Blade element momentum theory

Blade element momentum theory is a theory that combines both blade element theory and momentum theory. It is used to calculate the local forces on a propeller or wind-turbine blade. Blade element theory is combined with momentum theory to alleviate some of the difficulties in calculating the induced velocities at the rotor. 1 2 W 2 N c C y = 4 π U ∞ ( 1 − a ) × Ω a ′ r 2 {displaystyle {frac {1}{2}}W^{2}NcC_{y}=4pi U_{infty }(1-a) imes Omega a'r^{2}}     (1) 1 2 ρ W 2 N c C x = 4 π ρ [ ( a ′ Ω r ) 2 + U ∞ 2 a ( 1 − a ) ] r {displaystyle {frac {1}{2}} ho W^{2}NcC_{x}=4pi ho leftr}     (2) sin ⁡ ϕ = U ∞ W ( 1 − a ) → sin 2 ⁡ ϕ = ( U ∞ W ( 1 − a ) ) 2 {displaystyle sin phi ={frac {U_{infty }}{W}}(1-a) ightarrow sin ^{2}phi =left({frac {U_{infty }}{W}}(1-a) ight)^{2}}     (3) Blade element momentum theory is a theory that combines both blade element theory and momentum theory. It is used to calculate the local forces on a propeller or wind-turbine blade. Blade element theory is combined with momentum theory to alleviate some of the difficulties in calculating the induced velocities at the rotor.