On Thursday, August 21, 2014 11:08:12 PM UTC-7, Andrew Ouellet wrote:
In many of Johnson's flight test reports, he refers to something like 'the square root of the wing loading' method to unify glide polars taken from different gliders at different wing loadings down to a common wing loading in order to be effectively compared. Can someone explain what this is and how to do this?



I have a strong engineering background so no need to mince words.

Thanks!

First you need to have the polar in the form of a quadratic: ax^2+bx+c. If you don't have that you can take any graphical depiction of the polar and use any standard mathematical technique to pick three points and fit a quadratic (I use matrix algebra for three equations with three unknowns). You need to have the reference weight for the polar: W. To get the polar for any other weight (W') you need three new coefficients for a new quadratic representation of the polar: a'x^2+b'x+c', where a'=a/(W'/W)^0.5, b'=b and c'=c*(W'/W)^0.5. It's that simple. (Pardon the Excel notation for multiplication and exponents).

There are a bunch of aerodynamic reasons why this is true that as to do with the relationship between weight and lift (need to be equal), the relationship between lift and lift coefficient and velocity and the relationship between induced drag and lift coefficient and velocity. You don't need to derive all the aerodynamic formulae to translate the polar so I won't belabor it.

9B