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, 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 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. _____________.
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