“What Price Speed? Specific Power Required for Propulsion of Vehicles”, 1950 ():
[Introduction of the von Kármán-Gabrielli diagram by Giuseppe Gabrielli & Theodore von Kármán showing a Pareto frontier of transport methods;
It has been updated; Rik van Hemmen:
Figure 1 is the Gabrielli von Kármán plot (GvK plot) it was developed in the 1950’s and provided a very interesting insight into transportation efficiencies. It is not necessary to go into the mathematics, but if a technology finds itself lowest on the plot for a certain speed range it tends to be most efficient…This plot was updated a number of years ago by Dr. Neu at Virginia Tech as a student project and populated with more modern technology and shows that we have made a little headway with regard to ships (mostly by making them bigger) and airplanes (mostly by increasing their efficiencies).That update of the graph resulted in an interesting observation by Dr. Neu and me. If you draw a line along the waterborne modes of transport only, there is another line that shows the limits on waterborne transportation technology. I modestly have called that line the Neu van Hemmen line (The NvH line). It shows that, if you operate on the water, you can go faster, but you cannot beat efficiencies of other higher speed modes of transportation.
van Hemmen also discusses the possibility of “Wing In Surface Effect Ship” approaches in breaking the line.]
In this short study, the problem of comparative merits of various means of locomotion is considered merely from an engineering point of view. The power required for transportation of unit weight is used as a measure for the comparison. Evidently for a definite system of locomotion, the minimum of power necessary for transportation of unit weight is determined by the physical laws of the resistance of the medium, the efficiency of the method of propulsion, the unit weight and fuel consumption of the particular type of power plant, and many other factors. Nevertheless, it appears that if one throws all data together, a general trend, almost a kind of universal law, can be found for the power required per unit gross weight of the vehicle as a function of maximum speed. The demonstration of this general trend is the subject of the present contribution. One has to realize that the material is necessarily approximate and incomplete, and the conclusions are of a rather tentative nature.
The data for power, weight, and maximum speed are taken, in general, from publications; the data concerning the products of the Fiat concern, from records of this firm. No classified material was used in the plotting of the diagrams.