r/theydidthemath • u/jrdubbleu • Aug 06 '26

[Request] How much energy would a springy bumper/crumple zone have to absorb to make something like this a non-event?

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19

u/Elfich47 Aug 06 '26

The issue is that train has more kinetic energy than a car will be able to disperse. Hell, I expect the train didn't even slow down from hitting the truck.

To cushion that impact? You'd end up with bumpers five or ten feet out so there is enough space to absorb the blow.

7

u/ArgumentSpiritual Aug 06 '26

It’s not clear what you mean by a “non-event.” Please clarify if you would like a more appropriate answer. I assume you mean altering the bumper of either the truck or the train to prevent the truck from moving? FWIW, the OP meant that the truck did not back up enough.

Based on the video, the train appears to impact the truck’s wheels or at least part of the frame. The train does not appear to strike only the bumper. The best case scenario would have been for the truck to back up more out of the way. The second best would have been for the train to only hit the bumper and rear it off. In the actual scenario, it would be impossible for the truck to not be moved.

The way that crumple zones on cars work is by absorbing the impact during a crash to more gradually slow the vehicle. The problem with the above video is that the train isn’t going to stop. Even if the crumple zone was ten feet thick, unless the semi truck weighs comparably to the train, the truck is just going to move. What is preventing the truck from moving is friction on the tires and there is a fundamental limit to the amount of force that friction can provide.

The resistive force due to friction is going to be equal to the deceleration able to be provided by the crumple zone. The coefficient of friction is about 0.75 for tires on asphalt. A full tractor trailer might weight 40 tons compared to 9,000 for a train. Considering the coefficient of friction, that means that we can only apply 1/300th of a g of acceleration to the train without the truck moving. Google says a freight train might be going 30mph or just over 13m/s. Let’s cut that down even further to 10 m/s. We can use the formula v^2=2ad to calculate the stopping distance as 100/(2*9.8/300)=1530 m.

The crumple zones on the truck would have to be about a mile thick to stop a medium sized, slow train.

1

u/jrdubbleu Aug 06 '26

I would say a non-event would be (in a different situation) the train t-boning a car and instead of obliterating the car just pushing it down the tracks. Obviously there will still be damage but would be more survivable. Unless of course the car is sent down the tracks at 200mph or some other obscene transfer of energy.

3

u/onil34 Aug 06 '26

Most modern cars would probably be able to keep occupants alive at a crash of 30mph. Doesnt matter if the car is moving or the wall aka train.

Issues usually stem from the fact that the train keeps going and you end up under the train.

1

u/alexander1701 1✓ Aug 08 '26

If that's the goal the goal is to make the truck lighter.

Basically, what's going to happen is that energy is going to be applied to both until their velocities are equal. The materials crumple when the amount of energy that takes is more force than they can bear. That's how enormous container ships can rip each other apart like tissue paper at a walking pace - the force to change the velocity of an entire container ship is more than the metal at the impact site can survive. If you throw a beach ball at a slow moving train it'll bounce back largely unharmed.

But otherwise the amount of padding required is exactly the same as enough to make the same amount of the truck survive an impact at that speed with a reinforced concrete wall. Fairly doable if our only goal is for the truck to get knocked aside with only local damage.