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James R. Davis
 Administrator
14909 Posts
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Houston, TX
USA
Honda
GoldWing 1500
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 Posted - 12/20/2006 : 1:16 AM
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[The concepts and most of the math contained in this article were derived from an engineering technical paper published by the Society of Automotive Engineers (SAE 950354 by James A. Neptune, et.al.) but the wording is entirely mine.]
In the literature there are endless dissertations on how to properly use skid marks in the reconstruction of an accident. The vast majority of these articles, though sounding relatively simple and obvious, and drawing conclusions that accident reconstructionists have used in court for many years, are wrong - fundamentally. That is, they ignore the fact that the calculations used violate (actually, misrepresent) the First Law of Thermodynamics. About that, later.
First, I want you to see a diagram of an accurately measured deceleration curve for the situation in which a vehicle's wheels are locked - i.e., max braking used. (We all know this is not good - especially on a motorcycle.)
Note that the height of the curve is shown as a deceleration rate. Specifically, the height is shown in terms of Gravity so that the highest point on the curve shown represents a deceleration rate of slightly more than 1g. (Where 1g = 32.2 ft/sec/sec)
A motorcycle tire, in good shape, on good concrete, can support about 1.1g's of deceleration before losing traction so this is an excellent graph to make the points I am about to make for you.
Notice that the majority of the curve is virtually flat at a deceleration rate of about .7g's.
That is representative of your maximum deceleration rate while your brakes are locked and the tire is skidding on the roadway. Said another way, once you have exceeded the maximum deceleration rate supported by the traction of your tires, you will quickly lose about 25% of the traction you had. Or, you have moved from traction using the static coefficient of friction available to a rolling tire to that of the dynamic coefficient of friction available to a skidding tire.
You all know that where the tire is skidding it leaves a solid, DARK, skid mark on the pavement. But do you know that the tire leaves a lighter, sometimes intermittent mark, prior to that dark solid mark? This is known as the 'impending skid mark'. When you are doing a maximum braking effort you can actually hear the front tire 'chirp' as it leaves that impending skid mark.
So now, I suspect, you realize that the total length of the skid mark, including the impending skid mark portion, does NOT represent the time where the wheel is locked. And, further, you understand that using the length of that skid mark and a calculated coefficient of friction (u) CANNOT accurately tell you how fast the vehicle was moving at the time the brakes were first applied!!
I think there is at least one misunderstanding still running around in your head about this. My guess is that you think the skid marks started on the down side of the highest deceleration rate curve somewhere around where I marked this next chart.
However, in fact, the skid mark (actually, the 'impending skid mark) started much earlier than that as shown below.
(Remember, please, that you attain maximum braking by getting as close to the point where a skid occurs as possible without going past that point. While you are there you are leaving a 'chirpy' faint skid mark on the roadway.)
I think you are about to have a eureka moment! An accident reconstructionist calculates the speed the vehicle was moving when he applied his brakes by first calculating the dynamic coefficient of friction (u), in this case about .7, and uses that along with the length of the skid mark (I will show the formula later). In other words, the area within the red outlined rectangle in the diagram below is used to calculate the starting speed.
What that actually does is calculate the speed slightly more than .2 seconds AFTER the brakes were first applied. That is, there was a transient braking period of about .2 seconds that is not accounted for in these calculations. And it should be obvious to you that during that .2 seconds the vehicle was SLOWING DOWN so that the speed the vehicle was moving at the time braking began MUST HAVE BEEN HIGHER than the calculation will indicate.
What was the rate of deceleration during those .2 seconds? Well, it started at a rate of zero and got up to slightly more than .7g's within .2 seconds, and if you assume that it grew linearly, then the average rate of deceleration during that time would be half of .7, or approximately .35g's.
Note that there is a slight lag between when the brakes were first applied and when deceleration actually began (shown below as about .05 seconds.) In the case of a vehicle with air brakes that delay is noticeably longer than .05 seconds.
The way modern analysts calculate that average is by using exactly one half of the dynamic coefficient of friction. This is shown below.
And now we see that by combining the grayed out areas we have a more useful (and accurate) representation of the braking energy used to slow the vehicle and as a result of that we have a more accurate tool for calculating the speed the vehicle was moving when the brakes were applied.
I know, by now you are wondering 'So what?' This correction in the calculation can't make a significant difference, or can it?
I assure you that it makes a difference - especially in a court of law.
Let me give you a hypothetical example ...
You are riding your bike on a road that has a posted speed limit of 45 MPH, but you are going somewhat faster than that. Suddenly a pedestrian steps into the street in front of you, notices you and freezes in place. You notice the person and do a panic stop. Not good enough - you run into that person and cause serious injury.
You are sued. An accident reconstructionist who is well qualified calculates that you were moving at 37 MPH when you hit the individual and from your skid marks and having done a skid sled measurement to determine the dynamic coefficient of friction at the site, calculates that you were going 52 MPH when you started braking and that you were 59 feet from the impact point when you did so. You cannot argue that you were not speeding. Science (and possibly witnesses) proves that you were indeed going faster than the posted 45 MPH limit.
Is that all there is to it?
Well, actually, not at all. You see, if you can demonstrate that even if you were going only 45 MPH you could not have avoided hitting that person, then that person's actions were obviously a contributing factor and, thus, you can not be held solely responsible for the action.
Traditional analysis will show that had you been going 45 MPH instead of faster when you began braking you would have started your braking effort 87 feet before the impact site and would have stopped 13 feet beyond the point of impact so that, clearly, the accident (impact) was unavoidable.
HOWEVER, the plaintiff's attorney has found a modern analyst who understands that you HAD TO HAVE BEEN moving faster than 52 MPH when you began to brake because he took into account the transient braking time while the traditional analyst did not. His calculations demonstrate that you had to have been going at a speed of 54 MPH when you began braking and you were 73 feet from the victim when you started that braking. Furthermore, had you actually been traveling at 45 MPH you would have begun your braking 93 feet away from the victim and would have stopped just at the point of impact - thus, the accident (at least the injury part of it) was avoidable had you simply been moving at the posted speed limit. You just had a bad day in court!!!
It's getting very late and I'm heading off to bed now so I will post the calculations in the next message.
Before I go, however, I want to plant another eureka moment in your minds ...
Since ABS prevents skidding by releasing braking energy just before you lose traction, it should be clear to you now that when you panic stop with a vehicle that is ABS equipped you WILL LEAVE SKID MARKS!
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nomad dan
Advanced Member
1276 Posts
Denver, Colorado
USA
Kawasaki
06 Vulcan Nomad 1600
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Posted - 12/20/2006 : 10:07 AM
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quote:
........... But do you know that the tire leaves a lighter, sometimes intermittent mark, prior to that dark solid mark? This is known as the 'impending skid mark'. When you are doing a maximum braking effort you can actually hear the front tire 'chirp' as it leaves that impending skid mark.
......(Remember, please, that you attain maximum braking by getting as close to the point where a skid occurs as possible without going past that point. While you are there you are leaving a 'chirpy' faint skid mark on the roadway.)
7 years ago a motorcycle cop showed me how to stop. He said you need to listen for your tires to "roar" and keep the braking in that area till you stop. Beyond that area is skidding and prior to that area isn't full braking.
That advice seems to fit with what you describe James. The roar would be just before the skid.
I've been able to stop with the roar sound, but it takes a lot of practice to go all the way up to that sound, but not excede it into a lock up. Most people I presume, even in parking lot practice, don't get all the way into the tire roar and therefore are not stopping as fast as is possible.
There is a lot of braking left even when you think you are doing a good hard stop, if you haven't heard the roar the whole way through. |
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BikeWhisperer
Standard Member
163 Posts
Alabaster, Alabama
USA
Honda
ST1100
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Posted - 12/20/2006 : 1:23 PM
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| Not to split hairs with anyone but does the type of tire come into play here? Harder compounds (more milege) as opposed to the softer type (more traction) would skid quicker than the latter. Given the same bike, same weight ratios, etc. wouldn't a softer compound tire yield quicker stopping and thereby throw arguments one way or another? |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 12/20/2006 : 2:17 PM
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Thanks for posting you observation.
While how hard the tire compound is does effect the results, they are INCLUDED in the dynamic coefficent of friction analysis. That is, you will have a higher or lower deceleration rate based on tire compound, but the length of the skid mark coupled with deceleration rate yields precicely accurate results nevertheless. |
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scottrnelson
Advanced Member
5247 Posts
[Mentor]
Pleasanton, CA
USA
KTM
990 Adv, ST2, XR650L
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Posted - 12/20/2006 : 3:23 PM
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How can you know for sure what the coefficient of friction is for a tire?
If the tire has sat out in the weather for a few years it's not going to have the same grip as a new one, or one that has been inside for its full life.
I don't see how you can get a precise deceleration rate without measuring the actual tires in question, and at the exact air pressure, tire temperature, and road temperature. I've had both car and motorcycle tires that had more grip when they were warm than when cold. I've also seen multiple articles in car magazines showing how the grip changes due to air pressure.
I remain a little bit skeptical about the "precisely accurate results". |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 12/20/2006 : 3:26 PM
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I will here demonstrate the logic and calculations used to support traditional skid mark analysis then show the more modern method and explain why that is preferable.
For an earlier treatment of this subject, one that uses only the traditional approach, please read my earlier discussion here.
The First Law of Thermodynamics says that energy cannot be created or destroyed. That is, the energy of a “system” is equal to the energy entering the “system” plus the work performed on the surroundings minus the energy leaving the “system.” A “system" being defined by a control volume which is established as a physical region on the roadway.
The traditional approach uses the kinetic energy of the vehicle at the onset of skidding and when that vehicle brakes to a complete stop, then all of the kinetic energy has been used to perform work. Provided that there is no collision, the work performed is solely the result of braking action.
The traditional formula for determining the initial speed of a vehicle that skids to a complete stop, therefore, states that the kinetic energy of the vehicle at the onset of skidding is equal to the work performed by the braking force applied through the skidding distance.
The deceleration rate during braking is the product of a drag factor, f, and the acceleration of gravity, g. We will simplify the calculations by assuming a zero grade so that the drag factor is simply the coefficient of friction (u) times gravity (g). Thus, the deceleration rate (a) is merely u times g.
Let’s put some givens in place so that we can work with the formulas.
Notice that I had to convert from ft/sec to get a familiar speed of mph.
Therefore, with a drag factor of 0.78, the vehicle was decelerating at the rate of 17.12 mph per second.
How long, then, did it take to stop this vehicle? If you divide the initial speed (37) by 17.12 you find that it took 2.16 seconds to come to a complete stop.
Now let’s look again at the diagram shown in the first message.
It is clear that this is NOT a diagram of the example I am working here. It shows a deceleration rate of 0.70g’s instead of 0.78g’s, and it took 2.7 seconds to stop instead of the 2.16 in our example. But you should be able to see that the grayed out area accurately represents the work performed by the brakes during the time of skidding and that is what has reduced the kinetic energy the vehicle had at entry down to zero at the completion of the full stop.
Now let’s also review the fact that you do NOT simply add the amount of speed scrubbed during the skid (37 mph) to the speed of impact at time of collision (also, it turns out, 37 mph) in order to determine how fast the vehicle was actually traveling at the onset of braking. Because that number is the result of finding the square root of another number, you must combine, not add, speeds. Entry speed is NOT 37 + 37, or 74 mph. Rather, that speed is calculated like this:
That’s what the defendant’s attorney used to ‘prove’ that his client was involved in an unavoidable accident – that even if he had been traveling at the posted speed limit he could not have avoided colliding with the pedestrian.
But you now know that his expert failed to consider the ‘transient braking period’ of .2 seconds that preceded the skid marks. You also now know that his client HAD to have been moving faster than 52 mph when he first began braking.
The plaintiff’s expert used the modern method of analysis. His conclusion was that the defendant was moving at a rate of speed of 55 mph instead of 52 mph, and that with further analysis he found that the accident (at least the injury resulting from it) was avoidable as the vehicle would have come to a complete stop at the point of impact – ‘hitting’ the victim at zero mph.
So how do you include the transient braking period? Well, you compute one half of the deceleration rate during the transient braking period of 0.18 seconds.
