Stone chips - mudspats calculations.

[BruceT]

I've used a little high school physics to do some calculations on whether mud spats will stop the stone damage to the leading edge of the rear wheel arch in the door aperture. Forgive me if this looks a little over the top, but my purpose is to work out if mud spats could stop stones kicked up by the front wheels from striking the rear of the car.

My basic assumption is that in order to stop the stones the mud spats must be close enough to the ground to block their path - i.e the stones can't just fly under the mud spats and still hit the wheel arch.

Dimensions assumed (measured):
Stones leave ground after being run over by front wheel, when at a point when wheel is 15mm above the ground.
Distance to strike point: 1800mm = 1.8metres.
Height of strike point = 280mm + = 0.28 metres +
Distance to mud spat = 250 mm = 0.25 metres.

The question is: How high is the stone at the mudspat if it is on a trajectory to hit the rear wheel arch?

The following calculations have been rounded.
First calculation: assume car speed 100 km/h ~ 28 m/s
Assume stone goes straight up (an down) and it's the car' forward motion that causes the strike. Time to hit car = 1.8m/(28m/s) = 0.065 sec
Vertical speed of stone when leaving ground = 4.6 m/s
Vertical speed of stone at time of strike = 4.0 m/s
(Such a stone will reach a maximum height of 1.1 metres before falling back down - it is a potential window breaker for an oncoming vehicle.)

Time to reach mudspat = 0.25m/(28m/s) = 0.009 sec
Height above ground at mudspat = 0.041 m = 41 mm = 4.1 cm.

When I repeated the calculation assuming the car speed was 72 km/h = 15 m/sec, I got a height of the stone at the mudspat of 0.047 metres = 4.7 cm.

Assuming a direct path with no effect of gravity (worst case) = 0.28*(0.25/1.8) = 0.039m = 3.9 cm.

CONCLUSIONS:
1) Mudspats must reach to within 4 cm of the ground (and be wide enough of course) to stop stone strikes on the lowest point of the rear wheel arch in the rear door aperture.
2) The stone trajectory is quite "flat". Over such a short time gravity does not slow its vertical speed by much.

I don't think the standard mudspats go this close to the ground. They may still stop strikes on the body work closer to the front wheels, but they won't work for this problem.