This is the wrong way to think of it. At some point the mass is irrelevant. If an inelastic lead object the size of a car hits you, the energy transfers is the same as if a lead 747 hits you at the same speed.
Both objects have an overwhelming amount of energy and momentum compared to a nearly stationary 100 kg person. They'll transfer enough energy to bring the person up to their speed, likely mangling them in the process.
Trauma depends on how quickly this energy is transferred to the individual.
More to your point, both a car and a truck have more than enough energy to not be meaningfully slowed down by a pedestrian. The difference is strike location, contact area, and crumple zones to slow the transfer.
Vehicle mass matters a lot in vehicle-to-vehicle collisions, where the energy and momentum of each vehicle is going to change a lot, but when a car collides with a person, the car's momentum is barely affected, because the car is already significantly more massive than the person. A 20x mass ratio is already practically infinite.
In a direct collision between a moving 1000kg car going 10 m/s and a stationary 50kg person, the person will end up moving somewhere between 9.5 m/s (perfectly inelastic collision) and 19.05 m/s (perfectly elastic). The car will end up moving 9.5 m/s (perfectly inelastic) and 9.05 m/s (perfectly elastic).
In a direct collision between a moving 10000kg car going 10 m/s and a stationary 50kg person, the person will end up moving 9.95 m/s (perfectly inelastic) and 19.90 m/s (perfectly elastic).
The car will end up moving somewhere between 9.95 m/s (perfectly inelastic) and 9.90 m/s (perfectly elastic).
Even though we 10x'd the weight of the car, we only increased the velocity of the person after impact by about 5%, and energy imparted on the person by about 10%.
I suspect vehicle size (or rather, the size/shape of the front of the vehicle) has way more effect on pedestrian survivability than the weight of the vehicle. SUVs and trucks will impart the force of impact directly to your torso and head, and then subsequently run you over. Sedans hit you in the legs and then roll you over the top of the vehicle.
I think the correlation between vehicle weight and injury to pedestrians requires some nuance.
The comments in the article imply that being hit by a heavy vehicle involves more force than being hit by a light vehicle but, other things being equal, the difference is likely to be negligible. Sure the heavy vehicle has more momentum, but neither will slow down significantly from hitting you, so the acceleration applied to a pedestrian that is hit will be more or less the same. Note this isn't true when one vehicle hits another - mass will matter then.
So what does make a difference? The shape of the front of the vehicle. With a regular car, you'll almost certainly be swept off your feet and go over the roof. Your legs will take the full force, but your torso never experiences a huge acceleration, so your chances of internal injuries are less. With a truck, there's a pretty good chance the front is vertical where it hits your torso, meaning the acceleration is much higher, and so the chance of internal injuries is much higher.
After you're hit by the flat front of the truck, where do you go then? There's a pretty good chance you go under it.
Now, heavier vehicles are also more likely to be taller, but the impact on pedestrian safety is a second order effect. If you really want to encourage safer roads for pedestrians and cyclists, maybe tax the height of the front of the bonnet (hood)?
Actually neither of those matter much anyway. The energy transferred is primarily a function of the velocity difference (squared) and the mass of the lighter of the two objects. That is, a pedestrian will experience a collision with a car and with a bus in much the same way.
If the two objects are close to the same mass, i.e. car vs. car, the energy transfer will be reduced by up to 75%, but otherwise the mass of the larger object is immaterial. That is, a car-car collision at 60 MPH does equal damage as a bus-car collision at 30 MPH.
The difference in mass between a pedestrian and any vehicle is so great that at the moment of collision, the pedestrian's velocity becomes that of the car, and the car's velocity is practically unchanged. (That is, energy transferred is a function of vehicle's velocity and pedestrian's mass.)
Mass of the vehicle only practically comes into play for stopping distance, and as a proxy for its frontal cross-section.
The vast majority of pedestrians survive getting hit by a car, not all incidents happen at highway speeds. A difference between a mass of 1 and 3 tons would absolutely make a difference in lethality.
> Physics dictates that mass has a significant impact on safety
I suspect that once you have enough mass though then it is velocity that determines the impact on safety. Getting hit at 50 mph by a Ford F-150 that has a total mass (truck plus cargo) of 9000 pounds is not going to be much more harmful to a pedestrian than getting hit by a similar shaped truck at the same speed that has half that mass.
