**Effects of Automatic Flight Control System on Chinook Underslung Load Failures**

Marilena D. Pavel

*Faculty of Aerospace Engineering, Delft University of Technology The Netherlands* 

## **1. Introduction**

32 Will-be-set-by-IN-TECH

150 Automatic Flight Control Systems – Latest Developments

Zhang, Y. M. & Jiang, J. (2008). Bibliographical review on reconfigurable fault-tolerant control

Zhou, Q.-L. (2009). *Reconfigurable Control Allocation Design with Applications to Unmanned Aerial Vehicle and Aircraft*, Master's thesis, Concordia University, Montreal, QC, Canada.

systems, *IFAC Annual Reviews in Control,* 32(2): 229–252.

One of the major helicopter attributes is its ability to transport cargo externally in the form of external slung loads (see Fig. 1). Commercial and military operators accept the fact that using a helicopter for external load transportation is usually expensive in terms of both money and time. However, helicopters still have the significant advantage of accessing unreachable sites. Operations of helicopters with external loads impose limitations to the use of the helicopter, as for example: helicopter maximum forward speed is usually severely reduced because of the danger on dynamic instabilities of the load; due to external load the aerodynamic drag can become excessive, resulting in power and control limitations on the helicopter. The problem addressed in this chapter concerns the behaviour of a helicopter following the premature breakdown of one of its cables sustaining the slung load. As a specific example, the Chinook helicopter CH-47B with an external load will be considered. The CH-47 (Chinook) is a twin-engine tandem rotor helicopter (see Fig. 1) designed for allweather, medium-sized transport type operations. The three bladed rotors are driven in opposite directions (front rotor rotates anticlockwise, rear rotor rotates clockwise) through interconnecting shafts which enable both rotors to be driven by either engine. The rotor heads are fully articulated, with pitch, flapping, and lead-lag hinges.

Fig. 1. Chinook helicopter transporting single and multiple loads (Courtesy of the Royal Netherlands Air Force)

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 153

found that operating with a long sling cable damps out the sling-load pendulum mode lateral oscillation and the helicopter longitudinal phugoid; however, the associated slingload pitch oscillation and the helicopter Dutch roll mode become unstable. Suspending the sling load from a point ahead of the helicopter centre of gravity was found to stabilize the helicopter lateral oscillation; suspending it from a point aft of the centre of gravity caused instability. (Sheldon, 1978) concluded from experiments that a large number of instabilities are initiated by load yawing motions. A relatively easy way of obtaining an increased yaw resistance is to use a multipoint suspension system rather than a single point suspension. His experiments have shown that an inverted 'V' suspension system provides significant yaw resistance, while also minimizing the load trail angle. (Prabhakar, 1978) developed a non-linear single rotor helicopter-slung load model in multipoint suspension showing that the number, spacing and placement of the suspension points and the topology of the suspension cables are all important. The load is capable of changing almost completely the helicopter rigid body modes, generally destabilizing. Also, there exists significant coupling between the load and the helicopter lateral modes. The helicopter longitudinal modes on the other hand are affected little by the presence of the load. Dynamic coupling between the Dutch roll and a lateral load mode has been shown to decrease the Dutch role damping. A more recent study of (Cicolani, Kanning& Synnestvedt, 1995) developed a comprehensive approach for slung-load modelling where generic simulation models for a tandem helicopter capable of carrying load in single or multiple points with one, two or more helicopters were investigated. (Fusato, Guglieri & Celi, 2001) developed a body-flap-lag model to study the flight dynamics of a single-rotor helicopter carrying a single-point suspended load, showing that the load affects trim primarily through the overall increase in the weight of the aircraft; the influence of cable length was negligible. (Stuckey, 2002), using the equations of motions developed by (Cicolani, Kanning& Synnestvedt, 1995) and an open-loop control for pilot modelling, developed a piloted simulation model for a tandem helicopter capable of carrying a mixed density slung loads. (Tyson.1999) developed a slungload simulation model composed on the GenHel UH-60 model and validated against flight test data. (Chen, 1998) built a non-linear simulation model for one rotor helicopter-slung system and investigated the sudden load movement causing the cables to slacken or collapse. (Kendrick&Walker, 2006), using the motion simulator at The University of Liverpool, investigated the stability and handling qualities of a single-rotor helicopter carrying a slung load showing that at hover and low speed the pilot found easier to fly the helicopter with external load due to the increased damping in pitch provided by the load. (Bisgaard, 2006) developed an intuitive and easy-to-use way of modelling and simulating different slung load suspension types by using a redundant coordinate formulation based

on Gauss' principle of Least Constraint using the Udwadia-Kalaba equation.

(Van der Kamp et. Al, 2005) (Reijm, Pavel&Bart, 2006) and (Pavel, 2010) investigated whether the three-strop suspension system – usually used to transport large loads (see righthand side in Fig. 1) can be safely replaced by a two-strop suspension. A three-strop suspension system is actually a two-strop suspension backed up by a third point, the socalled 'redundant HUSLE'. The redundant HUSLE is a redundant set of slings which comes into action if one of the normal strops fails. However, such a system is expensive in terms of both money and time. Therefore, questioning how reliable the two-strop suspension was when compared to the three-point suspension; the above references concluded that although, in general, flying with the redundant HUSLE resulted in less violent helicopter reactions after load failure, redundant HUSLE did not necessarily mean safer. More

The goal of the chapter will be to implement the advanced automatic flight control system AFCS of the Chinook CH-47 (analogue in Chinook D-version and digital in the latest version F) into a generic Chinook model developed at Delft University of Technology (Van der Kamp et. Al (2005), Reijm, Pavel&Bart (2006), Pavel(2007), Pavel(2010)) and investigate the effects that AFCS may have on the recovery prospects of the Chinook helicopter after a failure scenario of its load. In other words, this chapter proposes to analyse how the advanced AFCS, implemented in general in order to improve the handling qualities characteristics, may improve/degrade the CH-47 behaviour during emergency situations such as failure scenarios of its suspended load(s). Searching in the specialist literature for research on this particular area of load failures and the AFCS effects on assisting/hindering the pilot during load failure recovering revealed that the subject has not been really investigated. A few publications have been identified dealing with load failure scenarios they address mainly a rather different problem, i.e. the situation in which a load is moving within an aircraft before being dropped - and none considers the effects that AFCS may have on helicopter behaviour during such emergency situations. Some relevant publications for understanding the problems related to the dynamics of a helicopter with a slung load are given below.

(Lucasen and Sterk, 1965) developed a first theoretical study of the dynamics of a single rotor helicopter carrying a slung load in hovering flight using a 3-dof longitudinal helicopter model including translation and attitude of the helicopter and load displacement w.r.t. the helicopter. They demonstrated that the phugoid stability depended on the cable length, decreasing with increasing cable length. (Dukes, 1973a) studied the stability characteristics of a single rotor helicopter with slung load near hover showing that with large pitch damping, the translational motion is only weakly coupled to the attitude and load motions. In a second study (Dukes, 1973b) concentrated on the stability of the load during different manoeuvres (acceleration-deceleration, changing the hover location and arresting a pendulous load motion) identifying some fundamental features of load control which can be utilized as basis for an open loop control strategy. (Feaster, Poli & Kirchhoff, 1977) studied the stability in forward flight of a single-rotor helicopter carrying a container, showing that long cables, high speeds and low weights increased the stability of the loads. Their results were contradicted by (Cliff&Bailey,1975) who obtained that longer cables were destabilizing, this probably due to different load aerodynamics considered. Both last papers underlined the importance of the load aerodynamics in studying the stability of helicopterslung load systems, where dynamic instabilities can be triggered by unsteady load aerodynamics. The most dominant form of load aerodynamic instability is a yawing divergence that couples with the load lateral modes. (Gabel, 1968) studied the slung load "vertical bounce" phenomenon, i.e. a resonant condition inherent to elastic sling load systems that occurs when the natural frequency of the sling load is close to one of the rotor frequencies. This mode can be exacerbated by the pilot's inertial reaction to vertical accelerations, leading to a vertical force being transmitted to the collective stick. To account for vertical bounce phenomenon one has to consider elastic suspensions. The author proposed several solutions to the pilot induced vertical bounce problem, the most promising being a low gain boost system which was meant to produce very low output for small pilot inputs and normal output for normal pilot inputs. For forwards speeds above 40 knots, the author showed that the effects of rotor downwash on the load aerodynamics are not important. (Nagabhushan, 1985) developed a non-linear body-flap model of a single rotorhelicopter and studied the stability characteristics of the helicopter-slung load system. He 152 Automatic Flight Control Systems – Latest Developments

The goal of the chapter will be to implement the advanced automatic flight control system AFCS of the Chinook CH-47 (analogue in Chinook D-version and digital in the latest version F) into a generic Chinook model developed at Delft University of Technology (Van der Kamp et. Al (2005), Reijm, Pavel&Bart (2006), Pavel(2007), Pavel(2010)) and investigate the effects that AFCS may have on the recovery prospects of the Chinook helicopter after a failure scenario of its load. In other words, this chapter proposes to analyse how the advanced AFCS, implemented in general in order to improve the handling qualities characteristics, may improve/degrade the CH-47 behaviour during emergency situations such as failure scenarios of its suspended load(s). Searching in the specialist literature for research on this particular area of load failures and the AFCS effects on assisting/hindering the pilot during load failure recovering revealed that the subject has not been really investigated. A few publications have been identified dealing with load failure scenarios they address mainly a rather different problem, i.e. the situation in which a load is moving within an aircraft before being dropped - and none considers the effects that AFCS may have on helicopter behaviour during such emergency situations. Some relevant publications for understanding the problems related to the dynamics of a helicopter with a slung load are

(Lucasen and Sterk, 1965) developed a first theoretical study of the dynamics of a single rotor helicopter carrying a slung load in hovering flight using a 3-dof longitudinal helicopter model including translation and attitude of the helicopter and load displacement w.r.t. the helicopter. They demonstrated that the phugoid stability depended on the cable length, decreasing with increasing cable length. (Dukes, 1973a) studied the stability characteristics of a single rotor helicopter with slung load near hover showing that with large pitch damping, the translational motion is only weakly coupled to the attitude and load motions. In a second study (Dukes, 1973b) concentrated on the stability of the load during different manoeuvres (acceleration-deceleration, changing the hover location and arresting a pendulous load motion) identifying some fundamental features of load control which can be utilized as basis for an open loop control strategy. (Feaster, Poli & Kirchhoff, 1977) studied the stability in forward flight of a single-rotor helicopter carrying a container, showing that long cables, high speeds and low weights increased the stability of the loads. Their results were contradicted by (Cliff&Bailey,1975) who obtained that longer cables were destabilizing, this probably due to different load aerodynamics considered. Both last papers underlined the importance of the load aerodynamics in studying the stability of helicopterslung load systems, where dynamic instabilities can be triggered by unsteady load aerodynamics. The most dominant form of load aerodynamic instability is a yawing divergence that couples with the load lateral modes. (Gabel, 1968) studied the slung load "vertical bounce" phenomenon, i.e. a resonant condition inherent to elastic sling load systems that occurs when the natural frequency of the sling load is close to one of the rotor frequencies. This mode can be exacerbated by the pilot's inertial reaction to vertical accelerations, leading to a vertical force being transmitted to the collective stick. To account for vertical bounce phenomenon one has to consider elastic suspensions. The author proposed several solutions to the pilot induced vertical bounce problem, the most promising being a low gain boost system which was meant to produce very low output for small pilot inputs and normal output for normal pilot inputs. For forwards speeds above 40 knots, the author showed that the effects of rotor downwash on the load aerodynamics are not important. (Nagabhushan, 1985) developed a non-linear body-flap model of a single rotorhelicopter and studied the stability characteristics of the helicopter-slung load system. He

given below.

found that operating with a long sling cable damps out the sling-load pendulum mode lateral oscillation and the helicopter longitudinal phugoid; however, the associated slingload pitch oscillation and the helicopter Dutch roll mode become unstable. Suspending the sling load from a point ahead of the helicopter centre of gravity was found to stabilize the helicopter lateral oscillation; suspending it from a point aft of the centre of gravity caused instability. (Sheldon, 1978) concluded from experiments that a large number of instabilities are initiated by load yawing motions. A relatively easy way of obtaining an increased yaw resistance is to use a multipoint suspension system rather than a single point suspension. His experiments have shown that an inverted 'V' suspension system provides significant yaw resistance, while also minimizing the load trail angle. (Prabhakar, 1978) developed a non-linear single rotor helicopter-slung load model in multipoint suspension showing that the number, spacing and placement of the suspension points and the topology of the suspension cables are all important. The load is capable of changing almost completely the helicopter rigid body modes, generally destabilizing. Also, there exists significant coupling between the load and the helicopter lateral modes. The helicopter longitudinal modes on the other hand are affected little by the presence of the load. Dynamic coupling between the Dutch roll and a lateral load mode has been shown to decrease the Dutch role damping. A more recent study of (Cicolani, Kanning& Synnestvedt, 1995) developed a comprehensive approach for slung-load modelling where generic simulation models for a tandem helicopter capable of carrying load in single or multiple points with one, two or more helicopters were investigated. (Fusato, Guglieri & Celi, 2001) developed a body-flap-lag model to study the flight dynamics of a single-rotor helicopter carrying a single-point suspended load, showing that the load affects trim primarily through the overall increase in the weight of the aircraft; the influence of cable length was negligible. (Stuckey, 2002), using the equations of motions developed by (Cicolani, Kanning& Synnestvedt, 1995) and an open-loop control for pilot modelling, developed a piloted simulation model for a tandem helicopter capable of carrying a mixed density slung loads. (Tyson.1999) developed a slungload simulation model composed on the GenHel UH-60 model and validated against flight test data. (Chen, 1998) built a non-linear simulation model for one rotor helicopter-slung system and investigated the sudden load movement causing the cables to slacken or collapse. (Kendrick&Walker, 2006), using the motion simulator at The University of Liverpool, investigated the stability and handling qualities of a single-rotor helicopter carrying a slung load showing that at hover and low speed the pilot found easier to fly the helicopter with external load due to the increased damping in pitch provided by the load. (Bisgaard, 2006) developed an intuitive and easy-to-use way of modelling and simulating different slung load suspension types by using a redundant coordinate formulation based on Gauss' principle of Least Constraint using the Udwadia-Kalaba equation.

(Van der Kamp et. Al, 2005) (Reijm, Pavel&Bart, 2006) and (Pavel, 2010) investigated whether the three-strop suspension system – usually used to transport large loads (see righthand side in Fig. 1) can be safely replaced by a two-strop suspension. A three-strop suspension system is actually a two-strop suspension backed up by a third point, the socalled 'redundant HUSLE'. The redundant HUSLE is a redundant set of slings which comes into action if one of the normal strops fails. However, such a system is expensive in terms of both money and time. Therefore, questioning how reliable the two-strop suspension was when compared to the three-point suspension; the above references concluded that although, in general, flying with the redundant HUSLE resulted in less violent helicopter reactions after load failure, redundant HUSLE did not necessarily mean safer. More

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 155

This type of helicopter control implies that with increased velocity the thrust of both rotors has to be tilted forward to compensate for the higher helicopter body drag. The lack of longitudinal cyclic in the HRP-1 forced the pilot to apply initially more differential thrust. This introduced an increase in nose down pitch angle. As a result of this forward helicopter pitch angle, the drag of the helicopter increases dramatically (see Fig. 3 from (Prouty, 2001)) To compensate for the large pitch angle, the longitudinal stick of the Chinook CH47-D controls differential thrust. Longitudinal cyclic is controlled separately by airspeed, keeping the helicopter body in acceptable pitch angles, thus minimizing

Fig. 3. Tandem helicopter with only differential pitch (top) and with differential collective

An Advanced or Automatic Flight Control System (AFCS) employs the aerodynamic control surfaces to manipulate the forces and moments of an aircraft to control its velocity, attitude and position. The AFCS can do this with or without assistance from the pilot. The performance of the AFCS is largely governed by its flight control laws that translate the input of various sensors to control surface output. Just like the complete system, the design of these control laws, especially for military aircraft, is determined by the requirement to provide good handling qualities, over a wide range of operating conditions (including cargo transport), with a low pilot workload, while being easy to

For the Chinook helicopter, pilot control is done by varying the pitch of the blades either cyclically or collectively. This is done with the thrust control lever (collective), a cyclic control stick and the directional pedals, which are all coupled between the pilot and the co-

**2. Description of the Chinook Automatic Flight Control System** 

and longitudinal cyclic pitch (bottom), (Prouty, 2001)

helicopter body drag.

expand or modify.

specifically, they demonstrated that loads up to only two tonnes could be safely suspended only in two-points without the need of using redundant HUSLE.

