A long time ago, the running joke of the three laws of thermodynamics was introduced. They are the following:
- You cannot win.
- You cannot break even.
- You cannot get out of the game.
Abstract, “The effects of a kinematic field of velocity fluctuations on the loudness metrics of two waveforms are examined with a three-dimensional one-way propagation solver. The waveforms consist of an N-wave and a simulated low-boom from NASA’s X-59 QueSST aircraft. The kinematic turbulence is generated using a von Karman composite spectrum, which is dependent on a root mean square (rms) velocity and outer scale of the turbulence. A length scale is proposed to account for the effect of the rms velocity and integral scale on the focusing and defocusing of the sonic boom waveform. The probability density function of the location of the first caustic attains a maximum value when the propagation distance is equal to the proposed length scale. Simulation results indicate that for small values of the nondimensional propagation distance, the standard deviation of the loudness metrics increases linearly. The loudness metrics follow a normal distribution within a given range of the nondimensional propagation distance. Results indicate the potential to parameterize the loudness metric distributions by the rms velocity and integral length scale.”
Carr, A. N., Lonzaga, J. B., Miller, S. A. E., “Numerical Prediction of Loudness Metrics for N-Waves and Shaped Sonic Booms in Kinematic Turbulence,” The Journal of the Acoustical Society of America, Vol. 151, No. 3580, 2022. DOI: 10.1121/10.0011514 [Link via DOI][PDF][PDF Preprint]
One other aspect should be mentioned. When the program was transferred to El Segundo from Santa Monica, I naturally duplicated some runs. The printout was eight-decimal places, I believe. For a number of steps the new and old tab sheets would check exactly. But then after a while there would be a gradual drift; first the eighth place would not check, then the seventh, and finally down to the sixth or fifth, so that I could not be certain I met my goal of five place accuracy. I talked and worked with the computer staff on the problem for about two weeks and no explanation was found. The discrepancy could not be tolerated, so in desperation I sat down at a Marchant and, using exactly the same mathematics and roundoff procedures, set out to duplicate a run by hand. After about a day and a half of steady calculating I found my first disagreement. This gave some guidance as to where to look for the trouble. The deck of cards containing the program for this problem was about 0.9-in. thick. In order to reduce the frequency of reloading the deck in the hopper, eleven duplicate decks were made, making a dozen in all. What we found when we traced through all the decks was that one card had been misplaced so that eleven times instructions were correct but were wrong the twelfth time. The erroneous card determined the value of one of the last terms in the Taylor series extrapolation so the error was small. This experience has made me extremely cautious about trusting the output of a large scale computer on a complicated problem, because there are so many possibilities for error.
I was not sure of the propagation and growth of roundoff errors, so after finding all the solutions, I checked by rerunning them again with two more terms in the Taylor series and longer steps. Everything checked. I hope this chronicle gives you the flavor of automatic computers in the early days.Tuncer Cebeci in Legacy of a Gentle Genius: The Life of AMO Smith
When visiting NASA Langley I had Josh Blake kindly take my picture by the Variable Density Wind Tunnel. Pioneered by Max Munk, leading theoretician in aerodynamics in America in our early years of aviation.
National historical landmark: The test section and airflow passages built into the VDT pressure vessel formed a continuous flow of pressurized air around the circuit and past the model. The direction of airflow is shown by the arrows. Both complete airplanes in model form and wing section models were tested.
After this I got more into aerodynamic research. The area rule involves calculating the flow about a bumpy body of revolution. Existing methods for calculating it were very poor. K. E. Van Every, my boss, talked to me about looking over the available methods and seeing what was best. I did and discovered an entirely new method that was far more powerful than any of the existing ones. I got an OK to try to work out the details of a computer programming method and got it to work quite successfully. The method is now known as the Panel Method and is universally used for low speed flow analysis both in this country and in Europe (Water flows can be analyzed just as well as air flows.) Our first successful calculations were in early 1955 . The method is written up in the book Applied Computational Aerodynamics, Vol. 125 of Progress in Astronautics & Aeronautics, edited by P. A. Henne. Before this method, one could not even calculate the flow about a round body with a hemispherical nose. Afterwards such calculations came easy. Stuart Crump handled research contracts for the David Taylor Model Basin of the Navy. So, once when I saw him, he said the contract he had given us was the best one he had ever given out. For this work I received the Engineering Achievement Award of Douglas Aircraft in 1958.Biographical memoir of A. M. O. Smith
If someday I may die, though it is unlikely, I hope the people in the cafés will say, ‘Dali has died, but not entirely.’Salvador Dalí