Explanation Given information: The maximum downward air speed ( v ) is 80 ft / s . The diameter ( d ) of the slipstream is 30 ft . Total weight of the helicopter and the crew, W is 3 , 500 lb . The specific weight of air γ is 0.076 lb / ft 3 . Calculation: Sketch the free body diagram of slipstream as shown in Figure 1. Find the mass flow rate ( d m d t ) using the Equation as follows: mass = density × volume = density × ( area × length ) Δ m = ρ A B ( Δ l ) (1) Substitute ( v B × Δ t ) for Δ l in Equation (1). Δ m = ρ A B v B ( Δ t ) Δ m Δ t = ρ A B v B Δ m Δ t = γ g A B v B d m d t = γ g A B v B (2) Here, A B is area of the slipstream well below the helicopter and v B is the corresponding velocity in the slipstream. Substitute ρ for γ g in Equation (2). d m d t = ρ A B v B Find the thrust ( F ) on the helicopter using the relation as follows: F = d m d t ( v B − v A ) (3) Here, v A is located at top of the blade. Thus, the v A is zero. Substitute γ g A B v B for d m d t in Equation (3)

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 14.3, Problem 14.72P

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Find the maximum load such that helicopter can lift while hovering in mid-air.

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Chapter 14.3, Problem 14.71P

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Chapter 14 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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Find the maximum load such that helicopter can lift while hovering in mid-air.

Solution Summary: The author calculates the maximum load such that helicopter can lift while hovering in mid-air using the Equation as follows:

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