Göttingen 765: attempt 6: camber line plot

Stephen Endersby from the UK is another long-time researcher of the elusive Göttingen 765. He found an interesting graph in the 'Alexander M. Lippisch Papers' held by Iowa State University, Library Special Collections Department. In fact it is the only concrete data on Göttingen 765 uncovered so far. It shows the camber lines (or mean lines) of Göttingen 761 through 765. It this camber line could be combined with a thickness distribution, we would know the actual profile, but only this camber line is known! A strange aspect of the camber lines is that maximum camber occurs at 20%, whereas other sources place the max camber position at 25 or 30%.

I measured the scan digitally (courtesy of a software tool written by Tjarko de Jong). The data is listed at the end of the page, for anyone interested. The next graph shows the camber line from the above graph in blue, and the calculated camber lines of attempts 4 (Messerschmitt drawing) and 5 (German data) in red and green respectively. The agreement is pretty bad.

Another possible piece of the puzzle was found in 'The Aerodynamics of the Unconventional Air Vehicles of A. Lippisch' by Henry Borst. Page 5-13 showed something about the camber lines of the reflex sections Lippisch worked on. The camber lines were reportedly the sum of:

• y_p = h * ( 1 - (1 - 2x) ²ⁿ ) called P-curve
• y_s = lambda * ( (1 - 2x) - (1 - 2x) ^{2m + 1} ) called S-curve

The parameters m and n are integers. I tried to obtain a fit using the Solver tool in Excel, but I did not achieve a perfect fit. Best fit was achieved with h=0.005025, n=3, lambda=0.01795, m=2, shown below. Second best was h=0.005214, n=4, lambda=0.01863, m=2. But perhaps different software could yield better results. I also tried two sets of P and S curves, but this did not help either. I also tried to match the Goe761 camber line, but this did not work either.

The data digitized from the ISU graph: