Archive for December, 2009

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