**5. Results and discussion**

The pitch rate variation attained from flight data recorder (FDR) data, FlightGear, and JSBSim data shows similarities from the maxima and minima values. The pitch rate data of actual aircraft, i.e., PITR, from **Figure 3** depicts that during the cruise phase, aircraft pitching rate was within 1.5–1°/s. However, from the FDM perspective, i.e., for JSBSim and FG, it shows pitching motion rate maxima and minima between 2.25 to 3.5°/s and 2.25 to 1.5°/s, respectively. The depiction gives a clear understanding that the aircraft modeled using FDM is replicating the motion dynamics of the actual aircraft but with some deviation. Simulation results demonstrate greater rates than the actual aircraft because the CFD results plugged in the aircraft dynamic file are overpredicting the pitching rate of actual aircraft. Nevertheless, it does give insight to the reader that CFD can be helpful in the initial designing of FDM aerodynamic table [11]. The optimizations can be used to predict the actual behavior of the aircraft pitching rate. A note to remember for damping the motion and response dynamics of the aircraft from pitch axis, *Cmq* and *Cmα*̇ are the two variables that can be used for fine adjustments according to pilot's requirement. Before, it is necessary to have a correct initializing FDM model. The file that was being used with JSBSim-based simulator was introduced with the specific tables of *Cmq* and *Cmα*̇for assisting for specific cases of landing and takeoff phase. This was implemented as per pilot's observations.

gives a clear understanding that the aircraft modeled using FDM is replicating the motion dynamics of the actual aircraft. In addition, the simulative results of FG are in high degree of agreement to actual aircraft roll rate performance. However, JSBSim demonstrates greater roll rates, specifically in positive direction, than the actual aircraft, and this can be because the control dynamics on the JSBSim were being operated using a feedback-based control loading system; however, in an actual aircraft, relative wind component affects the feedback felt by pilot on the stick, hence adding an extra variability to aircraft control. Nevertheless, the roll rate performance was better than the pitching rate. For controlling the oscillation and damping effects in roll axis, *Clp* (i.e., coefficient of rolling moment due to damping) and *Clr* (i.e., effect of yaw rate on coefficient of rolling moment) are the major variables. Mostly, *Clp* is used for altering the damping effect. The effectiveness in rolling moment of the control surface is catered by *Clda* where da denotes the change in aileron deflection angle. In addition to *Clda*, the FDM file was constrained in such a way that the code for right and left ailerons was separately designed for giving correct effect of aerodynamic deflections. Nevertheless, in pitch similar steps were also followed for defining aerodynamics of positive elevator separately to that of the negative elevator deflection using *Cmde* variable; however this was causing oscillatory modes at maximum deflection of positive elevators, for this two major variables were given full consideration during the pilot phase optimization which

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)…*

. These two variables assisted in changing the damping and

The yaw rate variation attained from FDR, FlightGear, and JSBSim data shows high degree of resemblance from the maxima and minima values. The yaw rate data of actual aircraft, i.e., YAWR, from **Figure 5** depicts that during the cruise phase, aircraft yaw rate was within 2 to 2°/s. However, from the flight dynamic model perspective, i.e., for JSBSim and FG, it shows yaw rate minima and maxima between 2.5 to 1.05°/s and 6.45 to 2.45°/s, respectively. The depiction gives a clear understanding that the aircraft modeled using FDM is replicating the motion dynamics of the actual aircraft. In addition, the simulative results of JSBSim are in high degree of agreement to the actual aircraft yaw rate performance. However, FG demonstrates greater yaw rates, specifically in negative direction, than the actual aircraft, and this can be because the control loading used on the FG was being

were *Cmq* and *Cm<sup>α</sup>̇*

**155**

**Figure 4.**

oscillations caused due to pitching motion.

