Consider the possibility of using two rotating cylinders to replace the conventional wings on an airplane for lift. consider an airplane flying at 150 km/hr through the standard atmosphere at 2,000 m. each "wing cylinder" has a 1.0-m radius. the surface velocity of each cylinder is 20 km/hr. find the length ℓ of each wing to develop a total lift of 40 kn. assume potential flow and neglect end effects. hints: = 2 r v see example 6.6

27.35m

Explanation:

For the calculation of the Support Force we rely on the formula for obtaining the force in a cylinder of a certain length l,

Here each term is,

= Lift force

= density of air

= vortex strength

For this last equation, its mathematical representation is given by,

Here each term is,

a= 1m, radios of cylinder

, the velocity of cylinder surface.

In order to find the density of the area at 2000m we will refer to the table of Standard Atmosphere of the United States, that is

Replacing the values,

Clearing l and solving for it we have,

In this way we can conclude that the length of the cylinder must be 27.35m

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