Aeronautical Engineering

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### Transcript

In order to operate an aircraft in three dimensions, we must be able to control its attitude, or orientation, in three dimensions. Thus, we define three principal axes to describe an airplane's position and any changes made to it. The origin of these three axes is located at the aircraft's center of gravity, which is the average location of its mass.

The yaw axis is perpendicular to the aircraft's wings and describes its motion from side to side. The pitch axis is oriented parallel to the wing and perpendicular to the yaw axis. Pitch motion is the up and down motion of the nose. Finally, the roll axis runs the length of the aircraft and describes the vertical movement of the wings.

To evaluate the aerodynamic characteristics of an aircraft as it changes position in these directions, we can measure several different coefficients that describe lift, drag, and moment. The lift and drag coefficients are dimensionless values that enable us to model the complex effects of shape and flow on lift and drag.

The lift and drag coefficients are defined as shown, where L and D are lift and drag, and S is the reference area of the aircraft model. Rho and V are the density and velocity of the free stream. We can simplify rho V squared over two to the dynamic pressure, q.

Similarly, engineers measure the pitching moment coefficient, which is a dimensionless value that describes the torque produced by forces on the aircraft in the direction of the pitch axis, called the pitching moment.

Like the lift and drag coefficients, the pitching moment coefficient is defined as shown, where M is the pitching moment, q is the dynamic pressure, and S and C are the reference area and reference length of the aircraft.

Finally, we can measure the yaw moment coefficient, which describes the torque produced in the direction of the yaw axis. This coefficient is defined as shown, where N is the yaw moment, and B is the wingspan on the aircraft.

Engineers use these coefficients to study aircraft performance and stability. The stability derivatives, taken with respect to the pitch or yaw angles, indicate whether the aircraft is stable or unstable.

For example, if the angle of attack, alpha, is suddenly increased by a wind gust, the aircraft's response determines its stability.If the angle of attack keeps increasing indefinitely, the aircraft is unstable. This is shown by a positive stability derivative, showing that the pitching moment coefficient continues to increase with alpha.

The same is true for directional instability with respect to yaw angle beta, which gives a negative stability coefficient. If the angle of attack or yaw angle return to their initial values, then the aircraft is said to be stable. This is reflected in the stability derivatives, which are opposite to the unstable conditions.

In this experiment, we will examine a model aircraft as it is exposed to airflow at different pitch and yaw angles and determine its stability and performance with and without its tail.

In this experiment, we will examine a model aircraft as it is exposed to airflow at different pitch and yaw angles and determine its stability and performance with and without its tail.

For this experiment, you'll need to use an aerodynamic wind tunnel with a force balance that controls the angle of attack, also called the pitch angle, and the yaw angle externally during the experiment. You'll also need a DC-6B aircraft model that attaches to the force balance using struts.

To begin, lock the external balance and install the struts on the balance to analyze the effects of the struts alone, so they can be subtracted out of the airplane measurements. Set the yaw angle to 0 by adjusting the yaw motor knob.

Now turn on the computer and turn on the data acquisition system for the external force balance. Allow the system to warm up for 30 min prior to testing.

Once the system has warmed up, open the data acquisition software. Read the room pressure and temperature and record these values in your notebook. Correct the barometric pressure, using the barometer spreadsheet that accompanies the mercury barometer.

Now make sure that the test section and wind tunnel are free of debris and loose parts. Then close the test section doors. Unlock the external balance. Then set the wind tunnel speed dial to 0. Turn on the wind tunnel and the wind tunnel cooling system. Record the balance forces and moments with the wind speed at 0.

Now adjust the yaw angle to 5° using the yaw control. Then record the balance forces and moments again at 0 wind speed. Repeat these measurements again at a yaw angle of 10° and zero wind speed. Now set the yaw angle back to 0 and then set the dynamic pressure to 7 inches of water. Then record the balance forces and moments again.

Now, set the yaw angle to 5°, adjust the dynamic pressure back to 7 inches of water, if necessary, and then record the balance forces and moments. Repeat the same measurements at a yaw angle of 10°, resetting the dynamic pressure back to 7 inches of water, if necessary.After the measurements have been recorded, return the yaw angle to zero, and turn off the wind tunnel.

To begin calibration of the model DC-6B airplane, first lock the external balance and open the test section. Then install the DC-6B model with the tail on. Calibrate the pitch angle using an electronic level and make adjustments to zero if needed.