*Variation of roll rate obtained from different flight data.*

*DOI: http://dx.doi.org/10.5772/intechopen.91895*

The roll rate variation attained from FDR, FlightGear, and JSBSim data shows high degree of resemblance from the maxima and minima values. The roll rate data of actual aircraft, i.e., ROLLR, from **Figure 4** depicts that during the cruise phase, aircraft rolling rate was within 4 to 4°/s. However, from the flight dynamic model perspective, i.e., for JSBSim and FG, it shows rolling motion rate minima and maxima between 1.25 to 6.25°/s and 2.25 to 2.15°/s, respectively. The depiction

**Figure 3.** *Variation of pitch rate obtained from different flight data.*

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)… DOI: http://dx.doi.org/10.5772/intechopen.91895*

**Figure 4.**

After the hardware is set up and FDM .xml scripted file is tested, we are able to collect different flight data of interest for quantification of flight maneuvers. In the next section, results of responses generated for angular rates that are dependent on

The pitch rate variation attained from flight data recorder (FDR) data, FlightGear, and JSBSim data shows similarities from the maxima and minima values. The pitch rate data of actual aircraft, i.e., PITR, from **Figure 3** depicts that during the cruise phase, aircraft pitching rate was within 1.5–1°/s. However, from the FDM perspective, i.e., for JSBSim and FG, it shows pitching motion rate maxima and minima between 2.25 to 3.5°/s and 2.25 to 1.5°/s, respectively. The depiction gives a clear understanding that the aircraft modeled using FDM is replicating the motion dynamics of the actual aircraft but with some deviation. Simulation results demonstrate greater rates than the actual aircraft because the CFD results plugged in the aircraft dynamic file are overpredicting the pitching rate of actual aircraft. Nevertheless, it does give insight to the reader that CFD can be helpful in the initial designing of FDM aerodynamic table [11]. The optimizations can be used to predict the actual behavior of the aircraft pitching rate. A note to remember for damping the motion and response dynamics of the aircraft from pitch axis, *Cmq* and *Cmα*̇ are the two variables that can be used for fine adjustments according to pilot's requirement. Before, it is necessary to have a correct initializing FDM model. The file that was being used with JSBSim-based simulator was introduced with the specific tables of *Cmq* and *Cmα*̇for assisting for specific cases of landing and takeoff phase. This was

The roll rate variation attained from FDR, FlightGear, and JSBSim data shows high degree of resemblance from the maxima and minima values. The roll rate data of actual aircraft, i.e., ROLLR, from **Figure 4** depicts that during the cruise phase, aircraft rolling rate was within 4 to 4°/s. However, from the flight dynamic model perspective, i.e., for JSBSim and FG, it shows rolling motion rate minima and maxima between 1.25 to 6.25°/s and 2.25 to 2.15°/s, respectively. The depiction

the aerodynamic coefficients plugged in FDM file are discussed.

**5. Results and discussion**

*Computational Fluid Dynamics Simulations*

implemented as per pilot's observations.

*Variation of pitch rate obtained from different flight data.*

**Figure 3.**

**154**

*Variation of roll rate obtained from different flight data.*

gives a clear understanding that the aircraft modeled using FDM is replicating the motion dynamics of the actual aircraft. In addition, the simulative results of FG are in high degree of agreement to actual aircraft roll rate performance. However, JSBSim demonstrates greater roll rates, specifically in positive direction, than the actual aircraft, and this can be because the control dynamics on the JSBSim were being operated using a feedback-based control loading system; however, in an actual aircraft, relative wind component affects the feedback felt by pilot on the stick, hence adding an extra variability to aircraft control. Nevertheless, the roll rate performance was better than the pitching rate. For controlling the oscillation and damping effects in roll axis, *Clp* (i.e., coefficient of rolling moment due to damping) and *Clr* (i.e., effect of yaw rate on coefficient of rolling moment) are the major variables. Mostly, *Clp* is used for altering the damping effect. The effectiveness in rolling moment of the control surface is catered by *Clda* where da denotes the change in aileron deflection angle. In addition to *Clda*, the FDM file was constrained in such a way that the code for right and left ailerons was separately designed for giving correct effect of aerodynamic deflections. Nevertheless, in pitch similar steps were also followed for defining aerodynamics of positive elevator separately to that of the negative elevator deflection using *Cmde* variable; however this was causing oscillatory modes at maximum deflection of positive elevators, for this two major variables were given full consideration during the pilot phase optimization which were *Cmq* and *Cm<sup>α</sup>̇* . These two variables assisted in changing the damping and oscillations caused due to pitching motion.

