  # Autorotation Calculator

 Gross Weight $$lb$$ Collective Angle $$deg$$ Number of Blades $$-$$ Rotor Radius $$ft$$ Blade Chord Length $$ft$$ Induced Velocity $$ft/s$$ Drag Coefficient $$-$$ Air Density $$slug / ft^3$$ Descent Rate 33.2 $$ft/s$$ Descent Rate 1994 $$ft/min$$ Rotor Speed 245 $$RPM$$

## 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.

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