LOG: Understanding Car Crash Velocity and Acceleration Calculations

[bbrightbill]

I'm trying to figure out what information I'm lacking that I need and what formulas to use in order to calculate velocities and accelerations in a car crash. For the first part of the crash, it was a sideways slide in grass, and I've got that part. Then the side wheels catch and the car starts to roll. Wants the roll starts, the car travels 60 meters. I can't decide how to treat the motion of the car as it rolls (sideways) over that distance in order to calculate that acceleration. Any input would be great appreciated.

B

 

[94JZA80]

well you're looking for both the velocity and acceleration (there are two types of each - translational velocity/acceleration and angular velocity/acceleration) of the car from the moment it starts barrel-rolling on its side to the moment it comes to rest.

the average straight-line velocity (with respect to the ground anyways) is the 60m distance traveled divided by the time interval over which it all happened. if you plot enough data points of the car's position with respect to time, you can approximate its instantaneous translational velocity (velocity with respect to the ground at a particular instant in time). likewise, if you know your calculus, you could use that data set to approximate a position curve/function and differentiate it to find instantaneous translational velocity. sorry i can't help you with an exact equation (position function) off of the top of my head, but it would be a somewhat complex equation anyways, given all the forces at play (friction, rolling resistance, etc.).

the car's average angular velocity (the rate at which its orientation changes as it rolls, i.e. its rate of rotation) is simply the number of times the car rolled divided by the amount of time that elapsed between the moment the car started rolling and the moment it stopped. again, if you can plot data points of the car's orientation (or angle of rotation) with respect to time, you can approximate its instantaneous angular velocity. and again, if you can approximate a function for angular position, then you can differentiate it to find its instantaneous angular velocity at any given time during the roll. i also can't help you with an exact equation here, but i would imagine that it might be simpler than the above equation, as less forces affect the angular motion of the car than the actual translational motion (motion of the car with respect to the ground).

i would imagine equations describing both the car's translational acceleration and angular acceleration could be derived in similar fashion (this time by plotting both data points of the car's translational velocity and angular velocity with respect to time, as opposed plotting the car's position with respect to time). or again, if you know your calculus, you could take the translational and angular velocity functions derived/approximated above, and use curve sketching methods to approximate the translational and angular acceleration curves/functions....now the above descriptions of the car's velocities and accelerations may be quite rough in approximation, as there may be more factors/forces involved. but i hope that gets you going in the right direction.

Eric

 

[bbrightbill]

Unfortunately I don't know time intervals on the crash. Being forensics, it's based entirely on what was seen after the crash. This means knowing surfaces, materials, and being able to tell that the car slid half the distance and then rolled the remainder. Mass of the car is known, distances are known, but very little other information is easily available. I can probably estimate the number of rolls based on the distance and circumference of the car (which would be a very rough estimate, the actual number would probably be a little lower in terms of numbers of rotation due to some amount of sliding and deformation of the car).

The major question that I'm trying to answer is how fast was the car going at the start of the roll in order to travel that distance?