How to find drag polar equation of Cl vs Cd graph

[MattH150197]

Homework Statement

I plotted the drag polar graph (Drag coefficient vs. lift coefficient) for an aircraft and are required to find the equation of the drag polar to determine values for [C][/D0] and k, using the graph or any other method. I've plotted the graph which I've included.

Homework Equations

CD=CDO+K*CL^2 [/B]

The Attempt at a Solution

I know that CD0 is the point at which the graph intersects the x-axis but what is k is it the gradient of the linear part of the graph? And what is the other method of analysing it, just out of curiosity. Thanks

 

[FactChecker]

There is no good fit of the data to an equation of the form C_d = C_d0 + k(C_l²).
There is a better fit of the data to a curve of the form C_l = C_l0 + k(C_d-0.4)².
Approximately C_l = 0.184 + 0.4×(C_d-0.4)²

I wonder if you are being asked to determine the tangent line from (0,0) to the curve. That gives the greatest lift-to-drag ratio. That would be the line from (0,0) to about (0.275, 0.82).

EDIT: The OP noticed that the chart had the lift and drag axis switched. So all the lift and drag coefficients in this should have been switched.

 

[MattH150197]

What about if like you said I draw a tangent line and then simply allied y=mx + c so y = Cd m = k, x = Cl^2, c = Cdo do you think that would be correct?

 

[FactChecker]

What about if like you said I draw a tangent line and then simply allied y=mx + c so y = Cd m = k, x = Cl^2, c = Cdo do you think that would be correct?

Not exactly. Instead of C_l², it must be (C_l - C_l0)², where C_l0 is the minimal lift value. See the equation in https://en.wikipedia.org/wiki/Drag_polar

 

[FactChecker]

Just eyeballing the original data, I don't see why the regression didn't give (approximately) C_d0 = .25, C_l0 = 0.4 and k = 0.3. I wonder if I did the regression correctly. Or maybe it is sensitive to the original choice of C_l0 = 0.4 (which was eyeballed). Maybe C_l0 = 0.45 would have fit the upper C_l values better. The lower C_l values do not fit the model well. They are too low.