Autorotation Calculator
Description
This calculator estimates the descent rate and rotor speed of a helicopter
in steady autorotation (without power).
Equations
The following equations are used to estimate the inflow angle \( \phi \)
and descent rate \( v_z \) at
a "0 torque blade section" assumed to be at 65% radius (\( .65R \)) with drag
coefficient \( c_d \).
The equations assume this blade section provides average thrust (per unit blade length)
over the rotor to counter 90% of the weight \( W \) of the helicopter (10% of the weight is
countered by lift on the fuselage and stabilizer).
The blade section has the input induced velocity \( v_i \)
and lift coefficient of \( 2 \pi \alpha = 2 \pi ( \phi + \theta ) \),
where \( \theta \) is the input blade collective angle.
The air density \( \rho \) is input.
\[ 2 \pi ( \theta + \phi ) \sin \phi = c_d \cos \phi \]
\[ r = .65R \]
\[ \Omega^2 r^2 + (v_z  v_i)^2 = v^2 \]
\[ .9W = \frac{\rho R N_b v^2}{2} ( 2 \pi ( \theta + \phi ) \cos \phi + c_d \sin \phi) \]
\[ \tan \phi = \frac{ v_z  v_i }{\Omega r} \]
For more details including the derivation of these equations see
our article
on autorotation.
