Wing Aspect Ratio (Newbie to Aerodynamics)

[t.kennedy]

Homework Statement

A tailless aircraft of 9072kg mass has a delta wing with aspect ratio 1 and area 37m². Show that the aerodynamic mean chord of a delta wing,
$\frac{\int_0^{b/2} c^2 dy}{\int_0^{b/2} c\ dy}$
is two-thirds of its root chord and that for this wing it is 5.73m.

Homework Equations

$AR= \frac{b}{\bar{c}}$
$\frac{\int_0^{b/2} c^2 dy}{\int_0^{b/2} c\ dy}$

The Attempt at a Solution

Problem 1.
$AR= \frac{b}{\bar{c}}=1$
$b= \bar{c}$
I don't get it. If the wingspan equals to the mean chord then it won't be delta wing anymore, wouldn't it?

As you can see the root chord is smaller than the tip chord hence $\bar{c}$ must be smaller than b/2. Where do I get myself wrong?


Problem 2
$\frac{\int_0^{b/2} c^2 dy}{\int_0^{b/2} c\ dy}$
How do I find the equation for c to solve this integral? Is there any of other way? I know the bottom integral is the area of one wing but I don't know the other one.

 

[CWatters]

If the wingspan equals to the mean chord then it won't be delta wing anymore, wouldn't it?

I can't help with the rest of the problem but if I don't see a problem with the wingspan being equal to the mean chord. The plan form won't be an equilateral triangle but it would still be a triangle and classed as a delta.