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James R. Davis
 Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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 Posted - 04/08/2005 : 8:02 PM
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I have created a model that is useful in doing skid mark analysis. It is useful in determining the minimum speed at which a vehicle must have been traveling when it started to skid. The concepts and methodology are straight forward and might be useful to some of you in understanding what can be learned from an accident scene.
Would anybody want me to make that model available and to post an explanation of how it works here?
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Ben
Junior Member
28 Posts
San Jose, CA
USA
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Posted - 04/08/2005 : 4:42 PM
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quote:
Originally posted by James R. Davis
I have created a model that is useful in doing skid mark analysis. It is useful in determining the minimum speed at which a vehicle must have been traveling when it started to skid. The concepts and methodology are straight forward and might be useful to some of you in understanding what can be learned from an accident scene.
Would anybody want me to make that model available and to post an explanation of how it works here?
Absolutely! I have some empirical data that I would like to test the model with.
Thanks,
Ben |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 04/08/2005 : 6:00 PM
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Skid mark analysis is often used by accident reconstructionists to determine the minimum speed at which a vehicle was traveling at the time the skid marks began. In a court of law the results of this analysis are considered of prime value because they can be defended scientifically, assuming the analysis is done correctly. The analysis is often challenged, however, because there is a certain degree of uncertainty in all aspects of the process. Nevertheless, a critical review of the method used and the assumptions made will find the amount of uncertainty involved is relatively insignificant in the conclusions. Should the analysis, for example, show that the vehicle had to have been traveling at least 63.5 MPH when it began to skid, uncertainty analysis can demonstrate that the conclusion cannot be more than, say, 5% off which means that the vehicle had to have been traveling at a speed of no less than 60 MPH and in a 45 MPH posted speed zone there can be no argument that it had been speeding.
The essence of skid mark analysis is the following formula:  where
- S = Minimum Speed in MPH
- f = drag factor
- d = length of skid in feet
The drag factor (f) is a numerical value that accounts for three physical attributes of the vehicle and road surface: f = mn+m where
- f = drag factor
- m = tire-surface coefficient of friction
- n = braking percentage of the vehicle wheels
- m = the slope (percentage grade) of the road
The tire-surface coefficient of friction (m) is highly dependant upon the road surface material. For roads constructed of Portland cement, for example, this can range from .55 to as high as 1.2, for asphalt, on the other hand, it can range from .5 to .9, and for gravel it can range between .4 and .8. (Ice ranges between .1 and .25 while snow ranges from .1 to .55.) Please note that this is not the same as the rolling traction capability of the tire. It is, instead, the sliding friction coefficient. Thus, a motorcycle tire that can support about 1.1g of acceleration has a sliding coefficient of friction of about .80 on concrete.
The braking percentage refers to that portion of the vehicle’s weight which is supported on the wheels that are actually braking. In other words, if a car has four wheels and one of them has a defective brake and that wheel supports 17% of the car’s weight, then the braking efficiency would be 83%. In the case of a motorcycle, if the rear brake was the only one being used, then depending upon how high the bike’s CG is compared to its wheelbase length, weight transfer would shift most of the bike’s weight to the front wheel leaving something less than 40% on the wheel being braked. In that case, braking efficiency would be no more than 40%. If only the front brake were being used then braking efficiency could be as high as 100% but this is most unlikely as the bike being a single-track vehicle would quickly fall over ending the skid mark. Most motorcycle skid marks are from the rear tire while spotty intermittent skidding of the front tire is quite common. In other words, braking efficiency for a motorcycle using both brakes could range from as low as 40% to very close to 100%.
The road grade (m) can be either plus or minus (or zero). A modest incline might have a grade of +.02 (2%) while a modest decline would be -.02 (-2%).
