I'm a Spanish student of aerospace engineering and I'm doing my final bachelor work that consists in designing an unlimited aerobatic plane, and I wonder if it is possible to calculate an approximation of the roll rate depending on design parameters. ( I have aerodynamic analysis of the wing, CL, CD, MAC, W, ...)
And another question about it, how exactly the trailing edge sweep angle affects the stability? And some bibliography?
In order to determine the roll rate of an aircraft, all you need to do is to set the rolling moment from aileron deflection equal to the roll damping of the wing (actually, of the whole aircraft, but the wing dominates roll damping anyways). So you set $$c_{l\xi}\cdot\frac{\xi_{left}-\xi_{right}}{2} = -c_{lp}\cdot p = -c_{lp}\cdot\frac{\omega_x\cdot b}{2\cdot v_{\infty}}$$ $$\Rightarrow\omega_x = -\frac{2\cdot v_{\infty}}{b}\cdot\frac{c_{l\xi}}{c_{lp}}\cdot\frac{\xi_{left}-\xi_{right}}{2}$$
The symbols are:
$\kern{5mm} \xi\:\:\:\:\:$ aileron deflection angle
$\kern{5mm} v_{\infty}\:\:$ velocity
$\kern{5mm} b\:\:\:\;$ wing span
$\kern{5mm} c_{lp} \:\:$ coefficient of roll damping, using $\frac{b}{2}$ for its reference length
$\kern{5mm} c_{l\xi} \:\;$ coefficient of rolling moment due to aileron deflection
$\kern{5mm} p \:\:\:\;$ dimensionless roll rate
$\kern{5mm} \omega_x \:\:$ rolling speed in rad/sec
Damping decreases with altitude, and in this equation the increase of flight speed with altitude will make sure that roll damping decreases accordingly.
