Physics question about odd situation...

[Johnny1A.2]

DR is defined as the (rough) equivalent of 1/70 inch of rolled steel.

Now, there is a character in my world who is so psychically powerful that her personal psychokinetic 'defense shield' has an effective DR of over 32,000, roughly the equivalent of 39 feet of rolled steel. Now an enemy rams her with a car, striking her straight-on at about 50 miles/hour (80 km/hour).

Now, said car (a typical American sedan) striking a 39-foot-thick cube of steel would not even be a danger, it would just more or less be destroyed on impact. But a 39-foot cube of steel masses over 13,000 tons.

Our victim masses about 65 kilograms and is held in place only by her own weight. (This happens on Earth, so all conditions are Earth-surface-normal).

Obviously, she's going flying, or going to be knocked down, or come through the windshield, for all the strength of her psi-barrier. (She's hit from behind and caught by surprise, long story.)

But what happens to the car? How much of the car's momentum is going to transfer to the woman? How badly messed up is the car going to be for hitting an effectively indestructible but relatively small and light object at high speed? Is she more likely to end up going under the car, over it, or flying forward?

I'm not sure how this plays out...

[mr beer]

Well, if she's flung around like a normal person, I think the car takes about the same damage as it would for running into a normal 65kg woman, maybe more if she's a hard surface - kind of like driving into a hollow titanium statue, which gets flung away like a garbage can. It's certainly not like driving into a concrete wall.

You can work out the damage she takes and then give her knockback based on that. As far as going over or under, I think it depends on her posture and the model of the vehicle. I would use google to check out common results. Again, I think this is going to look very much like a normal car crash, except that she's not injured in any way.

[RyanW]

Unless she is short or crouching, the car most likely makes initially contact below her center of mass. She will tend to have her legs knocked out from under her. In a typical pedestrian impact, the pedestrian hits the front edge of the hood with their hip, the top edge of the hood or the windshield with their head. If the car is slowing down, the pedestrian usually winds up on the ground some distance ahead of the car. If the car maintains speed, the pedestrian may instead roll over the roof.

Running over usually only occurs with small children or very tall vehicles, or situations where the victim is already on the ground (e.g. fell into the path of the vehicle).

[Anthony]

Realistically, not appreciably more damaged than hitting any other reasonably durable 60 kg object -- once the target is more rigid than car structure (which for a car with a crumple zone isn't really that much), any surplus barely matters.

In GURPS, use the collision rules.

[whswhs]

This depends, in the first place, on whether telekinesis is subject to action-reaction or not. In many portrayals, it seems not to be. For example, telekinetics can exert an upward force upon themselves to levitate. If you weigh 125 lbs., and you exert an upward pull of 126 lbs. to move yourself gently upward, and action/reaction applies, your weight is going to exert a downward pull of 126 lbs. upon you. At best this will neutralize the lift; at worst you'll feel as if a 126-lb. person were standing on your shoulders. And yet we don't see such things happen; levitation is a common telekinetic feat.

In effect, in this version, the telekinetic force originates at some point in space away from your body, and pushes or pulls at whatever it contacts there. You may be guiding that force with gestures or with your gaze, but your person does not experience a comparable force. So if the car slams into the force field, the force field would exert enough force to stop it, but your body wouldn't be involved. (If you use straight telekinesis, that force will be in an area equal to that of your two hands, which will make a pretty deep hole in the car's front. If you have a force field, it will probably be distributed evenly over the front of the car.)

Or, alternatively, look at it like this. Your 125 lb. woman probably has ST 10 and can lift up to 160 lbs. two-handed. But if she has TK 50, her telekinetic "hands" can lift up to 4000 lbs. two-handed. Do her own hands feel a weight of 4000 lbs., or for that matter do her spine, hips, and legs? If they did, she'd be in the hospital! But she might conceivably experience a force of 160 lbs., with the TK acting as a force multiplier, as if she were wearing a powered exoskeleton. In that case, a car that she stopped telekinetically would impact her as if it had 1/25 the weight and the same speed.

Telekinesis is fiction; you can make the assumptions you like about its "physics."

[tbone]

It sounds like you want a simple game case of "collision between car and (non-rooted) 65-kg object." Any good game system should have at least a simple answer for damage to the car, adjusted for whether the car's target is hard or soft. (The car rolling over the character, or striking her with the windshield, would be additional special considerations.)

