Where Can I Find Resources for Calculating Rotor Forces During Auto-Rotation?

[rm446]

Hello,

Out of curiosity I've been trying to mathematically model the forces on a rotor during auto-rotation starting with the basic lift/drag equations used for analyzing basic fixed wing flight (i.e. our beloved L = 0.5*Cl*rho*A*v^2). At first I thought this shouldn't be too hard since it's essentially the same as a fixed wing traveling over an airflow that increased linearly as you go from one end of the wing to the other. However as soon as you add a vertical component to the wind velocity angle of attack begins to vary with distance from the center of the rotor as well as velocity. This basically boils down to a very ugly integration problem and I'm just not that great at this type of mathematics and I figure someone must have done this before in a textbook somewhere.

So I just wanted to ask if anyone knows a good textbook or internet resources that does the calculation I'm trying to do. This doesn't need to specifically be auto-rotation, but any calculation that uses the basic lift/drag calculation to determine the overall forces produced by a rotor which has some vertical speed component.

(Also I have a master's in Mech. Engineering, so I can understand high level math but I have almost no exposure to aeronautical engineering beyond basic fluid dynamics.)

Thanks in advance :)

 

[Cyrus]

Hello,

Out of curiosity I've been trying to mathematically model the forces on a rotor during auto-rotation starting with the basic lift/drag equations used for analyzing basic fixed wing flight (i.e. our beloved L = 0.5*Cl*rho*A*v^2). At first I thought this shouldn't be too hard since it's essentially the same as a fixed wing traveling over an airflow that increased linearly as you go from one end of the wing to the other. However as soon as you add a vertical component to the wind velocity angle of attack begins to vary with distance from the center of the rotor as well as velocity. This basically boils down to a very ugly integration problem and I'm just not that great at this type of mathematics and I figure someone must have done this before in a textbook somewhere.

So I just wanted to ask if anyone knows a good textbook or internet resources that does the calculation I'm trying to do. This doesn't need to specifically be auto-rotation, but any calculation that uses the basic lift/drag calculation to determine the overall forces produced by a rotor which has some vertical speed component.

(Also I have a master's in Mech. Engineering, so I can understand high level math but I have almost no exposure to aeronautical engineering beyond basic fluid dynamics.)

Thanks in advance :)

Get a book on blade-element-momentum-theory to describe what you're trying to do. It's a non trivial process.