Skid Marks, Drag Factor, and a Road That Has to Reopen
You are the first unit at a single-vehicle crash on a dry asphalt county road. The car crossed the centerline, struck a mailbox, and came to rest in a ditch; the driver has minor injuries and is being treated. The car left 132 feet of pre-impact skid marks. Your agency's quick-reference card gives the minimum speed formula S = sqrt(30 x d x f), where d is skid distance in feet and f is the drag factor; for dry asphalt with antilock brakes the card lists f = 0.75. The driver, who is alert, says he was 'going about 45.' The posted limit is 55 mph. Dispatch wants an estimate of when the road reopens. The tow truck is 18 minutes out; after the tow pulls away, debris removal takes 12 minutes plus 1 minute for every 10 feet of debris field, and the debris field measures 40 feet. It is 0525. Your crash report takes 40 minutes to write and the tow-and-clear paperwork takes another 15.
1. Compute the minimum speed from the skid marks. Compare it with the driver's statement and the posted limit, and state what the figure does and does not prove.
Read the worked answer
S = sqrt(30 x 132 x 0.75)
- 30 x 132 = 3,960
- 3,960 x 0.75 = 2,970
- sqrt(2,970) = 54.5 mph
So the minimum speed at the start of the skid was about 54.5 mph. That is roughly 10 mph above the driver's 'about 45' and just under the 55 mph limit.
What it proves: the car was traveling at least that fast when the brakes locked, on the assumption that all four wheels were braking on that surface.
What it does not prove:
- It is a minimum, not an estimate of impact speed. The car was slowing from that point forward.
- It assumes the stated drag factor and that the full 132 feet were on the same surface. A shoulder transition or a tire leaving the pavement would change the arithmetic.
- It says nothing about why the car crossed the centerline, which is the more important question for the report.
2. At what time can the road reopen, and can you complete the report and the tow-and-clear paperwork before the 0700 end of shift if you begin writing only after the road reopens?
Read the worked answer
Reopen time:
- Tow arrival: 18 minutes
- Debris removal: 12 + (40 / 10) = 12 + 4 = 16 minutes
- Total: 18 + 16 = 34 minutes after 0525 = 0559
Paperwork: 40 + 15 = 55 minutes.
Starting at 0559, you finish at 0559 + 55 = 0654 - six minutes before 0700.
That margin is too thin to rely on. Two conclusions follow:
- The arithmetic says you can make it, but any delay in the tow, any follow-up call, or any driver statement taken after 0600 pushes you past shift end.
- The practical move is to start the report while waiting for the tow rather than treating 0559 as your start time. If the scene runs long, notify the shift supervisor early rather than at 0658.
Report the reopen estimate to dispatch as 'approximately 0600' and note it is dependent on the tow.
3. How much does the drag factor assumption change your conclusion about speed? Compute an alternative and explain how you would present the range in a report.
Read the worked answer
The formula is sensitive to the drag factor because f sits inside the square root, so the speed scales with sqrt(f). Recompute with a conservative and a high value:
- f = 0.60: sqrt(30 x 132 x 0.60) = sqrt(2,376) = 48.7 mph
- f = 0.80: sqrt(30 x 132 x 0.80) = sqrt(3,168) = 56.3 mph
So the minimum-speed estimate moves roughly 8 mph across a plausible range of friction values.
How to present it:
- State the assumed drag factor and where it came from (the agency card), not just the final number.
- Give the computed figure for that assumption and note that a lower drag factor produces a lower minimum.
- Do not offer a false-precision single number as if it were measured.
Practical effect on a 55 mph limit: at f = 0.75 the minimum equals the limit; at f = 0.80 it exceeds it; at f = 0.60 it does not. That means the skid evidence alone is not strong enough to support a speed charge. The driver's own account, the damage, and the road evidence have to carry it, and the report should say so plainly.