One of the many features of the CH-47 is its automatic flight control system AFCS. The goal of this chapter is to implement an advanced flight control system (AFCS) replicating the longitudinal axis AFCS of a Chinook CH-47D and use this system switched on to determine how the AFCS influences the recovery prospects of the Chinook helicopter after a front suspension failure. The chapter is structured as follows:


## **1.1 Tandem helicopter control**

The pilot controls of a tandem helicopter are essentially the same as those for normal helicopters. A pilot has a stick to control longitudinal and lateral motion, a collective stick for thrust and pedals to control the yaw motion. However, the connections between controls and rotor hub angles are different. Collective input moves both swash plates equally up and down. Whereas a normal helicopter longitudinal control input tilts the swash plate longitudinally, this input results in differential collective in a tandem helicopter. Lateral motion is achieved by tilting both front and rear rotor in the same direction. The tail rotor that is used for yaw control, is missing. This function is replaced by lateral cyclic in opposite direction for front and rear rotor disc. It should be noted that pitch attitude is not only controlled by differential collective of the front and rear rotor heads. In the past many tests have been conducted in order to achieve acceptable pitch control. The first Piasecki tandem helicopter and the Bristol 173 (see Fig. 2) had longitudinal cyclic, both were either uncontrollable or could only fly backwards (Prouty, 2001). Therefore a later Piasecki model, the HRP-1 used differential collective for longitudinal control.

Fig. 2. Bristol 173 with cyclic pitch longitudinal control, Piasecki HRP-1 with differential pitch, www.aviastar.org

154 Automatic Flight Control Systems – Latest Developments

specifically, they demonstrated that loads up to only two tonnes could be safely suspended

One of the many features of the CH-47 is its automatic flight control system AFCS. The goal of this chapter is to implement an advanced flight control system (AFCS) replicating the longitudinal axis AFCS of a Chinook CH-47D and use this system switched on to determine how the AFCS influences the recovery prospects of the Chinook helicopter after a front

The second section develops the control laws for a longitudinal AFCS with pitch

The third section simulates an example of a failure scenario flown and determines the

 The fourth section defines safety envelopes as boundaries of the maximum helicopter forward velocity achievable when recovery is possible after a load failure as a function

Finally, general conclusions and potential further extension of this work are discussed.

The pilot controls of a tandem helicopter are essentially the same as those for normal helicopters. A pilot has a stick to control longitudinal and lateral motion, a collective stick for thrust and pedals to control the yaw motion. However, the connections between controls and rotor hub angles are different. Collective input moves both swash plates equally up and down. Whereas a normal helicopter longitudinal control input tilts the swash plate longitudinally, this input results in differential collective in a tandem helicopter. Lateral motion is achieved by tilting both front and rear rotor in the same direction. The tail rotor that is used for yaw control, is missing. This function is replaced by lateral cyclic in opposite direction for front and rear rotor disc. It should be noted that pitch attitude is not only controlled by differential collective of the front and rear rotor heads. In the past many tests have been conducted in order to achieve acceptable pitch control. The first Piasecki tandem helicopter and the Bristol 173 (see Fig. 2) had longitudinal cyclic, both were either uncontrollable or could only fly backwards (Prouty, 2001). Therefore a later Piasecki model,

Fig. 2. Bristol 173 with cyclic pitch longitudinal control, Piasecki HRP-1 with differential

only in two-points without the need of using redundant HUSLE.

suspension failure. The chapter is structured as follows: The first section describes the AFCS characteristics;

of the load mass that can be safely transported;

the HRP-1 used differential collective for longitudinal control.

attitude hold and airspeed hold;

AFCS effects for recovering;

**1.1 Tandem helicopter control** 

pitch, www.aviastar.org

This type of helicopter control implies that with increased velocity the thrust of both rotors has to be tilted forward to compensate for the higher helicopter body drag. The lack of longitudinal cyclic in the HRP-1 forced the pilot to apply initially more differential thrust. This introduced an increase in nose down pitch angle. As a result of this forward helicopter pitch angle, the drag of the helicopter increases dramatically (see Fig. 3 from (Prouty, 2001)) To compensate for the large pitch angle, the longitudinal stick of the Chinook CH47-D controls differential thrust. Longitudinal cyclic is controlled separately by airspeed, keeping the helicopter body in acceptable pitch angles, thus minimizing helicopter body drag.

Fig. 3. Tandem helicopter with only differential pitch (top) and with differential collective and longitudinal cyclic pitch (bottom), (Prouty, 2001)

## **2. Description of the Chinook Automatic Flight Control System**

An Advanced or Automatic Flight Control System (AFCS) employs the aerodynamic control surfaces to manipulate the forces and moments of an aircraft to control its velocity, attitude and position. The AFCS can do this with or without assistance from the pilot. The performance of the AFCS is largely governed by its flight control laws that translate the input of various sensors to control surface output. Just like the complete system, the design of these control laws, especially for military aircraft, is determined by the requirement to provide good handling qualities, over a wide range of operating conditions (including cargo transport), with a low pilot workload, while being easy to expand or modify.

For the Chinook helicopter, pilot control is done by varying the pitch of the blades either cyclically or collectively. This is done with the thrust control lever (collective), a cyclic control stick and the directional pedals, which are all coupled between the pilot and the co-

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 157

Fig. 4. Cockpit interior of a CH-47D, (Boeing Helicopters, 2004)

 Three integrated lower control actuators (ILCA's) Two differentials airspeed hold actuators (DASH) Two Longitudinal Cyclic Trim actuators (LCT)

Three control position transducers (CPT's)

 A cockpit control panel Two AFCS computers

Regarding the AFCS of a CH-47D, this consists of the following parts:

cockpit control driver actuator (CCDA) and a collective CCDA

Attached to the cockpit controls are 2 magnetic brakes for yaw and roll, a longitudinal

The AFCS cockpit control panel (number 1 in Fig. 4) contains 7 switches to control the many AFCS functions (see Fig. 5). On top, the flight director coupling switches that when pressed engage the coupling between the AFCS and the Flight Director. Only one flight director may be coupled at a time. The left lower side contains the switches that control the cyclic trim actuators. Normally the longitudinal cyclic trim (LCT) actuators are automatically operated by the AFCS computers, with computer 1 controlling the forward LCT and computer 2 governing the aft LCT actuator according to the LCT trim schedule. When the switch is flipped to manual setting, the pilot is able to independently direct the extension or retraction of both actuators. The AFCS system select switch can be found on the lower right side of the display. Usually both AFCS systems will be selected. When one AFCS system is switched

pilot's position. The stick and pedal movements are transferred with a system of bell-cranks, push-pull tubes and actuators to a control mixing closet, located in the small hallway connecting the cabin to the cockpit. In this mixing unit, the pilot control inputs are combined with the signals from the AFCS computers and then mixed to result in the required lateral cyclic and collective pitch of the two rotors.

Earlier models of the CH-47 only had a Stability Augmentation System (SAS) installed to assist the pilot in attitude stabilization. With the D-version, the AFCS was added, which brought a number of modifications and additions to the SAS. Still, the main objective remains attitude stabilization, including rate damping, of the helicopter about all three axes. However, it is extended with a number of features, that for example maintain the desired value of certain flight parameters such as airspeed, pitch attitude and bank angle. The CH-47F is to be the first of the Chinook family equipped with a digital AFCS (DAFCS), granting it Level I handling qualities and meeting the stringent ADS-33 requirements for operation in degraded visual environments. A few of its impressive features include position adjustment with 30 cm increments, automatic hover capture when the cyclic stick is released below 8 kts ground speed and an altitude hold mode that eliminates drift (Einthoven et. Al., 2006). Since the flight control actuation on the F-version remains unchanged from the D-version, the control system still contains mechanically linked actuators. Hence it does not qualify for the term fly-by-wire: this notion originated from the replacement of mechanical linkages by electric signalling.

The main features of the AFCS system as implemented in the Chinook version D consist of (Boeing Helicopters, 2004):


Fig. 4 presents the cockpit interior of a CH-47D. Looking at this figure one can identify: 1) the AFCS control panel; 2) co-pilot pitch-roll control (cyclic stick); 3) pilot thrust control; 4) AFCS computer; 5) co-pilot multifunction display MMFD; 6) instrument panel; 7) centre console; 8) pilot pitch-roll control (cyclic stick); 9) multifunction display (AVMFD).

Fig. 4. Cockpit interior of a CH-47D, (Boeing Helicopters, 2004)

Regarding the AFCS of a CH-47D, this consists of the following parts:


156 Automatic Flight Control Systems – Latest Developments

pilot's position. The stick and pedal movements are transferred with a system of bell-cranks, push-pull tubes and actuators to a control mixing closet, located in the small hallway connecting the cabin to the cockpit. In this mixing unit, the pilot control inputs are combined with the signals from the AFCS computers and then mixed to result in the required lateral

Earlier models of the CH-47 only had a Stability Augmentation System (SAS) installed to assist the pilot in attitude stabilization. With the D-version, the AFCS was added, which brought a number of modifications and additions to the SAS. Still, the main objective remains attitude stabilization, including rate damping, of the helicopter about all three axes. However, it is extended with a number of features, that for example maintain the desired value of certain flight parameters such as airspeed, pitch attitude and bank angle. The CH-47F is to be the first of the Chinook family equipped with a digital AFCS (DAFCS), granting it Level I handling qualities and meeting the stringent ADS-33 requirements for operation in degraded visual environments. A few of its impressive features include position adjustment with 30 cm increments, automatic hover capture when the cyclic stick is released below 8 kts ground speed and an altitude hold mode that eliminates drift (Einthoven et. Al., 2006). Since the flight control actuation on the F-version remains unchanged from the D-version, the control system still contains mechanically linked actuators. Hence it does not qualify for the term fly-by-wire: this notion originated from the replacement of mechanical linkages by

The main features of the AFCS system as implemented in the Chinook version D consist of

Pitch attitude and long term airspeed hold, taking the position of the longitudinal cyclic

Long term bank angle and heading hold in level flight, bank angle hold in turning flight

 Altitude hold by means of barometer or radar signals (this mode is valid in the CH 47D of the US Army; the Royal Netherlands Air Force replaced this mode by Flight

Improved manoeuvrability with the use of control position transducers for all cockpit

Electronic detent switching on lateral stick and pedals based on signals supplied by the

Longitudinal cyclic trim scheduling and automatic LCT positioning to ground mode

 Use of the HSI bug error (error between actual and desired heading, indicated by a small token on the HSI instrument) for heading select (only in the CH 47D of the US

Fig. 4 presents the cockpit interior of a CH-47D. Looking at this figure one can identify: 1) the AFCS control panel; 2) co-pilot pitch-roll control (cyclic stick); 3) pilot thrust control; 4) AFCS computer; 5) co-pilot multifunction display MMFD; 6) instrument panel; 7) centre

Army; the Royal Netherlands Air Force replaced this mode by Flight Director);

console; 8) pilot pitch-roll control (cyclic stick); 9) multifunction display (AVMFD).

A stable positive longitudinal stick gradient throughout the entire flight envelope;

Fine adjustment of bank angle and airspeed trim (Vernier beep trim);

cyclic and collective pitch of the two rotors.

electric signalling.

Director);

controls;

AFCS;

(Boeing Helicopters, 2004):

stick as a reference;

(performing coupled turns);

when the aft wheels touch the ground;


The AFCS cockpit control panel (number 1 in Fig. 4) contains 7 switches to control the many AFCS functions (see Fig. 5). On top, the flight director coupling switches that when pressed engage the coupling between the AFCS and the Flight Director. Only one flight director may be coupled at a time. The left lower side contains the switches that control the cyclic trim actuators. Normally the longitudinal cyclic trim (LCT) actuators are automatically operated by the AFCS computers, with computer 1 controlling the forward LCT and computer 2 governing the aft LCT actuator according to the LCT trim schedule. When the switch is flipped to manual setting, the pilot is able to independently direct the extension or retraction of both actuators. The AFCS system select switch can be found on the lower right side of the display. Usually both AFCS systems will be selected. When one AFCS system is switched

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 159

(a) Integrated Lower Control Actuator (b) Differential Airspeed Hold Actuator

The differential airspeed hold (DASH) actuator (see Fig. 6(b)) is installed between the cyclic stick and the pitch ILCA. The actuator is in fact a combination of two electro-mechanical linear actuators mounted end to-end inside a tube. Like an ILCA, the upper half is controlled by AFCS No. 1, the lower half by No. 2, so again both AFCS computers are required for full authority, which is equal to 50% of the longitudinal control range, taking about 5 seconds to complete full travel. The DASH extends and retracts with the purpose of long term stabilization of the pitch axis, arranging a positive stick gradient and maintaining airspeed about a fixed stick position. Its performance depends on the mode of operation, of

A normal mode in which it stabilizes 1) the airspeed when flying faster than 40 kts and

 A Differential Collective Pitch Trim (DCPT) mode. This is turned on in special conditions such as high cyclic stick rate, large pitch attitude or on the ground. This is to prevent an exaggerated response from the actuator that would occur in these instances

 The transition mode. This mode is entered when the DCPT conditions do not apply anymore and the AFCS is engaged. The system switches to a low rate driver (20% of the normal rate), forcing the DASH actuator to return to its normal position corresponding to the airspeed. This avoids a step-like control input when the DASH resumes normal

The two longitudinal cyclic trim (LCT) actuators installed under the swashplate have as primary task to minimize fuselage drag by reducing the nose down attitude as airspeed and altitude build up. To manage this, the AFCS transmits signals to the LCT actuators which in

Fig. 6. Chinook actuators connected in series to cockpit controls (Anon, 2002)

which there are three:

operation.

2) the pitch attitude at speeds below 40 kts.

with the DASH in normal mode.

off, the Flight Director coupling and LCT functions continue to operate. The latter even keeps working with neither AFCS in operation.

Fig. 5. AFCS control panel scheme, (Boeing Helicopters, 2004)

Two AFCS computers are located in the avionics compartment. Since the AFCS is a redundant system, in normal operation, each computer controls half of the input to the flight controls. This is described as "operation at half gain and half authority". Failure of one of the computers results in the other computer taking over at ¾ gain but like regular operation, it has only up to half of the maximum travel of the working system available. In that case the remaining system is said to function at ¾ gain and half authority (Anon., 2002). When operational, the computers receive flight data from sensors and convert this into command signals that are fed to the actuators. Each unit directs its signals to the actuators according to a different path. Each actuator provides a position feedback signal to the related AFCS computer.

The Integrated Lower Control Actuators (ILCA) (see Fig. 6(a)) span 3 channels: pitch, roll, yaw. They separate the pilot control forces from the forces required to move the swashplates, which are generated by the upper controls. The ILCA's consist of two parts: a lower boost actuator and a dual extensible link. The hydromechanical lower boost actuators assist the pilot in controlling the helicopter. They are mechanically linked to the cockpit controls and will extend or retract in response to pilot inputs. The hydroelectrical dual extensible links incorporate an upper link, controlled by AFCS computer 1, and a lower link, driven by computer 2. This means that for full travel (full authority) both computers have to supply input. The actuating cylinders move solely based on AFCS commands without any corresponding cockpit controller motion. In the case none of the AFCS computers are working, the extensible links act as rigid links. The thrust input is enhanced with a lower boost actuator without extensible links, thereby assisting the pilot in moving the thrust control without providing a hydroelectrical input for the AFCS.

158 Automatic Flight Control Systems – Latest Developments

off, the Flight Director coupling and LCT functions continue to operate. The latter even

Two AFCS computers are located in the avionics compartment. Since the AFCS is a redundant system, in normal operation, each computer controls half of the input to the flight controls. This is described as "operation at half gain and half authority". Failure of one of the computers results in the other computer taking over at ¾ gain but like regular operation, it has only up to half of the maximum travel of the working system available. In that case the remaining system is said to function at ¾ gain and half authority (Anon., 2002). When operational, the computers receive flight data from sensors and convert this into command signals that are fed to the actuators. Each unit directs its signals to the actuators according to a different path. Each actuator provides a position feedback signal to the

The Integrated Lower Control Actuators (ILCA) (see Fig. 6(a)) span 3 channels: pitch, roll, yaw. They separate the pilot control forces from the forces required to move the swashplates, which are generated by the upper controls. The ILCA's consist of two parts: a lower boost actuator and a dual extensible link. The hydromechanical lower boost actuators assist the pilot in controlling the helicopter. They are mechanically linked to the cockpit controls and will extend or retract in response to pilot inputs. The hydroelectrical dual extensible links incorporate an upper link, controlled by AFCS computer 1, and a lower link, driven by computer 2. This means that for full travel (full authority) both computers have to supply input. The actuating cylinders move solely based on AFCS commands without any corresponding cockpit controller motion. In the case none of the AFCS computers are working, the extensible links act as rigid links. The thrust input is enhanced with a lower boost actuator without extensible links, thereby assisting the pilot in moving the thrust

keeps working with neither AFCS in operation.

Fig. 5. AFCS control panel scheme, (Boeing Helicopters, 2004)

control without providing a hydroelectrical input for the AFCS.

related AFCS computer.

