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excelplotcurve

Excel plotting airfoil curves from a paper, faulty polynom?

I'm trying to plot airfoil camber lines in excel, given the polynomial and some constants.

Here is the given data, the final to reach is on the right top, with the (x,y) coordinates being used to create a CAD model of a wing that will be used for a 3-bladed wind turbine rotor.

Here is the given data, the final to reach is on the right top

For the moment I get this:

For the moment I get this

Is there a fault in the given polynomial?

Solution

  • It looks like the authors reported the a parameters in reverse order. What was reported as a0 is in fact a3, reported a1 is a2, reported a2 is a1 and reported a3 is a0. To give a specific example, the parameters when z' = 10 mm should be

    a0 = -0.8E-03
a1 = -8.44E-01
a2 =  2.99E-02
a3 = -3E-04

    and the equation when z' = 10 mm should be

    y' = yLE + [-0.8E-03]*(x'-xLE)^0 + [-8.44E-01]*(x'-xLE)^1 + [2.99E-02]*(x'-xLE)^2 + [-3E-04]*(x'-xLE)^3

    Note that the parameters as reported are multiplied by scale factors (e.g. 10^4) and you need to divide the reported values by those scale factors to get the true values.

    Here's my graph of the airfoil profiles enter image description here

    This could have happened if the authors used Excel's LINEST function to do data fitting, because LINEST reports curve fit parameters in high-to-low order (a[n], a[n-1], ... a[2], a1, a[0]). To me this is ordering counter-intuitive and can lead to confusion.

    Hope that helps