Square root wing loading conversion method

On Friday, August 22, 2014 2:08:12 AM UTC-4, 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!

It all comes from the lift equation which can be used to determine what airspeed (and sink rate) is needed to achieve the same glide ratio following a weight change. When I wrote this I forgot your original question was about wing loading. So, pretty much what you'd do is figure out what weight each glider needs to be to achieve the same wing loading and correct each of their polars to that weight and plot them together.

Here's the write up explaining how the weight correction can be derived...
https://dl.dropboxusercontent.com/u/...ght_change.pdf

On Friday, August 22, 2014 11:22:55 AM UTC-4, Andrew wrote:
On Friday, August 22, 2014 2:08:12 AM UTC-4, 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!



It all comes from the lift equation which can be used to determine what airspeed (and sink rate) is needed to achieve the same glide ratio following a weight change. When I wrote this I forgot your original question was about wing loading. So, pretty much what you'd do is figure out what weight each glider needs to be to achieve the same wing loading and correct each of their polars to that weight and plot them together.



Here's the write up explaining how the weight correction can be derived....

https://dl.dropboxusercontent.com/u/...ght_change.pdf

After thinking about it again I realized the final formula I gave doesn't necessarily have to use just weight or airspeed. It's possible to use weight or wing loading to suit ones goal. Also, one could use sink rates instead of airspeed. This is because the final formula deals in ratios of speeds and the square root of the weight or wing loading ratio.

V could be the airspeed or sink rate, and W could be the weight or wing loading...

V_light / V_heavy = sqrt( W_light / W_heavy )