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Robert Philbin

Physics 111 or 211

October 2000

Dodge Caravan Drag: Rolling and Air Resistance

Abstract - 12%

The rolling resistance of a Dodge Caravan was measured using a simple technique of rolling to a stop on a level, paved roadway. Assuming it to be independent of speed yielded a rolling coefficient m _roll = 0.013 ± 0.005. However, there is some evidence that the rolling resistance decreases with increasing speed. Recommendations for further study are given.

Introduction and Procedure - 8%

The purpose of this lab is to measure the drag forces on a Dodge Caravan and to better understand the rolling dynamics of an automobile. In particular, does the rolling resistance follow a μN type model, more weight implying more rolling resistance? And is that rolling resistance independent of speed?

I chose an little used, level road on a windless day, accelerated to 30 mph and shifted into neutral. Using a stopwatch with lap-time capability, I measured the times at 25, 20, 15, 10, 5, and 0 mph.

Theory - 20%

Figure 1 (at right) is the free body diagram of the van on a level road while coasting to a stop. From this we get

Eq. 1 F_net,x = -f_roll - f_air = ma_x where ax is defined as

Eq. 2 a_x = D v_x / D t, and

Eq. 3 F_net,y = N - mg = ma_y = 0 => N = mg

Air resistance was modelled using the standard model:

Eq. 4 f_air = ½× C_D× A× r _air× v² where A is the frontal area and C_D is the drag coefficient.

It may be that the rolling friction follows the μN model, in which case we can simply compute the rolling force and divide by N=mg to get the rolling coefficient.

Calculation - 32%

Data for the van came from www.4adodge.com/caravan/specs/feature3.html.

A = 113.3in * 76.6in = 5.60 m², N = weight = 4057lb (4.448N/1lb) = 18046N, so

mass = mg/g = (18046N)/ 9.80m/s² = 1844 kg. C_D is estimated here as 0.6 (Energy and Problems of a Technical Society, Kraushaar and Ristinen, 1988, pg 332). Finally, × r _air in Trinidad is about 1.1 kg/m³.

After converting to meters and seconds, the first acceleration is found using Eqn 2:

a_x = D v_x / D t = (11.2-13.4) / (10.94 - 0) = -0.204 m/s², using Eqn 1 gives us

F_net,x = ma_x = (1844 kg)(-.204 m/s²) = -376 N.

The air resistance during this interval is computed using the average speed,

v_ave = (13.4+11.2)/2 = 12.29 m/s, so using Eqn 4:

f_air = ½× (.60)× (5.60 m²)× (1.1 kg/m³)× (12.29 m/s)² = 279 N.

Finally, rearranging Eqn 2 to solve for f_roll = -F_net,x - f_air = -(-377) -279 = 98 N

thus μ_roll = 98N/(18046N) = 0.005; this is not far above the published value for steel wheels rolling on steel tracks, i.e., almost certainly too low. All of the calculations were performed on a spreadsheet, summarized here:

v (mph)	v (m/s)	t (s)	Accel (m/s/s)	f net (N)	F air (N)	Froll (N)	mu
30	13.4	0
25	11.2	10.94	-0.204	-377	279	98	0.005
20	8.9	20.22	-0.241	-444	187	257	0.014
15	6.7	34.56	-0.156	-287	113	174	0.010
10	4.5	47.21	-0.177	-326	58	268	0.015
5	2.2	60.26	-0.171	-316	21	295	0.016
0	0.0	72.4	-0.184	-339	2	337	0.019

Which results in m = 0.013 ± 0.005. Note that the first data value is nearly two standard deviations below the mean. If I adjust C_D to 0.7, I get m = 0.012 ± 0.006 and if I adjust C_D to 0.5, I get m = 0.014 ± 0.004.

Fig 2 Rolling Resistance Coefficient for a Dodge Caravan (with C_D=0.6)

Conclusions - 24%

The rolling resistance is quite low (compared to sliding resistances) as expected. Using reasonable values for the air resistance model, C_D between .5 and .7, yielded rolling resistance coefficient values which did not depend too strongly upon the choice of air resistance model. This is as expected because at these low speeds, the air resistance component should be rather small. Considering the curve in Fig 2, it does appear that rolling resistance does have some speed dependency, but because of the one point (9m/s, .015), that correlation could possibly be flat. A linear regression of this data yields a 74% correleation coefficient, not very convincing that m and v are correlated (the linear relation would be m = (-.0010 ± .0003)v + (.019 ± .002).

Discussion - 4%

If I had lots of time, I would measure the values more than once. I would also try to measure the C_D value by measuring the terminal velocity of the van on an incline, i.e., where the air resistance is exactly balanced by the downhill component of the van's weight, mgsin(slope angle).