# Part3 - Part 1 Recap • We looked at the history of...

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Unformatted text preview: Part 1 - Recap • We looked at the history of helicopters. • We studied ways of overcoming reactive torque – tail rotors, co-axial rotors, tilt- rotors, tip jets, NOTAR etc. • We looked at a number of ways predicting helicopter performance in hover, and climb. Momentum theory- Induced Velocities V V+v V+2v The excess velocity in the Far wake is twice the induced Velocity at the rotor disk. To accommodate this excess Velocity, the stream tube has to contract. Induced Velocity at the Rotor Disk Now we can compute the induced velocity at the rotor disk in terms of thrust T. T=2 ρ Av(V+v) A T A T V ρ ρ 2 v V Hover, In 2 2 2 V- v 2 = = + + = Ideal Power Consumed by the Rotor + + = A T V V T P ρ 2 2 2 2 In hover, ideal power A T T ρ 2 = Use this during conceptual design to size rotor, select engines Figure of Merit • Figure of merit is defined as the ratio of ideal power for a rotor in hover obtained from momentum theory and the actual power consumed by the rotor. • For most rotors, it is between 0.7 and 0.8. Hover in Power Actual Hover in Power Ideal = FM Non-Dimensional Forms ( 29 ( 29 ( 29 Q C = Ω = = Ω = = Ω = = Ω = = P 2 Q 3 P 2 T C Q P Torque locity x Angular ve Power hover, In R AR Q t Coefficien Torque C R A P t Coefficien Power C R A T t Coefficien Thrust C form. l dimensiona- non in expressed usually are Power and Torque, Thrust, ρ ρ ρ Blade Element Theory R dr r ∫ ∫-- = = Tip Out Cut Tip Out Cut dP b P dT b T dT Root Cut-out Use this during preliminary design, when You have selected airfoils, number of blades, Planform (taper), twist, solidity, etc. Typical Airfoil Section Z e r o L if t L in e U T = Ω r v V θ φ α i E ffective Ang le o f A ttack = θ-α i- φ Ω = Ω = r r V i v arctan arctan α φ Closed Form Expressions dr r C r r V r r V cba P dr r r r V cba T R r r d R r r 3 3 2 2 v v 2 1 v 2 1 ∫ ∫ = = = = + Ω + Ω Ω- Ω- Ω = Ω- Ω- Ω = θ ρ θ ρ Average Lift Coefficient • Let us assume that every section of the entire rotor is operating at an optimum lift coefficient. • Let us assume the rotor is untapered. ( 29 ( 29 σ σ π ρπ ρ ρ T T R C R bc R R T C R bc dr r c b T 6 C 6 C 6 C 6 C C 2 1 C t Coefficien Lift Average l l l 2 2 3 2 l l 2 l = = = Ω = Ω = Ω = = ∫ Rotor will stall if average lift coefficient exceeds 1.2, or so. Thus, in practice, C T / σ is limited to 0.2 or so. Use this to select solidity σ, during design. Combined Blade Element-Momentum Theory Equate the Thrust for the Elements from the Momentum and Blade Element Approaches R v , 8 8 2 Ω + = Ω = =- - + V R V where R r a a c c λ λ θ σ λ λ σ λ -- + - = 2 16 8 2 16 2 c c a R r a a λ σ θ σ λ σ λ...
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Part3 - Part 1 Recap • We looked at the history of...

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