I'm currently trying to do an initial design for a propeller. In order to do this I'm trying to use Xrotor. Xrotor allows the user to enter certain information about both the propeller geometry, flight conditions and the airfoil lift and drag data after which it performs its calculations. Xrotor requires the following values for the lift and drag data (example values are given):

1) Zero-lift alpha (deg):   0.00       7) Minimum Cd           : 0.0070
2) d(Cl)/d(alpha)       :  6.280       8) Cl at minimum Cd     : 0.150
3) d(Cl)/d(alpha)@stall :  0.100       9) d(Cd)/d(Cl**2)       : 0.0040
4) Maximum Cl           :  2.00       10) Reference Re number  : 2000000.
5) Minimum Cl           : -1.50       11) Re scaling exponent  : -0.2000
6) Cl increment to stall:  0.200      12) Cm                   : -0.100
                                      13) Mcrit                :  0.620

This information can be obtained from the drag polars of the airfoil.

<span class=$\alpha,C_l$ plot">

<span class=$C_d,C_l$ plot">

[360 degree extrapolated polar using JBlade

The 360 degree polar was made using JBlade. The only value that Xrotor requests that I am not sure on how to calculate is the d(Cd)/d(Cl^2) figure. I'm fairly confident that this can be obtained using the $C_d,C_l$ drag polar, but I'm not completely confident on how I should go about it. What is the correct way of determining this value?


1 Answer 1


$d C_d/dC_l^2 = dC_d/(2 \cdot C_l \cdot dC_l) = (1/(2\cdot C_l)) \cdot(1/$Slope of $C_d/C_l$ curve$)$.

Use a few $\alpha$s of interest and read the $C_l$s. Find the slope at those $C_l$s. The ratio should be consistant.

  • $\begingroup$ To elaborate, I found the following procedure myself: Find the $C_l$ and $C_d$ at various $\alpha$. Then you can plot the $C_d$ on the $y$-axis and the $C_l^2$ on the $x$-axis and then the slope of the graph represents the $dC_l/dC_l^2$ value. $\endgroup$ Jan 9, 2019 at 9:41
  • $\begingroup$ This assumes, of course, that we should take them literally. There is a coefficient for this, but it is not as well known as the others. The coefficient is sometimes scaled to make it more consistent as a non-dimensional quantity. In which case, you really need to read the manual to make sure you don't need some scaling factor as well. Note, this is the only nominally dimensional quantity requested, so I'm a bit suspicious. $\endgroup$
    – Phil Sweet
    Jan 9, 2019 at 11:51
  • $\begingroup$ The manual only states the quadratic drag dependence on CL. Which isn't a whole lot to go on. $\endgroup$ Jan 9, 2019 at 19:39

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