The yaw rate variation attained from FDR, FlightGear, and JSBSim data shows high degree of resemblance from the maxima and minima values. The yaw rate data of actual aircraft, i.e., YAWR, from **Figure 5** depicts that during the cruise phase, aircraft yaw rate was within 2 to 2°/s. However, from the flight dynamic model perspective, i.e., for JSBSim and FG, it shows yaw rate minima and maxima between 2.5 to 1.05°/s and 6.45 to 2.45°/s, respectively. The depiction gives a clear understanding that the aircraft modeled using FDM is replicating the motion dynamics of the actual aircraft. In addition, the simulative results of JSBSim are in high degree of agreement to the actual aircraft yaw rate performance. However, FG demonstrates greater yaw rates, specifically in negative direction, than the actual aircraft, and this can be because the control loading used on the FG was being

*σ* ¼

*xi* and μ are the population mean.

*DOI: http://dx.doi.org/10.5772/intechopen.91895*

**Table 6.**

**Figure 6.**

*maxima.*

**157**

*Standard deviation of the angular rates.*

s

JSBSim perspective, it can be depicted that the atmospheric model was not completely integrated to give the effects as it was found in FlightGear.

understand the difference between different operating platforms.

understand the difference between different operating platforms.

understand the difference between different operating platforms.

**Figure 6** shows the local maxima and minima of the actual aircraft roll rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to

**Figure 7** shows the local maxima and minima of the JSBSim aircraft roll rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to

**Figure 8** shows the local maxima and minima of the FlightGear aircraft roll rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to

**Rates Actual (°/s) JSB (°/s) FG (°/s)** P 0.64380827 1.24255506 0.56483048 Q 0.19825922 1.08843922 0.49144324 R 0.45549470 1.05413173 0.73910523

*Local maxima and minima on the actual (P) roll rate in °/s chart, where green are the minima and red are the*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>P</sup>ð Þ *xi* � *<sup>μ</sup>*

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)…*

*N*

where σ is the population standard deviation, N is the size of the population, and

It was found that the SD lied on a discrepancy of about 1 °/s from mean values, giving us a generic idea that the results deviation was nominal as seen from **Table 6**. It is found that the max deviation is mostly found in the JSBSim-based results. However, FG results deviation is similar to the deviation of the actual aircraft. From

2

(8)

**Figure 5.** *Variation of yaw rate obtained from different flight data.*

operated using a joystick control. Logitech extreme 3d edition flight joystick has a small moment in yawing direction, i.e., the maxima and minima is reached in just a slight deflection, causing it hard to deflect gradually, hence adding an extra difficulty during yawing moment while controlling through FlightGear. Therefore, it was found that the yaw rate demonstrated better performance using JSBSim than the FG. The stability derivatives that are used for optimizing the yaw performance of the aircraft were *Cnr*, *Cndr*, and *Cnβ*, where *Cnr* is coefficient of yaw moment due to yaw rate, *Cndr* is the yaw moment caused due to rudder deflection, and *Cn<sup>β</sup>* is yaw moment caused due to sideslip angle. *Cn<sup>β</sup>* and *Cnr* were adjusted using specific values; however, for *Cndr* table was defined as per to assist for landing and ground run effectiveness of the yaw moment due to rudder deflection.

#### **5.1 Data quantification of the results**

For the steady-state cases, the linear model with required changes according to pilot's input, satisfactory estimation of the aerodynamic response is achievable. However, if the pilot induces large-amplitude maneuvers or rapid divergences from the steady-state conditions, then nonlinear parameters need to be considered with the basic aerodynamic model. Klein and Morelli in their research state two ways of doing this: (a) using Taylor series expansion for defining nonlinear stability derivatives and (b) combining static terms and treating stability and control derivatives of aircraft as a function of explanatory variables, i.e., angle of attack, angle of sideslip, and Mach number [12]. Moreover, system identification technique is also good for validating the required results of the aerodynamic coefficients from FDR data by reverse engineering the states using observation matrix with specific input and outputs [13–16]. However, in this study as we are considering the steady-state flight dynamics, some mathematical techniques like standard deviation can be used for evaluating performance of the CFD attained variables. This quantification was carried out using Excel.

