A person is hit by a car

1. Jul 25, 2011

Noobert

A 60kg person is hit by a car traveling at 17m/s.

a) what is the force exerted on the 60kg person.
b) what would have been the difference to the persons injuries and the force they would have felt if the car did and did not have a bull bar.
c) would this person have survived the collision.

2. Jul 25, 2011

sophiecentaur

Hi
The amount of actual force would depend entirely on the duration of the collision. Hitting a brick wall or a bouncy castle at the same speed would involve very different forces although, in both cases you would start and end at the same speed.
A bull bare would be a pretty unforgiving surface to be hit by - much better to be hit by the rounded, mild steel curved front of a safety conscious modern saloon. In both cases, you could end up travelling at 17m/s (assuming the idiot who hit you had not braked at all) but the impact duration could be several times longer for the softer impact.

The momentum transfer would, in both cases, be 60 X 17 Newton seconds (the unit), which is about 1000Ns.
This would mean a force of 1kN spread over 1 second, 10kN over 0.1s and 100kN over 10ms. So how long is a piece of string? Very hard to say - take your pick but I think 100kN would be bad news.

3. Jul 25, 2011

Noobert

Tyvm! this really helped out, now all I need to do is type up a debate about bull bare vs crumple zones in built up areas and the difference between being hit by a bull bare versus crumple zone. backed up with physics ofc, but ty again, much appreciated!

4. Jul 25, 2011

sophiecentaur

I should have thought that the statistics would have said it all!?? It's not something you'd want to experiment with.

5. Jul 25, 2011

gsal

it depends if you want to analyse this problem from the theoretical point of view or from a reality point of view...

do you want to deal with this problem from the rigid body point of view? or from the real deformable body point of view...

can you represent this bodies as particles? or bodies with volume and mass?

if you have rigid body physics and bodies that can be modeled by particles at the center of mass, then, bull bar or no bull bar does not make a different and the transfer of momentum is pretty much mv, although the car speed should reduce slightly too...then, again, it has an engine that keeps putting energy into it, as oppose to a crash where the two bodies just collide without any external source of energy.

in reality, bull bar will make a different...also, the fact that if I get hit by a celica, it will probably brake my knees...then again, it will not give me an immediate momentum of mv, since my center of gravity is much higher than that....instead, it will probably send me rotating and possibly later hit me with the windshield and which hopefully will give some and extend the time to transfer some mv

...etc, etc., etc...

6. Jul 25, 2011

BobG

Sad, but true. Good news would be to have various body parts hit the car before you were flung up into the air and hopefully land in a position that will distribute the force of landing over a greater area.

But, the mass of the vehicle makes a big difference.

A Smart Car is only about 740 kg. With an 80 kg passenger, the total mass would go up to 820 kg and if the driver at least took his foot of the accelerator, the collision would slow the car down to just 15.8 m/sec. It would be absurd to mount a bull bar on a Smart Car.

On an SUV in the Ford Expedition/Toyota Sequoia/GMC Yukon class, you're looking at around 2700 kg. Toss in 4 150 kg football players and you're up to 3300 kg. The vehicle is only going to slow to about 16.7 m/sec. I know for a fact that Ford has good crumple zones when it comes to the passengers in the vehicle, but a 60 kg person isn't going to crumple a Ford Expedition very far.

My Jeep is about 1700 kg. Toss in the driver and his 2-year-old grandson and subtract the mass of the doors (don't need doors in the summer) and the mass is about 1770 kg. The passenger should slow the Jeep to about 16.4 m/sec. A Jeep doesn't have nearly as good a crumple zone as a Ford Expedition. Toss in a bull bar that's affixed to the frame and there won't be much give. Riding over rocks on the sliders (the bars on the side that look like they're there as a passenger step) leaves some pretty good gouges that depress the bars inward a fraction of an inch, but that's putting up to 16.7 kN of force to deflect those bars by a small fraction of an inch.

SUVs, Jeeps and pick-up trucks would be far more likely to have bull bars than small economy cars. I don't think the pedestrian has a very good chance of survival whether the vehicle has a bull bar or not.

I think the vehicle passengers have a very good chance of survival even in a Smart Car.

It's hard to convert the vehicles' crumple zones into some sort of spring constant since the construction of the vehicles' crumple zones are proprietary information. By watching NTSA crash videos, an outsider might be able to approximate a crumple zone, though.

But, acceleration 50 times Earth's gravity (about 490 m/sec^2) has a very good likelihood of being fatal or causing serious injury. So the acceleration of the pedestrian to about 17 m/sec has to be spread out over at least 35 milliseconds.

If you use Hooke's Law and conservation of energy, you can bypass finding a spring constant. For the smart car, I think the front of the car has to be compressed about 51 cm for the pedestrian to survive. For the SUV, I think the front of the vehicle has to be compressed about 57 cm for the pedestrian to survive. Some of that could be replaced by compression of the passenger, instead, but it's going to be counterproductive for him to absorb all of the compression.

I don't think the bull bar will compress anywhere close to far enough, but I don't think a pedestrian will compress the front of a Smart Car by nearly two feet, either (that's probably not a great example since Smart Cars are designed to shunt the force around the passenger compartment since there just isn't any room to compress the front of the car without compressing the passenger compartment).

The passenger of the Smart Car needs something (the front of the car or the pedestrian) to compress about 3 millimeters. The passengers of the SUV need something (vehicle or pedestrian) to compress about 0.2 millimeters.

Last edited: Jul 25, 2011