By David Daggett
(Disclaimer: The author doesn’t claim to be now, nor has he ever been, a collision reconstructionist. While having prosecuted many cases involving the science – and having once stayed at a Holiday Inn Express – he has nonetheless always relied upon the expertise and tutelage of crash investigators when prepping for trial. This article is designed with two objectives in mind: (1) help familiarize prosecutors with some of the very basics of crash reconstruction; and (2) point out to crash investigators some factors that can be beneficial to prosecutors in proving the requisite degree of negligence/recklessness.)
This article is a continuation from last month’s article.
Coefficient of Friction (Drag Factor)
Coefficient of friction, at its simplest, means the amount of friction that exists between a particular road surface and the tires traveling over it. For example, a road surface covered by a sheet of ice would have a drag factor on the lower end of the friction scale while a dry, newly-paved, asphalt surface would be at the higher end. It is imperative to know the coefficient of friction of the road surface at the scene of the crash, as that is one of the factors necessary to calculate an accurate stopping distance as well as helping to determine speed.
There are a number of methods that can be employed to determine coefficient of friction, including: (1) the use of a drag sled; (2) use of your State Highway Administration’s Pavement Friction tester; (3) using established average drag values for certain type of surfaces; and (4) driving a vehicle at a known speed over the roadway at the crime scene, locking the brakes and measuring the skid marks. The first seems to be the most common; the second is probably the most accurate and least assailable; the third is the easiest; and the fourth is the most fun. Whatever method used, it should be done under similar weather and roadway conditions that existed at the time of the crash, if possible.
There is an industry paper (Society of Automotive Engineers) currently in vogue that discusses averages, ranges and standard deviations and seems to be “gaining traction” in the field. Sorry. I couldn’t help myself.
Be sure to clarify with your reconstructionist as to how the coefficient of friction was determined in your case. If the drag sled method was employed, consider having two reconstructionists separately conduct friction tests and taking the average of the two. This seems to be an area commonly attacked by defense attorneys and defense experts and if successful, can call into doubt many of your calculations, including speed.
One formula using the skid test method in determining coefficient of friction is shown below. “S” represents speed; “d” is the length of the skid mark (distance); and “30” is an algebraic figure that remains constant no matter what speed is used in the numerator (Don’t ask me, ask Isaac Newton):
Using the fourth method (above), have your investigator drive his or her patrol vehicle at a known, fixed speed, at or near the crime scene and under similar roadway conditions, lock up the brakes and measure the length of the skid. For example, at 45 MPH, the formula might read:
Certainly, the same formula can used while driving at a slower speed, which will obviously result in shorter skid marks. It goes without saying that it is safer when conducted at lower speeds.
Whenever possible, try and arrange to have your local State Highway Administration come out and test the area of road where the collision took place. That would seem to be the most accurate measurement and the least susceptible to defense attack.
This formula is used to determine the distance it would take a vehicle to stop when the speed and friction/drag factor are known. The speed might be determined by use of EDR data, for example. “S²” is speed squared; “30” is an algebraic constant and “f” is the known friction:
A vehicle traveling 45 MPH over a roadway with a coefficient of friction of .84 would require roughly 80.36 feet to come to a halt, absent any intervening factors. This particular formula comes in handy when the area of impact and speed are known and the defendant is exceeding the posted speed limit. By way of comparison, if the speed limit on the roadway was actually 25 MPH, you can use a combination of this formula and the distance during reaction time to determine if the collision could have been avoided altogether.
When factoring in the additional 46.91 feet the defendant traveled during his perception and reaction time as a result of driving 20 MPH over the posted 25 MPH limit (1.466 x 25 MPH x 1.6 sec = 58.64 feet versus 1.466 x 45 x 1.6 = 105.55) the evidence would show that, had the at-fault driver been doing the posted speed limit, he would have had an additional 102.47* feet with which to avoid striking the victim. That shows negligence, and negligence of some degree is an essential element in most DUI Homicide cases.
* 105.55 – 58.64 = 46.91 80.36 – 24.80 = 55.56 46.91 + 55.56 = 102.47 Feet
This is a basic formula that is used when the coefficient of friction and the length of the skid marks are known and you want to determine speed. In this formula, “f” is the friction of the roadway, “d” represents the distance of the skid marks and “30” is a constant algebraic figure. For those of us who’ve not used math for some time, 45 is the square root of 2025.
Total Stopping Distance
Once speed, coefficient of friction and reaction time have been determined, the following formula is helpful in determining how far a vehicle would travel from the time the driver should have first perceived the danger, reacted to it and braked to a complete stop. It looks a lot more complicated than it is.