Similarly on the other end if velocity is low enough mass won't matter. Consider for example getting hit by a freight train at 1 mph. Unless the collision knocks you over and you fall under the train it probably won't be fatal (and likely won't even injure you). Even though that freight train would have 300 times the momentum and 6 times the kinetic energy of the 50 mph 9000 pound truck it would be fine.
Bigger vehicles are heavier; at the same speed as a passenger car, they have more kinetic energy. It is even worse when the victim is lighter, as per the momentum conservation principle. The study confirms the physics. What's unexpected is the last line of the abstract.
I suppose if you absorbed all of the energy from the car, rather than just being pushed back by it, then the damage might be more comparable. For example, I think if someone was standing against a wall and a car rolled into them at 10mpg it might be as terrible as being hit by a 200lb cyclist at 40 mph. Of course, I agree that 10 mph seems a lot less dangerous - it gives many more options to move out of the way, or to spread the impact over time (by walking backwards and pushing against the car). Just throwing out some thoughts on why the same energy from each seems to have such a different destructive force.
It's worth separating the momentum M*V you're referring to, from the energy M*V^2 that's dissipated in deformation in the collision.
Hmm I'm not quite satisfied even by my clarification. Car and truck chassis strength needs to scale with something closer to M*V^2, so the truck chassis is multiple times stronger.
Dubious claim. A vehicle might as well be a wall with infinite mass vs a pedestrian. Deformation, breaking and being passed out of the way are what counts.
Weight of a vehicle is one of the main risk factors for people in another vehicle in an accident. When you hit a pedestrian their weight is negligible, so it doesn't matter as much, but when another vehicle is involved, it makes a significant difference because you are largely doing a conservation of momentum problem.
For (~100kg) pedestrian, I am sure the difference in lethality from being hit by a 1000kg vehicle vs a 3000kg vehicle is insubstantial. Where the weight would matter is for vehicle-vehicle collisions.
A human being's weight hitting the ground at 30 mph (already a generously high figure) is far less serious than a multi-ton vehicle hitting them at 30 mph (already a generously low figure).
A Honda Civic is 2900-3100 lbs. A Honda CR-V is 3500-3600 lbs. That weight difference will not make much difference in a collision with a cyclist or pedestrian.
Even if they went with something heavier like a Tesla Model 3 (3900-4000 lbs) or a Tesla Model Y (4200-4400 lbs) or a Ford F-150 (4700 lbs) it would still not make much difference.
Yes, at a given speed a heavier vehicle will have more momentum and more kinetic energy than a lighter vehicle of the same shape, but momentum and kinetic energy aren't as directly correlated with how much a collision hurts a pedestrian as many here seem to think they are.
Once the vehicle is sufficiently more massive than the pedestrian that the collision causes very little change in the vehicle velocity a heavier vehicle at the same velocity is not really going to hurt the pedestrian more in the collision itself.
E.g., a large freight train hitting you at a slow walking pace is not going to be worse than a small car hitting you at the same speed, even though the train has way more momentum and kinetic energy. Speed that car up to highway speed and then it will greatly injure you even though it still will have much less momentum and kinetic energy than the slow train.
Much more important is the shape of the vehicle. Besides affecting what injuries are incurred from the collision itself it can affect what happens after. A shape that knocks the pedestrian away is probably safer than one that tends to draw the pedestrian to under the car where they get run over.
Consider a 9 000 pound car at 50 mph. If you are standing there and that hits you you are going to die or be seriously injured.
Compare to a large freight train hitting you at 1 mph. A bit of Googling suggests that the largest freight train had a mass of around 140 000 000 pounds.
The momentum of that freight train would be more than 300 tims the momentum of the car (and the kinetic energy would be 6 times that of the car). Yet a free standing person hit be that train probably won't be killed or even seriously injured by the collision.
> More mass means more force to impart at the same speed.
technically yes, but the effect of more mass in a vehicle-pedestrian collision is asymptotic. a small (3000 lbs) sedan is already 15-20x the mass of a typical human. the vehicle loses a very small fraction of its initial velocity to momentum transfer. it really doesn't make much difference if you double or triple the mass of the vehicle.
Both objects have an overwhelming amount of energy and momentum compared to a nearly stationary 100 kg person. They'll transfer enough energy to bring the person up to their speed, likely mangling them in the process.
Trauma depends on how quickly this energy is transferred to the individual.
More to your point, both a car and a truck have more than enough energy to not be meaningfully slowed down by a pedestrian. The difference is strike location, contact area, and crumple zones to slow the transfer.
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