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This article is guest blogged by University lecturer Dr. Vassilios McInnes Spathopoulos, author of An Introduction to the Physics of Sports. You can read my review in Introduction to the Physics of Sports.
With all the talk about Usain Bolt vs. Mo Farah, or Usain Bolt vs. Kenenisa Bekele at 600 meters, ever wonder what would happen with Bolt vs. an airplane?
Photo credits: British Airways
The Race of the Century: Usain Bolt vs Airplane
In Moscow, Usain Bolt managed to impress again. It seems as if for the time being, as far as his fellow humans are concerned, there is nobody that can challenge him, at least when it comes to the big races. So maybe the time has come to for him to compete with something else! How would he fare for example, when racing against an aircraft taking off? With the use of basic physics, we can create a virtual race and view some interesting results. The following is an excerpt from my book “An Introduction to the Physics of Sports” (or see, www.physicsandsport.com/en).
To make such a race possible we need to create two mathematical models, in other words a set of equations that represent, at least to a certain degree, the performance of the athlete and of an aircraft during the take off phase. We can then simulate a race in order to find out which of the two, the fastest athlete in the world or one of our greatest technological achievements, will come first.
The mathematical modeling, i.e. deriving the mathematical equations that represent the model, is quite complicated, so I will not go into it in detail. What I should point out, is that for an airplane, I chose the Northop T-38 Talon, twin engine, supersonic, trainer jet. This was the first supersonic trainer and one of the most popular ever, so we are certainly dealing with a tough competitor.
The fastest sprint races are those of the 100 meters and 60 meters. We will compare the performance of the two competitors in both distances. The results are presented in the following figures. The dark line represents the aircraft and the lighter one, Bolt.
At first glance we notice that the two competitors are very close to each other, especially for the 60m. A more detailed analysis reveals that the airplane wins the 100m, by a margin of 1.3s, whereas our athlete wins the 60m by about 0.2s! The representative of the human race starts off impressively and actually leads the race for the first 66m. It is a great achievement in any case, considering that each engine of the T38 produces a huge amount of thrust.
To fully understand what is happening, we need to study the variation of speed and acceleration (see figures 2, 3).
From the last figure we can see that the airplane maintains an almost constant acceleration, of just over 3m/s2 which drops very slightly due to the presence of air resistance. When we move with a constant acceleration the speed increases at a constant rate, as observed in figure 2. The final speed of the airplane after 100m is 24.7m/s, almost 89km/hr.
We also see that our athlete makes an explosive start. His initial acceleration is 9.7m/s2. This is almost the acceleration of someone descending freely towards Earth, so he starts off as if falling from the balcony of a high building! Due to his high initial acceleration his speed increases dramatically and reaches 10m/s (36km/hr), in about 2.2s.
Human power though has its limitations and as we see, his speed reaches a maximum that cannot be overcome (just over 12m/s) and, in fact, it falls slightly during the last few meters. In summary, Bolt starts off with a huge acceleration, more than three times that of the airplane, which is enough to win him the 60m section of the race. On the other hand, his acceleration starts to fall immediately and the aircraft, which maintains an almost constant acceleration, wins the 100m.
So according to our calculations, the race between human and airplane ends in a draw. It should be noted that the mathematical models used, especially that for the airplane, contain many simplifications and the scope of this example was to comprehend certain principles and not necessarily to announce a winner. In any case, I hope you enjoyed it!
About the Author
Dr. Vassilios McInnes Spathopoulos graduated from the University of Glasgow (UK), with a joint honours degree in Aerospace and Electronic Engineering, in 1995. The following year he completed a MSc course in Flight Dynamics at Cranfield University (UK). In 2001 he obtained his PhD from the University of Glasgow, conducting research on the validation of a rotorcraft mathematical model by means of flight testing a gyroplane. He teaches undergraduate subjects at the Department of Aircraft Technology, at the Technological Education Institute (TEI) of Chalkis, Greece. His research interests include the aerodynamics of sports balls and improving engineering education.
 The equations used are taken from: Helene O. and Yamashita M.T., “The force Power and energy of the 100 meter sprint” (2010), Am. J. Phys. 78 (3), 307-309 and Yechout T.R., Morris S.L., Bossert D.E., Hallgren W.F., “Introduction to Aircraft Flight Mechanics: Performance, Static Stability, Dynamic Stability, and Classical Feedback Control” (2003), AIAA Education Series.