McMullan Aircraft Design


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Birth of an Airplane

JayBird Design Page

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Calculating Tail Volume Coefficients

Now that the fuselage and wing have been "sized" for my airplane, I have to calculate the volume coefficients for the horizontal and vertical tails. I have sketched them out as seen on the previous page but now I have to make sure they are the correct size. As with all the steps in designing an airplane, there are trade-offs. I can make the tail surfaces very large and they will give great stability and control but on the down-side, the control surfaces may be very hard to move and the airplane may be very hard to control directionally in a strong crosswind. Using the software that comes with "Preliminary Design - Modern Aircraft Design for the Non-Engineer" I will plug in the required data and the size of the tail surfaces I have drawn. The software will then give me the volume coefficients of the tail surfaces as they are drawn. You will find out that airplane design is 90% math. This software greatly simplifies all of the calculations that would have to be done over and over. If I had not already drawn the tail surfaces, the software will tell me what the coefficients should be and I could draw the tail surfaces accordingly. So the software gives me two ways to go about determining the calculations we need. "Preliminary Design" gives more instruction and examples on how to go about determining the volume coefficients.

Using the software with "Preliminary Design - Modern Aircraft Design for the Non-Engineer" makes calculating volume coefficients easy.

The software asks for a "moment arm". This measurement is taken from the center of gravity of the aircraft to the center of the tail surfaces. The moment arm is a distance from a point at which the airplane rolls or pitches. In our case it is 156 inches. An airplane with a longer moment arm will require smaller tail surfaces and an airplane with a shorter moment arm will require larger tail surfaces. A longer moment arm will also provide more longitudinal and directional stability in the aircraft. The reason this works is that a longer moment arm, when moved, gives more torque at the point of rotation. Mechanics understand this principle. If they have a bolt that is too tight for them to remove with a normal wrench, they can add a piece of pipe, sometimes called a cheater, to the end of the wrench and it makes it easier for them to remove the bolt. By using the same amount of force that would not remove the bolt with the wrench, the added piece of pipe allows the bolt to be easily removed.

The horizontal tail volume coefficients for light airplanes ranges between 0.3 and 0.7. The drawings I have made have a horizontal tail volume coefficient of 0.55. The vertical tail volume coefficients on most light airplanes range from 0.02 and 0.05. Mine comes in at 0.04. The horizontal and vertical tail volume coefficients both fit suitably well without having to make any changes. If they did not, I would need to scale the drawings of the tail surfaces up or down, depending on the size I am looking for.

The tail moment arm determines the size of the airplane's tail surfaces. Directional and longitudinal stablility are affected by the length of the moment arm also.

Next, we will check the aspect ratio of our horizontal and vertail tails and then we will size the rudder and elevator. As in the main wing of an airplane, a higher aspect ratio is desired for the tail surfaces of the airplane. The horizontal tail, as drawn, has an area of 19.7 square feet and a span of 9' 7 1/6'. Using our formula, I get an aspect ratio of 4.66. The vertical tail's aspect ratio is 2.17.


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