Flutter Deliverable 1

Beech 99 Trim One

Team name: Flutter

Joaquin Escalante

Jaime Gutierrez

Jacob Jones

Basil Lee

Submitted on February 20, 2015

AE432 Flight Dynamics and Control

Richard Prazenica

Section number: 01

Embry-Riddle Aeronautical University

Daytona Beach, FL 32114

AE432 Project Deliverable #1

Beech 99 Modeling

A Beechcraft 99 aircraft, as shown in Fig. 1, is to be modeled using Matlab Simulink. The Beech 99

was designed in the 1960’s as a civil aircraft with a capacity of one or two crew members and up to

15 passengers in a two abreast configuration. It has two PT6A-20 turboprop engines that produce a

maximum power of 715 SHP each. With a gross weight of 11,300 lb, this aircraft has a range of 900

nm at the maximum cruise speed of 224 kts, and 1010 nm at a cruise speed of 190 knots. Another

important characteristic of the aircraft is its stall speed of 75.6 knots. At sea level it can climb at a rate

of 2090 ft/min with a service ceiling of 25,000 ft.

Figure 1. Beechcraft 99 with Jamaica Air Shuttle delivery

Based on the previously mentioned aircraft characteristics, a six-degree-of-freedom nonlinear

Simulink model was created. This Simulink model was created using an existing model for the Navion

aircraft. The existing model was modified to accommodate for the Beech 99. The most significant

change in the model was the addition of a simple prop engine model. The maximum power of the

aircraft, 715 SHP per engine, was used has a constant value for the engine configuration.

The Simulink model had to be further modified in order to account for compressibility effects.

Therefore, an extra term had to be added to the aerodynamic coefficients inside the model. This was

done to take into account mach effects experienced by the airplane. For the Beech 99, the drag and

moment are not affected by compressibility; only the lift coefficient is affected. To account for this

change, the partial of CL over the partial of Mach was multiplied by the change in Mach with respect

to the trim Mach. Although drag and moment coefficients are not affected by speed, the Simulink was

adapted to account for this effect in all three aerodynamic coefficients.

Similarly, a Matlab m-file was created with all the initial trim conditions and the control input histories

for the Beech 99. This Matlab file also included all the variables needed, mass/geometry properties

and the aerodynamic coefficients, to run the Simulink model. The longitudinal trim condition for the

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Beech 99 was then calculated using MATLAB at the given trim velocity of 340 ft/s. The trim angle of

attack resulted in -0.056 degrees, an elevator deflection angle of 1.485 degrees, and a trim thrust of

890.7 lbs. The power required at trim was then calculated using the trim velocity and trim thrust. The

trim throttle setting was calculated by dividing the trim power required and the total power available,

which consists of the two 715 SHP turboprop engines. The following Figures show the differences in

aircraft states between trim and non-trim conditions.

Figure 2. Translational velocities, no trim (left) and with trim conditions (right)

Figure 3. Angular velocities, no trim (left) and with trim conditions (right)

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Figure 4. Euler angles, no trim (left) and with trim conditions (right)

Figure 5. Inertial position, no trim (left) and with trim conditions (right)

Figure 6. Control inputs, no trim (left) and with trim conditions (right)

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With all the aerodynamic derivatives, geometric parameters, and trim conditions set, three cases

were run to test the response of the simulation. The first test simulates the airplane’s response to

elevator deflections, in these tests all the other parameters are left at trim condition except for the

control input that is being tested. The elevator starts at trim angle and from two to four seconds the

elevator deflects 0.5 degrees up, then from four to six seconds it deflects down 0.5 degrees from trim,

and finally it returns to its initial position until 500 seconds of the simulation are run. The control input

over time can be seen in Fig. 7, and it reflects the process previously stated. The other results from

the simulation can be seen in Fig. 8 to Fig. 11.

Figure 7. Control inputs for elevator deflection test

The results show what was expected from the control inputs. A change in angular velocity, q, can be

seen in Fig. 8. Also in Fig. 9 the pitch angle changes as expected from an elevator deflection. In Fig.

10 and Fig. 11 a change in the velocity in the z-direction is shown as well as an altitude change.

When elevator experiences a positive deflection, it produces lift in the negative z-direction and thus

creating a nose down pitching moment that will make the airplane descend, as seen in Fig. 11.

Figure 8. Angular velocity for elevator deflection test

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Figure 9. Euler angles for elevator deflection test

Figure 10. Translational velocity for elevator deflection test

Figure 11. Inertial position for elevator deflection test

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The first test proved that the simulation ran properly when elevator control was changed. The next

test is done to test the aileron response in the simulation. The ailerons starts at neutral position up to

two seconds, then the right aileron deflects 0.5 degrees up from two to six seconds, then it returns to

neutral position from 6 to 16 seconds. Then the right aileron is deflected down 0.5 degrees from 16 to

20 seconds and finally it returns to neutral position until 500 seconds of the simulation are run. The

control input over time can be seen in Fig. 12, and it reflects the process previously stated. The other

results from the simulation can be seen in Fig. 13 to Fig. 16.

Figure 12. Control inputs for aileron deflection test

For aileron deflection, more changes are seen from the simulation. As expected, the roll rate, p,

varies in the time the ailerons are deflected. As a result of that the other angular velocities are

affected as seen in Fig. 13. The euler angles in Fig. 14 show how roll affects yaw and pitch, the

adverse yaw at a turn can be seen in the figure. The change in transverse velocity in the y-axis shows

the variation of speed due to the aileron deflection and Fig. 15 also shows the changes in velocity in

the x and z direction due to roll. When the aileron is deflected up, the airplane rolls right and starts

going east as seen in Fig. 16. After the aileron is deflected down it turns left and stars correcting its

course. The aileron deflection also causes the airplane to descend and after the ailerons are returned

to neutral position, the airplane stabilizes.

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Figure 13. Angular velocity for aileron deflection test

Figure 14. Euler angles for aileron deflection test

Figure 15. Translational velocity for aileron deflection test

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Figure 16. Inertial position for aileron deflection test

The last test for control response was done for rudder deflection. To test the simulation the rudder

was left at neutral position for two seconds, from two to four seconds it was deflected 0.5 degrees

and from four to six it was deflected 0.5 degrees in the opposite direction. To see if the airplane would

stabilize after the rudder deflections, it was returned to neutral position from six to the end of the

simulation. The control inputs over time can be seen in Fig. 17, and the airplanes response can be

seen in Fig. 18 to Fig. 21.

Figure 17. Control inputs for rudder deflection test

The simulation responds as expected from a positive and then negative deflection of rudder. By

introducing a yawing moment, the airplane experiences motion in all axes, as seen in Fig. 18 to Fig.

20. When the rudder is deflected to 0.5 degrees the airplane yaws to the left as seen in Fig. 21 as the

airplane starts moving west and after the rudder is deflected -0.5 degrees the airplane goes east

again. Very small variations in altitude are also seen in Fig. 21 as the airplane loses stability and

starts pitching up and down.

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Figure 18. Angular velocity for rudder deflection test

Figure 19. Euler angles for rudder deflection test

Figure 20. Translational velocity for rudder deflection test

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Figure 21. Inertial position for rudder deflection test

It can be concluded that the modeled aircraft successfully performed every test. These results prove

the Simulink model was modified correctly and further modifications can be now performed.

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Flutter Deliverable 1

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