The Spitfire (http://members.tripod.com/~F15JEagle2/spit.html) was renowned as a "small, graceful, elliptical-wing fighter, champion at air-to-air duals, and they were routinely dived at velocities approaching the speed of sound." An elliptically-shaped wing incurs the least drag.  

Let us assume the entire wing of the Spitfire is an ellipse with the major axis equal to the wingspan. Using a web site for the Spitfire V (http://www.sccs.swarthmore.edu/~dlevin/supermarine.html#spitfire) , we find wingspan and area data which can be used to determine the length of the minor axis.

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2. Use this information to write an equation of the ellipse (in standard form, assuming a center at {0,0}).

    

3. Sketch the ellipse on x, y axes with the center of the ellipse at the origin. Label the coordinates of the extremities of the major axis (wing tips) and minor axis.

    

4. How is the minor axis related to chord length? _____________________.

     

5. Is the chord length constant? _____________________.

    

6. What is the chord length 1 m from the ellipse's wing's center? ____________________.
   
   2.8 m from the center? ___________________.
   
   5 m from the center?___________.

    

7. Using the chord length 2.8 m from the center, compute an aspect ratio. _____________.

Intro

Worksheet