# Coast down test for Rolling Resistance

1. May 25, 2004

### steven mosher

Is there a simple way to estimate the rolling resistance of a vehicle by rolling it down a known incline with a variety of weights?

In short, if the velocity of a vehicle rolling down a ramp is a function of the air resistance and the rolling resistence and if rolling resitence is proportional to vehicle weight ( is this correct? ) can one come up with estimates for
CdA and Rolling resistence by rolling the vehicle down a known incline with various changes of weight? If not, is there a methology whereby one can measure the rolling resistance of a vehicle or measure changes to that figure of merit in relative terms?

2. May 25, 2004

### krab

Assuming it is easy to get good data, but hard to vary the slope of a hill, I would go to a level road, and take speed to time coastdown data. The derivative is the deceleration. Now fit the acceleration versus speed to a quadratic a=c_2v^2+c_1v+c_0. c_2 gives the air drag coefficient, and c_1 gives the rolling resistance.

3. May 26, 2004

### steven mosher

The vehicle is not powered. more precisely the transmission is direct drive.. so a coast down test on a level surface, I suspect, would be complicated by the fact that the transmsission losses would be factored into the decleration.
since the rear axel is directly coupled back to the engine I wouldnt want interanl resistence in the power plant to corrupt the estimate. So I was planning on decoupling the engine from the rear axel and coasting the sucker down a known measureable slope.

I have some constant slope test areas identified ( abandoned parking garages ) where I can send the vehicle down the slope and measure its time over a given distance. Given this experiementalk constraint what would the maths be..

4. May 26, 2004

### turin

I don't understand how an incline solves the problem of the transmission. (I should admit that I don't understand the problem with the transmission in the first place; why can't you disengage it?)

5. May 27, 2004

### steven mosher

Here's how

In most level coast down tests you bring the vehicle up to a given speed, then coast down. in most vehicles the engine is not connected directly to the rear axel. In the vehicle I am testing.

1. there is no speedometer.
2. The rear axel is connected directly to the engine.

So, if you accelerated to say 30 MPH ( assuming you could measure it )
and then went to Idle to slow down the engine would still be driving the rear axel and if you cut the engine the deceleration would be coupled to the internal resitence in the engine.

For incline testing I can merely take the direct drive chain off so the egine and axel are decoupled. Gravity becomes the power source and I just need to be able to estimate Cd and Rolling resistence. I might also be able to tow the vehicle up to a certain speed on a level surface and then un tether it?

6. May 27, 2004

### krab

The equation is
$$m{dv\over dt}=mg\sin\theta-c_2v^2-c_1v-c_0$$
Ramps in parking garages sounds like you won't be getting up to enough speed for air resistance to matter. So we drop the v^2 term. The solution is
$$\exp(-t/\tau)=1-v/v_\infty$$
where
$$v_\infty={mg\sin\theta-c_0\over c_1}$$
is the terminal velocity, and $\tau=m/c_1$.
You could try to record v versus time, and fit the results to the above equation. If you cannot measure v, integrate once more to get
$$d=v_\infty(t-\tau(1-\exp(-t/\tau)))$$
It may be hard to get both c_0 and c_1 from measurements, so instead, I suggest measuring c_0 separately. This could be done by attaching a tether to the cart, with something like a spring fishing scale. Pull the cart on level ground at very slow constant speed, and read c_0 off the scale.

Last edited: May 27, 2004
7. May 27, 2004

### turin

What the H E double-hockey-sticks kind of vehicle is this? That sounds wierd. I do see why you want to use the incline, now.

8. Jun 7, 2004

Thanks Krab,