So, assuming a motorcycle left skid marks that were 169 feet long before it came to a dead stop which indicated that both brakes were used efficiently could have a braking percentage of 80%, and if the sliding coefficient of friction was also .80, on a modest 2% uphill grade, we could calculate that the drag factor (f) was equal to:
- f = .80 * .80 + .02
- = .66
From that we could calculate that the minimum speed it must have been traveling at when the skid marks began was
- S =
- =
- = 57.85 MPH
But what if the bike did not come to a dead stop after the skid mark but, instead, crashed into another vehicle at 30 MPH? Do we conclude that it must have been traveling at no less than 87.85 MPH when the skid began? The answer is a decided NO! You do NOT simply add the crash speed to the calculated minimum speed evidenced by the skid mark. As the calculations involve taking the square root of the factors you must combine the speeds, not add them. In other words, you must square the calculated minimum speed and add it to the square of the collision speed then find the square root of the sum.
An example of the model:
You may access the model here. (Model has been updated - see later messages.)
If anyone would like to discuss why the caculated speed is a minimum we can do that here. (It should be obvious, however, that the vehicle was braking before it began skidding so that it was scrubbing speed before the skid began.)
If anybody finds fault with the methodology I used I would very much appreciate feedback! I'd like the model to be worthwhile, not just an exercise.
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 04/09/2005 : 6:55 AM
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The model has been enhanced to show a graph of the best possible stopping distance for the vehicle assuming no skidding and 100% braking.
The stopping distance algorithm uses the calculated minimum speed, and charts a range of rolling coefficient of friction values against stopping distance.
The formula used is
d = v^2/(30*(m+G)) where
d = distance to stop in feet
v = speed in MPH
m = coefficient of friction (rolling, not skidding)
G = grade (%)
The example shows that the vehicle that had a collision at 30 MPH after skidding 169 feet, with a .80 coefficient of friction and 80% braking efficiency, had to be traveling at least 65.16 MPH at the start of the skid mark. Had that vehicle not skidded and had full use of its brakes, assuming the rolling coefficient of friction of 1.00, could have stopped in only 138.76 feet. In other words, it would not have had a collision!
A note about the assumed rolling coefficient of friction ... the model presumes the pavement was dry at the time of the skid. In that case the sliding coefficient of friction was about 20% less than the rolling coefficient of friction. However, if the surface was wet then sliding coefficient of friction would have been about 50% less. |
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Cash Anthony
 Administrator
1184 Posts
[Mentor]
Houston, Texas
USA
Honda
Magna 750
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Posted - 04/12/2005 : 10:29 AM
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This is a fascinating analysis. Thanks for creating the tool.
I wonder if anyone does skid mark analysis outside the context of accident reconstruction? Is it used, for instance, in brake design?
Just curious....
Cash |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 04/12/2005 : 10:46 AM
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As a skid mark demonstrates that the brakes have already provided all the stopping energy possible (you could apply any amount of additional braking energy without ANY consequence whatever as the wheel is already locked) I cannot imagine that skid mark analysis would be helpful in brake design work.
Well, there is something that motorcycle designers have looked at that is similar. They put a paint gun on the bike that sprays a paint marker on the ground from the instant that the brakes are applied. That paint mark is obviously going to appear on the ground before any skidding. They can analyze the paint mark as compared to the skid mark (and against speed recordings) to see how effective the rider was in using his brakes and, by inference, how efficient the brakes were before they got to the point of locking the wheel.
The longer the paint mark is before the skid mark starts, the faster the bike was going before the skid began. THAT is exactly why skid mark analysis is used to determine the MINIMUM speed the bike was moving at the time the skid mark began rather than how fast the bike was moving when its brakes were applied. |
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Alan_Hepburn
Standard Member
112 Posts
San Jose, Ca
USA
Suzuki
2007 Boulevard C50T
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Posted - 07/19/2005 : 4:25 PM
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quote:
I'm sure that there is some similar psychological model that could be built that would relate the size of skidmarks produced to the level of fear induced. The greater the skidmarks made must surely be exponentially related to the adrenalin rush culminating in the ultimate when a weak skidmark becomes a solid at the moment of impact.