Quantification of **Figures 5–13** was conducted using Excel through which the local maxima and minima were depicted on different charts for observing the exact value from specific plots. By the help of the local maxima and minima, standard deviation (SD) was also calculated using Eq. (8):

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)… DOI: http://dx.doi.org/10.5772/intechopen.91895*

$$
\sigma = \sqrt{\frac{\sum \left(\mathbf{x}\_i - \boldsymbol{\mu}\right)^2}{N}} \tag{8}
$$

where σ is the population standard deviation, N is the size of the population, and *xi* and μ are the population mean.

It was found that the SD lied on a discrepancy of about 1 °/s from mean values, giving us a generic idea that the results deviation was nominal as seen from **Table 6**. It is found that the max deviation is mostly found in the JSBSim-based results. However, FG results deviation is similar to the deviation of the actual aircraft. From JSBSim perspective, it can be depicted that the atmospheric model was not completely integrated to give the effects as it was found in FlightGear.

**Figure 6** shows the local maxima and minima of the actual aircraft roll rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

**Figure 7** shows the local maxima and minima of the JSBSim aircraft roll rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

**Figure 8** shows the local maxima and minima of the FlightGear aircraft roll rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.


#### **Table 6.**

operated using a joystick control. Logitech extreme 3d edition flight joystick has a small moment in yawing direction, i.e., the maxima and minima is reached in just a slight deflection, causing it hard to deflect gradually, hence adding an extra difficulty during yawing moment while controlling through FlightGear. Therefore, it was found that the yaw rate demonstrated better performance using JSBSim than the FG. The stability derivatives that are used for optimizing the yaw performance of the aircraft were *Cnr*, *Cndr*, and *Cnβ*, where *Cnr* is coefficient of yaw moment due to yaw rate, *Cndr* is the yaw moment caused due to rudder deflection, and *Cn<sup>β</sup>* is yaw moment caused due to sideslip angle. *Cn<sup>β</sup>* and *Cnr* were adjusted using specific values; however, for *Cndr* table was defined as per to assist for landing and ground

For the steady-state cases, the linear model with required changes according to pilot's input, satisfactory estimation of the aerodynamic response is achievable. However, if the pilot induces large-amplitude maneuvers or rapid divergences from the steady-state conditions, then nonlinear parameters need to be considered with the basic aerodynamic model. Klein and Morelli in their research state two ways of doing this: (a) using Taylor series expansion for defining nonlinear stability derivatives and (b) combining static terms and treating stability and control derivatives of aircraft as a function of explanatory variables, i.e., angle of attack, angle of sideslip, and Mach number [12]. Moreover, system identification technique is also good for validating the required results of the aerodynamic coefficients from FDR data by reverse engineering the states using observation matrix with specific input and outputs [13–16]. However, in this study as we are considering the steady-state flight dynamics, some mathematical techniques like standard deviation can be used for evaluating performance of the CFD attained variables. This quantification was

Quantification of **Figures 5–13** was conducted using Excel through which the local maxima and minima were depicted on different charts for observing the exact value from specific plots. By the help of the local maxima and minima, standard

run effectiveness of the yaw moment due to rudder deflection.

**5.1 Data quantification of the results**

*Variation of yaw rate obtained from different flight data.*

*Computational Fluid Dynamics Simulations*

**Figure 5.**

carried out using Excel.

**156**

deviation (SD) was also calculated using Eq. (8):

*Standard deviation of the angular rates.*

#### **Figure 6.**

*Local maxima and minima on the actual (P) roll rate in °/s chart, where green are the minima and red are the maxima.*

#### **Figure 7.**

*Local maxima and minima on the JSB (P) roll rate in °/s chart, where green are the minima and red are the maxima.*

#### **Figure 8.**

*Local maxima and minima on the FG (P) roll rate in °/s chart, where green are the minima and red are the maxima.*

**Figure 9** shows the local maxima and minima of the actual aircraft pitch rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

and minima in red and green color, respectively. Using this SD was calculated to

*Local maxima and minima on the JSB (Q) pitch rate in °/s chart, where green are the minima and red are the*

*Local maxima and minima on the actual (Q) pitch rate in °/s chart, where green are the minima and red are*

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)…*

*DOI: http://dx.doi.org/10.5772/intechopen.91895*

**Figure 13** shows the local maxima and minima of the JSBSim aircraft yaw rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to

**Figure 14** shows the local maxima and minima of the FlightGear aircraft yaw rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calcu-

After observing the SD, standard error measure was also calculated. **Table 7** demonstrates values of the standard error measure of angular rates of actual, JSBSim, and FlightGear responses. Standard error measure shows how varied data is acquired from the actual responses. It can be seen that the response variation from

understand the difference between different operating platforms.

