Freesteel Blog » SymPy powered classical aerodynamics burblings

SymPy powered classical aerodynamics burblings

Tuesday, November 6th, 2018 at 6:51 pm Written by:

Quite a lot of work in the last week (especially at the weekend) reading a big book called Tailless Aircraft: Their Design and Characteristics, published 1994, translated from German.

The blurb on the inside cover reads:

The authors are uniquely placed to compile the first practical and comprehensive treatment of this fascinating branch of aeronautics. They have for many years collaborated on the practical and theoretical development of flying wings, applying themselves to sailplanes and powered designs ranging from models to full-size craft. In 1988, together with Klaus R, they received the “Berblinger Award” from the City of Ulm for their investivation into the design for an optimum tailless hangglider.

What the heck is the “Berblinger Award”?

The winner of the 100,000 Euro Berblinger Flight Competition was declared on Sunday 17 April, in the Ulm town hall. In all, 36 participants competed for the prize, which focussed on the use of innovative, ecological and resource-saving technologies. Of the 36 applications received, 24 aircraft were initially admitted to the competition. 13 aircraft started successfully; due to insufficient financial backing, technical difficulties or the absence of the appropriate flying licenses the remaining competitors were not able to take part in the practical phases of the competition, which was carried out at the AERO global for general aviation, in Friedrichshafen. Eight participants successfully completed the exercise of flying from Friedrichshafen to Ulm.

Two anniversaries were celebrated with an extensive programme of events during this weekend in Friedrichsau Park and the Adlerbastei: 200 years ago, King Friedrich 1st gave the Friedrichsau Park to the people of Ulm. In honour of his visit, Berblinger performed his attempt to fly across the Danube.

Who the heck is Albrecht Berblinger?

One of Berblinger’s inventions was what appears to be a hang gliderKing Frederick I of W├╝rttemberg became interested in his work and sponsored him with 20 Louis. He tried to demonstrate the glider on the evening of 30 May 1811 in the presence of the king, his three sons and the crown prince of Bavaria. The king and a large number of citizens waited for the flight but Berblinger cancelled it, claiming that his glider was damaged. The next day he made a second attempt. The King had left by this time, but his brother Duke Heinrich and the princes stayed to watch. Berblinger waited so long for a good wind that a policeman finally gave him a push and Berblinger fell into the Donau (Danube).

It sounds like the experience on some of my takeoffs.

But enough of that rabbit-hole.

I’ve been attempting to replicate some of these graphs and diagrams from the book, like these ones:

After many days and many attempts, I got to this matching version:

This was not helped by the mistake in Formula (2.7.5)!

I could not replicate the other four lines for the “neutral point” (some details about dc_l/d(alpha) has been left out).

In the process of this I have wasted no pencil and paper, and proved the power of SymPy, which I think all mathematics should be written using.

The details are all on the Horten sailplanes Jupyter notebook. It’s probably a good thing I don’t have the technology to inline mathematics into this blog.

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