Yes, the premise sounds entirely reasonable, but when it comes to physics, "All else being equal" doesn't really apply, since "twice as bad" doesn't actually result in twice as severity of injury, twice the number of injuries, or twice the number of fatalities. So clearly, the parameters "all else being equal" doesn't apply, as "all else" isn't equal at all, not when actual physics gets involved.
In an overly simplistic illustration, which on the surface would almost confirm the "twice as heavy = twice as bad" theory, if a moving body crashes into a solid, non-yielding wall at 20 miles per hour, the kinetic energy dissipated in the crash = 1/2 M x 20 x 20 = 1/2 M x 400 = M x 200. But if it crashes into the wall at 40 miles per hour, the energy dissipated in the collision is 1/2 M x 40 x 40 = 1/2 M x 1600 = M x 800. Thus, four times as much energy is involved in the second crash as in the first (M x 800/M x 200 = 4). The speed has doubled but the energy has quadrupled. In this case, where kinetic energy alone is accounted for, twice as heavy (or twice as fast) would be four times as bad. The same holds true for wind resistance where twice as fast means four times the resistance.
But don't throw a party, yet, Leo. Several other factors must be accounted for, like the Friction of the tires of the stationary Buick, for example, with S(mph) = 5.5 x sqrt (Cd x length of skid).
The physics of a car cash include Newton's Laws of Motion, and the dynamic forces acting within Newton's Laws: mass, velocity, acceleration, among many others.
Newtons' Laws of Motion
First Law: "A body does not alter its state of motion without the influence of an external force." That is, there is no change in the velocity of a body (neither in magnitude nor in direction) unless some other force acts on that body.
Second Law: "The net resultant force applied to the body is equal to the first time-derivative of the momentum function."
Force = Mass x Acceleration.
This relationship is not so much a natural law as a rule for assigning a magnitude to forces which is necessary in these types of calculations.
Third Law: "For every applied force there is an equal and oppositely directed reactive force." You push on the wall, and the wall pushes back. The pusher and the pushed, the striker and the struck both experience forces of the same magnitude but of opposite direction.
We're dealing with force, mass, inertia, torque, velocity, acceleration, friction, momentum, work, energy, and power.
Not even accounting for the variations of the crash-force absorbing construction of the different vehicles (the results of many government and industry backed crash tests), which would make all else even less equal, let's do the math, shall we? For the sake of simplicity, I'll keep speed low, which will make it easier to extrapolate for higher speed crashes.
An 8000 pound cargo van runs into a 4000 pound Buick.
The road is asphalt and the coefficient of drag is 0.7, the van is going just 10 miles per hour, the Buick is at rest.
The momentum of the system before the collision is:
Momentum = Mass (van) x Velocity (van) + Mass (Buick) x Velocity (Buick)
= (8000 x 10) + (0 x 4000)
= 80,000
Let's assume the external forces acting on the system during the impact are minimal (the brakes of the van are off) momentum is conserved. Thus, after the accident the following relation holds true where V is post-impact Velocity of the vehicles:
Momentum before = Momentum after
80,000 = (80,000 x V) + (4,000 x V)
V = 80,000/84,000 = 0.95 mph
where "V" is now the post impact velocity of the vehicles. (We assume here that the van and the Buick are moving with the same velocity after impact. The introduction of the Buick being in Park would make a difference, but it's not necessary for this exercise, and would only complicate things). Thus, the van loses 9.05 mph = 13.3 ft/sec due to the action of the retarding impact force, acceleration and deceleration.
One "g" is an acceleration equal to that generated by a free fall in the earth's gravitational field, i.e., 32.2 feet per second per second. Thus, a body acted on by a 0.5 g acceleration experiences a force equal to half its weight. This force acts in the direction of the acceleration.
If the Buick is shortened about 8" in this impact, then the distance through which the retarding force acts is about 12" (the van starts moving during the impact; assume it moves about 4") so that the van travels about 1' during the impact with an average velocity of about 8 ft/sec. The duration of the impact can be estimated as follows:
Distance = Velocity x Time
Time = Distance/Velocity
T = 1 ft/(8 ft/sec) = 0.125 sec
So the van decelerates from 14.7 ft/sec to 1.3 ft/sec in a time of 0.125 sec. Its average deceleration is:
13.4 ft/sec / 0.125 sec = 107 ft/sec/sec = 3.33 g
The average force acting on the Buick then is 3.33 x 8,000 pounds = 26,260 pounds.
This is also the force that acts on the van (Newton's Third Law: Every force has an equal and opposite reaction force): So that the average acceleration of the van is: 8,000/9990 = 3 ft/sec/sec = 0.8 g
Now, do all of the same math for a 4000 pound car that hits the same 4000 Buick, and the end result is the average force acting on the Buick would be 19,695 pounds, and not the predicted 13,130 pounds. The reason is, less energy is lost due to friction, deceleration and other forces, and more of the force is retained within the moving vehicle and is transferred directly to the stationary Buick. A vehicle weighing twice as much, it turns out, is 1.5 times as bad, not 2.0 times as bad.
So, while an 8000 pound cargo van is clearly more dangerous than a 4000 car, it ain't all that much more dangerous. And certainly not more enough to require the same regulation as far heavier vehicles.
But other than not much, what does all this really mean to us expediters? Not much. All it means is that until cargo vans start causing more accidents and more fatalities, no amount of wishing from those who do log will get the DOT to regulate cargo vans.
