Speed from Skids (Pre-braking Speed)

This equation is used to estimate the minimum speed a vehicle was travelling before skidding to a stop. The pre-braking speed can be estimated using the length of the skid marks and the Coefficient of Friction* of the road surface.

Explanation:

Speed = √(30 x Coefficient of Friction x Distance)

or

S = √(30 x f x D)

Where:

S = Pre-Braking Speed (mph)

30 = Conversion factor (converts feet per second to mph)

F = Coefficient of Friction of Roadway Surface

D = Distance (length) of longest skid mark (feet)

* The coefficient of Friction quantifies the amount of adhesion between the road surface and the vehicle's tires. Slippery roads (wet, icy, etc.) have lower Coefficients of Friction than dry road surfaces. A range of Coefficients of Friction should be used to achieve a realistic range of answers.

Example Calculation:

A car left 150 feet of skid marks on new Portland cement before coming to a stop in an intersection. How fast was it travelling before braking?

Low : S = √(30 x f x D) = S = √(30 x 0.7 x 150) = 56 mph

High: S = √(30 x f x D) = S = √(30 x 0.95 x 150) = 65 mph

Answer: 56-65 mph

COEFFICIENTS OF FRICTION OF VARIOUS ROADWAY SURFACES DRY WET

ASPHALT OR CONCRETE From 0.70 to 0.95 From 0.40 to 0.75

GRAVEL From 0.40 to 0.80 From 0.40 to 0.75

SNOW From 0.10 to 0.35 From 0.30 to 0.60

ICE From 0.07 to 0.20 From 0.05 to 0.10

Stopping Distance from Speed

This equation is used to estimate how far it takes a vehicle to stop from a given speed with a maximum (100%) braking force. The stopping distance can be estimated using the speed before braking and the Coefficient of Friction* of the road surface. This equation is a rearrangement of the Speed From Skids equation.

Explanation:

Braking Distance = (Pre-Braking Speed)^2 / (30 x Coefficient of Friction)

Or: D = (S)^2 / (30xF)

Where:

D = Stopping Distance (feet)

S = Pre-Braking Speed (mph)

30 = Conversion Factor (converts feet per second to miles per hour)

F = Coefficient of Friction

*The Coefficient of Friction quantifies the amount of adhesion between the road surface and the vehicle’s tires. Slippery roads (wet, icy, etc.) have lower Coefficients of Friction than dry road surfaces. A range of Coefficients of Friction should be used to achieve a realistic range of answers.

Example Calculation:

A vehicle is traveling at 65mph on wet Asphalt. How far would it take the vehicle to come to a complete stop?

Low: D = (S)2 / (30xF) = D = (65)2 / (30x0.75) = 188 feet

High: D = (S)2 / (30xF) = D = (65)2 / (30x0.40) = 352 feet

Answer: 188 – 352 feet

COEFFICIENTS OF FRICTION OF VARIOUS ROADWAY SURFACES DRY WET

ASPHALT OR CONCRETE From 0.70 to 0.95 From 0.40 to 0.75

GRAVEL From 0.40 to 0.80 From 0.40 to 0.75

SNOW From 0.10 to 0.35 From 0.30 to 0.60

ICE From 0.07 to 0.20 From 0.05 to 0.10

Distance Traveled During Perception & Reaction time

This equation is used to estimate the distance a vehicle travels during the time it takes the driver to perceive and react to an impending hazard. The normally accepted range of Perception and Reaction time is 1 and 1.5 seconds. If this occurs for instance before braking, then the Perception of Reaction distance must be added to the braking distance.

Explanation:

Distance = Speed x Time

And with a conversion factor:

D = (1.467 x S x T)

Where:

D = Distance Traveled (feet)
1.467 = Conversion factor (converts mph to fps)
S = Speed (mph)
T = Time (in intervals of 1 second)

Example Calculation:

Vehicle 1 was traveling at 65mph when a deer ran across the highway. How far did the vehicle travel before the driver was able to begin braking?

@ 1 Sec.: D = (1.467 x 65 x 1) = 95 feet

@ 1.25 Sec.: D = (1.467 x 65 1.25) = 119 feet

@ 1.5 Sec.: D = (1.467 x 65 x 1.5) = 143 feet

Distance Traveled at Speed

This equation is used to estimate the location of a vehicle at various points in time, if the vehicle’s speed is known. It can be used to identify where a car was 1 second, 2 seconds, 3 seconds, 4 seconds and 5 seconds before arriving at a location, or after leaving a location.

