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MAE 466/566. Rotary-Wing Aerodynamics.Homework Assignment #1. Due January 23.

1. A Tail Fan. Several helicopters use a ducted tail fan (the French call it a fenestron) rather than a tailrotor as an antitorque device. The effect is similar to a ducted or shrouded propeller.

(a) Using a control volume analysis, find the total thrust produced by the ducted fan (fan area, ) interms of the induced velocity at the fan, 1. Note that the streamlines exiting the shroud are parallelso that the pressure does not change across the outlet face and is thus equal to

. You may assume

that you know the freestream velocity, (this would be a crosswind relative to the helicopter, isstraight in to the tail fan), the ambient density and the disk area of the fan. Assume that= 16.Be sure to list the assumptions you make in order to do this analysis.

(b) Find the power required by the fan. If the helicopter is in hover, = 0. For this case, find the power

in terms of thrust and other known quantities (not 1).

(c) Compare the efficiencies of the tail fan and the tail rotor for equal thrusts and disk areas in hover.

(d) One reason the ducted fan is more efficient than the open-rotor fan is that the induced flow overthe duct itself produces some of the thrust. Find the ratio of fan thrust to total thrust in hover (and

thus duct thrust to total thrust) in terms of known quantities. Can you think of any practical designconsiderations that might change the relative efficiencies?

2. A NOTAR. The NOTAR (NO TAil Rotor) provides a means for supplying the anti-torque required tooffset the effect of the main rotor drive. The figure shows a simplified sketch of the NOTAR system withfan, boom, and thruster. Assume that the circulation control slots do not affect the current analysis. Thefan area is and the thruster jet area is . It can be shown that there is no contraction of the jet afterit leaves the boom (not necessary to prove this). Use any simplifying assumptions necessary, such as thatof an incompressible fluid.

(a) Find the forces on the helicopter boom in terms of known quantities and 1, where 1 is the inducedvelocity at the fan. That is, find the thrust in the negative -direction, and the momentum dragin the -direction. Note: The thrust of the fan does not equal the thrust of the jet. You arenotrequired to find the fan thrust in this problem.

(b) If the required thrust to trim the helicopter in hover is , compare the anti-torque power requiredfor a NOTAR with that required for a tail rotor. Assume that = 4 and = 33 Note:the expression for the required power for the NOTAR is NOT the same as the expression for powerrequired for the tail rotor. Be sure to derive the new power expression.

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(c) Now assume that the circulation control system accounts for half of the thrust required for anti-torque.Make the same comparison as above, but with the NOTAR taking advantage of its circulation controlsystem.

V

Vj

A

Aj

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