# Check my math for rolling friction please

1. Jul 10, 2008

### IMK

Hello,
I was wondering if someone could check math that determines rolling friction please.

Basically I have been into Wikipedia doing a bit of research and put the following math together. The output of the function looks about OK against some test drives in my car, rolling a bottle across the carpet and an Excel results plot, but I would like someone to double check me please.

http://en.wikipedia.org/wiki/Rolling_resistance

F = Crr * (Weight * 1g ) = RollingResistance = 0.04 * ( 1000 * 9.81 )

http://en.wikipedia.org/wiki/Kinetic_energy#Kinetic_energy_of_rigid_bodies

Ek = ½ * (Weight * m/s) = Joules = Newtons

NewEk = Ek – F

Newms^2 = NewEk / (Weight / 2)

#define COEFFICIENT_OF_ROLLING_RESISTANCE 0.04 // Car tire
#define NORMAL_FORCE 9.81 // m/s2
#define INITIAL_SPEED_IN_MPH 10

double RollingResistance;
double KineticEnergy;
double NewKineticEnergy;
double NewSpeedMPS;

RollingResistance = ( WEIGHT * NORMAL_FORCE ) * COEFFICIENT_OF_ROLLING_RESISTANCE;

KineticEnergy = ((CurrentSpeedMPS * CurrentSpeedMPS) * WEIGHT ) / 2;

NewKineticEnergy = KineticEnergy - RollingResistance;

NewSpeedMPS = sqrt( NewKineticEnergy / (WEIGHT/2));

Results for a 10 mph run are below: (this more or less concurs with the average of several test drives 10 mph)

Many thanks in advance IMK

10.000000
9.801645
9.599193
9.392377
9.180904
8.964443
8.742625
8.515030
8.281183
8.040537
7.792464
7.536228
7.270969
6.995658
6.709060
6.409660
6.095571
5.764394
5.412992
5.037135
4.630872
4.185359
3.686391
3.108332
2.394572
1.343959

2. Jul 10, 2008

### uart

No that's not exactly correct.

Energy = Force x Distance and rollong resistance is a Force! It therefore needs to be multiplied by distance before it's subtracted from the KE. That is,

NewKineticEnergy = KineticEnergy - RollingResistance * Distance.

Anyway your "simulation" gives correct numerical results if the increment of distance between sucessive calculations is taken as unity (1 metre).

BTW. Those equations are pretty trivial to solve in closed form if you want a nice simple formula, like speed as a function of distance (or speed as a function of time if preferable).

Last edited: Jul 10, 2008
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