What about post-collision velocities? It's complex in reality, of course, but for simple game purposes, you can actually eyeball a good approximation, like this:

Basic data

The sedan has, say, 24 times the mass of the character. Together they have a total 25 "units" of mass; the sedan has 24/25 of the total, the character 1/25.

The impact velocity is 50mph. Assume a solid, head-on impact and no odd outcomes (like the car disintegrating).

"Soft" collision

Now, assume a "soft" collision – a normal "squishy" character, or a flexible/soft force field. You can guesstimate that each colliding object will have its velocity change by a fraction of 50mph – with that fraction being the other object's fraction of total mass (as above).

Much easier to show than say: Guesstimate that the car will change its speed by about 1/25 of that 50mph – i.e., it slows down by about 2mph to 48mph. Guesstimate that the character will change her speed by about 24/25 of 50 mph - i.e., she flies backward at 48mph. Both continue on at this velocity, with her presumably in the grill or draped over the hood or whatever...

BUT, that was a "squishy" collision. If your character's force field is like a steel-hard block, things will work a bit differently.

"Hard" collision

Assume for simplicity that both the force field and the car are perfectly non-deforming objects (reasonable enough for game purposes, for two hard and super solid objects). Things will work out similar to the above – but double the velocity change experienced by each object. The car slows down by about 4mph. The character goes rocketing off at about 96 mph – i.e., "bouncing" off the car like a baseball off of a bat.

The tricky part, of course, is that even if the force field is "perfectly solid" like that, a car likely isn't. It'll likely deform (dent, etc.) somewhat. Net result: The changes in velocity will be something between the above two extremes: say, each object's velocity changing by 1.5 times the amount in the "squishy" case (to make up a multiplier).

Blah blah

Anyway, that's a brief look at part of your question: changes in velocity. Again, whether or not the car goes over her is another matter you'll have to judge based on relative sizes, positions, etc. As for damage to the car, test things using the GURPS collision rules and see whether the results seem reasonable at all. (I'd expect damage to the car, but certainly less than if it hit an immobile object, or a heavy one like another car.)

Warning

If you want to explore that business of velocity change more, look up coefficient of restitution. (FWIW, the two examples above represent the two extreme cases: a coefficient of 0 for a perfectly inelastic or "squishy" collision, and 1 for a perfectly elastic or hard collision. The reality of this or most any situation will be somewhere in between 0 and 1. It's not a number you can easily pin down, as it's not inherent to the force field, or inherent to the car; it's a property of the unique collision of these two objects, and can further vary a bit with velocity, the shapes involved, the part of the car that hits, etc.)

But be careful: Anyone who even mentions "coefficient of restitution" in a discussion of a simple game situation is probably going off the deep end. Consult with a doctor and/or local public safety authorities.

[Nereidalbel]

If your psi takes knockback as if her shield is massless, treat her as a hard surface under the collision rules instead of as a soft object. If her shield prevents knockback as if it has a mass of over 13,000 tons? The car hit a brick wall, and follows the collision rules for such an impact.

As for the effects on the psi, assuming her shield is massless for knockback purposes? She's rolling over the top of the car, more than likely severely damaging the windshield, and, the airbag will most certainly deploy from the force of the impact. The driver should be fine, assuming the airbag doesn't cause them to veer into oncoming traffic or something.

[Anthony]

Originally Posted by Nereidalbel

As for the effects on the psi, assuming her shield is massless for knockback purposes? She's rolling over the top of the car, more than likely severely damaging the windshield, and, the airbag will most certainly deploy from the force of the impact. The driver should be fine, assuming the airbag doesn't cause them to veer into oncoming traffic or something.

It's not at all obvious that the airbag deploys, the total delta-V to the car is quite low (equivalent to a 2 mph collision with a solid barrier), though not delivered in the same way.

[Flyndaran]

Not all cars even have airbags making their perfect deployment an odd assumption.

[Bruno]

Originally Posted by Anthony

It's not at all obvious that the airbag deploys, the total delta-V to the car is quite low (equivalent to a 2 mph collision with a solid barrier), though not delivered in the same way.

"Not delivered in the same way" is pretty critical. The various little parts of your car are pretty dang smart and don't rely on only one sensor to do their thinking.