If you’ve been paying attention you know that v = velocity, t = reaction time for an average, sober driver, s² = speed squared, f = coefficient of friction and 30 is an algebraic constant. By plugging in our known figures the formula looks like this:
This equation is extremely powerful evidence when contrasted with the figures for a driver doing the proper speed limit and especially if you are able to factor in the additional slowed reaction time of an impaired driver. That is why it is imperative to have a toxicologist provide expert testimony regarding the effects of alcohol and certain drugs on a driver’s motor skills and coordination. To do this, simply do a side by side comparison of an average, sober driver obeying the speed limit (25 MPH) with a 1.6 second reaction time versus the impaired driver doing 45 MPH with an additional half-second or even full- second perception-reaction time:
- Average, sober person driving the speed limit of 25 MPH (.84 C of F):
83.44 feet to stop, including 1.6 seconds of perception and reaction time.
- Impaired driver at 45 MPH at 1.6 seconds of perception and reaction time:
185.91 feet to stop.
- Impaired driver at 45 MPH and adding 1/2 extra second for delayed P-R time:
218.90 feet to stop.
- Impaired driver at 45 MPH and adding 1 extra second for delayed P-R time:
251.88 feet to stop.
These contrasting figures will undoubtedly impact the fact finder in showing negligence on the part of the defendant. It is also helpful in situations where the victim might have pulled out in front of the impaired driver and the defense argues that it was therefore the victim’s negligence that caused the collision, not the defendants.
Speed at Impact
While this equation appears to be a bit more complicated, if I can figure it out, anyone can. Speed at impact is used to determine at what speed a vehicle would have been traveling when it collided with an object at a particular point in the skid. This is helpful when the defendant is claiming that he was only doing 30 MPH prior to hitting his brakes, yet the victim’s vehicle looks like it was hit by a tractor-trailer. For purposes of this equation, “V” is velocity; “f” represents friction; “d” equals the distance of the skid; and “g” equals gravity, which is the 32.2 figure. I have no idea how, or by whom, that figure was derived. Newton? Einstein? Kardashian? Ask your crash investigator to explain it to you. We already know that a vehicle doing 45 MPH would require 80.36 feet to stop (given a C of F of .84). In this example, let’s assume that the at-fault vehicle collided with a stationary object after laying down 30 feet of skid.
As the 52.24 figure represents feet per second (velocity), in order to convert it to MPH it must be divided by 1.466. Thus, the vehicle would have been traveling 35.63 MPH at impact, which is certainly helpful in impeaching the defendant’s story that he was only doing 30 MPH prior to hitting his brakes.
While these are just some of the simplest and most basic of equations, they are also among the more common and easily explainable to the fact finder. If the crash investigator and prosecutor can explain these to the jury in a clear and concise fashion, you will have a leg up on proving your case. If not, you might just as well be speaking Klingon and you’re liable to hear snoring reverberating throughout the courtroom.
Other Items of Interest
Anti-lock Brakes – Many newer model vehicles come equipped with anti-lock brakes, which can cause some issues with tire/skid marks. The theory behind anti-lock brakes is fairly simple – a skidding wheel (where the tire contact patch is sliding relative to the road) has less traction than a non-skidding wheel. By keeping the wheels from skidding while you slow down, anti-lock brakes allow the vehicle to stop faster and to enable the driver to steer while the vehicle comes to a stop. Since the tires are spinning, they won’t necessarily leave the same roadway markings as locked tires. Ask your crash investigator to explain to you if anti-lock brakes are part of his investigation and what, if any, part they played in the crash analysis.
Braking efficiency – This, in its simplest terms, is the percentage of overall braking that each wheel employs in a particular braking situation. This is usually dependent, among other things, on the amount of weight that is shifted to or from each wheel; on the mechanical condition of the brakes; whether the vehicle is front or rear wheel drive; whether the wheels were all braking on the same surface, as well as other factors. Braking efficiency can certainly play a factor in the equations listed above and you need to be aware of how they factor in.
Qualifying your Collision Reconstructionist as an “Expert.”
Your reconstructionist should maintain and provide you with an updated curriculum vitae well in advance of trial. A copy must be provided to the defense attorney, along with the final crash report and an expert witness letter. The prosecutor should enter curriculum vitae into evidence upon qualifying your witness as an expert. It can’t hurt to let the jury see, as well as hear, all of the special training he or she has received.
If the case works out to be a plea, ask the defense attorney if they will stipulate that the reconstructionist would have been declared an expert in the field. If they so agree (and they usually will) make sure to include that stipulation into the Statement of Fact. Be sure to notify the reconstructionist that this was done. This will allow them to update this case to their CV and will make it that much easier to have them certified as an expert in the field the next time they appear in court.
As I have tried to stress throughout this article, Crash Reconstruction can be a very difficult concept to grasp – both for the prosecutor as well as for the fact-finder. It is imperative that the crash investigator and prosecutor set aside a large block of time to go over this aspect of the case and determine the best, and simplest, strategy in presenting the evidence.
Speed and impairment usually play a part in these type cases. Making good use of your reconstructionist and your toxicologist will enable you to present those necessary elements of the crime to the fact-finder. Good luck
AS ALWAYS, PLEASE CONSULT WITH YOUR LOCAL STATE’S ATTORNEY’S OFFICE FOR ANY LEGAL ADVICE RELATED TO THIS SUBJECT MATTER