My calculus is pretty rusty, but it appears that the correct statement is "best L/D means that s(h) = h * s'(h)".

My thinking is that the glide ratio R(h) = L/D = h/s(h). The best glide ratio is the zero crossing of the slope of the R curve, R'(h). The product rule and the chain rule for derivation gives the result above.

Cheers,
...david

On Friday, December 22, 2017 at 3:22:05 PM UTC-5, lharri...@gmail.com wrote:

On Friday, December 22, 2017 at 11:28:11 AM UTC-5, Tony wrote:

There is a spreadsheet that allows comparison of quite a few polars here: https://www.gliding.com.au/assets/docs/Polar10.xls

This is interesting data to me, but I open it up, and look at the "gliders" table of the raw data, and I cannot make any sense of what I am seeing.

What is "G/F" ... and then after that looking across the table, look at the first line, for an ADSH-25e ... yes, pretty high-performance sailplane ... but it says the units are "mps" (surely meters per second ?) ... but then the first entry is of 80?

80 what? 80 m/s ... yowsa, that's ≈ 160 kts!

and at "80" the value in the table is is 0.62 ... what is that? If that were the sink speed in m/s then the L/D would be 80/0.62 = 129 ... no way! So what are the numbers?

Can somebody explain WTF I am looking at here?

At this point I should mention that I really have been looking for these data. and I am an applied mathematician/scientist by trade and have been studying risk tradeoff optimization in speed-to-fly problems, this is also basically the same problem as

optimal handicapping in disguise.

Is there interest in discussion of these issues? I could point out some issues where the current methods aren't entirely right or complete, that do have pretty straightforward solutions.

One other point I would make ... for all calculational purposes, you want to reduce the polef data to a fitted function of some sort, and boy ... are polynomials convenient for this purpose in this case. The standard "McCready Speed to Fly" just

assumes the polar from best L/D on up is fitted with a quadratic, after trivial calculus and a little algebra the speed-to-fly is computed by solving the quadratic equation. This is easy to generalize to better fits.

And when you see this, and go through just a little math, what you see you want for the polar are stated minimum sink and best-L/D speeds & sinks, and then at least one, preferably 2 or 3 data-points at higher speeds ... and you don't need anything

more than that.

The reason minimum sink and best-L/D are so important to defining the polar should be intuitively obvious, but there's a mathematical reason too ... these provide additional important equation constraints on the fitted function

minimum sink is of course s'(h) = 0

best L/D means that s(h) = h / s'(h)

where h is the horizontal speed (that what's really the independent variable in a polar, NOT airspeed, although at the very high L/Ds of gliders the differences between these two is negligible) s(h) is the sink rate at horizontal speed h, and ' means

first derivative.

Forth these two "special" points you get two constraint equations, not one. Playing around with real polar data it takes a 5 to 6 order polynomial to really fit one well, and for manipulating all the ensuing calculations it is the coefficients of that

polynomial that is wanted.

Also, I don't see listed gross weights for these test data? That is important ... to do ballast corrections etc.

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