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

http://www.ideas-inspire.com

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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