what is the formula used to determine the speed of a vehicle from the measurement of the skid marks left on the road surface.
does the formula take into account the road surface conditions, abs if fitted, etc.
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Kev.
In a nut shell:
1. Distance travelled from seeing the need to take action to actually taking action (re-action time = .68 second (average)
then Distance = 1.47 x Time x Speed.
2. We have now seen the need for action and slammed on and achieved lock up. We need to know the skid resistance factor of the road (drag factor which is variable) and for purposes of Highway Code dry road stopping distances is 0.6. Wet slippery road about 0.2 or 3. Higher than .6 if it is new Shellgrip(Drag factor can be established by doing test runs and skidding).
Still with me?
Then the distance required to stop =
Distance = 0.033 x S(squared on lock up) over Drag factor.
Add the distance during reaction time to that to stop and you have an overall distance.
3. If you know the Drag factor and length of skid mark all locked then then to work out speed on lock up:
Speed = ______________________________
5.5/ Distance skids x Drag factor:
In case post does not show properly then 5.5 divided into square root of Distance time Drag factor
4. The above is in relation to a motor vehicle not fitted with ABS or brake reduction valves. ABS was not in when I did the Course with metpol but understand that there is formula to cover this which is not known by me.
As an insight if you can get hold of book Accident Investigation by Mathematics by J. Stannard-Baker (an ex Highway Patrol man) then you will get an insight as to what is involved.
A further avenue is to have a word with Police Collision Unit Officers. I feel sure they will help.
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DVD
You don't give any units in your post - length of skid in ft / metres? Speed in mph / kmh / snails per year?
Also you equation in 3 does not make sense - it is suggesting that the speed in inversely proportional to the square root of the length of the skids - eg longer skid = slower speed! Or have I misread it? I was trying to work out the data based on Kev's post below, but come out with 1.96 speed (mph maybe?) which don't seem right!
Can you enlighten us again?
Richard
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Well spotted Richard W 3 should be times not divide.
From my 30 year old notes:
Possible range of Drag Factors for rubber tyres on wet travelled asphalt or tar ranges from .45 to .7
To obtain the speed (S) in mph from skid marks left where (D) = length of mark in feet and (F) = Drag Factor.
Then S = 5.5. times the square root of D x F
= 18.07 mph (F = .45)
= 22.54 mph (F = .7)
To obtain the distance (D in feet) a vehicle will travel to a stop when speed (S in mph) and Drag Factor are known,i.e. slide to a stop:
Then D = 0.033 x speed squared over F
Speed = 20mph
= 29ft at .45F or 18ft at .7F
From the marks left in that mentioned, the minimum speed at lock up appears to be just under 20mph.
These equations for Court purposes had to be verified by a Physicist/Forensic Lab and if I remember correctly they allowed a margin of error of 2%
DVD
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Plus DVD we don't know the full story (as usual in these cases)but it also depends how much energy was dissipated in the impact, assuming there was one and the evidence can be collected.
for example cyclist catapulted a distance x means that a certain amount of energy was transferred and not lost through braking. Likewise vehicle damage though I always thought that bit was black magic, and I'm not talking chocolates.
Given any three estimates one can "prove" anything.
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A friend who is a magistrate told me of a case when he was still learning the "trade" where a driver was about to be locked up and the keys thrown away because of the absence of skidmarks. He must have been negligent as he didn't try to brake or avoid the accident. Friend asks what car he was driving and did it have ABS. To a man (person?) other magistrates said "what's that and what's it got to do with it?"
So I suspect the answer to your final question is "no".
Terry
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But what about the distance you travel whilst braking without locking up the wheels? a good drive should bring the car to a stop quickly without locking up. Also I thought it was known that most people don't brake hard enough in an emergency (one of the reasons for the invention of 'Brake Assist' which puts brakes on full for the driver when it thinks an emergency stop is being attempted.)
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Very interesting but what is behind your question have you been involved in an accident investigation.
Peter
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the reason for asking is because a friend of mine has been accused of exceeding the 20mph max speed limit when he knocked down a cyclist. the length of the skid marks was approx 8m on a wet/damp concrete surface. he states that the speed was below 20mph, so how can the truth be proved?
