quick question, i read all of your math and it all seems very logical. ive been following this thread for a couple of days, and agree with all of your reasoning. my only question is, when you hit a bump, the suspension compresses and rebounds, sending the rear of the truck into the air once the bumpstop bottoms out, when you drop it off a 56' drop, the truck has no where to go, wouldnt this change the math a little? am i explaining my question right?
Great question. I struggled with explaining it clearly.
The comparison is equal if you only allow the drop to compress the suspension 12". (and then somehow stop the fall/truck)
The main issue here is the time the suspension has to work on the truck to "move it up". Lets look at it this way, (which is another way to analyze it):
Basically in .0166 seconds the bottom of the tire moves up 12" (forced to by the ground). This is 1/60th of a second. If you assume that the tire squashes 3", the suspension takes up 6" (the amount it has when loaded), that means to avoid a nasty crash between the steel axle and steel frame, you need the suspension to move the truck up by 3".
Ok but how reasonable is that? Can't the suspension move the truck up 3" in that timeframe? It can't, and here is why:
The mass of the truck on the rear suspension is roughly 3,000 pounds. Lets assume that the force supplied by the suspension to the truck is constant (we know it isn't, but this will give us the SMALLEST force required).
x = .25' (3")
a = constant because force is constant
t = .0166
so knowing that v_initial is zero:
x = 1/2 * at^2
leaves a = 1814.5 ft/s^2
Great now what? Well this acceleration is equal to 56 "g"s. So the suspension must exert 56 times the weight of the truck on the rear axle to move it up 3" in that amount of time OR about
170,000 pounds of force MINIMUM.
There is no way this suspension is exerting more force than the weight of an M1A1 main battle tank on your truck. Ergo, you have a big, nasty impact between the rear axle and the frame rail, which kinks the frame (and ANY frame would kink), and makes you a Raptor with the dump truck look.
Better explanation?