Fig. 6. Chinook actuators connected in series to cockpit controls (Anon, 2002)

The differential airspeed hold (DASH) actuator (see Fig. 6(b)) is installed between the cyclic stick and the pitch ILCA. The actuator is in fact a combination of two electro-mechanical linear actuators mounted end to-end inside a tube. Like an ILCA, the upper half is controlled by AFCS No. 1, the lower half by No. 2, so again both AFCS computers are required for full authority, which is equal to 50% of the longitudinal control range, taking about 5 seconds to complete full travel. The DASH extends and retracts with the purpose of long term stabilization of the pitch axis, arranging a positive stick gradient and maintaining airspeed about a fixed stick position. Its performance depends on the mode of operation, of which there are three:


The two longitudinal cyclic trim (LCT) actuators installed under the swashplate have as primary task to minimize fuselage drag by reducing the nose down attitude as airspeed and altitude build up. To manage this, the AFCS transmits signals to the LCT actuators which in

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 161

control decoupling and automatic control of the helicopter take place. Generally, an AFCS comprises the sensors, the filters, the stability and control augmentation system (SCAS) and the autopilot which can completely take over the pilot in order to execute certain control

Fig. 7 (Reijm, Pavel & Bart, 2006) displays for example the pitch control laws connected to the generic helicopter model. Generally, the pitch control laws have 6 input paths: pitch attitude, pitch rate, yaw rate, bank angle, limited airspeed and the longitudinal control position. These signals arrive from the gyros, CPT and pressure sensor and are manipulated to steer the pitch ILCA extensible links to provide pitch rate damping and the DASH actuator to maintain airspeed and a positive stick gradient. The actuation system is quite a complicated mechanism with its own feedback control designed to ensure that the response and stability to control inputs has good performance. Helicopters fitted with an AFCS usually incorporate a limited authority series SCAS actuators, The SCAS authority, i.e. the amount in which a SCAS can overrule the pilot is limited to amplitudes of ±10% of the full actuator throw. For this work, it is assumed that each actuation element can be represented as a first order lag, although this assumption is a crude approximation of the complex

Fig. 7. Pitch control laws for the longitudinal AFCS (Reijm, Pavel & Bart, 2006)

Looking at Fig. 7, one can distinguish the various parts of the control laws. Starting with location 1, this is the primary input for the ILCA path: the pitch rate. It passes through washout functions which act like a sink and filter the signal for certain frequencies. These washout transfer functions can be tuned to select a desired filter strength and a frequency that should be eliminated from the signal. Moving to location 2, the filtered pitch rate signal is compensated by the yaw rate and roll attitude, presumable to cater for the effects of the coupling between the longitudinal and lateral flight dynamics. In location 3 the compensated

tasks.

behaviour of the servo-elastic system.

turn increase the longitudinal cyclic pitch angle of the fore and aft rotor. This way blade flapping is also reduced, lowering stresses on the rotor shafts. The pilot can also manually select the LCT actuator positions.

## **3. Modelling the Chinook tandem helicopter and its Automatic Flight Control System**

## **3.1 Modelling the Chinook tandem helicopter with external load**

A general non-linear six degree-of-freedom (6-dof) rigid body model for a generic tandem helicopter was first developed for piloted simulations ((Van der Kamp et. Al, 2005, Pavel, 2010). In a general non-linear 6-dof model the helicopter motion is represented by three translations and three rotations around the body axes-system centred on the helicopter centre of gravity, see Figure A 1 in Appendix A. The helicopter is modelled by dividing it into main components (front rotor, rear rotor, fuselage, horizontal stabilizer, vertical fin) and summing up the contribution of each part to the general system of forces and moments. The following main assumptions were made: 1) Aerodynamic forces and moments are calculated using the blade element theory and integrating along the radius and azimuth to obtain their average effect; 2) The fuselage is modelled with linear aerodynamics; 3) Rotor disc-tilt dynamics (the so-called 'flapping dynamics') are neglected and only steady-state rotor disc-tilt motion is considered; 4) The dynamic inflows of both front and rear rotors are included in the model as state variables and can be described as a quasi-steady dynamic inflow by means of time constants of a value 0.1 sec; 5) The rotors are modelled with a centrally flapping hinge; 6) There are no pitch-flap or pitch-lag couplings; 7) The lead-lag motion of the blades is neglected; 8) The blades are rectangular; 9) There are no tip losses; 10) Gravitational forces are small compared to aerodynamic, inertial and centrifugal forces; 11) The flapping and flow angles are small; 12) The front rotor angular velocity is constant and anticlockwise, the rear rotor angular velocity is constant and clockwise; 13) No reverse flow regions are considered; 14) The flow is incompressible; 15) The blades have a uniform mass distribution; 16) The blade elastic axis, aerodynamic axis, control axis and centre of mass axis coincide; 17) The blades are linearly pre-twisted twist= - 9.14 deg. For the expressions of the forces and moments acting on the helicopter components, the reader is referred to APPENDIX A. The equations of motion describing the motion of the helicopter in the 6-dof model are presented in APPENDIX A. To this model, a 6-dof model for the load has been added. The helicopter has three suspension points i=1,2,3 underneath its floor as seen in Figure A6, the tension force in one cable j being Sij. The slings are modelled as linear springs without mass and it is assumed that they have small internal damping. The damping coefficient is set large enough to prevent the oscillating load from inducing a pendulum-like motion. In APPENDIX A more detail is given on the calculation of load sling forces (see eqns. (24) and (25)). The load is modelled as a 6-dof body, the helicopter slings being connected to the load as seen in Figure A7. The slings are modelled as linear weightless springs with a small internal damping. Appendix B presents the Chinook data for the helicopter and load.

## **3.2 Developing control laws for the longitudinal AFCS**

Next, AFCS control laws for operating the Chinook helicopter are added to the presented flight mechanics model. In a classical AFCS, the computation of signals for stabilization, 160 Automatic Flight Control Systems – Latest Developments

turn increase the longitudinal cyclic pitch angle of the fore and aft rotor. This way blade flapping is also reduced, lowering stresses on the rotor shafts. The pilot can also manually

**3. Modelling the Chinook tandem helicopter and its Automatic Flight Control** 

A general non-linear six degree-of-freedom (6-dof) rigid body model for a generic tandem helicopter was first developed for piloted simulations ((Van der Kamp et. Al, 2005, Pavel, 2010). In a general non-linear 6-dof model the helicopter motion is represented by three translations and three rotations around the body axes-system centred on the helicopter centre of gravity, see Figure A 1 in Appendix A. The helicopter is modelled by dividing it into main components (front rotor, rear rotor, fuselage, horizontal stabilizer, vertical fin) and summing up the contribution of each part to the general system of forces and moments. The following main assumptions were made: 1) Aerodynamic forces and moments are calculated using the blade element theory and integrating along the radius and azimuth to obtain their average effect; 2) The fuselage is modelled with linear aerodynamics; 3) Rotor disc-tilt dynamics (the so-called 'flapping dynamics') are neglected and only steady-state rotor disc-tilt motion is considered; 4) The dynamic inflows of both front and rear rotors are included in the model as state variables and can be described as a quasi-steady dynamic inflow by means of time constants of a value 0.1 sec; 5) The rotors are modelled with a centrally flapping hinge; 6) There are no pitch-flap or pitch-lag couplings; 7) The lead-lag motion of the blades is neglected; 8) The blades are rectangular; 9) There are no tip losses; 10) Gravitational forces are small compared to aerodynamic, inertial and centrifugal forces; 11) The flapping and flow angles are small; 12) The front rotor angular velocity is constant and anticlockwise, the rear rotor angular velocity is constant and clockwise; 13) No reverse flow regions are considered; 14) The flow is incompressible; 15) The blades have a uniform mass distribution; 16) The blade elastic axis, aerodynamic axis, control axis and centre of mass axis coincide; 17) The blades are linearly pre-twisted twist= - 9.14 deg. For the expressions of the forces and moments acting on the helicopter components, the reader is referred to APPENDIX A. The equations of motion describing the motion of the helicopter in the 6-dof model are presented in APPENDIX A. To this model, a 6-dof model for the load has been added. The helicopter has three suspension points i=1,2,3 underneath its floor as seen in Figure A6, the tension force in one cable j being Sij. The slings are modelled as linear springs without mass and it is assumed that they have small internal damping. The damping coefficient is set large enough to prevent the oscillating load from inducing a pendulum-like motion. In APPENDIX A more detail is given on the calculation of load sling forces (see eqns. (24) and (25)). The load is modelled as a 6-dof body, the helicopter slings being connected to the load as seen in Figure A7. The slings are modelled as linear weightless springs with a small internal damping. Appendix B presents the Chinook data

**3.1 Modelling the Chinook tandem helicopter with external load** 

select the LCT actuator positions.

for the helicopter and load.

**3.2 Developing control laws for the longitudinal AFCS** 

Next, AFCS control laws for operating the Chinook helicopter are added to the presented flight mechanics model. In a classical AFCS, the computation of signals for stabilization,

**System** 

control decoupling and automatic control of the helicopter take place. Generally, an AFCS comprises the sensors, the filters, the stability and control augmentation system (SCAS) and the autopilot which can completely take over the pilot in order to execute certain control tasks.

Fig. 7 (Reijm, Pavel & Bart, 2006) displays for example the pitch control laws connected to the generic helicopter model. Generally, the pitch control laws have 6 input paths: pitch attitude, pitch rate, yaw rate, bank angle, limited airspeed and the longitudinal control position. These signals arrive from the gyros, CPT and pressure sensor and are manipulated to steer the pitch ILCA extensible links to provide pitch rate damping and the DASH actuator to maintain airspeed and a positive stick gradient. The actuation system is quite a complicated mechanism with its own feedback control designed to ensure that the response and stability to control inputs has good performance. Helicopters fitted with an AFCS usually incorporate a limited authority series SCAS actuators, The SCAS authority, i.e. the amount in which a SCAS can overrule the pilot is limited to amplitudes of ±10% of the full actuator throw. For this work, it is assumed that each actuation element can be represented as a first order lag, although this assumption is a crude approximation of the complex behaviour of the servo-elastic system.

Fig. 7. Pitch control laws for the longitudinal AFCS (Reijm, Pavel & Bart, 2006)

Looking at Fig. 7, one can distinguish the various parts of the control laws. Starting with location 1, this is the primary input for the ILCA path: the pitch rate. It passes through washout functions which act like a sink and filter the signal for certain frequencies. These washout transfer functions can be tuned to select a desired filter strength and a frequency that should be eliminated from the signal. Moving to location 2, the filtered pitch rate signal is compensated by the yaw rate and roll attitude, presumable to cater for the effects of the coupling between the longitudinal and lateral flight dynamics. In location 3 the compensated

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 163

times design strength, which is equal to the design strength of suspension points on the external loads. For the Chinook, the tensile strength are calculated with a design load of 17000lb (7.6x104 N) for each cable/hook and 25000lb (11.1x104N ) for a combined fore and aft cable/hook (31). During the failure simulations it became clear that the tension in the cables is very high when recovering to normal flight. On many occasions the EOL strength was exceeded and sometimes the BOL strength as well. As it was difficult to decide when a sling reaches its ultimate/breaking strength and snaps, the actual snapping point was set to

First, to fly the helicopter/slung load system in the front cable failure scenario, simple PID controllers have been developed to generate all control positions. Generally, in a PID controller, it is considered that the collective controls the altitude, the longitudinal cyclic controls pitch attitude, the lateral cyclic controls the roll motion and the pedal controls the

*z req* int\_ *z req <sup>w</sup> coll K z z K z z dt K w*

*req* int\_ *req <sup>q</sup> long K K dt K q*

*req* int\_ *req <sup>p</sup> lat K K dt K p*

*fus* int\_ *fus <sup>r</sup> pedal K K dt K r*

At the guidance level, the required pitch attitude is controlled by an altitude hold controller

*req h req K h h K h h dt K h* int\_ *h req hdot*

*req y req K* int\_ *y req ydot*

The longitudinal and lateral pilot inputs are mixed at the level of swashplate as given in

*cf cf pilot fus sf pilot fus sf cf pilot fus sf pilot fus cr cr pilot fus sr pilot fus sr cr pilot fus sr pilot fus*

 

 

 

 

> 

Next, the initial PID controlled model is replaced with the longitudinal AFCS controlled system of Fig. 7, the other inputs remaining still PID controlled. This new pilot model is used to simulate different failure scenarios of the front cable. The following steps are taken

Use Bilinear Transformation to map the continuous time transfer functions to the

cos sin sin cos cos sin sin cos

 

 

 

> 

1 1, 1 , 1 1, 1 , 1 1, 1 , 1 1, 1 ,

*y y <sup>K</sup> y y dt K <sup>y</sup>*

 

 

> 

 

 

 

(1)

(2)

(3)

the BOL strength as this represented a worst-case scenario.

to complete a failure scenario with the longitudinal AFCS switched on:

 

Calculate the trim state for a desired airspeed;

(Ostroff, Downing and Rood, 1976).

discrete domain;

and the required roll angle is controlled by a lateral position hold controller.

sideslip, i.e.:

signal passes through a feedforward loop; the combination of a feedback and feedforward loop increase the responsiveness of a system, decreasing the time to return to the desired state after a disturbance. The longitudinal control position (location 4 in the figure) also contributes to the ILCA signal with the purpose of control augmentation. The CPT signals pass via a direct path and high gain path, which incorporates a *rate limiter*. The rate limiter constricts the appliance of the CPT signal to repress the effects of rapid stick movement, which could otherwise result in overreaction of the system. The direct and rate limited signals are summed and together form the resulting longitudinal CPT signal to be used for the ILCA and DASH actuator. Before the CPT signal reaches the ILCA, it is modified by a special construction involving the regular signal subtracted by the signal that has been filtered by a *lag function*. Generally, the task of a lag function is to cancel high frequency throughput to prevent

saturation. They are defined by the transfer function <sup>1</sup> *s* 1 in which is the time constant

that defines the effectiveness of the filter. The higher the time constant, the better is the capacity of filtering high frequencies. The time constant is typically between 25 and 100ms, giving actuation bandwidths between 40 and 10 rad/s/. For this study a time constant of 100ms was chosen, resulting in a system with lower actuation bandwidth which shows that the actuation inhibits pilot rapid control actions. Then at location 5 one can see the *washout circuit* designed to only produce output during the transient period, cancelling the steady-state throughput. This behaviour is exactly what is required for control augmentation: the assistance by the boost actuators should be generated only when the pilot is moving the stick, not when keeping it steady. The resulting longitudinal CPT signal not only directs ILCA extension, but also controls the DASH actuator. The signal is supplemented with the pitch attitude that enables pitch attitude hold (location 6). The pitch attitude also works as input for the velocity control circuit in location 7. This velocity control circuit enables the DASH system to provide a positive stick gradient, but also includes feedback and feedforward loops to act on attitude changes caused by gusts.

## **4. Simulating front cable failure scenarios**

The generic control scheme of Fig. 7 is next implemented in the generic tandem helicopter + load model.

The generic helicopter/slung load model as presented above is used next to simulate failure scenarios of the front cable. A tandem V-shape suspended load is assumed to hang underneath the helicopter so that failure of the front hook means actually failure of the two front cables.

In analysing the pilot recovery chances after a front cable failure without dropping the external load, the following question arose: what happens if the remaining cables are not strong enough to carry the load and they snap so that the pilot looses the load. Therefore the tension in the remaining cables was analysed to determine the cases in which the pilot would loose the load. After a cable failure the tension in the remaining cables increases rapidly and may cause them to snap. The snapping of the other cables may cause extra piloting problems, even loss of control and a possible destruction of the rotor above. Generally, generic sling specifications demand a guaranteed life of four years. At the Beginning Of Life (BOL) they must withstand 7 times the designed tensile strength. At the end of their service or End Of Life (EOL) this number has dropped to a minimum of 4.2 162 Automatic Flight Control Systems – Latest Developments

signal passes through a feedforward loop; the combination of a feedback and feedforward loop increase the responsiveness of a system, decreasing the time to return to the desired state after a disturbance. The longitudinal control position (location 4 in the figure) also contributes to the ILCA signal with the purpose of control augmentation. The CPT signals pass via a direct path and high gain path, which incorporates a *rate limiter*. The rate limiter constricts the appliance of the CPT signal to repress the effects of rapid stick movement, which could otherwise result in overreaction of the system. The direct and rate limited signals are summed and together form the resulting longitudinal CPT signal to be used for the ILCA and DASH actuator. Before the CPT signal reaches the ILCA, it is modified by a special construction involving the regular signal subtracted by the signal that has been filtered by a *lag function*. Generally, the task of a lag function is to cancel high frequency throughput to prevent

that defines the effectiveness of the filter. The higher the time constant, the better is the capacity of filtering high frequencies. The time constant is typically between 25 and 100ms, giving actuation bandwidths between 40 and 10 rad/s/. For this study a time constant of 100ms was chosen, resulting in a system with lower actuation bandwidth which shows that the actuation inhibits pilot rapid control actions. Then at location 5 one can see the *washout circuit* designed to only produce output during the transient period, cancelling the steady-state throughput. This behaviour is exactly what is required for control augmentation: the assistance by the boost actuators should be generated only when the pilot is moving the stick, not when keeping it steady. The resulting longitudinal CPT signal not only directs ILCA extension, but also controls the DASH actuator. The signal is supplemented with the pitch attitude that enables pitch attitude hold (location 6). The pitch attitude also works as input for the velocity control circuit in location 7. This velocity control circuit enables the DASH system to provide a positive stick gradient, but also includes feedback and feedforward loops to act on attitude

The generic control scheme of Fig. 7 is next implemented in the generic tandem helicopter +

The generic helicopter/slung load model as presented above is used next to simulate failure scenarios of the front cable. A tandem V-shape suspended load is assumed to hang underneath the helicopter so that failure of the front hook means actually failure of the two

In analysing the pilot recovery chances after a front cable failure without dropping the external load, the following question arose: what happens if the remaining cables are not strong enough to carry the load and they snap so that the pilot looses the load. Therefore the tension in the remaining cables was analysed to determine the cases in which the pilot would loose the load. After a cable failure the tension in the remaining cables increases rapidly and may cause them to snap. The snapping of the other cables may cause extra piloting problems, even loss of control and a possible destruction of the rotor above. Generally, generic sling specifications demand a guaranteed life of four years. At the Beginning Of Life (BOL) they must withstand 7 times the designed tensile strength. At the end of their service or End Of Life (EOL) this number has dropped to a minimum of 4.2

*s* 1 in which is the time constant

saturation. They are defined by the transfer function <sup>1</sup>

**4. Simulating front cable failure scenarios** 

changes caused by gusts.

load model.

front cables.

times design strength, which is equal to the design strength of suspension points on the external loads. For the Chinook, the tensile strength are calculated with a design load of 17000lb (7.6x104 N) for each cable/hook and 25000lb (11.1x104N ) for a combined fore and aft cable/hook (31). During the failure simulations it became clear that the tension in the cables is very high when recovering to normal flight. On many occasions the EOL strength was exceeded and sometimes the BOL strength as well. As it was difficult to decide when a sling reaches its ultimate/breaking strength and snaps, the actual snapping point was set to the BOL strength as this represented a worst-case scenario.