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The skid marks cannot give the actual speed at the start of the braking process but if you assume thinking distance plus skid distance this will give the MINIMUM speed the car was doing based on simple physics. The car may well have been going far faster than this if (as mentioned above) a substantial amount of speed was removed by braking without skidding.
So the skid marks will indicate that it was likely that
the car was travelling at or in excess of a calculated speed.
If this calculated speed is under 20mph then no problem it cannot be proved from the skid marks that the car was doing any more than this speed. If the minimum speed is over 20mph then your friend is in the proverbial.
regards
Ian
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Ian
I may be missing something here, but surely the concept of thinking distance in these calculations is a bit of a red herring.
The car will lose very little speed during the 'thinking distance' (it will lose a litle as it it will be travelling on a closed throttle for part of the time) but the only valid calculation that can be made involves the skid marks, and these alone, as you say will indicate a minimum speed. Any other assessments can only be approximations.
Regards
John S
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John,
You are correct.....I was trying to eliminate the effect of the
braking but not skidding distance to indicate that the skid marks will only give the minimum speed of the car at the start of the skid. I should have eliminated both effects and concentrated on the actual skid.
regards
Ian
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8m seems a long way to skid at 20mph, even if the road was wet.
And I would have thought that if you were sliding on a wet surface you wouldn't leave skidmarks, or am I being naive ?
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Lets see now - highway code says combined stopping distance at 20 mph (thinking & braking) = 12 metres (actual braking distance 6 metres)
And this guy skidded for 8 ?
I think somebody's looking for a get out of jail card they don't deserve
I have to grow old - but I don't have to grow up
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Sqeegee effect Mark, like rubbing a rubber window cleaner down wet glass, plus there are particles of grit etc that get scratched along the road in some of the burnt rubber. This later point shows more lock up than what you can see of the black rubber and can add a couple of feet to that actually seen.
DVD
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actually this has been investigated and the scuff marks left during ABS braking have been identified, categorised and data can be fed into the new equations.
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If skidmarks are produced, it means that the wheel(s) have stopped rotating but the vehicle continues to move.
To achieve 100% braking, the braking force has to equal the vehicle weight.This will give a retardation of (g), which is 32.2ft/sec/sec, or 9.81 m/sec/sec. In practice this is rarely(if ever achieved). Usually it is about 80%.
The coefficient of friction between tyres and road will be approx 0.7 on dry tarmac.
Therefore the actual retardation will be: 32.2 x 0.8 x 0.7 = 18m/sec/sec.
Then using the formula: V x V = (u x u)-2as
where V = final velocity
u = initial velocity
a = decelaration
s = distance
We have s = (u x u)/2a
Thus for 20mph (29.3ft/sec) the stopping distance would be;
(29.3 x 29.3)/(2 x 18) = 23.84 feet.
if we assume 100% braking then distance would be 19.07 feet.
All this assumes that the retardation is constant and the thinking distance ignored.
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If skidmarks are produced, it means that the wheel(s) have stopped rotating but the vehicle continues to move.
Not at all. You can have skidmarks when the wheels are rotating, but at a lesser speed than the vehicle is moving. I understood that maximum friction is obtained when there IS slip between road and tyre. On a clear, unused bit of road, slam an ABS equipped cars brakes on - I think you WILL see rubber marks on the road.
Martin
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Both the police and local authorities have devices which check the co-efficient of friction of the road surface.One for investigations and the other for need for re-surfacing.
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If skidmarks are produced, it means that the wheel(s) have stopped rotating
Not necessarily so. You can also produce skid marks by wheel spinning it away from the lights ;o)
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Dynamic Dave.
In that case the vehicle is stationary whilst the wheels revolve.
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Dynamic Dave. In that case the vehicle is stationary whilst the wheels revolve.
You don't necessarily have to be stationary to cause the wheels to spin.
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You see this after the start of a Grand Prix. Not skidding - friction burn? There is a name for it which escapes me.
With a skid mark it come on faint and get heavier along the line of travel.
Friction burn is the opposite. Also if the mark is on a curve then there will side striations in the mark from a rotating wheel.
DVD
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