Helicopter hovering in crosswind with tail rotor

[Hey_Ducky]

Homework Statement

A helicopter is hovering in a steady cross wind at a gross weight of 3,000lb. The helicopter has 275 hp delivered to the main rotor shaft. The tail rotor radius is 2.3 ft and has an induced power factor of 1.15. The tail rotor is located 15.3 ft away from the main rotor shaft. Determine the crosswind conditions (velocity and direction) in which tail rotor effectiveness may be reduced or lost. If the center of gravity is assumed to lie on the rotor shaft axis, determine the feasible yawing angular velocity that the pilot can demand that may also result in a loss of tail rotor effectiveness

Homework Equations

My understanding is that the torque of the tail rotor needs to counteract, ie, be equal to the torque created by the main rotor. For that reason, my first goal is to right down torque equation for each scenario. Leishman, my textbook, uses Q = Torque, T = Thrust (here, same as weight in hover).

Qrotor = T * Vinduced/(Vtip/R)
Qtail = r x f = |r| |f| sin(theta)
--> Figure out under what circumstances Qtail < Qrotor

I'm interested in exploring the angle of the crosswind, so theta is fine.
Known (or solvable): T, R, Vi, r
Vi = sqrt(T/ (2*A*rho))
Unknown: Vtip (how do I deal with this?)
Not sure: f ? and theta

F must be the thrust exerted by the tail rotor. So, call it Ttail ?
In rotorcraft P = T * Vi.
Here's where I'm stuck. How do I use the induced power factor to get Ptail? How do I get Vi,tail? I don't have area or disk loading or really any information about the tail?

Am I on the right track? Your help would be greatly appreciated.

The Attempt at a Solution

 

[rcgldr]

There seems to be insufficient information. It's not clear to me what an induced power factor of 1.15 at the tail rotor means. The main rotor size is not stated either. Also it takes less power to hover in a crosswind versus zero wind, but I don't know if your textbook explains this.

 

[theOrange]

Homework Statement

A helicopter is hovering in a steady cross wind at a gross weight mass* of 3,000lb.
My understanding is that the torque of the tail rotor needs to counteract, ie, be equal to the torque created by the main rotor. For that reason, my first goal is to right down torque equation for each scenario. Leishman, my textbook, uses Q = Torque, T = Thrust (here, same as weight in hover).

I don't have area or disk loading or really any information about the tail?

Right, so in what situation (can you think of) would the torque caused by the tail rotor be lower compared to the torque of the main rotor?

You do have a radius, could you not find the area using that?

Also, remember that since the helicopter is in hover, the downward thrust is equal to the weight.

$$Weight = mass * gravity$$

 

[rcgldr]

Right, so in what situation (can you think of) would the torque caused by the tail rotor be lower compared to the torque of the main rotor?

Typically, the tail rotor moves at some fixed multiple of the speed of the main rotor, and the pitch of the blades on the tail rotor is changed to vary the amount of torque on the tail rotor. Instead of a cross wind situation, imagine flying a helicopter sideways; I'm not sure of the limits for flying full scale helicopters sideways, but aerobatic radio control model helicopters can be flown at top speed sideways, with the top speed is reduced due to the drag of the fuselage being flown sideways. The limitaion on sideways speed is due to the main rotor, not the tail rotor which is essentially a variable pitch propeller.

Also, remember that since the helicopter is in hover, the downward thrust is equal to the weight.

And for some given period of time Δt, the impulse (thrust x Δt ) equals the change in momentum of the air. Assuming some fixed amount of mass of air flowing per unit time mdot, then change in momentum = mdot Δv. The change in momentum must deal with the induced vortice flow, which is greater when hovering compared to forward or sideways flight at sufficient speed. Links:

http://www.copters.com/aero/hovering.html

http://www.copters.com/aero/translational.html

 

[theOrange]

Typically, the tail rotor moves at some fixed multiple of the speed of the main rotor, and the pitch of the blades on the tail rotor is changed to vary the amount of torque on the tail rotor. Instead of a cross wind situation, imagine flying a helicopter sideways; I'm not sure of the limits for flying full scale helicopters sideways, but aerobatic radio control model helicopters can be flown at top speed sideways, with the top speed is reduced due to the drag of the fuselage being flown sideways. The limitaion on sideways speed is due to the main rotor, not the tail rotor which is essentially a variable pitch propeller.

An for some given period of time Δt, the impulse (thrust x Δt ) equals the change in momentum of the air. Assuming some fixed amount of mass of air flowing per unit time mdot, then change in momentum = mdot Δv. The change in momentum must deal with the induced vortice flow, which is greater when hovering compared to forward or sideways flight at sufficient speed. Links:

http://www.copters.com/aero/hovering.html

http://www.copters.com/aero/translational.html

I know, I'm giving the OP some questions to think about.