### Example: Braking/Tractive Force input tables

In a collision event that you are reconstructing with the m-smac program, a collision occurs at 0.50 sec and V1 has the right front wheel locked as a result of the collision. Also, the vehicle is in gear during the spinout phase so it is assumed to have 0.10 G engine braking subsequent to the collision. The calculation of the inputs for the braking force on the four wheels of the vehicle follows.

First some assumptions for the vehicle so you can calculate the appropriate inputs.

Vehicle Mass      = 10.352 lb-sec2/in                     (m-smac input on card 4, field 5)

Weight                         = 4000 lbs.

A                      = 48 inches                   (m-smac input on card 4, field 1)

B                      = 52 inches                   (m-smac input on card 4, field 1)

Mu                    = 0.70                           (m-smac input on card 12, field 5, coefficient of friction )

G                      = 386.4 in/sec2                             ( Local Acceleration of gravity constant)

Rear Wheel Drive Vehicle

Inputs Required to Lock the RF Wheel:

Calculate the weight on the wheel and put a sufficient amount of braking force on that wheel to exceed the maximum friction force.

The weight on the wheel is:           Weight on axle             =  Vehicle Mass * G * ( B/(A + B))

Weight on RF     =  1/2 * Vehicle Mass *G *  ( B / (A + B))

= 0.50 * 10.352 lb-sec2/in * 386.1 in/sec2 * (48 in / (48 in  + 52 in) )

=  960.0 lbs.

The force required to exceed the maximum friction force and lock the wheel:

Force to Lock     = Weight on Wheel * Friction Coefficient

= 960.0 lbs * 0.70

> 672.0 lbs.

Inputs Required to Include Engine Braking:

In many accident situations, subsequent to a collision, the driver is normally no longer applying control inputs (braking or steering). The condition where a vehicle is coasting while in gear is referred to as engine braking. The engine coasting in gear is applying a drag on the drive wheels. The range of drag on the vehicle for engine braking is normally from 10 to 15 % of the total vehicle weight distributed equally between the drive wheels.

For the above vehicle, the engine braking force will be applied at the rear drive wheels. If we assume the engine braking to be 10% of the vehicle weight:

Total Engine Braking       =  10% * Vehicle Mass * G

=  0.10 * 10.352 lb-sec2/in * 386.1 in/sec2

=  400 lbs

To distribute equally between the two drive wheels      =  -200 lbs per wheel.

Timing Consideration

The use of a time history table as inputs to  m-smac is to permit simulating the changes in the wheel forces as a function of time. In our hypothetical case, lets assume that we simulate the collision occurring at 0.50 seconds.  Normally, the collision event occurs over approximately 100 ms (0.10 sec) duration. Therefore,  for our example, the wheel drag should start after the initial contact, 0.50 to 0.60 seconds, and then remain constant. Therefore, we will use a time history table which starts at 0.40 seconds until 0.70 second in 0.05 sec increments.

The resulting input table would be as follows:

# Sample Input Table: RF lock and Rear engine braking; collision at 0.50 sec

0.4     0.70    0.05                                                           8

0.40    0.0     0.0     0.0     0.0                                        1   8

0.45    0.0     0.0     0.0     0.0                                        2   8

0.50    0.0     0.0     0.0     0.0                                        3   8

0.55    -337.5  0.0     -100.   -100.                                      4   8

0.60    -672.   0.0     -200.   -200.                                      5   8

0.65    -672.   0.0     -200.   -200.                                      6   8

0.70    -672.   0.0     -200.   -200.                                      7   8

More: Example: PCTOPT (% Force inputs option) inputs