Seen a few films lately where the hero runs on top of a moving train, for example "Under Siege 2". It gives the impression that the train is moving quite fast (presumably its normal operating speed on a straight section, of order 100 km/hr $\approx$ 30 m/s). Is it realistic that a man sized object could run along the top of the train? What sort of forces would he have to overcome to stay on the roof and what speed of train could he/she safely manage?
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1$\begingroup$ physics.stackexchange.com/q/41934 $\endgroup$– user65081Jan 3, 2020 at 0:52
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2 Answers
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Running is certainly unrealistic, crawling might be possible if there is something to hold on to.
This being Physics SE, we should run some numbers. Below you see the drag force of a typical human being in different postures. This is from Sighard Hoerner's book "Fluid Dynamic Drag", page 3-14
Running would be best approximated by the standing human; let's assume his drag area is a bit below those 9 ft². Drag area is the drag force divided by dynamic pressure. In case of a 30 m/s headwind the dynamic pressure in standard atmospheric conditions (air density 1.225 kg/m³) is 550 N/m². With a drag area of 8 ft² the drag force on that average human is 410 N or more than half his weight. Just standing in that breeze would require to lean forward by more than 30° (which reduces the drag area a bit). Running would only be possible if the friction between shoes and train roof would allow to transmit this horizontal force of 410 N - with one foot lifted up!
answered Jan 3, 2020 at 22:29
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If the train is moving at constant velocity, in order for the the man to walk on top of it in the direction of travel he would need to exert a force overcome the force of air resistance. On the other hand, he could easily walk opposite the direction of travel of the train since the force of the air at his back will cause him to accelerate.
Bottom line is the velocity of the train is irrelevant if it is constant, were it not for the air resistance. If, for example, the train were moving at constant velocity in a vacuum (no air), the man could walk freely in either direction only needing to apply the necessary force to accelerate his mass in the desired direction. The velocity of the train would have no effect on him.
I accept that in a vacuum no particular issues, but did have the tag aerodynamics.
In that case in air it would be unreasonable for the man to run along the top of the train towards the front of the train since, even with no wind with the train still, the relative velocity of the air against the man would be 100 km/hr (62 miles per hour) which is nearly hurricane force winds. On the other hand, he would be accelerated towards the back of the train requiring no effort.
Hope this helps.
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$\begingroup$ I accept that in a vacuum no particular issues, but did have the tag aerodynamics. $\endgroup$– jimJan 3, 2020 at 0:18
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$\begingroup$ I'd point out that if the train is accelerating, a person can only run on it if the acceleration of the train is smaller than the product of the coefficient of friction and the acceleration due to gravity. $\endgroup$– user87745Jan 3, 2020 at 1:11
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$\begingroup$ @DvijMankad Yes, but I read the question as the train is going at constant velocity. If it isn't, it's a different question. $\endgroup$– Bob DJan 3, 2020 at 1:29
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$\begingroup$ I see. I thought that the example of a constant velocity motion that the OP mentioned was only an example and they were asking for the general case. $\endgroup$– user87745Jan 3, 2020 at 2:51
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$\begingroup$ @Dvil Mankad I think if that was the OP’s intent the OP would have stated it. We aren’t mind readers $\endgroup$– Bob DJan 3, 2020 at 12:36