## Friday, March 14, 2014

### Math for Calculating Area of Vertical Fin

To keep an airplane flying straight normally a vertical fin is needed, the position is usually above the horizontal stabilizer. For a sport rubber model 10% of the wing area is good proportion to try. What would be the area for the vertical fin using the 36 square inches of wing area?    [3.6 sq. in.]  After computing the square inches of the vertical fin, what function would you use on this area to get equal length sides?   [square root]

 Side View of Rubber Powered Model Airplane

You decide that for the shape of the vertical fin part of the area to the front will be a right triangle. You decide the rear part of the fin will now be a square with sides 1.5” long.  How much area will this be? [ 2.25 sq. in].  What do you think the next step will be?   Yes, [ 3.6” – 2.25” = 1.35 sq. in.] Now we need a right triangle of 1.35 sq. in. with the opposite side 1.5” long to match up with a side of the square with sides that are 1.5" long. How long will the adjacent side of this triangle be?

I started looking for a formula to compute the adjacent side given the area and the opposite side but did not find one. My reasoning was to create a rectangle by drawing in another triangle and doubling the area. This would make it easy to compute the adjacent side. 1.35 sq. in. x 2 = 2.7 sq. in for rectangle area.  Divide this by 1.5” which equals  1.8“ for the bottom side (adjacent side).

 Entire Vertical Fin

To check my method I divided the area of rectangle 1.5” x 1.8” /2 = 1.35 square inches. I could now put the triangle and square together to form a vertical fin with 3.6 square inches of area.

If anyone has another solution to find the missing dimension of the triangle comment below.

Bill Kuhl

For an explanation of many aspects of simple aerodynamics with math problems check out my article Basic Aerodynamics With a Lesson

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