The new formula would be:
= 52.44 + 2.26
= 54.7
= 55 (rounded) Enough about the formulas for the moment. I want now to point out a few empirically confirmed observations that might be important for you to know.
You may have noticed the PDR number in the givens of 1.5 seconds. That is VERY OFTEN used by reconstructionists to represent the amount of time it took the vehicle operator to notice a threat, decide what to do about it, and finally to react to that decision. It is a HUGE fudge factor in their analyses. It is used to calculate how far the vehicle traveled before braking began. As a motorcyclist you probably have a PDR of about 1.0 seconds if you are alert. (Your fingers ARE covering your front brake, right?) Imagine how much that factor determines whether or not an accident can be shown to have been ‘avoidable.’
The dynamic coefficient of friction is NOT a function of speed!!! That is, regardless if you are braking from 60 mph down to zero or from 20 mph down to zero, the dynamic coefficient of friction is relatively constant. That is VERY IMPORTANT for you to know because traditional reconstructionists tend to use a CALCULATED dynamic coefficient of friction in their analyses. And, their calculations of that factor result in different numbers based on speed.
The rate of deceleration and the dynamic coefficient of friction are ‘derived’ quantities. For example, the dynamic coefficient of friction is determined by measuring the speed of a test vehicle at the onset of braking, the skidding distance and the grade of the roadway and these numbers, in turn, are used to ‘derive’ that coefficient. Unfortunately, by using such measurements you get a dynamic coefficient of friction that DECREASES with speed. That is a violation of the First Law of Thermodynamics!!! For example, in a typical series of tests, the ‘derived’ dynamic coefficient of friction for a test vehicle with an onset speed of 20 mph was found to be 1.25 while it was found to be .80 with an onset speed of 50 mph. That discrepancy is significant! It results in significant error at lower speed. (If the coefficient was really 1.25 at 20 mph then the deceleration curve should indicate a steady state deceleration of approximately 1.25 times gravity when skidding at that speed. There are no vehicles on the public roads that can manage such a deceleration rate.
The minimum transient braking time measured ranged from 0.11 seconds to as much as 0.25 seconds. That is remarkably close and constant and its variability reflected roadway surface with the lowest being from new asphalt and the highest being from new chip-sealed surfaces. This factor is noticeably higher when air brakes are involved to account for the air actuation delay.
Been in an accident and being sued? You better get hold of the accident reconstructionist's report and look it over closely. You might well find a way to ‘prove’ your point of view that the reconstructionist failed to notice.
Or, better still, avoid the accident.
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 12/20/2006 : 6:25 PM
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I get frustrated and weary beyond words when I read criticisms such as those that preceded this message - criticisms that seem to infer that either science in general or math are imprecise. They are not. They are what allow precision.
Nevertheless, I quite understand that math and unfamiliar science cause many people to be skeptical and to voice that skepticism rather than acknowledge that they simply do not understand or have facility with the material. 'Face saving' is often an unconscious activity.
As to the comment that what I presented above raises doubt about the precisely accurate results ... I did not claim that ANY formula can calculate the exact speed the vehicle was moving at the onset of braking. Instead, I claimed that the formulas themselves yielded precisely accurate answers - they yield answers to whatever level of accuracy you wish to use. Let me be clear about that, if the values used in the formulas are accurate, the result of the calculations DO show the amount of kinetic energy consumed by the braking effort and, if you believe (and understand) the laws of physics, that, in turn, means you can with extremely high confidence (indeed, certainty!) determine how much speed the vehicle lost as it came to a dead stop.
How is that different than claiming that they can determine the actual speed at the onset of braking? Well, as I pointed out in the article, there are MINOR errors in all of the measurements used in the calculations and as a result anybody who uses these equations will claim in court that the MINIMUM SPEED the vehicle was traveling at the onset to braking was the result of the calculations. Those errors add up to slight UNDER calculations in the result. Nobody will claim, in the hypothetical example I used, that the vehicle was traveling at precisely 52 or 54 mph at braking onset, only that it had to have been traveling AT LEAST that fast.
These formulas are designed to precisely and accurately calculate an APPROXIMATE speed. They do so - no ifs or buts about it.