First, to fly the helicopter/slung load system in the front cable failure scenario, simple PID controllers have been developed to generate all control positions. Generally, in a PID controller, it is considered that the collective controls the altitude, the longitudinal cyclic controls pitch attitude, the lateral cyclic controls the roll motion and the pedal controls the sideslip, i.e.:

$$\begin{aligned} \text{coll} &= K\_{\varepsilon} \left( z\_{m\eta} - z \right) + K\_{\text{int\\_v}} \int \left( z\_{m\eta} - z \right) dt + K\_{w} d\upsilon \\\\ \text{clong} &= K\_{\rho} \left( \theta\_{m\eta} - \theta \right) + K\_{\text{int\\_v}} \int \left( \theta\_{m\eta} - \theta \right) dt + K\_{\text{e}} q \\\\ \text{lat} &= K\_{\rho} \left( \phi\_{m\eta} - \phi \right) + K\_{\text{int\\_v}} \int \left( \phi\_{m\eta} - \phi \right) dt + K\_{r} p \end{aligned} \tag{1}$$
 
$$\text{prod} = -K\_{\varphi} \mathcal{B}\_{f\text{s}} + K\_{\text{int\\_v}} \int \left( -\mathcal{B}\_{f\text{s}} \right) dt - K\_{r} r$$

At the guidance level, the required pitch attitude is controlled by an altitude hold controller and the required roll angle is controlled by a lateral position hold controller.

$$
\boldsymbol{\Theta}\_{n\boldsymbol{\eta}} = \boldsymbol{K}\_{\boldsymbol{h}} \left( \boldsymbol{h}\_{n\boldsymbol{\eta}} - \boldsymbol{h} \right) + \boldsymbol{K}\_{\operatorname{int}\_{-} \boldsymbol{h}} \left[ \left( \boldsymbol{h}\_{n\boldsymbol{\eta}} - \boldsymbol{h} \right) \boldsymbol{d} + \boldsymbol{K}\_{\operatorname{hbar}} \dot{\boldsymbol{h}} \right. \tag{2}
$$

$$
\boldsymbol{\phi}\_{n\boldsymbol{\eta}} = \boldsymbol{K}\_{\boldsymbol{y}} \left( \boldsymbol{y}\_{n\boldsymbol{\eta}} - \boldsymbol{y} \right) + \boldsymbol{K}\_{\operatorname{int}\_{-} \boldsymbol{y}} \left[ \left( \boldsymbol{y}\_{n\boldsymbol{\eta}} - \boldsymbol{y} \right) \boldsymbol{d} \boldsymbol{t} + \boldsymbol{K}\_{\operatorname{ybar}} \dot{\boldsymbol{y}} \right. \tag{3}
$$

The longitudinal and lateral pilot inputs are mixed at the level of swashplate as given in (Ostroff, Downing and Rood, 1976).

$$\begin{aligned} \boldsymbol{\theta}\_{1\boldsymbol{\phi}} &= \boldsymbol{\theta}\_{1\boldsymbol{\epsilon},\operatorname{pliv}} \cdot \cos \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} + \boldsymbol{\theta}\_{1\boldsymbol{\epsilon},\operatorname{pliv}} \cdot \sin \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} \\ \boldsymbol{\theta}\_{1\boldsymbol{\phi}} &= \boldsymbol{\theta}\_{1\boldsymbol{\epsilon},\operatorname{pliv}} \cdot \sin \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} - \boldsymbol{\theta}\_{1\boldsymbol{\epsilon},\operatorname{pliv}} \cdot \cos \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} \\ \boldsymbol{\theta}\_{1\boldsymbol{\sigma}} &= \boldsymbol{\theta}\_{1\boldsymbol{\sigma},\operatorname{pliv}} \cdot \cos \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} + \boldsymbol{\theta}\_{1\boldsymbol{\sigma},\operatorname{pliv}} \cdot \sin \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} \\ \boldsymbol{\theta}\_{1\boldsymbol{\sigma}} &= -\boldsymbol{\theta}\_{1\boldsymbol{\sigma},\operatorname{pliv}} \cdot \sin \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} + \boldsymbol{\theta}\_{1\boldsymbol{\sigma},\operatorname{pliv}} \cdot \cos \boldsymbol{\beta}\_{\boldsymbol{\mu}\boldsymbol{u}} \end{aligned} \tag{3}$$

Next, the initial PID controlled model is replaced with the longitudinal AFCS controlled system of Fig. 7, the other inputs remaining still PID controlled. This new pilot model is used to simulate different failure scenarios of the front cable. The following steps are taken to complete a failure scenario with the longitudinal AFCS switched on:


Effects of Automatic Flight Control System on Chinook Underslung Load Failures 165

A typical failure simulation can be seen in Fig. 8. The case considered is the helicopter flying forward at 50 kts when a front failure occurs with a 2-point suspended load of 2 tonnes. It is considered that the pilot reaction starts 1 sec after the failure. The controls remain unchanged from the moment of failure to the moment of pilot reaction (i.e. for 1 second). Looking at this figure it appears that the pilot can control this failure, being close to the upper limit for the longitudinal controller and well within the limits for the collective and

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

Fig. 8. Helicopter and load snapshot to a front cable failure scenario from 50 kts initial

velocity, 2-point suspension, 2000 kg load, 1 sec delay in pilot reaction

lateral controllers.


To determine the limits within which the pilot can control the recovery, the ADS-33 standard (ADS-33, 2000), section 3.1.14.4 'Transients Following Failures' has been used. According to ADS-33, for rotorcraft without failure warning and cueing devices, the perturbations encountered shall not exceed the limits as given in Table 1 (equivalent with Table III from ADS-33). Also, according to pilot experience it appeared that the pilot can react within 1 or 2 seconds after the load failure. Therefore, the pilot reaction time in the simulations performed in this paper has been adjusted to 1 and maximum 2 seconds.



164 Automatic Flight Control Systems – Latest Developments

 Simulate the first 25 seconds with a full PID control. This is done because when the AFCS is turned on in flight after it has been switched off, or it leaves ground mode, a DASH error signal could exist. This means that DASH actuator operation and the longitudinal stick position are out of sync, requiring a small period of time for the actuator to cancel the error signal after which it is able to resume normal operation. This is done with the Transition Mode of the DASH. Discussions with RNLAF test pilots

At 25 seconds, switch to longitudinal AFCS with all other inputs (collective, lateral and

At t = 26 seconds, a cable failure will be introduced. The control laws will keep

 From the start of the failure until the specified pilot reaction time of either 0, 1 or 2 seconds, the PID controllers will enter a stick-fixed mode, remaining at the position

 When the reaction time period has expired, the PID controllers will kick in and the simulation will again run in mixed mode until it is finished, covering the same 5

To determine the limits within which the pilot can control the recovery, the ADS-33 standard (ADS-33, 2000), section 3.1.14.4 'Transients Following Failures' has been used. According to ADS-33, for rotorcraft without failure warning and cueing devices, the perturbations encountered shall not exceed the limits as given in Table 1 (equivalent with Table III from ADS-33). Also, according to pilot experience it appeared that the pilot can react within 1 or 2 seconds after the load failure. Therefore, the pilot reaction time in the

Flight condition

Both Hover and Low Speed and Forward Flight Up-and-Away requirements apply

Both Hover and Low Speed and Forward Flight Up-and-Away requirements apply

Both Hover and Low Speed and Forward Flight Up-and-Away requirements apply

Forward Flight

Near-Earth Up-and-away

10 sec

5.0 sec

10 sec

Stay within OFE. No recovery action for

Stay within OFE. No recovery action for

Stay within OFE. No recovery action for

simulations performed in this paper has been adjusted to 1 and maximum 2 seconds.

Hover and Low speed

No recovery action for 3.0 sec

No recovery action for 3.0 sec

No recovery action for 3.0 sec

Table 1. Transients following failures (ADS-33, 2000)

3o roll, pitch, yaw 0.05g nx, ny, nz

10o attitude change 0.2g acceleration

24o attitude change 0.4g acceleration

provided the indication that approximately 25 seconds is a realistic value;

operating, immediately responding to the changing helicopter states.

Compute the new pilot input value for smooth transition;

pedal) PID controlled;

they were in at t = tfailure.

seconds from t = tfailure.

Level

1

2

3

A typical failure simulation can be seen in Fig. 8. The case considered is the helicopter flying forward at 50 kts when a front failure occurs with a 2-point suspended load of 2 tonnes. It is considered that the pilot reaction starts 1 sec after the failure. The controls remain unchanged from the moment of failure to the moment of pilot reaction (i.e. for 1 second). Looking at this figure it appears that the pilot can control this failure, being close to the upper limit for the longitudinal controller and well within the limits for the collective and lateral controllers.

Fig. 8. Helicopter and load snapshot to a front cable failure scenario from 50 kts initial velocity, 2-point suspension, 2000 kg load, 1 sec delay in pilot reaction

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 167

Fig. 10 shows the helicopter pitch rate, attitude and velocities after a cable failure in the case of a PID controlled helicopter (left hand side of the figure) and an AFCS controlled helicopter (right hand side). The case considered is the helicopter flying forward at 50 kts when a front failure occurs with a 2-point suspended load of 2000 kg. It is considered that the pilot PID control will start to react at 1 sec after the front suspension point has failed. The controls remain unchanged from the moment of failure to the moment of pilot reaction (i.e. for 1 second). It is interesting to discuss how the AFCS affects the simulation. While the PID controller is restrained by the pilot reaction time, the AFCS control laws immediately start reacting to the change in helicopter pitch attitude caused by the swinging of the load. This should result in a lower maximum pitch rate, an expectation confirmed by the results. The maximum pitch rate qmax of the PID controlled helicopter is equal to 8.6 deg/sec (27th second), whereas the qmax resulting from AFCS control comes to 7.6 deg/sec (2nd second), an 11% attitude reduction. Concerning the pitch attitude, one can see that the AFCS controller clearly has trouble to maintain the trimmed pitch attitude, allowing it to increase to 8 degrees. This immediately has its effect on the forward velocity that begins to decline as soon as the pitch angle starts to build up at about 27 seconds. The filtering of the pitch attitude control also has its effect on the vertical velocity, but this is neither vital to the survival of the helicopter nor relevant to the ADS-33 handling limits. Simulating different scenarios it was observed that the DASH control circuit fails to maintain airspeed when flying faster than 40 kts. Though it appears more and more likely that the implementation of the DASH control circuit does not wholly agree with the real-life situation, the pitch ILCA is still doing its job just as intended, keeping the pitch rate within handling limits and making

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -10

time[s]

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -3

time[s]


PID controlled AFCS controlled Fig. 10. Helicopter motion after front suspension load failure, 50kts, two-point suspension,

q [deg/s] [deg]

 u [m/s] v [m/s] w [m/s]

0

5

10

recovery possible.


2 tonne mass load

q [deg/s] [deg]

 u [m/s] v [m/s] w [m/s]

0

5

10

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -10

time[s]

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -3

time[s]

Concerning the time responses of the servo commands control actions, Fig. 9 displays the pitch control law of the actuator servo commands during a 30-second level flight at 50 kts.

Fig. 9. Pitch control low for the DASH and SAS actuator command during the 50 kts forward flight

Looking at this figure, one can see that there is a 25-second settling time that the DASH actuator requires before reaching a steady state value of about 6.3 cm.. Such behaviour seems to agree with the RNLAF CH-47D flight manual ((Anon, 2004),section 8.3). The manual states that when the AFCS is turned on in flight after it has been switched off, or it leaves ground mode, a DASH error signal could exist. This means that DASH actuator operation and the longitudinal stick position are out of sync, requiring a small period of time for the actuator to cancel the error signal after which it is able to resume normal operation. This is done with the Transition mode of the DASH as described above. The manual does not mention how long this period actually lasts, but, from discussions with Chinook pilots, it appears that this period it would amount to approximately 25 seconds, value similar to the one encountered in Fig. 9.

Furthermore, the following scenarios are considered:


166 Automatic Flight Control Systems – Latest Developments

Concerning the time responses of the servo commands control actions, Fig. 9 displays the pitch control law of the actuator servo commands during a 30-second level flight at 50 kts.

Fig. 9. Pitch control low for the DASH and SAS actuator command during the 50 kts

Looking at this figure, one can see that there is a 25-second settling time that the DASH actuator requires before reaching a steady state value of about 6.3 cm.. Such behaviour seems to agree with the RNLAF CH-47D flight manual ((Anon, 2004),section 8.3). The manual states that when the AFCS is turned on in flight after it has been switched off, or it leaves ground mode, a DASH error signal could exist. This means that DASH actuator operation and the longitudinal stick position are out of sync, requiring a small period of time for the actuator to cancel the error signal after which it is able to resume normal operation. This is done with the Transition mode of the DASH as described above. The manual does not mention how long this period actually lasts, but, from discussions with Chinook pilots, it appears that this period it would amount to approximately 25 seconds,

 the load is suspended on two-point or three-point suspension systems. In the threepoint suspension the redundant set of slings (between the front and rear hook) come

the load can be suspended either in a nose-down position (so-called 'nose-down rigged

 the helicopter is flying initially in level flight at velocities varying between 10 and 100 kts the helicopter can carry three different container of 2 tonnes, 6 tonnes or 10 tonnes. the pilot reaction time to failure varies from instantaneously reaction (ideal case) to a

load') or in a horizontal position (so-called 'level rigged load').

forward flight

value similar to the one encountered in Fig. 9.

into action when the front cables fail.

delay in response of 1 and 2 seconds.

Furthermore, the following scenarios are considered:

Fig. 10 shows the helicopter pitch rate, attitude and velocities after a cable failure in the case of a PID controlled helicopter (left hand side of the figure) and an AFCS controlled helicopter (right hand side). The case considered is the helicopter flying forward at 50 kts when a front failure occurs with a 2-point suspended load of 2000 kg. It is considered that the pilot PID control will start to react at 1 sec after the front suspension point has failed. The controls remain unchanged from the moment of failure to the moment of pilot reaction (i.e. for 1 second). It is interesting to discuss how the AFCS affects the simulation. While the PID controller is restrained by the pilot reaction time, the AFCS control laws immediately start reacting to the change in helicopter pitch attitude caused by the swinging of the load. This should result in a lower maximum pitch rate, an expectation confirmed by the results. The maximum pitch rate qmax of the PID controlled helicopter is equal to 8.6 deg/sec (27th second), whereas the qmax resulting from AFCS control comes to 7.6 deg/sec (2nd second), an 11% attitude reduction. Concerning the pitch attitude, one can see that the AFCS controller clearly has trouble to maintain the trimmed pitch attitude, allowing it to increase to 8 degrees. This immediately has its effect on the forward velocity that begins to decline as soon as the pitch angle starts to build up at about 27 seconds. The filtering of the pitch attitude control also has its effect on the vertical velocity, but this is neither vital to the survival of the helicopter nor relevant to the ADS-33 handling limits. Simulating different scenarios it was observed that the DASH control circuit fails to maintain airspeed when flying faster than 40 kts. Though it appears more and more likely that the implementation of the DASH control circuit does not wholly agree with the real-life situation, the pitch ILCA is still doing its job just as intended, keeping the pitch rate within handling limits and making recovery possible.

Fig. 10. Helicopter motion after front suspension load failure, 50kts, two-point suspension, 2 tonne mass load

PID controlled AFCS controlled

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 169

than if he reacts one second later ( =1sec point dotted line). This can be explained as follows: the AFCS is actually first attempting to converge to reference (trim) values. If the pilot reacts immediately to the failure, the AFCS has difficulties in combining pilot inputs with its own convergence algorithm. But as soon as the circumstances favour the AFCS controller, i.e. the pilot reaction time becomes 1 or 2 seconds, the advantage of its

Especially with a 2 second reaction time the contribution of the AFCS to the helicopter recovery emerges as invaluable. This can be seen when comparing Fig. 12(a) with Fig. 12(b), showing even more than doubling the envelope area when =2 sec and when instead of using PID controller the AFCS is switched on. This means that, when compared to a basic PID controlled helicopter, the AFCS is offering a much broader flight regime in which under slung loads can be transported. While the PID only stabilizes the helicopter motions by limiting the

Comparing the two-point and three-point suspension for an AFCS controlled helicopter (i.e. Fig. 12(b) with Fig. 13(b)) it appears that a three-point suspension is safer. However, this does not mean that the two-point suspension is not safe for a certain condition. For example, if a 6 tone load needs to be transported, one can choose for a two-point suspension with the condition of not exceeding 70 kts in level flight. Above this velocity the chance to recover in

rate at which the attitude changes, the AFCS is attempting to converge to trim values.