Explanation:

Distance = Speed x Time

And with a Conversion Factor:

D = (1.467 x S x T)

Where:

D = Distance traveled (feet)
1.467 = Conversion factor (converts mph to fps)
S = Speed (mph)
T= Time (in intervals of 1 second)

Example Calculation:

Vehicle 1 was traveling at 55mph when it collided with stationary vehicle 2. How far was vehicle 1 at one through five seconds before the collision?

@ 1 Sec.: D = (1.467 x 55 x 1) = 81 feet

@ 2 Sec.: D = (1.467 x 55 x 2) = 161 feet

@ 3 Sec.: D = (1.467 x 55 x 3) = 242 feet

@ 4 Sec.: D = (1.467 x 55 x 4) = 323 feet

@ 5 Sec.: D = (1.467 x 55 x 5) = 403 feet

Acceleration: Time to Speed

This equation is used to estimate the time it takes to reach a given speed, at a pre-determined level of acceleration.

Explanation:

Time = Change in Speed / Acceleration

or

T = 0.0455 x (Sf – Si)

A

Where:

T = Time (seconds)

0.0455 = Conversion factor (converts mph to fps)

Sf = Final Speed (mph)

Si = Initial Speed (mph)

A = Acceleration (g’s)

Example Calculation:

How long would it take a passenger car to accelerate from 0 to 30 mph at a normal rate?

Low: T = (0.0455 x (St – Si)) / A = (0.0455 x (30-0)) / (0.2) = 6.8 Sec.

High: T = (0.0455 x (St – Si)) / (A = (0.0455 x (30-0)) / (0.1) = 13.7 Sec.

Answer: 6.8 – 13.7 Seconds

AVERAGE ACCELERATION OF DIFFERENT VEHICLES Acceleration (g's)

From To

Passenger cars, Normal Acceleration

Less than 30 mph 0.1 0.2

More than 30 mph 0.05 0.1

Passenger cars, Brisk Acceleration

Less than 30 mph 0.2 0.4

More than 30 mph 0.1 0.2

Large or Loaded Trucks, Normal Acceleration

Less than 30 mph 0.05 0.1

More than 30 mph 0.025 0.05

Large or Loaded Trucks, Brisk Acceleration

Less than 30 mph 0.1 0.2

More than 30 mph 0.05 0.1

Acceleration: Distance to Speed

This equation is used to estimate the distance it takes to reach a given speed, at a pre-determined level of acceleration. This equation is rearrangement of the Acceleration: Time to Speed equation

Explanation:

D = (Final Speed^2 – Initial Speed^2)

Acceleration

or

D = (Sf^2 – Si^2)

(30 x A)

Where:

D = Distance Traveled (feet)
Sf = Final Speed (mph)
Si = Initial Speed (mph)
30 = Conversion (converts feet per second to miles per hour)
A = Acceleration (g’s)

Example Calculation:

How far would a passenger car travel while accelerating from 30 to 60 mph at a brisk rate?

Low: D = (Sf2 – Si2 ) / (30 x A) = (602 – 302 )/ (30 x 0.2) = 450 feet

High: D = (Sf2 – Si2 )/ (30 x A) = (602 -302 )/ (30 x 0.1) = 900 feet

Answer: 450 – 900 feet

AVERAGE ACCELERATION OF DIFFERENT VEHICLES Acceleration (g's)

From To

Passenger cars, Normal Acceleration

Less than 30 mph 0.1 0.2

More than 30 mph 0.05 0.1

Passenger cars, Brisk Acceleration

Less than 30 mph 0.2 0.4

More than 30 mph 0.1 0.2

Large or Loaded Trucks, Normal Acceleration

Less than 30 mph 0.05 0.1

More than 30 mph 0.025 0.05

Large or Loaded Trucks, Brisk Acceleration

Less than 30 mph 0.1 0.2

More than 30 mph 0.05 0.1

TECHNICAL REFERENCE Accident Reconstruction Calculators

Speed from Skids (Pre-braking Speed)

TECHNICAL REFERENCE
Accident Reconstruction Calculators