Are we clear? Science and math are both precisely accurate. Results derived from both are well understood and defendable and duplicatable. As I showed in all of my examples, results are usually rounded. Any objections to doing that? Does doing so invalidate the results?
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scottrnelson
Advanced Member
5247 Posts
[Mentor]
Pleasanton, CA
USA
KTM
990 Adv, ST2, XR650L
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Posted - 12/21/2006 : 9:55 AM
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Well I hope you haven't taken my comments as criticism, since I feel that being able to find the exact coefficient of friction is important here. You mentioned the example of a study estimating initial speed at 52 mph, but with a bit more analysis, they determined it was 54 mph.
Is there any chance that the driver had old, cold tires at a pressure that is not optimal for braking that would give a reduced coefficient of friction that could have made the same skid marks from 50 mph, or maybe 45? That would be an important point to the defendant in the case where a few miles per hour makes the difference between guilt and innocence.
Overall, I appreciate the information you've presented here and feel that it has helped increase my understanding of what occurs during braking. I'm just concerned that the coefficient of friction might be a bigger variable than presented here. |
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jmerenda
Junior Member
77 Posts
Massapequa, NY
USA
Harley-Davidson
FXDLI
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Posted - 01/31/2007 : 8:28 PM
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| Somehow, I seemed to have missed this topic when it was originally posted! Personally, I am fascinated by this type of analysis and find the information both useful and interesting. Thanks for making the P&T forum such a wonderful source of information. |
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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 : 11:46 AM
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| It has been my pleasure to explore these topics here. Feedback from members like yourself prove how wrong I was when a year or so ago I didn't think there would be much real interest. |
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Jerry Godell
Senior Member
441 Posts
Kansas City, kansas
USA
Harley-Davidson
FXD SuperGlide
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Posted - 02/01/2007 : 1:15 PM
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My police days go back to the 70's when on several occasions we took the vehicles that struck pedestrians and locked up the brakes to get the coefficient of friction of that vehicle. The tests were at the site of the accident. Surprisingly we had a labratory that determined speed by the deformation of metal.
The formulas are familiar. We also used wheel hop in the determinations. Accident reconstruction is a science.
GPS and Lasers are used now. I got in trouble in court one time. I used a fireplug for a reference. I couldn't prove that the fireplug was still in the same spot when the reconstruction was done.
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Thom Thumb
Advanced Member
1592 Posts
[Mentor]
Jordan, MN
USA
Harley-Davidson
Sportster XL883
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Posted - 02/01/2007 : 4:44 PM
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quote:
Originally posted by Jerry Godell
. . . I got in trouble in court one time. I used a fireplug for a reference. I couldn't prove that the fireplug was still in the same spot when the reconstruction was done.
You're kidding!?  What was the outcome of that one?
TT
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Jerry Godell
Senior Member
441 Posts
Kansas City, kansas
USA
Harley-Davidson
FXD SuperGlide
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Posted - 02/01/2007 : 7:49 PM
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quote:
Originally posted by Thom Thumb
quote:
Originally posted by Jerry Godell
. . . I got in trouble in court one time. I used a fireplug for a reference. I couldn't prove that the fireplug was still in the same spot when the reconstruction was done.
You're kidding!? What was the outcome of that one?
TT
One of those lawyer things. Streets get widened. Utilities moved. Anything to win a case. Need to reference the fireplug to something else. Local police now use GPS. Several reference points. Including the grade of the road at the accident scene.
I can see a laptop, Google Earth. Overlaid with the accident photo's? |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
Peer Review:
1
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Posted - 03/22/2007 : 12:38 PM
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An interesting PM was sent to me along the lines of this thread and because the author specifically said I could quote that message in public I have done so below.
quote:
Good day to you. please excuse the rambling intrusion and my question.I'm new here, and have, with interest, read your posts on skidding and the associated calculation of speed from the marks. I'm interested in learning more about the subject, and wonder whether you might enlighten me on the questions below, or point me towards some published research work. As a newbie, I was unsure of how or whether to post the questions, but would be happy for you to post it on my behalf, if you think it of interest to the group.
