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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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