**Figure 9.**

*the maxima.*

**Figure 10.**

*maxima.*

**159**

understand the difference between different operating platforms.

lated to understand the difference between different operating platforms.

**Figure 10** shows the local maxima and minima of the JSBSim aircraft pitch rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

**Figure 11** shows the local maxima and minima of the FlightGear aircraft pitch rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

**Figure 12** shows the local maxima and minima of the actual aircraft yaw rate during a steady-state flight condition. The figure gives an idea of the local maxima *Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)… DOI: http://dx.doi.org/10.5772/intechopen.91895*

#### **Figure 9.**

*Local maxima and minima on the actual (Q) pitch rate in °/s chart, where green are the minima and red are the maxima.*

#### **Figure 10.**

**Figure 9** shows the local maxima and minima of the actual aircraft pitch rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to

*Local maxima and minima on the FG (P) roll rate in °/s chart, where green are the minima and red are the*

*Local maxima and minima on the JSB (P) roll rate in °/s chart, where green are the minima and red are the*

**Figure 10** shows the local maxima and minima of the JSBSim aircraft pitch rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to

**Figure 11** shows the local maxima and minima of the FlightGear aircraft pitch rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calcu-

**Figure 12** shows the local maxima and minima of the actual aircraft yaw rate during a steady-state flight condition. The figure gives an idea of the local maxima

understand the difference between different operating platforms.

**Figure 7.**

*Computational Fluid Dynamics Simulations*

*maxima.*

**Figure 8.**

*maxima.*

**158**

understand the difference between different operating platforms.

lated to understand the difference between different operating platforms.

*Local maxima and minima on the JSB (Q) pitch rate in °/s chart, where green are the minima and red are the maxima.*

and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

**Figure 13** shows the local maxima and minima of the JSBSim aircraft yaw rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

**Figure 14** shows the local maxima and minima of the FlightGear aircraft yaw rate during a steady-state flight condition. The figure gives an idea of the local maxima and minima in red and green color, respectively. Using this SD was calculated to understand the difference between different operating platforms.

After observing the SD, standard error measure was also calculated. **Table 7** demonstrates values of the standard error measure of angular rates of actual, JSBSim, and FlightGear responses. Standard error measure shows how varied data is acquired from the actual responses. It can be seen that the response variation from

#### **Figure 11.**

*Local maxima and minima on the FG (Q) pitch rate in °/s chart, where green are the minima and red are the maxima.*

**Figure 12.**

*Local maxima and minima on the actual (R) yaw rate in °/s chart, where green are the minima and red are the maxima.*

mean is in similar constraints to each other. The standard error deviation for pitch rate (i.e., Q) is higher for JSB and FG to that of the actual model because the values chosen for the aerodynamic coefficients are generating greater pitching moment; nevertheless, here the control column perspective should not be neglected as this has also a greater impact on variability of the results.

### **6. Conclusions**

The study has compiled a way for designing FDM tables using CFD obtained results and pilots response from FDR data. The performance of CFD-designed FDM was tested and compared with the FDR data with similar steady-state conditions as prevailed during actual flight scenario. It was found that the response

characteristics of the simulated angular rates were in correspondence with the actual rates. In addition to this, a standard deviation error measure was below 0.1 for all the rates from the mean position, giving us a confidence on the values of the aerodynamic coefficients plugged in the FDM. Moreover, 1°/s SD of the angular rates explained that the CFD data is useful for initially designing the FDM;

*Local maxima and minima on the FG (R) yaw rate in °/s chart, where green are the minima and red are the*

*Local maxima and minima on the JSB (R) yaw rate in °/s chart, where green are the minima and red are the*

