Finding the lift of a propeller

[Alkhimey]

Is there any formula to find the lift genetated by a helicopter propeller?

 

[Alkhimey]

Anybody?
Can you give me at least the formula for the lift force of a normal airplane wing?

 

[FredGarvin]

There are so may factors that effect this that a simple plug and chug equation will not suffice. There are a lot of things about helicopter aerodynamics that complicate the process that a fixed wing doesn't have to deal with.

The basic equation for lift is:
$$F_L = \frac{1}{2} C_L \rho V^2 A$$ where:

$$F_L$$= Lift force
$$C_L$$ = Coefficient of lift
$$\rho$$ = Density
$$V$$ = Velocity
$$A$$ = Area

The coefficient of lift is the tough part to determine and is usually an experimentally deduced value. Also, this is a one dimensional look at lift. The lift characteristics, especially of a helicopter blade change from root to tip. It can get as complicated as you like.

 

[Alkhimey]

Thank you for your reply.
I have few questions.
What density do you mean? Density of the air or density of the wing?
Area of what do you mean?
Can you suggest an experiment to find a coefficient of lift?
I guess plane desiners have other ways to find it. No one would let them crash a plane just to find out what is the maximum weight it can carry.

In my opinion the only difference between a helicopter wind and an airplane wing is that hellicopter wing moving a cillcular orbit (or if the helicopter going up than it is a spiral orbit) while the airplane wing is moving in a 2d line. I think in both cases the lift should be same. Am I right?

sorry for my bad english

 

[Danger]

Fred's definitely the expert here, but I'll stick in a comment or two just to keep my typing fingers nimble. One is that the lift of a helicopter rotor constantly changes because of the way they're controlled. You have both cyclic (steering) and collective (lift) pitch controls that determine how much lift you get and in which direction it is applied. Also, rotors are quite long in proportion to their width and thickness, so there's a lot more flex than in a fixed wing or a standard aeroplane prop.
Experimental testing of aerodynamic surfaces is traditionally done with models or full-scale prototypes in a wind tunnel with instrumentation and visual markers such as smoke. Computer modelling is probably quite prevailent in that arena as well.

 

[FredGarvin]

The density is the air density. The area is the plan form area of the wing in question.

The big difference in rotary wing is that there are two aspects to consider. The first is the effects of the wing as it is advancing into the relative wind. The second is as the wing is retreating in the second half of the rotation in the same direction as the relative wind in the first half. This is where the situation of "retreating blade stall" can rear it's ugly head. It is also the reason for asymmetrical lift.

Also you normally have to incorporate the notion that the blade is not traveling through nice still air. In a lot of cases but it is going through air that has been disturbed by the rotor in front of it. It can and does get very complicated modeling the flows through a rotor disk.

Here are some links to give you some reading on the subject:
Asymetrical Lift
Blade Flapping
Retreating Blade Stall
http://www.cavalrypilot.com/aerodynamics/transverse.html
http://www.cavalrypilot.com/aerodynamics/rotational_vel.html
http://www.synchrolite.com/B270.html

 

[Alkhimey]

Thank you for the info.
What want do to is to preform a simple experiment that demonstrates how helicopters work. Any suggestions on how to do this? Maybe someone already done something similar and already have the parameters for the propeller? I want to make a 50-100 gram constuction to hover stably several centimeters above the ground.
Can you give me hints to how helicopters keep their stability?

 

[Danger]

Longitudinal stability in a single-rotor machine is provided by a horizontal prop called the tail rotor which serves to counteract the rotational reaction of the fusilage. It's speed is geared to the main rotor, and the rudder pedals control the pitch to determine the precise thrust (for turning left or right). In some newer designs, the engine exhaust is routed out of louvres in the tail to act as a control jet rather than using a rotor.
Dual-rotor 'copters have the main's counter-rotating to eliminate yaw effects.

 

[FredGarvin]

Thank you for the info.
What want do to is to preform a simple experiment that demonstrates how helicopters work. Any suggestions on how to do this? Maybe someone already done something similar and already have the parameters for the propeller? I want to make a 50-100 gram constuction to hover stably several centimeters above the ground.
Can you give me hints to how helicopters keep their stability?

That's going to be a bit on the tough side. The first thing that comes to my mind is to have a stationary shaft that rotates a rotor disk. Have 4 or more load cells placed about the disk. As you rotate the rotor blades, you can change the pitch of the blades and display the effect around the disk by the readouts of the load cells. This does mean that you would have to replicate the blades, the swashplates, the control linkages, etc... It would be a fair amount of work and possibly too complicated.

You may take a look into available radio controlled helicopters, especially the electric ones. Then there you will be trading complexity for cost.

 

[Danger]

Wolram might be helpful in the model department. I understand that he has extensive experience.