Velocity (kts)

=0 sec =1 sec =2 sec 2 4 6 8 10 Load mass (tones)

2 4 6 8 10 Load mass (tones)

*(b) Longitudinal AFCS control*

*(b) Longitudinal AFCS control*

=0 sec =1 sec =2 sec

*Load failure safety envelopes for different pilot reaction time*

=2 sec

=0 sec =1 sec

=0 sec =1 sec =2 sec

=0 sec =1 sec =2 sec

*Load failure safety envelopes for different pilot reaction time*

Velocity (kts)

=0 sec =1 sec =2 sec

application becomes clear.

*Load failure safety envelopes for different pilot reaction time*

*(a) PID control*

*Load failure safety envelopes for different pilot reaction time*

*(a) PID control*

=2 sec

=2 sec

Velocity (kts)

Velocity (kts)

2 4 6 8 10 Load mass (tones)

=0 sec =1 sec

Fig. 12. Safety envelopes for a two-point suspension

2 4 6 8 10 Load mass (tones)

Fig. 13. Safety envelopes for a three-point suspension

=1 sec

=0 sec

Fig. 10 clearly shows the advantage of the running AFCS: the pitch ILCA picks up on the increasing pitch rate right after the cable failure, resulting in a lower maximum pitch rate compared to PID control with a one second reaction time delay. The PID controlled pitch rate ranges from -4 to +8 deg/s, the AFCS improves on this with a range of -2.5 to +7.5 deg/s.

The difference in helicopter motions result in a small difference in the way the load swings. But surprisingly, the change is not to be found in the axis in which the controller actually differs. Fig. 11 presents the pitch, roll and yaw motions of the container. Apart from the deviation in shape, the longitudinal AFCS controller causes an increased negative load roll rate and larger overall yaw rate amplitude. The swinging of the load may even result in a destructive collision between the container and helicopter hull before the load can be safely detached. This danger should be investigated in future research.

Fig. 11. Load motion after front suspension cable failure

## **5. Defining safety envelopes for the load failures**

The numerous failure scenarios simulated have been plotted in safety envelopes giving the velocity when recovery was possible as a function of load mass carried. Fig. 12 and Fig. 13 present the envelopes for a two- and respectively three-point suspension level rigged container after the front suspension point failed as a function of pilot reaction time to recover. Two controls are analysed: (a) a PID controller and (b) an AFCS controller. Looking at Fig. 12 one can see that in case of a two-point suspension, the PID control covers a larger envelope area than the partial AFCS control when the pilot reacts instantaneously to the failure (= 0 sec). However, in case of a three-point suspension this difference is not present. Fig. 12(b) shows a kind of inverse trend in safety when switching on the AFCS: if the pilot reacts instantaneously to the failure (=0 dotted line envelope) he has less chances to recover 168 Automatic Flight Control Systems – Latest Developments

Fig. 10 clearly shows the advantage of the running AFCS: the pitch ILCA picks up on the increasing pitch rate right after the cable failure, resulting in a lower maximum pitch rate compared to PID control with a one second reaction time delay. The PID controlled pitch rate ranges from -4 to +8 deg/s, the AFCS improves on this with a range of -2.5 to

The difference in helicopter motions result in a small difference in the way the load swings. But surprisingly, the change is not to be found in the axis in which the controller actually differs. Fig. 11 presents the pitch, roll and yaw motions of the container. Apart from the deviation in shape, the longitudinal AFCS controller causes an increased negative load roll rate and larger overall yaw rate amplitude. The swinging of the load may even result in a destructive collision between the container and helicopter hull before the load can be safely

> -50 0 50

> > 50

0

r

PID controlled AFCS controlled

The numerous failure scenarios simulated have been plotted in safety envelopes giving the velocity when recovery was possible as a function of load mass carried. Fig. 12 and Fig. 13 present the envelopes for a two- and respectively three-point suspension level rigged container after the front suspension point failed as a function of pilot reaction time to recover. Two controls are analysed: (a) a PID controller and (b) an AFCS controller. Looking at Fig. 12 one can see that in case of a two-point suspension, the PID control covers a larger envelope area than the partial AFCS control when the pilot reacts instantaneously to the failure (= 0 sec). However, in case of a three-point suspension this difference is not present. Fig. 12(b) shows a kind of inverse trend in safety when switching on the AFCS: if the pilot reacts instantaneously to the failure (=0 dotted line envelope) he has less chances to recover

l [deg/s]

ql [deg/s]

pl [deg/s]

0 1 2 3 4 5 6

Load yaw rate

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -50

time[s]

Load roll rate

Load pitch rate

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -200

detached. This danger should be investigated in future research.

0 1 2 3 4 5 6

Load yaw rate

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -50

time[s]

Fig. 11. Load motion after front suspension cable failure

**5. Defining safety envelopes for the load failures** 

Load roll rate

Load pitch rate

<sup>0</sup> <sup>1</sup> <sup>2</sup> <sup>3</sup> <sup>4</sup> <sup>5</sup> <sup>6</sup> -200

+7.5 deg/s.


50

0

r

l [deg/s]

ql [deg/s]

pl [deg/s]

than if he reacts one second later ( =1sec point dotted line). This can be explained as follows: the AFCS is actually first attempting to converge to reference (trim) values. If the pilot reacts immediately to the failure, the AFCS has difficulties in combining pilot inputs with its own convergence algorithm. But as soon as the circumstances favour the AFCS controller, i.e. the pilot reaction time becomes 1 or 2 seconds, the advantage of its application becomes clear.

Fig. 12. Safety envelopes for a two-point suspension

Fig. 13. Safety envelopes for a three-point suspension

Especially with a 2 second reaction time the contribution of the AFCS to the helicopter recovery emerges as invaluable. This can be seen when comparing Fig. 12(a) with Fig. 12(b), showing even more than doubling the envelope area when =2 sec and when instead of using PID controller the AFCS is switched on. This means that, when compared to a basic PID controlled helicopter, the AFCS is offering a much broader flight regime in which under slung loads can be transported. While the PID only stabilizes the helicopter motions by limiting the rate at which the attitude changes, the AFCS is attempting to converge to trim values.

Comparing the two-point and three-point suspension for an AFCS controlled helicopter (i.e. Fig. 12(b) with Fig. 13(b)) it appears that a three-point suspension is safer. However, this does not mean that the two-point suspension is not safe for a certain condition. For example, if a 6 tone load needs to be transported, one can choose for a two-point suspension with the condition of not exceeding 70 kts in level flight. Above this velocity the chance to recover in

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 171

The system of equations describing completely the motion of the helicopter in an inertial

*u g <sup>X</sup> rv qw <sup>m</sup> v g Y ru pw*

 

*w g q Z u pv*

*m*

*m*

2 2 2

*y z z xz xy x y z z xz x z xz*

*rq I I I I pqI I I I I L I N*

*xz x y z x x y xz xz x x z xz*

> sin cos cos cos sin sin

 

*rqI I I I pq I I I I I L I N*

*II I*

*q r*

*q r*

 

 

In order to describe completely the helicopter motion w.r.t. the Earth system, the equations

 

cos sin cos sin cos cos sin sin cos sin cos sin sin cos sin cos

To these systems of equations, two differential equations are added for the dynamic inflow of the front main and rear rotors, describing the dynamic inflow as a "quasi-steady inflow"

> *f if T Elem f T Glau f r ir T Elem r T Glau r*

where CT,elem and CT,Glau are the rotor thrust coefficients as expressed in blade element theory and respectively Glauert theory. The total forces and moments acting on the helicopter centre of gravity consist of the sum of front and rear rotors (with indices Rf and Rr), rotor torque (Q) and helicopter body aerodynamics (B). For the load, a suspension point component (S) is considered which is added when the load is attached underneath the

 

*C C C C*

,, ,, ,, ,,

 

 

 

(6)

 

 

*p*

*xu v w v w yu v w v w*

 

 

 

2 2 2

(4)

(5)

sin

 

sin cos cos cos

 

2 2

*<sup>p</sup> II I*

*<sup>q</sup> <sup>I</sup>*

*r*

of trajectory can be added:

 

by means of time constants:

helicopter model.

*z x xz y*

*M pr I I I r p*

 

 

 

sin sin cos cos

 

*zu v w*

 

system are:

case of a load failure is questionable. In case of a 10 tones load, the AFCS for a two-point suspension cannot contribute to the pilot efforts to recover the load if the failure occurs above 30 kts. In this case it is safer to choose a three-point suspension for load transportation.

## **6. Conclusion**

The purpose of this chapter is to determine how the AFCS influenced the recovery prospects of a Chinook helicopter with an external sling load when one of its cables brakes. This can be of vital importance for deciding whether to replace the safer three-point redundant suspension to a two-point suspension during Royal Netherlands Air Force operations. The chapter presented the flight control laws for a longitudinal automatic flight control system (AFCS). The general conclusion that could be drawn was that the assistance of the AFCS expanded the number of occasions at which the helicopter motions stayed within the handling limits during recovery of a cable failure. In many cases, the AFCS cancelled the negative effect of a delayed pilot response, supporting the supposition that the combination of active pilot control and AFCS backup could push the flight envelope boundaries even further. The chapter proposed safety envelopes covering the areas that define the conditions at which a cable failure at a suspension point could happen without presumable fatal consequences. It was demonstrated that since the longitudinal part of the AFCS was operating continuously, it was not bound by the obstruction of the imposed pilot reaction time. For this reason, partial AFCS control gained an advantage when the pilot reaction was delayed. Flying with a two-point suspension is just as safe as a three-point suspension stipulating that the safety envelope boundaries are obeyed.

## **7. Appendix A**

## **7.1 Derivation of the equations of motion in a six degree-of-freedom model**

In a general 6-dof non-linear body model the helicopter motion is represented by three translations and three rotations around the body axes-system *EXYZ B BB B* centred in the helicopter centre of gravity, see Fig. A1.

Fig. A1. System of coordinates used to express the helicopter motion in the 6-dof model

170 Automatic Flight Control Systems – Latest Developments

case of a load failure is questionable. In case of a 10 tones load, the AFCS for a two-point suspension cannot contribute to the pilot efforts to recover the load if the failure occurs above 30 kts. In this case it is safer to choose a three-point suspension for load

The purpose of this chapter is to determine how the AFCS influenced the recovery prospects of a Chinook helicopter with an external sling load when one of its cables brakes. This can be of vital importance for deciding whether to replace the safer three-point redundant suspension to a two-point suspension during Royal Netherlands Air Force operations. The chapter presented the flight control laws for a longitudinal automatic flight control system (AFCS). The general conclusion that could be drawn was that the assistance of the AFCS expanded the number of occasions at which the helicopter motions stayed within the handling limits during recovery of a cable failure. In many cases, the AFCS cancelled the negative effect of a delayed pilot response, supporting the supposition that the combination of active pilot control and AFCS backup could push the flight envelope boundaries even further. The chapter proposed safety envelopes covering the areas that define the conditions at which a cable failure at a suspension point could happen without presumable fatal consequences. It was demonstrated that since the longitudinal part of the AFCS was operating continuously, it was not bound by the obstruction of the imposed pilot reaction time. For this reason, partial AFCS control gained an advantage when the pilot reaction was delayed. Flying with a two-point suspension is just as safe as a three-point suspension

stipulating that the safety envelope boundaries are obeyed.

helicopter centre of gravity, see Fig. A1.

**7.1 Derivation of the equations of motion in a six degree-of-freedom model** 

In a general 6-dof non-linear body model the helicopter motion is represented by three translations and three rotations around the body axes-system *EXYZ B BB B* centred in the

Fig. A1. System of coordinates used to express the helicopter motion in the 6-dof model

transportation.

**6. Conclusion** 

**7. Appendix A** 

The system of equations describing completely the motion of the helicopter in an inertial system are:

$$\begin{aligned} \dot{u} &= -g\sin\theta + X\Big/\_{m} + rv - qw \\ \dot{v} &= g\sin\phi\cos\theta + Y\Big/\_{m} - ru + pv \\ \dot{w} &= g\cos\phi\cos\theta + Z\Big/\_{m} + qu - pv \end{aligned}$$

$$\begin{aligned} \dot{p} &= \frac{rq\left(I\_{y}I\_{z} - I\_{z}^{2} - I\_{zx}^{2}\right) - pqI\_{xy}\left(I\_{z} - I\_{y} + I\_{z}\right) + I\_{z}L + I\_{xz}N}{I\_{z}I\_{z} - I\_{zx}^{2}} \\ \dot{q} &= \frac{M + pr\left(I\_{z} - I\_{z}\right) + I\_{zx}\left(r^{2} - p^{2}\right)}{I\_{y}} \\ \dot{r} &= \frac{-rqI\_{zx}\left(I\_{z} - I\_{y} + I\_{z}\right) + pq\left(I\_{z}^{2} - I\_{z}I\_{y} + I\_{zx}^{2}\right) + I\_{zx}L + I\_{z}N}{I\_{z}I\_{z} - I\_{zx}^{2}} \end{aligned} \tag{4}$$

$$\begin{aligned} \dot{\psi} &= \frac{\left(q\sin\phi + r\cos\phi\right)}{\cos\theta} \\ \dot{\theta} &= q\cos\phi - r\sin\phi \\ \dot{\phi} &= p + \dot{\psi}\sin\theta \end{aligned}$$

In order to describe completely the helicopter motion w.r.t. the Earth system, the equations of trajectory can be added:

$$\begin{aligned} \dot{x} &= \left( u\cos\theta + \left( v\sin\phi + w\cos\phi \right) \sin\theta \right) \cos\psi - \left( v\cos\phi - w\sin\phi \right) \sin\psi\\ \dot{y} &= \left( u\cos\theta + \left( v\sin\phi + w\cos\phi \right) \sin\theta \right) \sin\psi + \left( v\cos\phi - w\sin\phi \right) \cos\psi\\ \dot{z} &= -u\sin\theta + \left( v\sin\phi + w\cos\phi \right) \cos\theta \end{aligned} \tag{5}$$

To these systems of equations, two differential equations are added for the dynamic inflow of the front main and rear rotors, describing the dynamic inflow as a "quasi-steady inflow" by means of time constants:

$$\begin{aligned} \pi\_f \dot{\mathcal{A}}\_{\circ} &= \mathsf{C}\_{\,^{\circ}, \mathrm{Elim}, f} - \mathsf{C}\_{\,^{\circ}, \mathrm{Clim}, f} \\ \pi\_r \dot{\mathcal{A}}\_{r} &= \mathsf{C}\_{\,^{\circ}, \mathrm{Elim}, r} - \mathsf{C}\_{\,^{\circ}, \mathrm{Clim}, r} \end{aligned} \tag{6}$$

where CT,elem and CT,Glau are the rotor thrust coefficients as expressed in blade element theory and respectively Glauert theory. The total forces and moments acting on the helicopter centre of gravity consist of the sum of front and rear rotors (with indices Rf and Rr), rotor torque (Q) and helicopter body aerodynamics (B). For the load, a suspension point component (S) is considered which is added when the load is attached underneath the helicopter model.

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 173

the pilot moves the collective up; 4) Longitudinal cyclic for front and rear rotor1sf and 1sr are assumed positive when the pilot moves the stick forward; 5) Lateral cyclic for front and rear rotors 1cf and 1cr are assumed positive when the pilot moves the stick to the right for

cyclic pitch to the right.

Fig. A3. Longitudinal axis Chinook control (side view)

Fig. A4. Lateral axis Chinook control (front view)

$$\begin{aligned} \mathbf{X} &= \mathbf{X}\_{\mathbb{N}\_{\mathcal{Y}}} + \mathbf{X}\_{\mathbb{N}\_{\mathcal{Y}}} + \mathbf{X}\_{\mathbb{s}} \left( + \mathbf{X}\_{\mathbb{s}} \right) \\ \mathbf{Y} &= \mathbf{Y}\_{\mathbb{N}\_{\mathcal{Y}}} + \mathbf{Y}\_{\mathbb{s}r} + \mathbf{Y}\_{\mathbb{s}} \left( + \mathbf{Y}\_{\mathbb{s}} \right) \\ \mathbf{Z} &= \mathbf{Z}\_{\mathbb{N}\_{\mathcal{Y}}} + \mathbf{Z}\_{\mathbb{s}r} + \mathbf{Z}\_{\mathbb{s}} \left( + \mathbf{Z}\_{\mathbb{s}} \right) \\ \mathbf{L} &= \mathbf{L}\_{\mathbb{Q}'} + \mathbf{L}\_{\mathbb{Q}r} + \mathbf{L}\_{\mathbb{s}\mathcal{Y}} + \mathbf{L}\_{\mathbb{s}r} + \mathbf{L}\_{\mathbb{s}} \left( + \mathbf{L}\_{\mathbb{s}} \right) \\ \mathbf{M} &= \mathbf{M}\_{\mathbb{N}'} + \mathbf{M}\_{\mathbb{s}r} + \mathbf{M}\_{\mathbb{s}} \left( + \mathbf{M}\_{\mathbb{s}} \right) \\ \mathbf{N} &= \mathbf{N}\_{\mathcal{Q}'} + \mathbf{N}\_{\mathbb{q}r} + \mathbf{N}\_{\mathbb{s}\mathcal{Y}} + \mathbf{N}\_{\mathbb{s}r} + \mathbf{N}\_{\mathbb{s}} \left( + \mathbf{N}\_{\mathbb{s}} \right) \end{aligned} \tag{7}$$

The rotor forces and moments consist of front and rear vertical thrust components Tf and Tr, drag forces HXf and HX,r, lateral forces HYf, and HYr and rotor shaft torques MQf and MQr as seen in Fig. A2.

