**3.2.4 Program results**

The program has been tested on the VUK-T sailplane project developed at the Institute of Aeronautics, at Faculty of Mechanical Engineering in Belgrade. The obtained numerical results fully agree, and in some cases are complementing with the flight test results obtained for this sailplane.

Fig. 28. Basic diagram (left), SE greater 40% (right)

In the paper is presented computer analysis of hydraulic servo-actuator transient state between its engage and full pressure recovering. In different mathematical forms hydraulic actuator dynamic model is assumed without any geometrical and physical discontinuities and ambiguity of initial pressure conditions. Hydraulic actuator can be assumed with two serial connected compressible fluid flows controlled by supply and return variable fluid flow restrictors enclosed in control servo-valve and separated by actuator piston, expressed by equivalent mass, viscous damping and arbitrary external force. Presented mathematical model includes transient state of hydraulic actuator, which can be described and determined by ambiguity of the initial pressure conditions in actuator chambers as result of the final state of its previous operations and existing fluid leakage which can produce arbitrary value of initial pressure. Initial condition of pressure is primarily caused by external force, which is arbitrary value during actuator operations. Pressure surge in the moment of change direction of piston motion as result of geometric and flow asymmetry of actuator and its control servo-valve is included in the model also. Hydraulic actuator is usually assumed with compressible fluid flow including the effects of its viscosity. Fluid compressibility is assumed as quasi-static change of its density depending of static pressure. Each of the mentioned effects produces local pressure drop and surge and corresponding actuator operational time delay, which is the limiting factor of its cyclic velocity. Dominant influence on actuators time delay (less than 3% of unit step discrete control piston stroke time) is caused by fluid volumetric compressibility. In the paper following problems are treated: pressure discontinues changes in reverse of piston motion direction; nonlinear effects of

Any direction change of actuator motion produces pressure discontinuity in its source and return pipelines. This is caused by inversion of fluid flow which produce connection change between supply pipeline and actuator chambers. In the moment of fluid flow direction change each of actuator chambers inter-change connections with system pump and return pipeline and produce corresponding discrete change of pressure in actuator chambers. Possible pressure drop or surge is also caused by geometric asymmetry of servo valve.

Any change of direction of actuator motion produces pressure discontinuity in its both pipelines. This discontinuity is caused by inversion of fluid flow which produce the change of connection between supply pipeline and both actuator chambers. In the moment of change of fluid flow direction each of actuator chambers change connections with system pump and return pipeline, producing corresponding discrete changes of pressure in actuator chambers. Possible pressure drop or surge is also caused by geometric asymmetry

On figure 30 is shown actuator motion asymmetry between direct and reverse modes. This asymmetry is result of pressure distribution along supply and return streamlines, shown on diagrams a) and c) on figure 32. Diagram a) corresponds to direct mode of actuator function

**4.1 Modeling of transient state and pressure recovering in aircraft proportional** 

**4. Systems, subsystems and equipments** 

actuator behavior; actuator dynamic model linearization.

of servo valve. These effects are explained on the following figures.

**4.1.1 Effects of system discontinuities** 

**hydraulic servo-actuators** 

Fig. 29. Basic diagram (left), SR smaller 40% (right)

In the process of sailplane analysis, influence of variation of elevator and ruder areas has been tested very effectively through the previously described model. The results obtained for two different elevator (SE) and rudder (SR) areas are presented in Fig's. 28 & 29 respectively.

The results present variations of height, speed, and the characteristic angular velocities and angles of the sailplane during the first 20 seconds of spin. Practical application of this software has shown that computational design in flight mechanics gives exceptional results, allowing the designer to follow the development of calculation with a large number parameters in detail, and continuously be able to fulfill the criteria of technical demands, performing all necessary optimizations.

In the process of sailplane analysis, influence of variation of elevator and ruder areas has been tested very effectively through the previously described model. The results obtained for two different elevator (SE) and rudder (SR) areas are presented in Fig's. 28 & 29

The results present variations of height, speed, and the characteristic angular velocities and angles of the sailplane during the first 20 seconds of spin. Practical application of this software has shown that computational design in flight mechanics gives exceptional results, allowing the designer to follow the development of calculation with a large number parameters in detail, and continuously be able to fulfill the criteria of technical demands,

Fig. 29. Basic diagram (left), SR smaller 40% (right)

performing all necessary optimizations.

respectively.