I'm considering the full process of braking insofar as it relates to a modern sports motorcycle, and particularly at the front wheel. I note the onset of braking, the transfer of weight, a period of braking which climbs rapidly to a peak value, and the eventual lock of the front wheel, resulting in a fall of the bike. I would like to get a handle on the duration of each phase, and the (-ve) acceleration values achieveable in each one. I have seen front wheel tyre marks of between 20 and 30 metres (say 60-90 feet)or so in length. The mark typically commences with (call this part A) a short conical taper, then maintaining an even and constant width where grey (not black) deposit is left on the roadway. Then (part B) Towards the end of the mark, typically, there is a shallow curve to one side, where the mark narrows and becomes quite black (tyre now locked, I suspect) followed by the inevitable fall over.
I have understood that that some of your mathematical illustrations concentrate on the locked wheel/tyre part of the process. I would like to understand or establish guidelines or calculations on the part (A) and how much speed may be lost during the maximum braking under weight transfer BEFORE actual full wheel lock, and the duration of that phase, and then (B) the duration and decelaration value of the locked phase before fallover. If one were to carry out a test of the coefficient of friction of the roadway, and find it to be, for example, 0.7g, with a sled or skid test how does this correlate to the amount of deceleration at the wheel in both phases?
Simply put, how much speed can you lose BEFORE you lock the wheel. How long will the bike stay up when you do?.
Best wishes
WAC
(Aynsley Cooper)
In other words, WAC has said that he wants to better understand what skid marks can tell him about braking where those skid marks are not primarily the result of a locked brake.
Here is my response:
quote:
Welcome aboard.
You would post a question such as you posted in the Private Message in the Physics and Theoretical forum where you have already read similar posts.
If the roadway coefficient of friction is, as you say, only .70, that means that your motorcycle can attain a deceleration rate of no more than .70g before it's tires skid. Anything greater than that will result in a wheel lock.
It takes approximately 1.0 seconds to perceive a threat, decide what to do about it, and then react (PDR). Braking begins after the PDR.
It takes approximately .2 seconds of transient braking time for about 75% of weight transfer to complete. During that .2 seconds your deceleration rate has averaged about .26g (half of the available DYNAMIC coefficient of friction - about 75% of the STATIC coefficient of friction).
At that point you begin to show light skid marks (what you describe as grey.) Deceleration rate increases as weight transfer continues and, if you are particularly skilled, you enter the realm of 'threshold braking' where you are very close to, but not beyond, the limit of STATIC coefficient of friction. Meaning, for example, that you could go from transient braking and get to maximum possible braking (a deceleration rate of approximately .7g) in another .2 or .3 seconds.
A superbly skilled rider need never go beyond that deceleration rate. In other words, he could maintain a deceleration rate of approximately .7g's until his bike was stopped. No need to lock the front tire at all.
A less skilled rider would attempt excessive braking pressure and exceed the amount of available static friction in so doing, and as a result, lock the front brake, begin a hard (black) skid, and dump the bike.
The scenario I just described fails to account for the fact that you specifically mentioned a sportbike. No matter as you also specified a coefficient of friction of only .70. Had the surface provides a static coefficient of friction closer to 1.0, then your actual maximum deceleration rate would be limited by that rate at which the bike does a stoppie (typically close to .96.)
So, let's see what that means in terms of braking (speed reduction) in the scenario he posted.
Since the vast majority of the skid mark was not black and solid, but was indicated to be a continuous line of grey that extended most of the 60 to 90 feet before turning black and solid, the indications strongly suggest that this rider is extremely proficient at threshhold braking. That is, he maintained a deceleration rate of nearly .7g's for most of his braking effort until he exceeded the available traction provided by the static coefficient of friction and locked his front brake. For arguments sake, let's say that he maintained a deceleration rate of .68g's most of the way.
The first about .5 seconds (following the PDR) had an average deceleration rate of somewhat more than .35g's.
Since .35g's = 11.27 ft/sec., that accounts for the first 5.6 feet of skid mark. That is, the bike scrubbed 3.8 MPH from its speed during the first .5 seconds.
Let's guess that the length of the black skid mark at the end was 5 feet and let's also decide that the length of the entire skid mark was 75 feet. That means that the remaining part of the grey skid mark was 63.5 feet long. This part of the skid was created while the bike was decelerating at the rate of .68g's or 21.9 ft/sec.