Ed
Would there be some kind of correlation between the skid mark left on the road and the skid mark left in your trousers?  |
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BadaBing
Moderator
1196 Posts
[Mentor]
Houston, TX
USA
Harley-Davidson
Heritage Classic 04
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Posted - 10/13/2005 : 3:59 PM
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quote:
Originally posted by Alan_Hepburn
quote:
I'm sure that there is some similar psychological model that could be built that would relate the size of skidmarks produced to the level of fear induced. The greater the skidmarks made must surely be exponentially related to the adrenalin rush culminating in the ultimate when a weak skidmark becomes a solid at the moment of impact.
Ed
Would there be some kind of correlation between the skid mark left on the road and the skid mark left in your trousers?
Hey Ed,
Ubet!!! Plus I can analyze them easier.
Ciao,
BadaBing
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pmdean
Junior Member
71 Posts
Burnsville, MN
USA
BMW
K1200LT
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Posted - 01/11/2006 : 12:52 PM
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| In calculating the distance of the skid are you looking at the distance of the mark alone? I have heard that, at least on asphalt, the mark doesn't start until friction has created enough heat and that the mark is actually the oil from the asphalt and not rubber from the tire. |
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md2lgyk
Standard Member
223 Posts
Harpers Ferry, WV
USA
Suzuki
Marauder 800
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Posted - 01/11/2006 : 1:38 PM
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| It wasn't as rigorous as what you've presented, but I was taught skid mark analysis at the police academy. |
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Jody Hudson
New Member
16 Posts
New Bern, North Carolina
USA
BMW
R1150RS
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Posted - 01/11/2006 : 9:38 PM
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As a point of interest: I was recently treated to a tour of the local PD (voluntary! - it was part of a Citizens Police Academy session), and saw a section of an automobile tire in their garage that was partially filled with cement, with an eye bolt allowing it to be lifted and another eye bolt allowing it to be dragged. This is the drag sled used in accident analysis to measure the actual coefficient of friction at the actual location of an accident. A scale is used to weigh the device, and a scale is used to pull the device over the road surface, and the coefficient of friction is obtained by simple division.
The officer giving the tour said that officers investigating an accident used PDAs with software that utilized the observed conditions to come up with accident parameters.
I know that it is a bit of a leap to go from the friction of a dummy, cement-filled (hence lightly-loaded) tire pulled at very low speed to a heavily loaded, locked tire sliding at highway speeds, but it is probably better than pulling numbers out of a table of typical values.
I would be curious to know if an effect of the prevalence of ABS has been to make accident reconstruction much more difficult, if not impossible. Does an ABS'd tire leave any skid marks at all?
[BTW, thanks for posting the model. I look forward to trying it out when I have a bit more time.]
[No, no, no -- I meant on my computer -- I am not going to go out and make skid marks and then measure them.] |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 02/01/2007 : 9:52 PM
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After a year or so of working with various scenarios I needed to upgrade the model. The current version is now available here.
Here is a sample run with the new model:
There are three fundamental differences in the model over the last version:
- It now shows how much speed was scrubbed while braking - prior to any collision that might have occurred
- It now calculates minimum speed at start of braking including transient braking time
- It now reflects the fact that the dynamic (sliding) coefficient of friction is about 25% less than the static coefficient of friction instead of 20%
Transient Braking Time is the elapsed time from when you first start braking until weight transfer has occurred and you have reached maximum braking effort. It is very close to .2 seconds for almost all cars and motorcycles. If air brakes are involved, then Transient Braking Time can be considerably longer. [See this thread for a complete discussion about Transient Braking Time.]
It is important that you realize that the 'Minimum Speed scrubbed by skid' result is actually what the speed would have been if the vehicle had come to a complete stop. Thus, instead of adding that speed to the collision speed to determine minimum speed at start of braking, you COMBINE, not ADD, those speeds. Combining involves adding the square of both speeds and then finding the square root of the sum. In the example run above, therefore, the minimum speed at start of braking is correctly found to be nearly 66 MPH (SQRT(30^2 + 56.07^2)) instead of 86 MPH (30 + 56.07). |
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