HALL - CARPENTER, CO.
By Edwin T. Scallon, Copyright © 1990, 1995, 2008 All Rights Reserved
ACCIDENT RECONSTRUCTION AND BAC CALCULATION PROGRAMS
MINIMUM SPEED FROM SKID MARKS
As the name implies speed from skid marks will provide the investigator with the vehicle's minimum speed. Unlike critical speed which provides the investigaor with the exact speed of the vehicle, minimum speed is just that. What that means simply, is that the vehicle could not possibly be going any slower than the calculated minimum speed, but the vehicle's actual speed might be faster. If the vehicle ends up in a collision with anything, such as another motor vehicle or a rigid object, the vehicle's crush or deformation will be added to the minimum speed in calculating the vehicles speed. In that event we will use the combined speed formula. Likewise, if the vehicle skids between different surfaces such as from asphalt onto grass, the drag factor both surfaces must be measured and included in the combined speed formula. Also, in the same vein if the left side tires were skidding on asphalt and the right side tires were skidding on a different surface, like grass, we then utilize a speed formula derived by changing the constant to 1/2 that of the minimum speed formula and then adding the two different drag factors, one for the asphalt road for the right tires and the drag factor of the grass surface for the left tires..
The minimum speed formula is derived from a more complex algebraic formula and you should be familiar with the derivation of the minimum speed formula so you can visualize the mathematical progression.
The formula is based on known Kinetic Energy formula of Ke=1/2m*(v2)
Ke = Kinetic energy or energy in motion
g = Acceleration of gravity or 32.2 fet per second squared
w = weight in pounds
S = Speed in miles per hour (Mph)
v = Velocity in feet per second (Fps)
f = Drag Factor (Coeficient of Friction)
d = distance in feet
m = Mass, which is the same as the weight of an object dividedby the acceleration of gravity (m=w/g)
30 = A constant that arises in the proess of derivation
1.466 = Feet per Second. A conversion factor of a mile = 5280 feet divided by time in seconds (60 minutes *60 seconds)
Now for the derivation:
First make a conversion from miles per hour to feet per second. This is used in every formula derivation.
In a skidding vehicle energy is equal to firctional force. The frictional force is equal to the weight of the vehicle ressing down on the sliding tires (w) times the drag factor of the road (f) times the distance infeet the vehicle will slide (d)
Ke=1/2m(v2)
Ke=wfd
1. So a skidding vehicle wfd = 1/2m(v*v)
2. Change m to w/g and divide out w
wfd/w = 1/2 w /g v2 /w which leaves
fd = 1/2 * 1/g * v2
fd =1/2g * v2
3. To get v2 alone multiply both sides of the equation by 2g
fd= 1 v22 / 2g 2g/1
v2 = 2g fd
4. We will change g to 32.2 and multiply it by 3 which changes 2g into 64.4
v2 = 64.4 fd
Next v2 is changed to miles per hour
(S * 1.466)2 = 64.4 fd
Next, squae 1.466 and divide out 2.149 to get S alone
5. S2 * 2.149/2.149 = 64.4 fd / 2.149 which leaves
√S2 = √30 fd
Now extract the square root from each side of the ewuation
6. S = √30df +/- f *be
So we have a formula for minimum speed which is Speed = Square root of 30 times Distance skidded time the Drag Factor and if using the chart +/- road grade. If you you used a drag sled or determined speed using a vehicle, then the grade does not come into play. However, be is the breaking efficiency of the vehicle. If all four tires are locked and skidding you have 100% breaking efficiency so the be = 1. Each front tire has a breaking efficiency of 30% each for a total frontal breaking efficiency of 60%. The rear tires have a breaking efficency of 20% for each tire for a total breaking efficiency of 40% for the rear tires.
For Example, in the drag factor section we determined that our asphalt rural rode had a drag factor of 0.8 Now we measured the tire marks and the length of the tire marks are 120 feet long. Since all four tires were locked and skidding we have 100% breaking efficiency. Using the minimum speed formula we find
S = √ 30 * 120 * 0.8
S = √ 3600 * 0.8
S = √ 2880
S = 53.66 Mph
The formula for a vehicle tires skidding on two surfaces at the same time, like the example above where the right tires are skidding on asphalt and the left tires are skidding on grass calculate the drag factor for both surfaces by pulling the drag sled in the same direction as the skid and utilize the below formula:\
S = √15 * (f1 + f2) * D
Let's assume that the left tires are skidding on the same 10 year old rural asphalt road with a drag factor of 0.8g and when we measured the drag factor of the gtrass we find it has a drag factor of 0.5. and the skids marks are 120 feet long. Using the above formula we can calculate the minimum speed of this vehicle.
S = √15* (.08 + .04) * D
S= √15 * (1.2) * 120
S = √2160
S = 46 Mph
Now rather than a drag sled you utilize test skids using a vehicle. For this example we will drive a calibrated vehicle, which is one that has been tested with a radar gun to verify the speedometer is accurate. We then drive the vehicle at a constant speed, which is arbitrary, so lets drive it at 60 Mph. Once the vehicle is traveling a constant 60 Mph in the direction of the skid, the vehicle's breaks will be applied which causes all four wheels to lock and begin skidding. After the vehicle comes to rest, measure the length of the skid mark, for this example we skidded 5 feet, now input that data into the below formula:
f = S2 /30 D
f = 602 * 30 * 120
f = 3600/30 * 5
f = 3600/300
f = 24 Mph
For the next example, let's assume that the vehicle traveling on this 10 year old rural asphalt road skids for 20 feet on the asphalt then goes off the road onto a grass field and continues to skid for an additional 30 feet. Again the drag factors for both surfaces are determined. For this example we will use 0.8g for the asphalt surface and 0.4 for the grass surface. We have determined that all four wheels were locked and skidding through out the entire skid. We would then use the Combined Speed formula below to find the vehicle's minimum speed.
St = √S12 + S22
Total speed ( St ) is the speed of the vehicle using the square root of the first calculated minimum speed of the vehicle on the asphalt and added to the calculated minimum speed of the vehicle on the grass surface. The first thing is to determine the minimum speeds using the minimum speed formula, above:
S1 = √30 * D *f S2 = √30 * D * f
S1 = √30 * 20 * .08 S2 = √30 * 30 * 0.4
S1 = √480 S2 = √360
S1 = 21.9 S2 = 18.97
Now using the combined speed formula we find:
St = √S1 + S2
St = √21.9 + 18.97
St = √408.7
St = 22 Mph