# A few calculations

It's still way too windy outside, so lets do some calculations.

We have the rotation rate at which the copter lifts, and the construction details. This means we should be able to get the (average) coefficient of lift $C_l$ from the lift force $L$ and the wing area $S$.

$C_l = 2L/(rho v^2 S)$

$v = omega r$

$C_l = 2L/(rho omega^2 r^2 S)$

Due to the square relation to the radius, just taking half the span of the wing (0.3m) isn't really valid, and it gives a $C_l$ of about 1, which seems pretty high for the sorry excuse of a wing profile that I use.

So, if I grok this (and I'm absolutely not sure I do), we need $root3(1/2) = 0.7937$ of the span, that gives $r = 0.476$ and $C_l = 0.4$, which is way more believable.

(The idea behind this is that $int x^2 = 1/3 x^3$, so with $x=1$ we have $1/3 x_(avg)^3 = 1/6$.)

On to the drag, which has the same formula:

$C_d = 2F/(rho omega^2 r^2 S)$

Which gives $C_d = 0.29$. Seems high, even including the drag from the rest of the copter besides the wing. Is that an effect of induced drag? A quick calculation gives a result on the order of $0.1N$, so probably not, even if it really is for wings with elliptical lift distribution etc.pp.

Constants:

- $L = 1.619 N$ (165g)
- $F = 1.17 N$ (120g)
- $rho = 1.293 (kg)/m^3$ (at 0°C)
- $omega = 21.36 s^-1$ (3.4 Hz)
- $S = 0.06 m^2$