After closing the test section doors, unlock the external balance, press the nose down button to set the pitch angle to -6°. Now record the balance forces and moments with the wind tunnel off to acquire the correction needed to account for the model's weight.

Change the pitch angle to -4° and repeat the measurement of the force and moments as before. Conduct the test for angles of attack up to 10° with 2° increments. Then return the pitch angle to zero. Now conduct the same test for the yaw angles 0,5,and 10°. When all of the angles have been tested, lock the external balance, open the test section, and remove the DC-6B model tail.

Then install the tail cone, so that we can measure the model weight contribution with the wind tunnel off. Now close the test section, set the yaw angle to zero, and record the force and moment measurements for all of the pitch angles from -6 to 10°, as before.

Once those measurements are complete, repeat the test again at a pitch angle of0 for the three yaw angles. When complete, lock the external balance.

Now we'll run the experiment with a non-zero wind speed. To begin, check the test section for debris and loose parts. Then, close the test section doors.

Next, set the pitch angle to zero and unlock the external balance. Set the wind tunnel speed dial to zero, then turn on the wind tunnel. Record the balance forces and moments before turning on the airflow. Now turn on the airflow with the dynamic pressure equal to 7 inches of water. Then set the pitch angle to -6°, and adjust the dynamic pressure back to 7 inches of water, if needed, before recording the balance forces and moments for this setting.

Repeat the measurement for each of the pitch angles tested in the calibration steps. Then return the pitch and yaw angles to zero. Adjust the dynamic pressure again if needed, and then record the balance forces and moments. Like before, repeat the measurements for the yaw angles tested during the calibration.

Once all of the measurements have been taken, slowly decrease the air speed to zero. Now lock the external balance and open the test section. Remove the DC-6B tail cone and install the complete tail. Then close the test section and repeat the measurements for all of the pitch angles and yaw angles tested previously with a wind tunnel dynamic pressure of 7 inches of water.

In this experiment, we obtained performance and stability characteristics of a DC-6B aircraft model in two configurations, with the conventional airplane tail and with the tail removed.

For each configuration, adjust the measured forces to remove the weight of the strut by subtracting the forces with the model off and wind off from the forces with the model off and the wind on.

Then remove the effect of the weight of the model by subtracting the forces with model on and wind off from the forces with the model on and wind on. Then remove the aerodynamic effect of the struts by subtracting the weight adjusted forces of the struts from the weight adjusted forces of the model.

Using these adjusted forces, we can calculate the lift coefficient and drag coefficient using these equations. Here, L is the lift and D is the drag, which were measured in the experiment. S is the model reference area and q is the dynamic pressure.

Now if we plot the lift and drag coefficients against the pitch angle, we can see that the tail on the aircraft increases the maximum lift, but the tail also increases the drag. Next, let's look at the pitching moment coefficient.The pitching moment, M, was measured in our experiments.

Then, we'll plot the pitch moment coefficient against the pitch angle. Remember that if the pitch moment increases with increasing angle of attack, the aircraft is unstable, as it is unable to return to level heading. But if the pitch moment decreases with increasing angle of attack, the pitch moment acts to prevent the pitch angle from increasing or decreasing indefinitely; thus, ensuring more stability in the aircraft.

For the tail off configuration, the pitch coefficient increases with the increase of the pitch angle, showing that the aircraft is unstable in this configuration. On the other hand, the tail on configuration exhibits the opposite behavior, where the pitch coefficient decreases as the pitch angle increases, showing that the tail adds stability to the aircraft.

Similarly, we will calculate the yaw moment coefficient. The yaw moment, N, was measured in our experiments. Here we show a plot of the yaw moment coefficient versus the yaw angle.

For directional stability, a positive side slip angle beta means that the aircraft nose is pointing to the left of the direction of motion, and to the right if beta is negative. The yaw moment coefficient is positive to the right and negative to the left.

However, if the yaw moment decreases as beta increases, as it does for the tail off configuration, the airplane does not tend to return to the zero beta position and is unstable. Therefore, we can conclude that the airplane tail is necessary to achieve stability, even though it results in some performance reduction.

In summary, we learned how the aerodynamic characteristics of an aircraft are described by its lift, drag, and moment coefficients. We then measured the aerodynamic forces experienced by model DC-6B airplane in a wind tunnel to analyze its flight performance and stability.