*Rf Tf Hf Rf Tf Hf Rf Tf Hf X XX Y YY Z ZZ Rr Tr Hr Rr Tr Hr Rr Tr Hr X XX Y YY Z ZZ* (8) 1 1 *Rf Rf f Rf Qf Rf Rf f Rf f Rf Rf Rf f Qf L Yh Z f L M Xh Zl N X f Yl N* 1 1 *Rr Rr r Rr Qr Rr Rr r Rr r Rr Rr Rr r Qr L Yh Z f L M Xh Zl N X f Yl N* 

Fig. A2. Forces and Moments on the rotors

The model uses the following sign conventions (see Fig. A3 and Fig. A4): 1) Longitudinal disc tilt for front and rear rotors a1f and a1r are assumed positive for backward tilted rotor disc plane; 2) Lateral disc tilt for front and rear rotor b1f and b1r are positive for rotor disc plane tilted in the direction of azimuth angle =90(i.e. b1f >0 to the right and b1r>0 to the left, backside view); 3) Collective pitch for front and rear rotor 0f and 0r are positive when 172 Automatic Flight Control Systems – Latest Developments

*Qf Qr Rf Rr B S Rf Rr B S*

*NN N N N N N*

The rotor forces and moments consist of front and rear vertical thrust components Tf and Tr, drag forces HXf and HX,r, lateral forces HYf, and HYr and rotor shaft torques MQf and MQr as

*LL L L L L L MM M M M*

The model uses the following sign conventions (see Fig. A3 and Fig. A4): 1) Longitudinal disc tilt for front and rear rotors a1f and a1r are assumed positive for backward tilted rotor disc plane; 2) Lateral disc tilt for front and rear rotor b1f and b1r are positive for rotor disc plane tilted in the direction of azimuth angle =90(i.e. b1f >0 to the right and b1r>0 to the left, backside view); 3) Collective pitch for front and rear rotor 0f and 0r are positive when

 

*Rf Rr B S Rf Rr B S Rf Rr B S*

*XX X X X YY Y Y Y ZZ Z Z Z*

*Rf Tf Hf Rf Tf Hf Rf Tf Hf*

1

*X XX Y YY Z ZZ*

1

Fig. A2. Forces and Moments on the rotors

*Rf Rf f Rf Qf Rf Rf f Rf f Rf Rf Rf f Qf*

 

*L Yh Z f L M Xh Zl N X f Yl N*

 

seen in Fig. A2.

 

 

*Qf Qr Rf Rr B S*

*Rr Tr Hr Rr Tr Hr Rr Tr Hr*

1

*Rr Rr r Rr Qr Rr Rr r Rr r Rr Rr Rr r Qr*

 

*L Yh Z f L M Xh Zl N X f Yl N*

1

*X XX Y YY Z ZZ*

 

(7)

(8)

the pilot moves the collective up; 4) Longitudinal cyclic for front and rear rotor1sf and 1sr are assumed positive when the pilot moves the stick forward; 5) Lateral cyclic for front and rear rotors 1cf and 1cr are assumed positive when the pilot moves the stick to the right for cyclic pitch to the right.

Fig. A3. Longitudinal axis Chinook control (side view)

Fig. A4. Lateral axis Chinook control (front view)

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 175

<sup>3</sup> <sup>1</sup> 23 2 2 *f r zf r if r l*

, , 1, , , ,

 

 

2 1, 0, 1, 1, , , 0, 0, 0,

2 2

 

> 

*xf r df r f r xf r zf r if r l*

*a a b*

, 1,

*Tf r f r*

*C b*

, , , ,, 2 +( - ) ) *CT Glau if r xf r if r zf r*

 , <sup>2</sup> , , ,, , ,, 1 4.7

The advance ratios of front/rear rotors xf,r, xf,r, xf,r are calculated by projecting helicopter

; *f fr r f f f r rr f f r r*

and then by non-dimensionalizing (uf,r, vf,r, wf,r) by R while neglecting the yaw rate r. This

*fff*

*rrr*

*u h q v h p w l q RRR*

*u hq v hp w lq RRR*

*u u f r h q u u f r h q v v lr h p v v lr h p w wl q fp w wl q fp*

1 1

1 1

(18)

<sup>2</sup> *C C CC df* ,0 , *r d dt T <sup>f</sup> <sup>r</sup>* (19)

*C CC*

 

*Qf r xf r Tf r zf r if r xf r HXf r*

2 2 42 4

*C b a b a a*

*fr fr fr fr zf r if r f r fr fr <sup>l</sup>*

, , ,, ,

 

, , 1, , 2 2 0, 1,

*zf r if r f r xf r fr fr*

24 6

 

 

 

velocity vector (u,v,w) on the plane of front/rear rotor hub as (uf,r, vf,r, wf,r):

leads to the following expressions for the front/rear rotor advance ratios:

The blade drag coefficient Cdf,r of front/rear rotors is calculated as:

*xf yf zf*

*xr yr zr*

22 32 2

*Tf r T elem f r xf r*

*C C a*

 

*<sup>C</sup> C C*

, 0 ,

*C*

*HXf r f r l*

3( )

, , 0, 1, ,

The main rotor thrust coefficient in Glauert theory is:

8 *df r*

*C*

*HYf r xf r f r f r xf r*

*C a a*

3

 

0, 1, , , 1, 0, 1,

 

*b b a a*

*fr fr zf r if r f r fr fr*

The rotor torque coefficient can be expressed as:

346

*C*

0 , , ,

 

   

3 3

0, 1, , 1,

*a a C a*

*f r f r Tf r f r*

(12)

(13)

 

(15)

(16)

(17)

(14)

The contributions of these components to the front rotor thrust and the horizontal and side forces in the helicopter body system are:

$$\begin{aligned} X\_{\eta\eta} &= T\_f \sin\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) \cos\left(\theta\_{1\circ f} + b\_{1\circ}\right) \\ X\_{\eta\eta} &= -H\_{\chi\eta} \cos\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) - H\_{\eta\circ} \sin\left(\theta\_{1\circ f} + b\_{1\circ}\right) \sin\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) \\ Y\_{\eta\eta} &= T\_f \sin\left(\theta\_{1\circ f} + b\_{1\circ}\right) \cos\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) \\ Y\_{\eta\eta} &= H\_{\eta\circ} \cos\left(\theta\_{1\circ f} + b\_{1\circ}\right) \\ Z\_{\eta\eta} &= -T\_f \cos\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) \cos\left(\theta\_{1\circ f} + b\_{1\circ}\right) \\ Z\_{\eta\eta} &= -H\_{\chi\circ} \sin\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) + H\_{\eta\circ} \sin\left(\theta\_{1\circ f} + b\_{1\circ}\right) \sin\left(\theta\_{1\circ f} - a\_{1\circ} + i\_f\right) \\ L\_{\eta\circ} &= M\_{\eta\circ} \sin i\_f \\ N\_{\eta\circ} &= -M\_{\eta\circ} \cos i\_f \end{aligned} \tag{9}$$

For the rear rotor, these components are (note the opposite direction of the lateral flapping angle b1r with respect to the front rotor equations):

$$\begin{aligned} X\_{ir} &= T\_r \sin\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) \cos\left(\theta\_{1\text{sr}} - b\_{1r}\right) \\ X\_{ir} &= -H\_{\text{ir}} \cos\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) + H\_{\text{ir}} \sin\left(\theta\_{1\text{sr}} - b\_{1r}\right) \sin\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) \\ Y\_{ir} &= T\_r \sin\left(\theta\_{1\text{sr}} - b\_{1r}\right) \cos\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) \\ Y\_{ir} &= -H\_{\text{ir}} \cos\left(\theta\_{1\text{sr}} - b\_{1r}\right) \\ Z\_{ir} &= -T\_r \cos\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) \cos\left(\theta\_{1\text{sr}} - b\_{1r}\right) \\ Z\_{ir} &= -H\_{\text{ll}} \sin\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) - H\_{\text{lr}} \sin\left(\theta\_{1\text{sr}} - b\_{1r}\right) \cos\left(\theta\_{1\text{sr}} - a\_{1r} + i\_r\right) \\ L\_{\text{\texttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttexttext$$

The front and the rear rotor thrust (Tf and Tr), horizontal force (drag force) (HXf, HXr), lateral forces (HYf, HYr) and torque (MQf, MQr) are expressed by their non-dimensional coefficients:

$$\begin{aligned} T\_{f,r} &= \mathbb{C}\_{\gamma f, \sigma} \rho \left(\Omega \mathbf{R}\right)^2 \pi \mathbf{R}^2 \\ H\_{\chi\_{\mathbf{y},r}} &= \mathbb{C}\_{\pi \mathbf{y}, r} \rho \left(\Omega \mathbf{R}\right)^2 \pi \mathbf{R}^2 \\ H\_{\chi\_{\mathbf{y}',r}} &= \mathbb{C}\_{\pi \mathbf{y}', r} \rho \left(\Omega \mathbf{R}\right)^2 \pi \mathbf{R}^2 \\ M\_{\chi\_{\mathbf{y}',r}} &= \mathbb{C}\_{\chi\_{\mathbf{y}',r}} \rho \left(\Omega \mathbf{R}\right)^2 \pi \mathbf{R}^3 \end{aligned} \tag{11}$$

The non-dimensional coefficients for rotor thrust, horizontal and lateral forces and torque can be calculated using the blade element theory by integration of the lift and drag forces on each blade element along the blade and around the azimuth. Their non-dimensional coefficients w.r.t. the disc plane (non-dimensionalized by <sup>2</sup> <sup>2</sup> *R R* ), for the front and rear rotors, are:

174 Automatic Flight Control Systems – Latest Developments

The contributions of these components to the front rotor thrust and the horizontal and side

cos sin sin

 

*X H ai H b ai*

*Hf Xf sf f f Yf cf f sf f f*

*sf f f*

*r sr rr*

*a i*

(11)

*R R* ), for the front and

*a i*

(9)

(10)

1 1 11 11

 

1 1 11 11

 

1 1 1 1

 

11 11

1 1 1 1

sin sin

1 1 1 1

 

sin sin

11 11

1 1 1 1

, ,

*f r Tf r Xf r HXf r Yf r HYf r Qf r Qf r*

, ,

, ,

, ,

coefficients w.r.t. the disc plane (non-dimensionalized by <sup>2</sup> <sup>2</sup>

1 1 1 1

1 1 cos

The front and the rear rotor thrust (Tf and Tr), horizontal force (drag force) (HXf, HXr), lateral forces (HYf, HYr) and torque (MQf, MQr) are expressed by their non-dimensional

The non-dimensional coefficients for rotor thrust, horizontal and lateral forces and torque can be calculated using the blade element theory by integration of the lift and drag forces on each blade element along the blade and around the azimuth. Their non-dimensional

*T C RR H C RR H C RR M C RR*

 

 

2 2

 

2 2

2 2

2 3

 

 

 

 

cos sin sin

 

*X H ai H b ai*

*Hr Xr sr r r Yr cr r sr r r*

*Tr r cr r sr r r*

*YT b ai*

sin cos

cos

sin cos

*Qr Qr r Qr Qr r*

*LMi NM i*

 

coefficients:

rear rotors, are:

*Hr Yr cr r*

*YH b*

sin cos

*XT ai b*

*Tr r sr r r cr r*

1 1

cos cos

*Z T ai b*

*Tr r sr r r cr r Hr Xr sr r r Yr cr*

*Z H aiH b*

*Hf Xf sf f f Yf cf f*

*Z H ai H b*

1 1 sin

For the rear rotor, these components are (note the opposite direction of the lateral flapping

 

1 1 1 1

*Tf f cf f sf f f*

*YT b a i*

sin cos

cos

*YH b*

*Hf Yf cf f*

sin cos

angle b1r with respect to the front rotor equations):

*Qf Qf f Qf Qf f*

*LM i NMi*

  sin cos

*XT ai b*

*Tf f sf f f cf f*

1 1

cos cos

*Z T ai b*

*Tf f sf f f cf f*

forces in the helicopter body system are:

$$\mathbb{C}\_{\Upsilon\_{l',r}} \approx \mathbb{C}\_{\Gamma\_{l,\text{dim},\ell,r}} = \frac{\sigma \mathbb{C}\_{\text{la}}}{\mathfrak{2}} \left[ \frac{\theta\_{0\_{\ell,r}}}{\mathfrak{3}} \left( 1 + \frac{\mathfrak{3}}{2} \mu\_{\eta^{\ell,r}} \right) + \frac{\mu\_{\eta^{\ell,r}} - \lambda\_{\eta^{\ell,r}}}{\mathfrak{2}} \right] \tag{12}$$

$$\begin{split} \mathbf{C}\_{\text{H}\&,r} &= \frac{\sigma \mathbf{C}\_{\text{lur}}}{2} \Bigg[ \frac{\mu\_{\text{r}/r} \mathbf{C}\_{\text{d}\_{f,r}}}{2 \mathbf{C}\_{\text{lur}}} + \theta\_{0f,r} \Bigg( \frac{a\_{1f,r}}{3} - \frac{\mu\_{\text{s}/r}}{2} \frac{\mu\_{\text{r}/r} - \lambda\_{\text{s}/r}}{2} \Bigg) + \\ &+ \frac{\Re(\mu\_{\text{s}/r} - \lambda\_{\text{s}/r})a\_{1f,r}}{2} + \frac{\mu\_{\text{s}/r}}{4} \Big( a\_{0f,r}^{-2} + a\_{1f,r}^{-2} \Bigg) - \frac{a\_{0f,r}b\_{1f,r}}{6} \Bigg) - \mathbf{C}\_{\text{fl},r}a\_{1f,r} \end{split} \tag{13}$$

$$\begin{split} \mathbf{C}\_{H\boldsymbol{\upbeta},r} &= \frac{\sigma \mathbf{C}\_{\boldsymbol{u},r}}{2} \Big[ \boldsymbol{\mu}\_{\boldsymbol{\upbeta},r} \left( \frac{\mathbf{b}\_{1/r} \boldsymbol{\theta}\_{0,r}}{2} - \mathbf{a}\_{0,r} \mathbf{a}\_{1/r} \right) + \boldsymbol{\mu}\_{\boldsymbol{\upbeta},r} \cdot \left( \frac{\mathbf{a}\_{1/r} \boldsymbol{\upbeta}\_{1/r}}{4} + \frac{\mathbf{3} \left( \boldsymbol{\mu}\_{\boldsymbol{\upbeta},r} - \boldsymbol{\upbeta}\_{0,r} \right) \mathbf{a}\_{0,r}}{2} - \frac{\mathbf{3} \mathbf{a}\_{0,r} \boldsymbol{\upbeta}\_{0,r}}{4} \right) + \\ &+ \frac{\boldsymbol{\Theta}\_{0,r} \cdot \mathbf{b}\_{1/r}}{3} + \frac{\mathbf{3} \left( \boldsymbol{\mu}\_{\boldsymbol{\upbeta},r} - \boldsymbol{\upbeta}\_{\boldsymbol{\upbeta},r} \right) \mathbf{b}\_{1/r}}{4} + \frac{\mathbf{a}\_{0,r} \cdot \mathbf{a}\_{1/r}}{6} \Big] - \mathbf{C}\_{\boldsymbol{\upbeta},r} \boldsymbol{b}\_{1/r} \end{split} \tag{14}$$

The main rotor thrust coefficient in Glauert theory is:

$$\mathbf{C}\_{\mathbf{r}\_{\text{'},\text{'}\text{'}\text{'}}} = \mathbf{2}\boldsymbol{\lambda}\_{\mathbf{r}\_{\text{'},\text{'}}} \sqrt{\boldsymbol{\mu}\_{\text{z}\_{\text{'},\text{'}}} + (\boldsymbol{\lambda}\_{\text{'},\text{'}} \cdot \boldsymbol{\mu}\_{\text{z}\_{\text{'},\text{'}}})^2} \tag{15}$$

The rotor torque coefficient can be expressed as:

$$\mathbf{C}\_{\mathbf{Q}\_{\mathbf{f},r}} = \frac{\sigma \mathbf{C}\_{\mathbf{d}\_{\mathbf{f},r}}}{8} \left( \mathbf{1} + 4.7 \,\mu\_{\mathbf{r}\mathbf{f},r} \right) - \mathbf{C}\_{\mathbf{f}\mathbf{f},r} \left( \mu\_{\mathbf{r}\mathbf{f},r} - \lambda\_{\mathbf{f},r} \right) - \mu\_{\mathbf{r}\mathbf{f},r} \mathbf{C}\_{\mathbf{H}\mathbf{X}\mathbf{f},r} \tag{16}$$

