Archive for the ‘Todd Hutchison’ Category

Speed Calculation in a Motorcycle Accident

Friday, December 18th, 2009

“I never saw him, he came out of nowhere, he must have really been flying” are common familiar sayings in motorcycle accidents. This article deals with the vault formula and slide to stop method for calculating the speed of a motorcycle involved in a crash where another vehicle pulls out in front of an oncoming motorcycle. In crashes where the front of the motorcycle impacts into the front or rear sections of an automobile, pickup or some object that allows the rider to vault over the handle bars and continue flying through the air until it impacts the ground, the vault formula method may be used.

In cases where the motorcycle impacts into a large vehicle where the occupant does not clear the collision area such as when it impacts into a semi tractor or trailer, the formula can not be used.  An example of the type of impact where the vault formula can be used is seen in diagram 1.

In order to calculate the departure speed of the motorcycle operator several bits of information are needed:
  • The horizontal distance that the operator travels from the point of impact to the first touch point on the roadway and the final rest location
  • The departure/takeoff angle of the motorcycle operator
  • The height of the center of mass of the motorcycle operator above the first touch point
  • The coefficient of friction between the operator’s clothing and roadway surface
The distance needed for the vault portion of the calculation is the horizontal distance from the location where the motorcycle operator is located at the point of impact with the car, pickup truck or object to the point on the roadway or grass where the driver or rider lands.  The distance needed for the slide to stop portion of the calculation is the horizontal distance from the location where motorcycle operator first touches the ground to its final rest position. Sometimes there is good evidence on the roadway apparent at the scene investigation of where the motorcycle operator impacted the ground and many times there is not. A thorough scene inspection at the earliest time after the accident by a trained eye will have the best opportunity to find this evidence. A scale diagram will normally be made to document the impact point, final rest locations and other pertinent information from which measurements can be made to determine the proper distances for the calculations.

The takeoff angle for a motorcycle operator is generally between 10 to 20 degrees. The takeoff angle for the passenger varies depending on the type of motorcycle and operator position of the particular accident and can be as low as 18 to 20 degrees and  as much as 45 degrees.

When making the field measurements with total station technology or other methods, (steel tape and level) elevation changes between the roadway at the point of impact and the landing point need to be made. This will allow an accurate measurement of the vertical  distance that the operator traveled from the point of impact to the first touch point.

Adding the height of the center of mass of the driver (located usually at the belly button point) from the top of the seat height of the motorcycle will give the  starting height at the point of impact. Subtracting the elevation change to the ground level and then adding ½ the thickness of the body will give the height above the ground distance needed in the calculation. An estimate can be made by bracketing the distance if the exact height is not known.
The formula is as follows:


V = feet per second
g = acceleration due to gravity (32.2 feet per second squared)
d = total horizontal distance
A = components of 15º departure angle
Y = vertical height of driver or rider (negative value if below takeoff point)

Be sure to convert the feet per second calculated value to miles per hour by dividing feet per second by 1.467. After calculating the vault speed, the next calculation checks the calculation by calculating the slide to stop speed from the first touch point to the final rest point. Measure the distance from the first touch point to the final rest of the operator. Use the measured distance in the slide to stop formula and compare the answer with the vault speed. If the two speeds are roughly the same it’s a good indication that the answer is valid.

Slide to stop formula:

S = √ (30df)

S = √ (30*37.5*1)

S= √ 1125

S = 33.54 mph


S = miles per hour
d = total horizontal distance of motorcycle driver or rider slide
f = coefficient of friction of motorcycle driver or rider (either sliding or tumbling based on                                    injuries and scene data)
g = gravity (32.2 feet per second squared)

Studies show that the coefficient of friction between the operator’s clothing and the roadway surface for cotton/ wool and polyester is between .7 to .85 g’s and for leather is between .6 to .7 g’s. When a body does not slide but tumbles the coefficient of friction is approximately 1.0 or higher. There may be a combination of sliding and tumbling so the slide to stop coefficient of friction may vary.

By using this method a calculation can be done with the vault formula and then the slide to stop calculation can  be done to check the vault speed. If the distance used in the vault formula produces a speed that is consistent  with the speed from the slide to stop formula then that speed is how fast the motorcycle was traveling at the point of impact. If the speed from the vault formula is to high to produce a speed low enough to match the slide to stop speed then use a shorter distance for the vault and a longer distance for the slide to stop formula. Narrowing in on the right distance by trial and error, the investigator will be able to find the solution that fits both equations and   that is the approximate speed that the motorcycle was traveling when the impact occurred.

