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# Drag on rotating airfoil (tail wind?)

## Drag on rotating airfoil (tail wind?)

(OP)
Hello,

I have a question regarding drag on a moving airfoil, as in a wind turbine. In the simplest form, say an airfoil is moving forward at zero angle of attack at a speed V with a tail wind of U. Is the drag:

a.) D = Cd*1/2*rho*A*(U^2-V^2)

b.) D= Cd*1/2*rho*A*(U-V)^2

Difference of the squares or square of the difference? (there are plenty assumptions in the above - one being that Cd is equal at 0 and 180 AoA, if it wasn't there would be a Cd term before each U and V).

Thank you.

### RE: Drag on rotating airfoil (tail wind?)

It probably doesn't matter what kind of machine or wing you're interested it.  This is about the basic concept of force on an aerofoil, regardless of its application.

In a simulation of an aerofoil or a wing, the wing is usually said to move with respect to the air.  In a wind tunnel, the air moves with respect to the wing.  A semantic difference to us now, but 100 years ago there was some discussion on the matter.

The wing doesn't really care if it is moving through the air, or if the air moves over it.  Forces will develop nonetheless.

In your case, find the net relative airspeed of the aerofoil through whatever situation the air is in, and that net velocity is your V vector.  This makes equation "b)" correct.

Steven Fahey, CET

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