The advance ratios of front/rear rotors xf,r, xf,r, xf,r are calculated by projecting helicopter velocity vector (u,v,w) on the plane of front/rear rotor hub as (uf,r, vf,r, wf,r):

$$
\begin{bmatrix} u\_f \\ v\_f \\ w\_f \end{bmatrix} = \begin{bmatrix} u + f\_i r - h\_f q \\ v + l\_f r + h\_f p \\ w - l\_f q - f\_i p \end{bmatrix} \quad ; \quad \begin{bmatrix} u\_r \\ v\_r \\ w\_r \end{bmatrix} = \begin{bmatrix} u + f\_i r - h\_i q \\ v - l\_r r + h\_r p \\ w + l\_i q - f\_i p \end{bmatrix} \tag{17}
$$

and then by non-dimensionalizing (uf,r, vf,r, wf,r) by R while neglecting the yaw rate r. This leads to the following expressions for the front/rear rotor advance ratios:

$$
\mu\_{\boldsymbol{\pi}^{\boldsymbol{\pi}}} = \frac{\left(\boldsymbol{u} - \boldsymbol{h}\_{\boldsymbol{\gamma}}\boldsymbol{q}\right)}{\boldsymbol{\Omega}\boldsymbol{R}} \qquad \qquad \mu\_{\boldsymbol{\pi}^{\boldsymbol{\pi}}} = \frac{\left(\boldsymbol{v} + \boldsymbol{h}\_{\boldsymbol{\gamma}}\boldsymbol{p}\right)}{\boldsymbol{\Omega}\boldsymbol{R}} \qquad \qquad \mu\_{\boldsymbol{\pi}^{\boldsymbol{\pi}}} = \frac{\left(\boldsymbol{w} - \boldsymbol{l}\_{\boldsymbol{\gamma}}\boldsymbol{q}\right)}{\boldsymbol{\Omega}\boldsymbol{R}} \tag{18}
$$

$$
\mu\_{\rm yr} = \frac{\left(\mu - h\_r q\right)}{\Omega R} \qquad \qquad \mu\_{\rm yr} = \frac{\left(\upsilon + h\_r p\right)}{\Omega R} \qquad \qquad \mu\_{\rm yr} = \frac{\left(\upsilon + l\_r q\right)}{\Omega R} \frac{\upsilon}{r}
$$

The blade drag coefficient Cdf,r of front/rear rotors is calculated as:

$$\mathbf{C}\_{\omega\_{\mathbf{f},r}} = \mathbf{C}\_{\omega\_0} + \mathbf{C}\_{\omega} \mathbf{C}\_{\mathbf{f},r}^2 \tag{19}$$

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 177

sin cos 1 sin

*B N fus fus fus fus*

*B Y fus B L fus fus*

*XCV YC V ZC V LCV MC V NC V*

 

cos sin sin sin cos

*S ij ij ij S ij ij ij S ij ij*

*X S Y S Z S*

the suspension point on the load.

when the load is oscillating around a fixed point.

 

cos cos

 

 

sin cos

where the fuselage angle of attack fus and fuselage sideslip fus are defined as seen as:

*fus fus fus fus*

cos sin cos cos

 

*S ij ij ij i j j j j*

*M S hs S fs S fs*

 

sin cos sin cos

tension force in one cable j being Sij. The total forces on the slings are:

<sup>1</sup>

 

sin sin cos

*S ij ij ij i ij*

*L S hs f*

 

 

*B L fus fus fus*

 

 

sin sin

*B FE fus fus*

*B M fus fus*

 

> 

sin cos 0.94sin 0.342 cos

2 2 2 2 2 2 2 2

1,3 1,3 1,3 2 2 2

 

cos sin sin sin sin sin

*S ij ij ij j j j j j j*

where ij and ij are the angles that the sling cable makes with the X and Z direction; fs1,2,3 and hs1,2,3 are the hook distances to the helicopter centre of gravity. The slings are modelled as linear springs without mass and have small internal damping. The tension force in each cable is determined by comparing the actual sling length lij to the zero tension sling length l0ij, see equation (27), where *j* is the cable number on the *ith* suspension point. The zero tension cable length as well as the cable stiffness are known, the actual length of each cable is computed by measuring the distance between the specific helicopter suspension point and

The damping forces inside the slings are determined using equation (28). In this equation *dV* is the relative velocity between the endpoints of a cable, in the direction of that cable. This requires that both endpoint velocities are known in the same axis system. The damping coefficient is set just large enough to prevent the load from increase in pendulum motion

 

*NS fS fs S fs*

 

1 1,3 1,3 1,3 1,3 2 2 2 2

 

> 

*S kl l ij* max 0, *ij ij* <sup>0</sup> (27)

*damp*,*ij ij damp <sup>l</sup> S dV c* (28)

 

 

 

*wu w uu w vu v uu v*

 

The helicopter has three suspension points i=1,2,3 underneath its floor as seen in Fig. A6, the

  (24)

(25)

(26)

with the values Cd0 and Cdt defined in Appendix B. The rotor interference is considered through interference factors expressed as in (Ostroff, Downing and Rood, 1976):

$$\begin{aligned} \text{dinterval}\_{\text{sow}} &= \left[ 0.356 + 0.321 \underline{\chi}\_{\text{y}} - 0.368 \underline{\chi}\_{\text{y}} \stackrel{\circ}{\text{}}^2 + 0.392 \underline{\chi}\_{\text{y}} \stackrel{\circ}{\text{}} \right] \left( 1 - \left| \sin \beta\_{\text{r}} \right| \right) + \\ &+ \left[ 0.356 + 0.0131 \underline{\chi}\_{\text{y}} - 0.0764 \underline{\chi}\_{\text{y}} \stackrel{\circ}{\text{}}^2 - 0.0085 \underline{\chi}\_{\text{y}} \stackrel{\circ}{\text{}} \right] \cdot \left| \sin \beta\_{\text{r}} \right| \end{aligned}$$

$$\begin{aligned} \text{dinterval}\_{\text{sow}} &= \left[ 0.356 + 0.151 \underline{\chi}\_{\text{v}} - 0.314 \underline{\chi}\_{\text{v}} \stackrel{\circ}{}^2 + 0.164 \underline{\chi}\_{\text{v}} \stackrel{\circ}{}^3 \right] \left( 1 - \left| \sin \beta\_{\text{r}} \right| \right) + \\ &+ \left[ 0.356 + 0.0131 \underline{\chi}\_{\text{v}} - 0.0764 \underline{\chi}\_{\text{v}} \stackrel{\circ}{}^2 - 0.0085 \underline{\chi}\_{\text{v}} \stackrel{\circ}{}^3 \right] \cdot \left| \sin \beta\_{\text{r}} \right| \end{aligned} \tag{20}$$

where If, Ir are the inflow angles of front and rear rotors defined as in Figure A5 and equation (21) and fr and rr are rotor sideslip angles defined in equation (22) and (17).

Fig. A5. Rotor inflow angle used to calculate front and rear rotor interferences

$$\chi\_{\mathbb{X}^{\mathbb{V}}} = \arctan\left(\frac{\mu\_{\boldsymbol{\pi}^{\mathbb{V}}}}{\lambda\_{\boldsymbol{\gamma}}}\right) \qquad \chi\_{\boldsymbol{\nu}} = \arctan\left(\frac{\mu\_{\boldsymbol{\pi}^{\mathbb{V}}}}{\lambda\_{\boldsymbol{\gamma}}}\right) \tag{21}$$

$$\begin{aligned} \sin \beta\_r &= \upsilon\_f \Big/ \sqrt{\mu\_f^2 + \upsilon\_f^2} & \cos \beta\_r &= \iota\_f \Big/ \sqrt{\mu\_f^2 + \upsilon\_f^2} & \iota\_f &\neq 0\\ \sin \beta\_n &= \upsilon\_r \Big/ \sqrt{\mu\_r^2 + \upsilon\_r^2} & \cos \beta\_n &= \iota\_r \Big/ \sqrt{\mu\_r^2 + \upsilon\_r^2} & \iota\_r &\neq 0 \end{aligned} \tag{22}$$

The interference factors are used to compute a new inflow ratio in the Glauert formula (15):

$$\begin{split} \mathcal{\lambda}\_{\boldsymbol{\gamma}\_{\text{-,new}}} &= \frac{\mathsf{C}\_{\text{\text{\textdegree}}}}{2\sqrt{\left(\boldsymbol{\mu}\_{\text{-\text{\textdegree}}}-\boldsymbol{\lambda}\_{\text{\textdegree}}\right)^{2}+\boldsymbol{\mu}\_{\text{\textdegree}}^{2}}} + d \text{interf}\_{\text{\textdegree}\text{\textdegree}} \frac{\mathsf{C}\_{\text{\textdegree}}}{2\sqrt{\left(\boldsymbol{\mu}\_{\text{w}}-\boldsymbol{\lambda}\_{\text{r}}\right)^{2}+\boldsymbol{\mu}\_{\text{r}}^{2}}} \\ \mathcal{\lambda}\_{\boldsymbol{\gamma}\_{\text{r},\text{aw}}} &= \frac{\mathsf{C}\_{\text{\textdegree}}}{2\sqrt{\left(\boldsymbol{\mu}\_{\text{w}}-\boldsymbol{\lambda}\_{\text{r}}\right)^{2}+\boldsymbol{\mu}\_{\text{w}}^{2}}} + d \text{interf}\_{\text{\textdegree}} \frac{\mathsf{C}\_{\text{\textdegree}}}{2\sqrt{\left(\boldsymbol{\mu}\_{\text{g}}-\boldsymbol{\lambda}\_{\text{g}}\right)^{2}+\boldsymbol{\mu}\_{\text{r}}^{2}}} \end{split} \tag{23}$$

The fuselage forces and moments are calculated through flat plate theory using (Ostroff, Downing and Rood, 1976):

176 Automatic Flight Control Systems – Latest Developments

with the values Cd0 and Cdt defined in Appendix B. The rotor interference is considered

0.356 0.0131 0.0764 0.0085 sin

0.356 0.0131 0.0764 0.0085 sin

 

 

 

where If, Ir are the inflow angles of front and rear rotors defined as in Figure A5 and equation (21) and fr and rr are rotor sideslip angles defined in equation (22) and (17).

 

interf 0.356 0.321 0.368 0.392 1 sin

interf 0.356 0.151 0.314 0.164 1 sin

Fig. A5. Rotor inflow angle used to calculate front and rear rotor interferences

*If Ir*

*if new*

Downing and Rood, 1976):

*ir new*

2 2

 

2 2

 

arctan arctan *xf xr*

2 2 2 2 2 2 2 2 sin cos 0 sin cos 0 *fr f f f fr f f f f rr r r r rr r r r r*

*v uv u uv u v uv u uv u*

 

 

 

The interference factors are used to compute a new inflow ratio in the Glauert formula (15):

interf

*<sup>C</sup> <sup>C</sup> <sup>d</sup>*

*Tf Tr*

*zr ir xr zf if xf*

interf

*zr ir xr zf if xf*

*Tr Tf*

*C C d*

, r-on-f 2 2 <sup>2</sup> <sup>2</sup>

, fonr 2 2 <sup>2</sup> <sup>2</sup>

The fuselage forces and moments are calculated through flat plate theory using (Ostroff,

 

*f r*

 

 

(21)

2 3

2 3

 

 

(20)

(22)

(23)

2 3

*If If If fr*

 

2 3

 

*If If If fr*

*Ir Ir Ir rr Ir Ir Ir rr*

through interference factors expressed as in (Ostroff, Downing and Rood, 1976):

f-on-r

r-on-f

*d*

*d*

$$\begin{aligned} \mathcal{X}\_s &= -\mathbb{C}\_{\varepsilon \varepsilon} \pm \rho V^1 \cos a\_{\mu \nu} \cos \mathcal{J}\_{\mu \nu} \\ \mathcal{Y}\_s &= -\mathbb{C}\_{\nu \rho} \pm \rho V^1 \sin \mathcal{J}\_{\mu \nu} \\ \mathcal{Z}\_s &= -\mathbb{C}\_{\varepsilon\_{\mu \rho \nu} \frac{1}{2}} \pm \rho V^1 \sin a\_{\mu \nu} \\ \mathcal{L}\_s &= -\mathbb{C}\_{\varepsilon \beta \frac{1}{2}} \pm \rho V^1 \sin \mathcal{J}\_{\mu \nu} \left| \cos \mathcal{J}\_{\mu \nu} \right| \left( 1 - \left| \sin a\_{\mu \nu} \right| \right) \\ \mathcal{M}\_{\mu} &= \mathbb{C}\_{\mu \alpha} \frac{1}{2} \rho V^1 \sin a\_{\mu \nu} \cos a\_{\mu \nu} \\ \mathcal{N}\_{\mu} &= -\mathbb{C}\_{\nu \rho} \frac{1}{2} \rho V^1 \sin \mathcal{J}\_{\mu \nu} \cos \mathcal{J}\_{\mu \nu} \left( 0.94 \sin a\_{\mu \nu} + 0.342 \cos a\_{\mu \nu} \right) \end{aligned} \tag{24}$$

where the fuselage angle of attack fus and fuselage sideslip fus are defined as seen as:

$$\begin{aligned} \sin \alpha\_{f\_{\text{fix}}} &= w \Big/ \sqrt{u^2 + w^2} & \cos \alpha\_{f\_{\text{fix}}} &= u \Big/ \sqrt{u^2 + w^2} \\ \sin \beta\_{f\_{\text{fix}}} &= v \Big/ \sqrt{u^2 + v^2} & \cos \beta\_{f\_{\text{fix}}} &= u \Big/ \sqrt{u^2 + v^2} \end{aligned} \tag{25}$$

The helicopter has three suspension points i=1,2,3 underneath its floor as seen in Fig. A6, the tension force in one cable j being Sij. The total forces on the slings are:

$$\begin{aligned} \mathbf{X}\_{s} &= \mathbf{S}\_{\bar{\eta}} \cos \alpha\_{\bar{\eta}} \sin \beta\_{\bar{\eta}} \\ \mathbf{Y}\_{s} &= \mathbf{S}\_{\bar{\eta}} \sin \alpha\_{\bar{\eta}} \sin \beta\_{\bar{\eta}} \\ \mathbf{Z}\_{s} &= \mathbf{S}\_{\bar{\eta}} \cos \beta\_{\bar{\eta}} \\ \mathbf{L}\_{s} &= -\mathbf{S}\_{\bar{\eta}} \left\{ \sin \alpha\_{\bar{\eta}} \sin \beta\_{\bar{\eta}} \| \mathbf{s}\_{i} - \cos \beta\_{\bar{\eta}} \mathbf{f}\_{1} \right\} \\ \mathbf{M}\_{s} &= \mathbf{S}\_{\bar{\eta}} \cos \alpha\_{\bar{\eta}} \sin \beta\_{\bar{\eta}} \| \mathbf{s}\_{i} - \mathbf{S}\_{\mathbf{1},3\bar{\eta}} \cos \beta\_{\mathbf{1},3\bar{\eta}} \| \mathbf{s}\_{i,3} + \mathbf{S}\_{\mathbf{2},i} \cos \beta\_{\mathbf{2},j} \| \mathbf{s}\_{\mathbf{2},j} \\ \mathbf{N}\_{s} &= \mathbf{S}\_{\bar{\eta}} \cos \alpha\_{\bar{\eta}} \sin \beta\_{\bar{\eta}} \mathbf{f}\_{1} + \mathbf{S}\_{\mathbf{1},3\bar{\eta}} \sin \alpha\_{\mathbf{1},3\bar{\eta}} \sin \beta\_{\mathbf{1},3} \| \mathbf{s}\_{\mathbf{1},3} - \mathbf{S}\_{\mathbf{2},j} \sin \alpha\_{\bar{\eta}} \| \mathbf{s}\_{\mathbf{2},j} \end{aligned} \tag{26}$$

where ij and ij are the angles that the sling cable makes with the X and Z direction; fs1,2,3 and hs1,2,3 are the hook distances to the helicopter centre of gravity. The slings are modelled as linear springs without mass and have small internal damping. The tension force in each cable is determined by comparing the actual sling length lij to the zero tension sling length l0ij, see equation (27), where *j* is the cable number on the *ith* suspension point. The zero tension cable length as well as the cable stiffness are known, the actual length of each cable is computed by measuring the distance between the specific helicopter suspension point and the suspension point on the load.

$$S\_{\bar{\eta}} = \max\left\{0, k\{l\_{\bar{\eta}} - l\_{a\bar{\eta}}\}\right\} \tag{27}$$

The damping forces inside the slings are determined using equation (28). In this equation *dV* is the relative velocity between the endpoints of a cable, in the direction of that cable. This requires that both endpoint velocities are known in the same axis system. The damping coefficient is set just large enough to prevent the load from increase in pendulum motion when the load is oscillating around a fixed point.

$$S\_{\rm{damp},\bar{\text{yl}}} = dV\_{\bar{\text{yl}}} \mathbf{c}\_{\rm{damp}} \tag{28}$$

Effects of Automatic Flight Control System on Chinook Underslung Load Failures 179

*l C Bl l C Bl l C Bl l C Bl l C Bl l C Bl*

The contributions of each cable and of the load aerodynamics are given in equations (30) and (31) respectively. Note that the cable component is valid only for a V-suspension.

sin sin cos cos

cos sin cos cos

 

The magnitude of the sling forces is given by equation (27). The load aerodynamics are taken from the flat plate theory, using the empirical equations of reference (Ostroff,

sin cos 1 sin

hf 2.093 m hr 3.527 m lf 6.425 m lr 5.450 m f1 0 m fs1 2.28092 m fs2 1.78308 m fs3 0.19812 m hs1,2 1.309 m hs3 1.509 m

*Bl N l sl sl sl sl*

Chinook dimensions (see Fig. B1)

*i li li cgl i li li l cgl*

*S w S w w*

*L S h S w S ww M S h S l S ll*

 

*C ij lij lij cgl i li cgl i li l cgl C ij lij lij cgl j l j cgl j l l cgl*

 

> 

11 22

s sin

 

> 

sin cos 0.94sin 0.342 cos

1 1 2 21

2 2

   

 

*l j l j l cgl*

 

*l l*

1 1

 

cos sin sin sin cos

*C ij lij lij C ij lij i C ij lij*

*X S Y S Z S*

 

Downing and Rood, 1976), see equation (31).