After calculating the motorcycle’s impact speed then use the skid to stop formula using the pre-impact skid distance of the motorcycle to obtain the skid-to-stop speed for the pre-impact skidding of the motorcycle. Then take that answer and combine that speed with the impact speed of the motorcycle by using the combined speed formula to calculate the start of skid speed of the motorcycle. The combined speed formula is as follows:

The combined speed formula

S = √ (S1²+S2²)

Example:   Motorcycle pre-impact skid distance is 34.6 feet. The coefficient of friction used in the calculation is .7 g’s. Assume that the motorcycle is able to obtain 100% of the coefficient of friction.

Slide to stop:                            Combined Speed:

S1 = √ (30*34.6*.7)                  S = √ (33.5²+26.9²)

S1 = √726.6                             S = √ (1122.25+723.6)

S1 = 26.95                                S = 42.96 mph

The start of skid speed of the motorcycle in this case is approximately 43 mph.

Todd Hutchison

Conservation of Linear Momentum

Friday, July 24th, 2009

The Conservation of Linear Momentum method is a well established scientific too utilized by the reconstructionist to determine the impact speeds of vehicles involved in collisions. It is one of the many useful techniques that an accident reconstructionist has at their disposal. Others include Conservation of Energy, Critical Speed Analysis, and the Crush Factor Method. Conservation of Linear Momentum utilizes several inputs that require careful evidence collection and analysis. Additionally, some of these inputs are more sensitive than others depending on the particular situation. Next we will list the inputs and discuss some of the methods used for determining the proper value to use.

Needed Inputs:
  • Angle at Start of Post Impact Rotation
  • Angle at End of Post Impact Rotation
  • Lock-up value per Wheel
  • Weight distribution per Wheel
  • Post Impact Drag Factor
  • Post Impact Travel Distance
  • Grade in Area of Post Impact Travel
  • Approach Angle
  • Departure Angle
  • Total Weight
Accurate documentation of the vehicles, roadway, and crash scene markings is necessary. This can be done with total station technology or some other accurate method of measurement. A drag sled can be used to determine drag factors on various surfaces. Other methods such as skid tests or drag factor tables in certain instances are necessary. This documentation which is used to make an accurate scale diagram is then utilized to obtain values for the above variables. Data from the vehicle and crash scene markings will be used to determine the inputs for the lock up factor which in turn will be used for the departure speeds. Other values like the weights of the vehicles are normally obtained from professional databases like expert auto stats and then combined with the estimated weights of the occupants and cargo.

Conservation of Linear Momentum analysis, which is a scientifically sound method used by reconstructionists for calculating impact speeds and other information about crash vehicles, yields good information when proper data is inputted. The method requires several inputs some of which may be sensitive. Consequently, it is imperative that a detailed analysis and an experienced professional evaluation of the data be performed to obtain accurate results.

Todd Hutchison

The Skid Mark / Crush Factor Method

Thursday, February 7th, 2008

When investigating an accident a common question that arises is, “How fast were the vehicles going?” If the skid distance of the striking vehicle and the maximum crush depth of the target vehicle are known, a simple estimate of the speed of the striking vehicle can be made. This is done by determining the impact speed of the striking vehicle by measuring the maximum crush depth of the target vehicle and inputting the distance in the Crush Factor Formula.

The Minimum Speed Formula uses the pre-impact skid distance of the striking vehicle and the roadway drag factor.

Both the Crush Factor Formula and the Minimum Speed Formula are then combined in the following way to determine the Striking Vehicle Start of Skid Speed.

30 - Mathematical Constant in the formula

d1 - Striking Vehicle’s Pre-Impact Skid Distance (measured in feet). Note: Measure the skid marks from the start to the point of impact (offset in the mark) and then subtract the wheelbase (front to rear axle distance of the skidding vehicle) from the skid distance.

f - The adjusted drag factor of the vehicle leaving the skid marks on the roadway surface. Note: if the vehicle is a passenger car, van, SUV or pickup truck and all four wheels left skid marks and the roadway was level, the roadway coefficient of friction is the vehicles drag factor. For a dry traveled asphalt surface the coefficient of friction is usually within the range .6 to .8 g’s. If the roadway surface is wet or has gravel on it, the coefficient of friction can be significantly less.

d2 - The target vehicle’s maximum crush depth (measured in feet from the normal undamaged position to the maximum permanent crushed position) of either the side or rear surface. Note: this calculation can not be used for head on collisions. This may only be used for t-bone or rear end collisions.

cf - The crush factor of the target vehicle is vehicle specific, but the average crush factor for the side and rear surface is 27. The crush factor values are based upon statistical analysis of 1000 vehicles involved in accidents where the speeds of the vehicles were verified by independent means.

