# Drag of flat plate at any orientation in 3D

I am trying to calculate the force vector on a flat plate caused by wind, when that plate is not perpendicular to the wind.

Imagine a sailboat, and assume that its sail is a rectangular flat plate. If the boat is upright, then the lift/drag can be computed easily because the plate is perpendicular to the air flow and the angle of attack is the angle between the wind and the "sail".

However, if the boat heels, then this creates a second "angle of attack". I can't figure out how to compute the resulting force vector in this case.

I'm pretty sure that the 3D force vector is perpendicular to the flat plate, as it is in 2D. But how do I compute the magnitude of this force vector?

EDIT: I think I found the answer: the angle of attack is equal to the angle between the wind vector and the flat plate's normal vector, minus 90 degrees. The area to use in calculating the lift and drag is simply the area of the plate. Does this make sense?

• Possible duplicate: aviation.stackexchange.com/questions/21391/… – ja72 Mar 28 at 15:38
• Also google "cl cd vs angle of attack flat plate" – ja72 Mar 28 at 15:39
• @ja72: This question is not a duplicate of the one you linked. That one was about using a flat plate for the 2D cross section of a wing. This one involves tilting a sail in 3D, where the flat-plate cross section is merely incidental. – D. Halsey Mar 28 at 22:41
• It's not simple. You really need to understand airfoils and the Kutta condition. The force felt by the "wing" depends seriously on the angle of attack. Read this great e-book: av8n.com/how – Mike Dunlavey Mar 30 at 0:43