This second phase of the braking effort, therefore, lasted 2.9 seconds which, in turn, means that the bike scrubbed another 43.2 MPH from its speed during that time.
The third phase had the bike slowing at the rate of only about .525g's (about 75% of static coefficient of friction). Since it was 5 feet long, it took only about .3 seconds (5 feet divided by 16.9 ft/sec) and scrubbed an additional 3.5 MPH from the bike's speed.
Thus, we know that the bike had to have been moving at a rate of speed in excess of 50.5 MPH when braking began. But how much faster was he actually going? That can only be determined if we know how fast the bike was moving when it hit the ground and that can only be estimated by how much damage was done to the bike/rider by that impact and subsequent slide, and the length of that slide.
I did this rather quickly and suspect that I may have made an error or two in the process. But I did it in order to demonstrate, consistent with the theme of this thread, that there is a lot to learn from skid mark analysis.
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1olbull
New Member
19 Posts
Tacoma, WA
USA
Kawasaki
VN2000
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Posted - 03/23/2007 : 9:03 AM
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Why are you attempting to split hairs regarding the transient portion of the braking process and the measured skid mark? The slide to stop formula you quoted takes into account that the deceleration rate (cof times g) is an average and that a skidding vehicle does not actually decelerate at a constant rate, but at a lower rate in the beginning than at the end of a skid mark. The cof is also not constant, it is a percentage; the Force divided by the Mass. The slide to stop formula is NOT fundamentally wrong. It produces a minimum speed estimate (read not precise). Since the analysis produces a reasonable "estimate", I fail to see why you find a 2 mph difference significant. Given the many unknown variables, the science used here just can not call it that accurately.
I have testified in court hundreds of times over the past 38 years. Believe me when I say that no competent reconstructionist would be so cavalier as to rest his case on a two mph calculated difference. Additionally, no PI attorney would invest his money in a case, or expert for that matter, that would be decided over 2 mph.
Regarding your alarmist comments about court cases and collision reconstructionists in general; Sir, you are just flat incorrect.
PS
Mr. Davis, you provide a great service with this forum and I thank you for the opportunity to comment and to share a common love of motorcycles. |
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WAC
Starting Member
4 Posts
Stoke on Trent, Staffordshire
United Kingdom
Honda
VF1000RF
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Posted - 03/23/2007 : 9:40 AM
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This has perhaps arisen out of my own attempt to consider whther the braking could be considered in two parts, but perhaps not in the proportions considered within James. R Davis' original SAE referenced post.
I have seen that applying "average" (derived) decelerations to locked wheel CAR tyre marks to determine speed lost is a normal technique.
For my own part, I am interested in views as to whether applying a similarly derived "average" value to a motorcycle tyre mark for its whole displacement is a correct approach for all occasions, because of the part of that mark that MIGHT be attributed to a high level of non-locked deceleration, and the part of the mark that can definitely be attributed to wheel lock.
It also occurred to me to ask the forum how long a locked FRONT wheel might persist before the bike fell down.
Just a thought, looking for inspiration and guidance, here!
I would be grateful to be pointed at ANY research material on this aspect of motorcycle behaviour, and in particular, work that attempts to assess the time period that a locked FRONT wheel condition might prevail, and after locking, HOW LONG it might take the bike to fall. |
Edited by - WAC on 03/23/2007 9:45 AM |
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scottrnelson
Advanced Member
5247 Posts
[Mentor]
Pleasanton, CA
USA
KTM
990 Adv, ST2, XR650L
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Posted - 03/23/2007 : 10:08 AM
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quote:
Originally posted by WAC
It also occurred to me to ask the forum how long a locked FRONT wheel might persist before the bike fell down.
Just a thought, looking for inspiration and guidance, here!
I would be grateful to be pointed at ANY research material on this aspect of motorcycle behaviour, and in particular, work that attempts to assess the time period that a locked FRONT wheel condition might prevail, and after locking, HOW LONG it might take the bike to fall.
