Are bigger vehicles safer?

First, a few qualifiers:

1. The biggest factor influencing safety is the awareness and caution of the driver
2. Back-of-envelop calculations have limits

Having gotten that out of the way, what can we learn from some simple back-of-the-envelop type calculations?

The test

Note that the car is pitching forward.

The simplest test is to run a vehicle into a flat, vertical, immovable barrier at some speed that will stress the vehicle structure and safety systems.  The Federal government decided that speed would be 30 miles per hour.

That is a reasonably accurate simulation of a head-on collision between two identical vehicles with a closing speed of 60 miles per hour (30 mph per vehicle) with neither driver attempting to avoid the accident or hitting the brakes.

Let's look at what happens in a collision between America's best selling automobile and best selling truck.

Delta Velocity

America's best selling passenger car has a curb weight of about 3300 pounds (1500kg).  America's best selling light truck has a curb weight of 6000 pounds (2730 kg).  Imagine a head-on collision between these two vehicles.  Imagine that both are traveling at 30 mph when they collide.

The center of gravity of the system (car + truck) is traveling in the same direction as the truck at 8.7 mph before they hit.  It is also traveling at 8.7 mph in the direction of the truck's original travel after they collide.  This is known as conservation of momentum.

Assuming the vehicles stick together and do not rebound, then the truck went from 30 mph to about 9 mph forward velocity.  The passenger car went from 30 mph to traveling in the reverse direction at 9 mph.  So the truck saw a change in velocity of 21 mph and the car saw a change in velocity of 39 mph.

The function of the restraint system is to safely dissipate the kinetic energy of the occupants.  Kinetic energy is 1/2 * mass * velocity * velocity.  That means that the restraint system of the passenger car must cope with more than three times as much kinetic energy as the passenger in the truck for the same collision.

Heights

Not to scale.

Another factor to consider is the relative heights of the primary motor rails.  The motor rails on the passenger car are centered about 18 inches (470mm) above the ground while the truck's frame rails are about 4 inches (100mm) higher.

At the instant of contact, the vehicles have a closing speed of 26.8 mm/ms or very close to one inch per millisecond.  The bumper and frame of the truck kiss the top of the passenger car's bumper and frame.  It will be at least 20 milliseconds before they encounter anything substantial.

The bumper of the truck crushes the fascia, front of the hood and the headlamps.  The structure of the passenger car's bumper encounters....air.

Then the bumper of the truck slices through thin (about 0.028" thick, half the thickness of a well worn penny) steel that comprises the sides of the engine compartment, the fenders and the fender rails.  It crumples like paper.  Empirical studies by Magee and Thornton suggest that the most important factor for retaining force during axial crush is the metal's thickness.  Factors like yield strength and the size of the section are much less significant. 

The structure of the car's bumper encounters.....more air.

Which brings us to the air bags.  The little black box that triggers the air bags has an accelerometer in it.  The processor is looking for a very specific acceleration trace before firing the air bags.  A huge amount of effort was expended in engineering a system that reliably discriminates between "deploy" and "non-deploy" events.  Many of the "non-deploy" events were "suggested" by the Insurance Institute.  For example, one of the "non-deploy" events involves hitting a 160 pound deer at 45 mph.  That deer produces an acceleration trace very similar to the early part of the truck collision because it is bending up the same metal.

Eventually, the truck hits the strut caps and generates enough decell to trigger the passenger car's air bags.

The air bags

Energy is dissipated by squeezing a fluid through small holes.  This is what you would see if you took a shock absorber apart.  The air bag dissipates energy by squeezing hot gasses through the holes in the porous cloth as the occupant's head is slowed down.  The bag quickly inflates....like a shotgun shell going off...and is deflated by the force of the occupant's head hitting the bag.

Two things interact to derail this plan.  The forces generated within the passenger car ramp up very quickly so the air bag deploys late in the event.  There is a fairly high chance that the occupant will hit the air bag while it is still inflating.  Then, instead of dissipating energy that "shotgun shell" will add energy to the occupant's head.

The other thing that is happening is that the passenger car experiences negative pitch.  The forces exerted upon the passenger car are at a higher elevation than anticipated.  That negative pitch and the effect of the strut caps being driven back in the structure can result in the air bag being below the path of the driver's head rather than centered in its path.

Conclusion

Are full sized trucks "safer" in collisions than a typical passenger car?  You betchya.  The physics of momentum are ruthless and "star ratings" rarely inform the shopper that most of those tests simulate collisions between identical vehicles.

Federal Motor Vehicle Safety Standards for passenger cars mandate that both front and rear bumpers protect a zone from 16" above the ground to 20" above the ground.  Those standards could be amended to raise the front bumper zone to 18"-to-22" to increase the chances of triggering an airbag deploy in the event of a collision with a taller vehicles.  An alternative would be to require that the "protection zone" be raised to from 20" to 22" in the area immediately in front of each motor rail.

Additionally, it would make sense to lower the FMVSS requirement for rear bumper bars by two inches to negate the effect of braking-induced-pitch.  In a typical, real life, rear-end collision, the bullet car submarines beneath the target car due to braking-induced-pitch.