Question #249173
A helicopter of gross weight W with rotor diameter D hovers at Sea level achieving a figure of merit M using momentum theory calculate the % of change in actual rotor power at 1 KM above sea level at same M density change 8% per KM may be assumed near sea level
1
Expert's answer
2021-10-10T09:34:40-0400

P=vT

But v=T2ρaBut \ v=\sqrt{\frac{T}{2\rho a}}

Thus P=T2ρaTP=\sqrt{\frac{T}{2\rho a}}*T

%∆P=\frac{P'-P}{P} P=PPP∆P=\frac{P'-P}{P}

P=1000T21.08ρaTP'=\sqrt{\frac{1000T}{2*1.08\rho a}}*T

P=(1000T21.08ρaT)T2ρaTT2ρaT∆P=\frac{(\sqrt{\frac{1000T}{2*1.08\rho a}}*T)-\sqrt{\frac{T}{2\rho a}}*T}{\sqrt{\frac{T}{2\rho a}}*T}

=30.42-1=29.42

=29.42%


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