Here’s the question I sent to Cecil, and the reply said to post my question here. So here it is:
If a car weighing 5000 lbs collides broadsides (T-bone) with a parked car of equal weight at exactly 40 mph at the time of impact, would the extent of injury to the occupant(s) of the moving car be greater or less if, at the time of impact, the moving car was applying full braking force or if the moving car was applying full acceleration?
This was really hard to lay down in words, and I hope you understand it. Assume that all factors are equal except that one of the moving cars is accelerating and the other is braking. Make sense?
I seem to think that the accelerating car’s occupant(s) would suffer less injury due to the a reduction in deceleration forces experienced by the body.
This has puzzled me for a while, and I can’t find a study of this type of collision anywhere on the internet so far, so I thought I would ask you for the answer.
Assuming they are wearing seatbelts (in both cases), I’d expect the braking car occupants to be less likely to be injured. They’d already be pressed against the belts, rather than getting thrown against them during the crash.
If there are airbags involved, I couldn’t guess. I suspect it would depend on details about how airbags are designed to deploy.
If you assume that at the time of impact the car does not continue to brake or accelerate (as the case may be), then they physics of the crash is exactly the same. That is, both drivers take their feet off the pedals at the instant of impact. All other things being equal, the outcome is the same as long at the speed at the time of impact is 40 MPH and nothing other than the impact affects its rate of deceleration.
However, all other things are not quite equal–the positions of the passengers within the car is different in the two situations. As **ZenBeam **points out, the accelerating car is going to have the passengers plastered back into their seats, with a longer distance (relative to the car) to traverse compared to the braking car where they are already pitched forward into their belts. But I’m still not sure which group has an advantage. From the moment of the crash, both groups will have the same rate of deceleration and therefore the same force against the seat belt, although the former group will have to travel a few inches before getting there.
If, OTOH, they are not wearing seat belts at all, the acceleration of the occupants will be very high as they hurtle towards the windshield and the extra distance traveled by the occupants who are back against their seats will probably not make that much difference in the final “second impact” with the windshield.
But if your intuition is telling you that an accelerating vehicle is going to hit harder than one that is braking, that is incorrect. The only thing that matters is the speed at the instant of impact.
The force transferred into the car will be the same as 40 MPH is 40 MPH.
The difference will be in the position of the passengers.
When accelerating hard, the occupants will be back in their seats.
At the instant of the accident the seat belt tensioners will fire and reel up the slack in the belts (up to about 4" with about 20lbs of force)
This means that when the frontal bags deploy the driver and passenger will be as far away as possible.
This is a good thing
When in a panic stop the driver and passenger will be thrown forward against the belt, and the belt will be tight. The belt tensioners won’t do anything as they are not powerful enough to overcome the weight of the people pushed against them.
Depending on the amount of slack in the belt, the occupants could wind up a lot closer to the airbag deployment than is optimal.
This could be bad.
There are three collisions in a car crash: The cars hitting each other and crumpling, the bodies hitting the interior of the cat and both crumpling, and the internal organs hitting bone and crumpling. The more time you can prolong the third one (lowering ‘G’'s) is better.
Let car A be the one approaching the crash at 40 MPH, and let car B be the parked car.
First, “time of impact” is non-zero. The impact is not an instantaneous thing: there is an instant of first contact when the bumper of car A first contacts the door of car B, but each car deforms over the course of a fraction of a second, inducing many g’s of acceleration for the occupants of each car (here I am using acceleration as a scalar, not a vector). The peak force/acceleration a vehicle undergoes in an accident will be proportional to the maximum vehicle deformation incurred during the collision.
Second, “applying full acceleration” is probably better expressed as “applying full accelerator”. That is, the driver of car A presses the right pedal to the floor; whether the car’s speed actually increases from this point on will depend on the sum total of all forces are acting on the car.
In the present case, let us first suppose driver A exerts no pedal input during the collision. The cars experience a peak of 20 g’s of acceleration, with car B achieving some maximum speed (and car A also traveling at that same speed) before the whole mess begins decelerating due to drag from car B’s tires being dragged sideways. Ouch.
