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Kinetic Energy vs Momentum in a Car crash

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ScottH

Mon May 22 2017, 02:30PM

Registered Member #61373 Joined: Sat Dec 17 2016, 01:45PM
Location: San Antonio, TX
Posts: 87

I know the difference between the two, but I am wondering if it's the ke of the collision, or the g forces alone that do the majority if the damage.

If a car hit a tree at 60mph vs 120mph, would the driver experience 4x the force from the ke, or will he feel 2x the force from the momentum change (120mph)? Ignore the car deformations effect on stopping distance, for the sake of simplicity.

I know the sudden stop and the forces experienced cause damage, but I just wanted to understand real life examples of ke vs momentum.

2Spoons

Mon May 22 2017, 09:49PM

Registered Member #2939 Joined: Fri Jun 25 2010, 04:25AM
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Its probably a bit more complicated than that IRL because the forces involved are also dependent on the deceleration time, which is dependent on a huge number of mechanical factors, such as structural failure modes, which are in turn dependent on energy, force and rate.

Very messy.

Carbon_Rod

Mon May 22 2017, 10:01PM

Registered Member #65 Joined: Thu Feb 09 2006, 06:43AM
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impact and impulse are very different properties:

And yes, things get complex very quickly, but we tend to use stuff like OpenFOAM for CFD problems:

Uspring

Tue May 23 2017, 10:49AM

Registered Member #3988 Joined: Thu Jul 07 2011, 03:25PM
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In a complex mechanical situation all quantities like momentum, energy and forces interact in some way with each other. Forces e.g. arise from 2 different sources:

a) mechanical deformation like compression of material

b) change of speed of masses, i.e. their acceleration and deceleration

The speed of masses is related to their kinetic energy. You cannot attribute crash damage to a single quantity alone, since they all interact. There is no proportionality between either kinetic energy nor momentum to crash damage.

Dr. Slack

Tue May 23 2017, 07:33PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

ScottH wrote ...

... Ignore the car deformations effect on stopping distance, for the sake of simplicity.

You could, but that's getting **too** simple, if you want to distinguish the effects of KE and momentum. What do you think 'crumple zones' are, and how they work? They change where the KE is absorbed, but of course do nothing to the total momemtum balance.

One of the things that does damage to a person is the peak force. Force is change of momentum per unit time. If you have a lot of time to slow the car down, then the peak force is lower than if you have less time. Whether you have time to slow it down is a function of the distance you have. A crumple zone *builds distance into the vehicle* that will shorten at low force, to allow the vehicle to be brought to rest with a smaller peak force.

Consider the difference between a more or less free-flying head being stopped by 5mm of padding on a steering wheel, or being stopped by the 200mm thickness of an inflated air-bag. You do need to consider the deformations of the structure when assessing potetnial to do damage.

hen918

Wed May 24 2017, 01:36PM

Registered Member #11591 Joined: Wed Mar 20 2013, 08:20PM
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Dr. Slack has it exactly right. If you completely ignored deformation, the time taken to come to a stop would be 0, therefore the power dissipated would be infinite, and damage done would be likewise incalculable. The best (simplistic) way of looking at it, is if the deformation determines the deceleration, and from that we can estimate damage.

ScottH

Fri May 26 2017, 11:33AM

Registered Member #61373 Joined: Sat Dec 17 2016, 01:45PM
Location: San Antonio, TX
Posts: 87

I'll list another two scenarios.

1. Would a driver experience the same damage if he crashed head on with an identical car moving at the same speed, or a solid wall? I know the deceleration is the same, but the 2 cars crashing have the ke of both cars involved, or 2x the ke.

2. Would a baseball hitting you in the face be 2x or 4x more dangerous if it was going 120mph vs 60mph?

Dr. Slack

Fri May 26 2017, 04:22PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

ScottH wrote ...

I'll list another two scenarios.

1. Would a driver experience the same damage if he crashed head on with an identical car moving at the same speed, or a solid wall? I know the deceleration is the same, but the 2 cars crashing have the ke of both cars involved, or 2x the ke.

If the wall was perfectly solid (in the physics 'spherical cow' sense), in other words an 'immovable object', then the two situations are exactly equivalent. Consider a plane normal to the velocity of both cars, exactly between them. As each piece of car meets that plane, it meets its twin coming in the other direction, and each twin comes to rest symmetrically about the plane. That plane is the perfectly solid wall.

There's a total of twice as much KE to be dissipated, but with two cars, the other car loses its energy on the other side of the plane.

ScottH wrote ...

2. Would a baseball hitting you in the face be 2x or 4x more dangerous if it was going 120mph vs 60mph?

Define 'dangerous', do you mean deposited energy, depth of penetration, cost of reconstructive surgery? What is the yield versus force graph for the face? All you can say absolutely is that the 120mph would be no less damaging than the 60mph impact.

This isn't just being picky, because the damage depends on the strength of the face, and when it breaks. Compare 1mph and 2mph. Neither causes damage. Compare 1000mph and 2000mph. I suspect the damage would be identical. At some speed, there will be yield of structures bringing the ball to rest. Breaking of skin cells results in bruising. Breaking of bones at the front results in trauma. Breaking of bones at the back results in a real mess.

What this means is that you can't really do physics without sufficient information, or, you have to simplify down to some point where the behaviour is idealised, but still sufficiently rich to capture what you're thinking about. Consider a couple of more or less limiting cases.

For instance, consider the ball is thrown at a compression spring, that breaks above a certain stress (bone). For input energies that do not break the spring, the deflection is proportional to the incoming speed, or sqrt(KE), as the energy stored in a spring is proportional to its deflections squared. If the spring breaks, the deflection is unlimited.

As an alternative, consider the ball is thrown at a thick slab of rigid gel (like expanded polystyrene for instance) which does not flow sideways and which crushes to zero volume at a pressure of (say) 10MPa, that is, exerts a constant stopping pressure of 10MPa (brain(ish (very ish))). How far does the ball travel into the gel at each speed? Answer, the depth of penetration is proportional to KE, as all of the incoming KE does work at a constant rate per distance.

Once you're happy with those answers, you can complicate things by making the stopping structure heterogeneous, so a few mm of skin, a few of bone, 200mm of brain, each with defined density, modulus, yield strength. Or you can say the structure is so complicated that it's more practical to simply do the experiment and see what happens, like french surgeon Rene La Fort did around the 1900s -
wikipedia

, and pdf

If you read the pdf, you'll see why a face might be a particularly tricky subject to model well through physics.

I was particularly interested in this type of injury a few years back when I was on my bike doing about 15mph, and a motorcyclist's leather-clad shoulder doing perhaps 30mph did what you imagine a baseball doing, giving me a La Fort 2. Happily that sort of injury tends not to be life-changing, though it does slow you down a bit at the time. My wife's comment to the surgeon before I went to theatre was 'could you make him a bit more Brad Pitt, and bit less Jimmy Durante'.

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