I have no scientific information, just my own personal experience in 1986 of locking a front wheel on clean, dry pavement. I was on the ground sliding on my face within about half a second of the front wheel locking. Much faster than I could have reacted to my riding mistake. |
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James R. Davis
Administrator
14909 Posts
[Mentor]
Houston, TX
USA
Honda
GoldWing 1500
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Posted - 03/23/2007 : 10:51 AM
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quote:
Additionally, no PI attorney would invest his money in a case, or expert for that matter, that would be decided over 2 mph.
Regarding your alarmist comments about court cases and collision reconstructionists in general; Sir, you are just flat incorrect.
LOL  Pretty strong statements there, friend.
Let me ask you a couple of questions. When you provide such an analysis in a court proceeding do you have to specify what formula you use to round your numbers? Do you round at hundredths of a MPH, tenths, even MPH, or nearest 5 MPH?
Unless you do the last (round to the nearest 5 MPH) then this statement is unambiguously wrong:
quote:
... I fail to see why you find a 2 mph difference significant.
As to your statement that:
quote:
The cof is also not constant
That is similarly wrong. What you and other reconstructionists do is derive that number. Indeed, you derive the DYNAMIC cof as a function of starting speed as compared to the length of skid. Because the transient time between when braking starts and when full braking skid begins is a LARGER portion of the total skid length for slower starting speeds than for higher, your derived cof is necessarily in error and that error causes a non constant cof exemplar for you to work with. For example, if the starting speed is 20 MPH, then the CALCULATED DYNAMIC cof is about 1.25 when an actual measurement of that cof is only .82. (What, pray tell, kind of surface do you know of that has a dynamic cof as high as 1.25?)
Here is a chart to demonstrate how much your calculated cof varies from measured values based on vehicle speed.
Finally, your assertion that
quote:
a skidding vehicle does not actually decelerate at a constant rate, but at a lower rate in the beginning than at the end of a skid mark.
Is entirely disproved by the first diagram I provided earlier
which is an accurately MEASURED deceleration curve.
Making very strong claims that someone else is 'flat wrong' is probably not the best way to further your point of view. |
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WAC
Starting Member
4 Posts
Stoke on Trent, Staffordshire
United Kingdom
Honda
VF1000RF
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Posted - 03/23/2007 : 11:17 AM
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James: Thanks for re-posting the graph here.
I may have unintentionally misled you when I mentioned 0.7g. I meant to refer to the DYNAMIC portion of the curve, rather than the STATIC portion.
In effect, I wonder whether a motorcyle (skilled rider, high level of front braking without wheel lock, maintained for some time) might have a STATIC portion of the graph which is rather longer than that illustrated in the SAE paper example. This, it seems to me, would render the "average" dynamic deceleration approach likely to UNDER estimate speed loss.
Here, we seem to have a roughly two second locked wheel time, if I read the information correctly. Is this typical for a bike?
Scott: Noted and fully understood. Personally, I was amazed at how hard the road was when I tapped it with my teeth... |
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James R. Davis
Administrator
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Posted - 03/23/2007 : 11:50 AM
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The chart is representative of a full lock skid. It could easily be of a motorcycle's REAR tire but it simply could not be of a motorcycle's front tire.
Using a .70 dynamic cof you could easily go back to my example and assume a static cof of approximately 1.0 and then assume something like a .98 threshold braking effort instead of .68 in order to do your analysis.
I believe that I have seen a study indicating that it takes at least 1/4 second for a motorcycle to fall to its side during a front wheel lock skid. If the bike was dead vertical at the time that a front wheel skid began, and NO FURTHER STEERING INPUT WAS EXPERIENCED (such as a sloping roadway), then it is possible to release the front brake and recover from the lock. But it is highly unlikely that steering input would NOT be experienced during the skid so you can reliably predict that the rider will quickly be eating asphalt as a result of locking the front brake. |
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WAC
Starting Member
4 Posts
Stoke on Trent, Staffordshire
United Kingdom
Honda
VF1000RF
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Posted - 03/23/2007 : 12:06 PM
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quote:
Using a .70 dynamic cof you could easily go back to my example and assume a static cof of approximately 1.0 and then assume something like a .98 threshold braking effort instead of .68 in order to do your analysis.
This is just the point that I was attempting to get to; thanks. Formal research references anyone? |
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