1112

*C j l j l j cgl j*

Data for the helicopter and load used in the simulation model

*N S lS*

*Bl FEl l Bl Y l l sl Bl L l l sl*

*XCV YC V ZCV LCV MC V NCV*

 

**8. Appendix B** 

sin sin co

1 11 2 22

 

cos sin cos sin

sin sin  

 

 

 

*Bl M l sl sl*

sin cos

*Bl L l l sl sl sl*

(29)

  (30)

(31)

*XX X YY Y ZZ Z LL L M M M NN N*

 

Fig. A6. Hooks and slings loads

## **7.2 Load model**

The load is modelled as a 6-dof body, the helicopter slings being connected to the load as seen in Fig. A7.

Fig. A7. Container load with local axes and sling numbering

The forces and moments acting on the load centre of gravity, besides load gravitational forces, consist of cable forces indexed with *C* and aerodynamic forces, which are determined using flat plate theory, indexed *Bl*. The summation of these forces and moments is given by equation (29).

$$\begin{aligned} \mathbf{X}\_{l} &= \mathbf{X}\_{c} + \mathbf{X}\_{\mathcal{M}} \\ \mathbf{Y}\_{l} &= \mathbf{Y}\_{c} + \mathbf{Y}\_{\mathcal{M}} \\ \mathbf{Z}\_{l} &= \mathbf{Z}\_{c} + \mathbf{Z}\_{\mathcal{M}} \\ \mathbf{L}\_{l} &= \mathbf{L}\_{c} + \mathbf{L}\_{\mathcal{M}} \\ \mathbf{M}\_{l} &= \mathbf{M}\_{c} + \mathbf{M}\_{\mathcal{M}} \\ \mathbf{N}\_{l} &= \mathbf{N}\_{c} + \mathbf{N}\_{\mathcal{M}} \end{aligned} \tag{29}$$

The contributions of each cable and of the load aerodynamics are given in equations (30) and (31) respectively. Note that the cable component is valid only for a V-suspension.

 1 1 11 22 1 1 2 21 1112 cos sin sin sin cos sin sin cos cos cos sin cos cos sin sin co *C ij lij lij C ij lij i C ij lij C ij lij lij cgl i li cgl i li l cgl C ij lij lij cgl j l j cgl j l l cgl C j l j l j cgl j X S Y S Z S L S h S w S ww M S h S l S ll N S lS* 2 2 1 11 2 22 s sin cos sin cos sin *l j l j l cgl i li li cgl i li li l cgl l l S w S w w* (30)

The magnitude of the sling forces is given by equation (27). The load aerodynamics are taken from the flat plate theory, using the empirical equations of reference (Ostroff, Downing and Rood, 1976), see equation (31).

$$\begin{aligned} \mathcal{X}\_{\mathcal{U}} &= -\mathcal{C}\_{\text{ref}} \frac{1}{2} \rho V\_{l}^{2} \\ \mathcal{Y}\_{\mathcal{U}} &= -\mathcal{C}\_{\text{v}\mu} \pm \rho V\_{l}^{2} \sin \beta\_{\mathcal{A}} \\ \mathcal{Z}\_{\mathcal{U}} &= -\mathcal{C}\_{\text{l}\boldsymbol{\omega}} \pm \rho V\_{l}^{2} \sin \alpha\_{\boldsymbol{\omega}} \\ \mathcal{L}\_{\mathcal{U}} &= -\mathcal{C}\_{\text{l}\boldsymbol{\omega}} \pm \rho V\_{l}^{2} \sin \beta\_{\boldsymbol{\omega}} \left| \cos \beta\_{\boldsymbol{\omega}} \right| \left( 1 - \left| \sin \alpha\_{\boldsymbol{\omega}} \right| \right) \\ \mathcal{M}\_{\mathcal{U}} &= \mathcal{C}\_{\text{l}\boldsymbol{\omega}} \pm \rho V\_{l}^{2} \sin \alpha\_{\boldsymbol{\omega}} \cos \alpha\_{\boldsymbol{\omega}} \\ \mathcal{N}\_{\mathcal{U}} &= -\mathcal{C}\_{\text{v}\boldsymbol{\omega}} \frac{1}{2} \rho V\_{l}^{2} \sin \beta\_{\boldsymbol{\omega}} \cos \beta\_{\boldsymbol{\omega}} \left( 0.94 \sin \alpha\_{\boldsymbol{\omega}} + 0.342 \cos \alpha\_{\boldsymbol{\omega}} \right) \end{aligned} \tag{31}$$

## **8. Appendix B**

178 Automatic Flight Control Systems – Latest Developments

The load is modelled as a 6-dof body, the helicopter slings being connected to the load as

The forces and moments acting on the load centre of gravity, besides load gravitational forces, consist of cable forces indexed with *C* and aerodynamic forces, which are determined using flat plate theory, indexed *Bl*. The summation of these forces and moments is given by

Fig. A7. Container load with local axes and sling numbering

Fig. A6. Hooks and slings loads

**7.2 Load model** 

seen in Fig. A7.

equation (29).

Data for the helicopter and load used in the simulation model


Effects of Automatic Flight Control System on Chinook Underslung Load Failures 181

Blade control angle to stick displacement conversion factors Collective front rotor 0.734 deg/cm Collective rear rotor 0.734 deg/cm Longitudinal front rotor 0.242 deg/cm Longitudinal rear rotor -0.242 deg/cm Lateral front rotor 0.752 deg/cm Lateral rear rotor -0.752 deg/cm Pedal front rotor 1.25 deg/cm Pedal rear rotor - 1.25 deg/cm Collective front/rear neutral 7.85 deg

Blade control system limits deg cm stick Collective range front rotor 0 – 16 deg 0 – 21.8 cm

Longitudinal cyclic range front rotor - 0.5 – 2 deg -2 – 10.33 cm

Lateral cyclic angle front rotor - 10 – 10 deg -13 – 13 cm

Container load mass and dimensions ml 2000, 6000 and 10000 kg ll 6.058 m wl 2.438 m hl 2.591 m lCG l (½ ll) m wCG l (½ wl) m hCGl (½ hl) m

Load moments of inertia Ixx l <sup>1</sup> 2 2

Iyy l <sup>1</sup> 2 2

Izz l <sup>1</sup> 2 2

Ixz l 0

<sup>12</sup> *mw h ll l*

<sup>12</sup> *mh l ll l*

<sup>12</sup> *mw l ll l*

Collective range rear rotor 0 – 16 deg

Longitudinal cyclic range rear rotor - 0.5 – 2.5 deg

Lateral cyclic angle rear rotor - 10 – 10 deg

Fig. B1. Chinook dimensions




180 Automatic Flight Control Systems – Latest Developments

Rotor characteristics mbl 161 kg 0.08459 N 3 if 9 deg ir 4 deg 23.562 rad/s 12.8 twist - 9.14 deg R 9.144 m c 0.81m Cl 5.75 rad-1 Cdo 0.0098 Cdt 38.66

Chinook mass and moments of inertia m 14968.6 kg <sup>x</sup> 50386.3 kg m2 y 273536 kg m2 <sup>z</sup> 257685 kg m2 xz 19838.3 kg m2 Ibl 3110.2 kg m2

Chinook CH-47B aerodynamics

CFE 3.5 m2 CL fus 32.5 m2 CL 6.57 m3 CM 142 m3 CN 51.5 m3 CY 43.4 m2

Fig. B1. Chinook dimensions





Effects of Automatic Flight Control System on Chinook Underslung Load Failures 183

Dukes, Theodor, A. (1973) Maneuvring Heavy Sling Loads Near Hover Part II: Some

Dukes, Theodor, A. (1973) Maneuvring Heavy Sling Loads Near Hover Part II: Some

Einthoven P., et al. (2006) Development of Control Laws for the Chinook Digital AFCS

Fusato, Dario, Guglieri, Giorgio, Celi, Roberto (2001) Flight Dynamics of an Articulated

Gabel, Richard, Wilson, Gregory, J. (1968). Test Approaches to External Sling Load Instabilities, *J. of American Helicopter Society*, Vol. 13, No.3, July 1968, pp. 44-54 Kendrick, Stephen, A., Walker, Daniel, J. (2006) The Modelling, Simulation and Control of

Lucassen, L.R., and Stenk F.J.(1965) Dynamic Stability Analysis of a Hovering Helicopter with a Slung Load", *J. of the American Helicopter Society*, 10( 2), pp.. 1965 Nagabhushan, B.L. (1985). Low-Speed Stability Characteristics of a Helicopter with a Sling

Ostroff A.J., Downing, D.R. And Rood, W.J. (1976) A technique using a non-linear helicopter

Pavel, M.D.(2007) Mathematical Modeling of Tandem Helicopters with External Sling Loads

Pavel, M.D. (2010) Investigation of Chinook helicopter operations with an external slung load after cable failure. *The Aeronautical Journal,* 114(1156), pp. 345-365 Feaster, L., Poli, C. & Kirchhoff, R. (1977) Dynamics of a Slung Load, *J. of Aircraft*, Vol. 14,

Prabhakar, A. (1978) Stability of a Helicopter Carrying an Underslung Load, *VERTICA*,

Prouty, R.W. (2001) *Longitudinal cyclic control for tandem-rotor helicopters*, VERTIFLITE

Reijm, Rogier, Pavel, Marilena D&, Bart, Jacob (2006), Effects of Automatic Flight Control

Sheldon, D.F. (1977) An Appreciation of the Dynamic Problems Associated with the

Stuckey, R.A. (2002) *Mathematical Modelling of helicopter Slung-load systems*, DSTO Aeronautical and Maritime Research Laboratory, Victoria Australia, 2002 Tyson, Peter, et. al. (1999). Simulation Prediction and Flight Validation of UH-60A Black

System on Chinook Underslung Failures, *32nd European Rotorcraft Forum*,

External Transportation of Loads from a Helicopter-State of the Art, *VERTICA*, Vol.

Hawk Slung load Characteristics, *55th American Helicopter Society Annual Forum*,

pp. 3-13

pp. 3-13

Arizona

No. 1, January 2001, pp. 3-12

Center Hampton, Va, May 1976

Vol.2, No.2, 1978, pp. 121-143

magazine, vol. 47, no. 3. 2001

May 25-27, 1999, Montreal, Canada

No. 2, pp. 115-121

1, 1977

*Helicopter Society*, May 9-11, 2006, Phoenix, AZ

Load", *VERTICA*, Vol. 9, No.4, 1985, pp. 345-361

and Exhibit, Hilton Head, South Carolina, IAA-2007-6617

Maastricht, The Netherlands, September, 12-14, 2006

Elementary Maneuvres, *J. of the American Helicopter Society*, Vol. 18, No. 3, July 1973,

Elementary Maneuvres, *J. of the American Helicopter Society*, Vol. 18, No. 3, July1 973,

program, *62nd American Helicopter Society Annual Forum*, May 9-11, 2006, Phoenix,

Rotor Helicopter with an External Load, *J. of the American Helicopter Society*, Vol. 46,

Helicopters Operating with External Loads, *62nd Annual Forum of the American* 

model for determining trims and derivatives, NASA TN D-8159, Langley Research

for Piloted Simulation, AIAA Modeling and Simulation Technologies Conference



## **9. Acknowledgment**

The subject of this research was initiated as collaboration between Delft University of Technology, TNO Defence, Security and Safety and Royal Netherlands Air Force (RNLAF). Sincere thanks for all support given by the Chinook pilots to judge the results.

## **10. References**


182 Automatic Flight Control Systems – Latest Developments

Load moments of inertia Ixx l <sup>1</sup> 2 2

Sling aerodynamics

The subject of this research was initiated as collaboration between Delft University of Technology, TNO Defence, Security and Safety and Royal Netherlands Air Force (RNLAF).

ADS-33 (2000) *Aeronautical Design Standard-33E-PRF, Performance Specification, Handling* 

Anon. (2002) *Technical Manual, Aviation Unit and Aviation Intermediate Maintenance Manual* 

Anon, (2004), *Boeing Integrated Defense Systems, ICH-47D-10: Flight Manual International CH-*

Bisgaard, Morten, Bendtsen, Jan Dimon, la Cour-Habo, Anders (2006) Modelling of Generic

Boeing Helicopters (2004), *Flight Manual International CH-47D Helicopter*, The Boeing

Chen, C., Lim, K.Y. and Seah, C.S.P.(1998) Modeling and Dynamic Analysis of Helicopter

Cicolani, Luigi S., Kanning, Gerd, Synnestvedt, Robert (1995) Simulation of the Dynamics of

Cliff, E.M. and Bailey (1975) D.B., Dynamic Stability of a Translating Vehicle with a Simple

Exhibit, 21-24 Aug. 2006, Keystone, Colorado, AIAA 2006-6816

Company, Philadelphia, Pennsylvania, Rev 4, 30 September 2004.

*Qualities Requirements for Military Rotorcraft*, US Army AMCOM, Redstone,

*CH-47D Helicopter*, TM 55-1520-240-23-9, Headquarters, Department of the Army,

Sling Load System, AIAA Modeling and Simulation Technologies Conference and

Underslung System", *AIAA Modeling and Simulation Technologies Conference and* 

Helicopter Slung Load Systems. *J. of the American Helicopter Society*, Vol. 40, No. 4,

Iyy l <sup>1</sup> 2 2

Izz l <sup>1</sup> 2 2

Ixz l 0

k 7.25 10<sup>5</sup>

Inormal ij 4 m Ired 5.2 m cdamp 10 kg/s

kred 1 10<sup>5</sup>

Sincere thanks for all support given by the Chinook pilots to judge the results.

Rev. 19 Sept. 2002, chapter 11, section IX, page 1012

*Exhibit*, 10-12 Aug. 1998, Boston, MA, AIAA-98-4358

Sling Load, *J. of Aircraft*, Vol. 12, No. 10, Oct. 1975

*47D Helicopter*, The Boeing Company, 2004

October 1995, pp. 44-61

**9. Acknowledgment** 

**10. References** 

Alabama

<sup>12</sup>*mw h ll l*

<sup>12</sup>*mh l ll l*

<sup>12</sup>*mw l ll l*

N/m

 m2 /rad


**7** 

*1,2The Netherlands* 

*3Germany* 

**Tool-Based Design and** 

Hafid Smaili1, Jan Breeman2 and Thomas Lombaerts3 *National Aerospace Laboratory NLR/Delft University of Technology* 

*1NLR Cockpit & Flight Operations Department, Amsterdam,* 

*2NLR Avionics & Systems Department, Amsterdam, 3DLR Institute of Robotics and Mechatronics, Wessling,* 

**Evaluation of Resilient Flight Control Systems** 

A large transport aircraft simulation benchmark (REconfigurable COntrol for Vehicle Emergency Return RECOVER) has been developed within the European GARTEUR Flight Mechanics Action Group 16 (FM-AG(16)) on Fault Tolerant Control (2004-2008) for the integrated evaluation of fault detection, identification (FDI) and reconfigurable flight control systems. The benchmark includes a suitable set of assessment criteria and failure cases, based on reconstructed accident scenarios, to assess the potential of new adaptive control strategies to improve aircraft survivability. The application of reconstruction and modeling techniques, using accident flight data for validation, has resulted in high fidelity non-linear aircraft and fault models to evaluate new Fault Tolerant Flight Control (FTFC) concepts and

their real-time performance to accommodate in-flight failures (Edwards et al., 2010).

This chapter will give an overview of advanced flight control developments and pilot training related initiatives to reduce the amount of in-flight loss-of-control (LOC-I) accidents. The GARTEUR RECOVER benchmark, validated with accident flight data and used during the GARTEUR FM-AG(16) program, will be described. The modular features of the benchmark will be outlined that address the need for tool-based design of modern resilient flight control systems that mitigate potentially catastrophic (mechanical) failures

Fault tolerant flight control (FTFC) enables improved survivability and recovery from adverse flight conditions induced by faults, damage and associated upsets. This can be achieved by "intelligent" utilisation of the control authority of the remaining control effectors in all axes consisting of the control surfaces and engines or a combination of both. In this technique, control strategies are applied to restore stability and maneuverability of

the vehicle for continued safe operation and a survivable landing.

**1. Introduction** 

and aircraft upsets.

**2. Program overview** 

Van der Kamp, Reinier., et. al. (2005). Investigation on the Chinook operations with an external sling load after cable failure", *31st European Rotorcraft Annual Forum,* Florence, Italy, September 13-15, 2005
