
Elliptical
Wing Problems
If so instructed by your teacher, print out a worksheet page for these
problems.
The Spitfire
(http://members.tripod.com/~F15JEagle2/spit.html) was renowned as a "small,
graceful, ellipticalwing fighter, champion at airtoair duals, and they
were routinely dived at velocities approaching the speed of sound." An
ellipticallyshaped 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 Mk
V (http://en.wikipedia.org/wiki/Supermarine_Spitfire)
, we find wingspan and area data which can be used to determine the length
of the minor axis.
 State the lengths
of the major and minor axes of the elliptical wing _______________.

Use
this information to write an equation of the ellipse (in standard
form, assuming a center at {0,0}).
 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.
 How is the minor
axis related to chord length? _____________________.
 Is the chord length
constant? _____________________.
 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?___________.
 Using the chord
length 2.8 m from the center, compute an aspect ratio. _____________.
