# Calculating Lift-To-Drag ratio of a rotating propeller with zero forward velocity

I'm simplifying some blade element theory problems by assuming that the propellers are perpendicular to the ground and their motion is constrained to being purely vertical (without forward velocity).

Im having some trouble calculating gamma, which is the arctan of the coefficient of drag divided by the coefficient of lift. This is related to the lift-to-drag ratio, as it is the arctan of its inverse. This gave me the idea to use lift-to-drag equations (like total drag = induced + zero lift) for finding gamma

However, lift-to-drag ratios are typically used for things like aircraft blades and not rotating propeller blades. Since the motion of the blades is contributed entirely by the blades rotation (no forward velocity), Would it be possible to use these equations if I assume the tangential velocity of the blade to be the equivalent airspeed in the equations?

• I think this answer is what you are looking for. May 23, 2023 at 21:25
• Are you working from a particular resource when writing your BEM? It might be easier to point us at a particular equation with a given set of nomenclature. When a BEM talks about cl and cd, it usually is referring to 2d sectional lift and drag coefficient -- not the combined coefficients of the propeller as a whole. The BEM works very logically through the process of finding the velocity and angle of attack at every blade station. That is the whole point of the BEM. May 23, 2023 at 21:35
• @RobMcDonald Im not working from a particular resource, per se, im trying to calculate the effective lift and drag coefficients of a propeller from APC propellers given their documented performance and geometry data (which dont include Cd and Cl sadly). May 23, 2023 at 21:52
• We don't normally book-keep propellers as having an overall lift and drag coefficient -- most of the time, that is meaningless. We typically care about a propeller's thrust and power coefficient. What are you actually trying to accomplish? Why do you think you want lift and drag coefficient of a propeller? May 23, 2023 at 22:47