A
tek said:
Hey, im trying to find a formula for calculating speeds of accidents from skid marks left on pavement. Im talking about a down'd bike here, sliding on its side. Pavement is a standard road mix, not ashfault(haha spelling?) with chunks of rocks and gravel in it. the bike will have slid on its left side, dragging the pegs and the stator cover mainly, little rubber contact with pavement. no frame sliders. no tumbling. scratch marks in pavement measured 155 ft +/-
so if anyone has some formulas for me that would rock, i know there are lots of different variables, so the numbers will not be really precise. Im just looking for close, like the insurance investigators use. that kind of thing.
i have a bit of data accessable from a local bike crash, and just wanted to come up with my own conclusion as to MPH traveled etc.
thanks for any ideas or input.
This is from a test I found at this link:
LINK
"
Police have used the formula
to estimate the speed
s (in mph) at which a car was travelling if it skidded
d feet. The parameter
C is the coefficient of friction determined by the kind of road (concrete, asphalt, gravel, tar) and whether the road was wet or dry. The following are some values of
C.
"
Don't know how true it is, but you can give it a shot to see if it gives reasonable results. Otherwise, here's my 2 cents of the physics:
The coefficient of friction of rubber against smooth pavement is 0.8. The Cf of steel on steel is 0.4. Knowing this, I'd take a wild guess that your bikes expensive bits sliding along the pavement would yield a Cf of about 0.5-0.6. THIS IS A GUESS! You would actually need to "experiment" to get a descent value.
1) Simple Newtonian physics yields this formula from a balance of forces:
ma = - (N.Cf + 0.5*Cd.rho*A*(v^2))
where:
m is the mass of the bike (170kg)
a is the average deceleration of your bike (?? - you want to find this, in m/s^2)
N is the normal force exerted by the ground on your bike = m.g (in Newtons, g is gravitational acceleration = 9.8m/s)
Cf is the coefficient of friction (approx 0.6 as stated above)
Cd is the coefficient of air resistance / drag (0.55 for our bike)
rho is the density of air (1.2kg/m^3)
A is the frontal / cross sectional area of the bike (in m^2, --> 1.8m^2 , for the direct frontal area I think)
v is the average velocity encountered during the skid (in m/s). Give a rough estimate. The second term in the RHS of the above equation should be small anyways.
NOTE: Again, this is only an estimate, as you would actually need to integrate the above function w.r.t time to get an accurate answer.
2) Linear equation of motion are as follows:
v^2 = u^2 + 2as
OR
v = u + at
where:
v is the final speed of your bike (in m/s. Zero, I presume. Although if its not, it won't make a difference)
u is the initial speed of your bike (in m/s, ?? - What you want to find)
a is the average deceleration of your bike (in m/s^2, found from Equation (1) above)
s is the distance that you skidded for (in metres)
t is the time that you skidded for (in seconds)
Hope this helps.
You can PM me if you need a hand with the numbers. I know I put in metric figures. Its what the rest of the world use... You should have no prob using imperial units, just convert the numbers I used. Else stick to metric and convert at the end.
TO THE REST OF YOU: This is the estimate that HE wanted. ESTIMATE DAMMIT!!!