The following example illustrates how the combined speed formula works:


The striking vehicle left 59.5 feet of pre-impact skid marks and had a wheel base distance of 9.5 feet. Subtracting the wheelbase distance from the total skid mark distance gives a pre-impact skid distance of 50 feet. The skidding occurred on a roadway that was level, dry asphalt. The drag factor was measured to be .7 g’s. The vehicle impacted into the side of another car and left 18 inches (1.5 feet) of permanent crush damage.

The combined formula was used to determine the start of skid speed.

This formula works as an approximation of the start of skid speed for situations where one car, van, SUV or pickup truck impacts into the side or rear of another car, van, SUV or pickup truck. This is a relatively easy way to determine if the vehicle was traveling in excess of the speed limit and to decide whether or not a more detailed accident reconstruction would be helpful. This simple estimate of the striking vehicle speed and the speed of the target vehicle can be confirmed by the conservation of linear momentum method. In collisions that involve vehicles that impacted either head-on or head-on at an angle, this skid mark / crush factor method can not be used. In those cases either conservation of linear momentum or some other method needs to be used to determine the speed of the vehicles.

Todd Hutchison

Tractor / Trailer Turning Maneuvers and Turn Times in Night-Time Accidents

Wednesday, November 7th, 2007

Tractor trailers usually take three times as long or longer to accelerate as a regular passenger car. That coupled with the large bulky structure of a tractor trailer unit makes for a very long acceleration time to clear an intersection once the tractor trailer starts to pull out onto a roadway. The fact that the trailer wheels do not track directly behind the tractor wheels when a turn is being made means that a wider then normal turn has to be made in many circumstances. This can lead to the tractor going partially off of the roadway as it’s making the turn before straightening up in its intended lane. All of these factors need to be considered when trying to analyze just how the accident occurred and just what would be visible to the oncoming motorist during night time accidents. The following discusses the approximate turning times and tractor paths throughout the turn and the headlight visibility and orientation to the oncoming motorist through the turn.

 Studies show that average acceleration factor for a tractor trailer is approximately .05. That is an acceleration rate of 1.6 feet / second / second. This means that the first second the truck accelerates a distance of 0.8 feet, after 2 seconds it has accelerated a distance of 3.22 feet and after 3 seconds it has accelerated a distance of 7.25 feet. This shows that as times goes on the vehicle is accelerating to a higher speed and is gaining speed and covering a greater distance each second. So as seen in the table below if a truck accelerates for 10 seconds from the time that it starts until it reaches the point of impact it travels a total distance of 80.5 feet. The first 3 seconds it only travels 7.25 feet but the last 3 seconds it travels a distance of 41.06 feet.












Distance Total

From Start

1 =



2 =



3 =



4 =



5 =



6 =



7 =



8 =



9 =



10 =




 Depending on the roadway configuration and the amount of available sight distance the oncoming motorist may only see a portion of the truck’s total turn time prior to the impact occurring. What is important to know, in an accident where the oncoming vehicle runs into the side of a trailer, is where the oncoming motorist is located and where the tractor / trailer is positioned when the motorist could first see it. For instance if at a certain speed the motorist can see the tractor / trailers acceleration for the last 6 seconds from the time it travels from 12.88 feet to 80.5 feet, the motorist should be able to see that a tractor / trailer is entering the roadway and should start to slow down and be more attentive to the roadway. If, however, the sight distance limits the oncoming motorist’s view to only seeing the last 3 to 4 seconds of the tractor / trailer acceleration, the angle of the headlights might be such that the glare could veil the side of the trailer so that it might not be very conspicuous. It may appear to the oncoming motorist that there is just another vehicle approaching in the opposite direction not realizing the impending danger of a trailer angled across the their lane just beyond the headlights. This is where a thorough investigation determining the roadway geometry, the tractor / trailer acceleration characteristics, and the approaching motorist speed becomes necessary in properly analyzing this type of accident.

 A scene investigation using a total station or some other acceptable means of measurement to make a scale diagram is needed along with information concerning the acceleration characteristics and speeds of the involved vehicles. An acceleration test with the same or similar type of tractor / trailer and load that was involved in the accident can help determine the acceleration rate of the vehicle involved. A speed calculation can usually be done of the approaching vehicles speed by either crush damage analysis, speed from skidding or a combination of the two. Remember the important factor is what each of the motorist could see and at what point they could see it.


