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Computer drawings of several fin planforms. The fin shapes
 are rectangular, trapezoidal, triangular and compound.

This slide shows the fin shapes for a variety of rockets as viewed from the side while looking onto the fin. This view is called a planform of the fin. You can see that fins come in many different planforms: rectangular, triangular, trapezoidal, or even elliptical. To determine the aerodynamic force that a fin generates, you must be able to calculate the area of any of these shapes. This skill is taught in middle school and used every day by design engineers. The area is the two-dimensional amount of space that an object occupies. Area is measured along the surface of an object and has dimensions of length squared; for example, square feet of material, or centimeters squared.

On the slide we have listed the formula to calculate the area of a variety of shapes: The area of a rectangle is equal to the height h times the base b;

A = h * b

The equation for the area of a trapezoid is one half the sum of the top t and bottom b times the height h;

A = h * [ t + b ] / 2

The area of a triangle is equal to one half of the base b times the height h;

A = .5 * b * h

Some fins are elliptically shaped. For an ellipse with a semi-axis a and semi-axis b, the area is given by:

A = pi * a * b

where pi is the ratio of the circumference to the diameter of a circle and is equal to 3.1415. A special case of the ellipse is a circle, in which the semi-axis is equal to the radius r. The area of a circle is:

A = pi * r^2

If the root of an elliptical fin is given by cr and the distance from the root to the tip is given by ct, the area of the fin is:

A = pi * cr *ct

For a compound configuration like the Space Shuttle, you have to break up the fin into simple shapes which you can compute, and then add them together.


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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Jun 12 2014

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