Repeat the collision, with driver A slamming on the brakes as soon as his bumper first touches the door of car B. Whereas the first scenario had only the impact forces decelerating car A, now the tires/brakes are also decelerating it at an additional 0.8 g’s. So car A experiences greater peak deceleration (20.8 g’s) than in the first scenario, and by the time the collision has ended, car B and car A are moving more slowly than in the first scenario. This means car B experienced less than 20 g’s peak acceleration - 19.2 g’s, in fact.
Take our bruised and battered occupants, herd them at gunpoint into two new cars, and repeat the scenario a third time, with the driver of car A slamming the accelerator pedal to the floor at the moment of first contact. At 40 MPH the engine is only capable of applying enough tractive force to accelerate the car at 0.25 g’s under normal conditions, so that’s the force available to counteract the collision forces. Instead of 20 g’s, car A experiences 19.75 g’s during the collision, and car B experiences 20.25 g’s. Our occupants, suffering the wear and tear of three severe car crashes, stagger and stumble away from the wreckage, calling lawyers, the police, and the media. We’d best be leaving now.
Some posters are talking about the occupants of car A shifting in their seats as car A undergoes acceleration or deceleration, but this assumes that pedal application is occuring before the start of the collision. If the pedal is not applied until moment of first contact, and if collision forces are assumed to be zero at the moment of first contact and to scale linearly with vehicle deformation, then yes, there will be a very short period after the moment of first contact when car A’s speed actually increases, but this increase will be negligibly small; peak speed for car A will be achieved when the vehicles are deformed enough to counteract the forces from car A’s driveline. Given that “full” deformation is inducing 20 g’s, then 1.2% deformation (and 1.2% of the total collision duration) is enough to counteract car A’s acceleration input; car A’s speed won’t increase much during that time, and the passengers won’t shift much.
Bottom line, the application of brake or accelerator makes a difference in the peak g loading, but not much - less than 5 percent for maximum braking, and about 1% for maximum acceleration (20 g’s for a 40-MPH collision is an estimate, but it’s probably in the right order of magnitude). The passengers of either car probably won’t incur significantly different injuries if driver A does anything (or nothing) with the pedals starting at the moment of collision. However, things can be much improved if driver A gets on the brakes before the collision and does his damndest to reduce speed. If a collision is unavoidable and imminent, you are best advised to stay on the brakes until it’s all over. As noted above, the forces of the collision will be slightly higher than they would be if you weren’t on the brakes during the collision, but the forces will be lower than they would be if you had never touched the brakes at all and collided at a higher speed.
I agree with this analysis, and it leads me to revisit the OP and wonder what the question was all about in the first place. Perhaps **rafffaelo **was actually asking about the effects of braking vs. flooring the gas pedal continuously through the collision, as this analysis posits. (I may have misinterpreted the question as a naive one about the forces in play at the point in time where the collision begins, assuming all else is equal from that point forward.)
I agree with this analysis to the extent that, in this scenario, getting on the gas will produce a lower g-force on the A occupants (although a greater force on the hapless B occupants).
I assumed that the selected pedal was already fully applied.
The problem with Machine Elf’s analysis is that he has not accounted for the time lag of the brakes/accelerator application until their having any effect on the momentum of the car. There will be a time lag. Particularly with the gas pedal if full throttle application would cause the automatic transmission to downshift.
Also depending on the car and the hit before the throttle input would have any effect the engine might not be producing any power due either from damage or via the SRS system deactivating the fuel pump or disconnecting the battery.
So due to this time lag your driver would actually have to depress the selected pedal before the moment of impact to have the effect arrive at the moment of impact.
Mechanically true but based on the wording of the OP it is reasonable to assume an idealized scenario where the car is either accelerating or braking at the moment of impact without regard to mechanical lag, human reaction time, etc.
That’s not how I would read it. It would seem like a logical thought experiment to ask, “Would the impact be different if the first car was accelerating to 40mph or decelerating to 40mph?”
Clearly the car starts decelerating at the moment of impact, so I can’t imagine how you would define “accelerating vs braking” starting at that point.
See my post upthread, in which I did in fact define “accelerating vs. braking” to refer to the pedal inputs rather than to whether the car was undergoing any change in velocity. In fact the OP speaks of “applying” full braking or acceleration, which suggests driver inputs.