Todd Hutchison 

Accident Reconstruction: The Scene Investigation

Friday, August 17th, 2001

Accurate measurements mean accurate answers. If the at-scene investigation is done in a proper manner, it will assist the accident reconstructionist in determining the contributing factors to the accident. That is why the investigator who gets to the scene early on, while the physical evidence is fresh, is so important to the overall process of determining who is at fault. If the accident is serious enough it is best to have the accident reconstructionist do the at-scene investigation. If not, it is sometimes necessary to have adjusters or accident technicians to gather and record the physical evidence. In the event someone other than the accident reconstructionist gathers the scene evidence, that person may be needed to testify if the case goes to court. Since the majority of smaller dollar value cases do not go to court, the scene evidence gathering may be effectively done by someone other than the accident reconstructionist.

The first people on the scene include police officers, emergency technicians, special investigative units and in a perfect world, the accident reconstructionist. If the accident involved a fatality or had serious injuries the police investigators may be more thorough in their documentation of the scene data. This is usually the best opportunity to see the roadway markings while they are fresh. Some evidence such as debris patterns and anti-lock skid marks, etc. are short lived and is best seen at this time. During this part of the  investigation the traffic is stopped and the investigator has time to log more information.

The second type of investigator that arrives on the scene, including insurance adjusters, private investigators, and accident reconstructionists, can still gather much useful evidence. Even though some evidence might be gone, other evidence can be gathered and used together with the police measurements and at-scene photographs to determine what happened.

Types of evidence that can be gathered include the location of pre-impact skid marks, offset marks and gouge marks. If gathered properly, these can help the accident reconstructionist to determine the pre-impact direction and speeds of the vehicles, the types of evasive action used by the drivers and ultimately who was at fault in the accident.

The Scene Investigation

“Safety First” is the phrase that needs to occupy the thoughts of the investigator the entire time the investigation is being done. Even though this slows down the investigation, obviously it is a necessary component to being available for the next assignment. Though the scope of this paper is not to show
methods to follow when conducting a scene investigation in a safe manner, it is a reminder to use proper safety methods. Remember the investigator is out there to gather evidence and not to cause another accident. When arriving at the scene be sure to park completely off of the roadway and as far off the
shoulder as possible. Be visible with proper safety equipment, including safety vests and always be thinking “Safety First”.

Once at the scene and after remembering “Safety First”, size up the scene and decide what needs to be logged and preserved. The physical evidence can be extremely helpful in assisting the accident reconstructionist in his job. This evidence includes pre-impact skid marks, which will show the
direction of travel and assist in determining the speeds of the vehicles and offset skid marks and gouge marks, which help to show where the impact occurred. Other useful information includes scratch marks, oil or fluid spills, which can be helpful in determining the vehicles final rest positions. When using
conservation of linear momentum calculations to determine vehicle speeds, the impact and departure angles and distances are necessary. A good scene investigation will help with this. This field data will then be put on a scale diagram and through computer analysis, angles and distances can accurately be made.

In addition to taking good photographs that visually recording the physical evidence, there are two methods
most commonly used to log the data on a field sketch. These are the coordinate method and the
triangulation method. These methods utilize either electronic measuring equipment, steel tapes, or in some cases roll tapes.

The coordinate method uses one reference point, such as a utility pole or fire hydrant and a reference line such as an edge of pavement or painted line. It also uses the direction the measurement is taken from
using north, south, east or west. A field sketch is useful as a picture to show what items were logged and what measurements were made. Be sure and put on the sketch what reference point and reference line were used for the measurements and what direction is north. Once the reference point, reference line, and the north direction are established, and once the pertinent marks are put on the field sketch, the measurements can be made and logged on that sketch. These marks will be logged in relationship to the point on the reference line that is perpendicular to the reference point. Each point being located will have two
measurements. Each point needs to be measured to determine how far it is north, south, east or west from the zero point measured along the reference line and how far north, south, east or west it is away from the reference line. Record all measurements in feet and tenths of feet.

The other method used to log roadway markings is the triangulation method. This involves locating two
reference points and making measurements from each reference point to the point that is being located. In using this system, it is necessary to have two points that are separated and in an area that can best log all of the marks. These reference points need to be far enough away from each other longitudinally down the road and latitudinal across the road to give the best results. Since this type of method is done by using some form of electronic measurement device or two people, each holding one end of the tape, it is usually
more practical to use the coordinate method.

Todd Hutchison