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)…*

*DOI: http://dx.doi.org/10.5772/intechopen.91895*

**Rates Actual JSB FG** P 0.0132808 0.025632 0.0116516 Q 0.0040898 0.0224528 0.0101355 R 0.0093961 0.0217451 0.0152466

**Figure 14.**

**Figure 13.**

*maxima.*

*maxima.*

**Table 7.**

**161**

*Standard error measure of the angular rates.*

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)… DOI: http://dx.doi.org/10.5772/intechopen.91895*

#### **Figure 13.**

*Local maxima and minima on the JSB (R) yaw rate in °/s chart, where green are the minima and red are the maxima.*

#### **Figure 14.**

*Local maxima and minima on the FG (R) yaw rate in °/s chart, where green are the minima and red are the maxima.*


#### **Table 7.**

mean is in similar constraints to each other. The standard error deviation for pitch rate (i.e., Q) is higher for JSB and FG to that of the actual model because the values chosen for the aerodynamic coefficients are generating greater pitching moment; nevertheless, here the control column perspective should not be neglected as this

*Local maxima and minima on the actual (R) yaw rate in °/s chart, where green are the minima and red are the*

*Local maxima and minima on the FG (Q) pitch rate in °/s chart, where green are the minima and red are the*

The study has compiled a way for designing FDM tables using CFD obtained results and pilots response from FDR data. The performance of CFD-designed FDM was tested and compared with the FDR data with similar steady-state conditions as

prevailed during actual flight scenario. It was found that the response

has also a greater impact on variability of the results.

**6. Conclusions**

**160**

**Figure 12.**

*maxima.*

**Figure 11.**

*Computational Fluid Dynamics Simulations*

*maxima.*

*Standard error measure of the angular rates.*

characteristics of the simulated angular rates were in correspondence with the actual rates. In addition to this, a standard deviation error measure was below 0.1 for all the rates from the mean position, giving us a confidence on the values of the aerodynamic coefficients plugged in the FDM. Moreover, 1°/s SD of the angular rates explained that the CFD data is useful for initially designing the FDM;

however, further modifications using system identification with least square method (LSM), Taylor series expansion, and filtering methods can be employed for increasing the accuracies of the results.

*ω* Eddy dissipation rate

*DOI: http://dx.doi.org/10.5772/intechopen.91895*

p roll rate q pitch rate r yaw rate *CL* lift coeffeicient *CD* drag coefficient *CY* side force coeffeceint *Cl* roll moment coefficient

u forward velocity in x-direction v lateral velocity in y-direction w normal velocity in z-direction

*Development of the Flight Dynamic Model (FDM) Using Computational Fluid Dynamic (CFD)…*

*Clp* roll moment coefficient due to roll rate *Clr* roll moment coefficient due to yaw rate *Clda* roll moment coefficient due to aileron input *Cldr* roll moment coefficient due to rudder input *Cl<sup>β</sup>* roll moment coefficient due to rudder input

*Cnp* roll moment coefficient due to roll rate *Cnr* roll moment coefficient due to yaw rate *Cnda* roll moment coefficient due to aileron input *Cndr* roll moment coefficient due to rudder input *Cn<sup>β</sup>* roll moment coefficient due to rudder input *Cy<sup>β</sup>* roll moment coefficient due to rudder input

σ the population standard deviation

Muhammad Saad Saeed<sup>1</sup> and Abdul Hameed Siddiqui<sup>2</sup>

3 Middle East Technical University, Ankara, Turkey

provided the original work is properly cited.

\*Address all correspondence to: adil.loya@pafkiet.edu.pk

, Muhammad Arsalan<sup>3</sup>

1 PAF Karachi Institute of Economics and Technology, Karachi, Pakistan

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

2 National University of Science and Technology, Risalpur, Pakistan

, Siraj Anis<sup>1</sup>

, Arsalan Khan1

,

*Cmq* pitch moment coefficient *Cm<sup>ά</sup>* pitch moment coefficient *Cmde* pitch moment coefficient *Cn* yaw moment coefficient

SD standard deviation

\*, Shoaib Arif<sup>2</sup>

**Author details**

Adil Loya<sup>1</sup>

**163**

N the size of the population *xi* and μ the population mean SDE standard deviation error
