Calculating foil drag

[CamCleat]

The simple example I would like to solve is for a dingy sailed upright with the sail force (F) exactly balanced by the centreboard force. I understand that…..

D = 0.5 ρ V^2 S (CDo + CL^2/( π λ e))

where…..

D = Centreboard drag force
ρ = Density of water
V = Boat speed through water
S = Area of centreboard
CDo = Drag coefficient
CL = Lift coefficient of centreboard = F / (0.5 ρ V^2 S)
λ = Centreboard aspect ratio
e = Oswald efficiency (= 1.0 for an elliptical foil)

Now, the question I have is whether the CL and CD are simply the 2D coefficients that you would obtain from X-foil or similar?

I thought that flow around the base of the centreboard which results in induced drag also reduces the lift coefficient towards the tip. This would result in the 2D lift coefficient varying along the foil. Do we need to calculate an effective 2D coefficient to use in the formula above?

Thanks in advance.

[jehardiman]

First of all, you are dealing with hydrodynamics, not aerodynamics so, some aero ways of doing things do not apply.

Second, e is never 1.00 in the real world. It would only be 1.00 for an ellipicly loaded foil (not an ellipitical foil, though it could be ellipiticaly loaded) in inviscid flow. Most likely it will be 0.6-0.8 depending on sweep. This accounts for the 3-D flow. Though it is nice to think of a foil as a bunch of short 2-D sections tacked together, that is incorrect given the spanwise flow caused by viscous effects. In your equation above, CL will most likely be a geometry based and CDo most likely experimental based. Use them directly and allow the experimentally based correction coefficents work it all out.

See this site for a better description of your equations above, including the root drag that you left out of your equations.

http://adg.stanford.edu/aa241/drag/induceddrag.html

[tspeer]

The variation in 2D lift coefficient shows up in two places. The CL in the equations you're using is the average lift coefficient of the whole board, and the factor e is determined by the spanwise distribution of lift along the board.

You might find this spreadsheet useful for accounting for the spanwise lift distribution.