### EFFICIENCY OF A DERBY RACER - Derby Tech - June, 1984

by Ollie Brower

The efficiency of a derby racer depends on two major factors. (1) Wind resistance, and (2) Rolling resistance. In recent years only wind resistance has been extensively investigated. After all, doesn't everybody know that significant improvements in maximum derbying speeds can be achieved only with a reduction in wind resistance?

That's fair enough as long as one considers top speeds only, but at lower speeds, much more typical of a racer going down the hill (starting from a dead stop, and not reaching terminal or maximum speed until near, or at the finish line), the effect of rolling resistance is of greater significance than is usually recognized.

Rolling resistance is defined as the effect of rolling friction between the tires and the road. This rolling friction is a combination of bearing friction, alignment of axles and bearings, roughness of spindle, and the mechanical properties of the racer, as they relate to the wheels rolling over the uneven surfaces of the track. (see Figure 1) Every time the wheel rolls over a small bump in the track, say 1/16", and the weight on this wheel is 62 1/2 lbs., and the mechanical properties of the racer are poor, your racer must change the direction of this weight to an upward direction of 1/16", which requires energy at the rate of .33 ft/lbs per bump. If the mechanical properties (resiliency) of these component parts return 80% of the energy that was used to roll to the top of each bump, a total loss of energy for each bump will be .067 ft/lbs. of energy (which is the average loss of component parts and construction materials). For poor mechanical properties, the energy return is about 68%. This would relate to the racer being 325" slower. If each of your wheels roll over 1500 of these bumps (there will be many more than 1500, and many will be larger than 1/16 of an inch) on it's way to the finish line, your racer will have lost 402 ft/lbs of energy rolling over these bumps. This loss alone is equivalent to 160".

The effort needed to overcome rolling resistance at a given speed may be expressed in units of energy lost: ft/lbs. (the racer in the starting blocks has so much potential energy, measured in ft/lbs. The total amount of potential energy is found by the determining the height Of the racer's center of gravity above the finish line, in feet, and multiplying it by the total weight of the racer and driver, in pounds. PE=HxW, Potential Energy equals the Height times the Weight.)

The magnitude of this rolling energy lost is calculated from the following formula: E = Cr x F x V

(see figure 2)

(The note in figure 1 says that "Every Irregularity in the track surface causes a loss of energy")

The critical factor is Cr, the coefficient of rolling resistance. All efforts to reduce rolling resistance must concentrate on attempting to reduce this factor, which has been shown to depend on the following individual factors:

• Wheel Diameter - Soap box derby wheels vary slightly, but is not a factor if both contestants race on the same wheels.
• Tire Quality - Resiliency is generally not a factor if both contestants race on the same wheels, but can be a factor due to weight differences.
• Suspension Quality - Different for every racer, and here's an area where improvements can be made.
• Road Surface Quality - Where to drive in a lane becomes important.
• Speed of Racer - Generally not a significant factor.
• Wheel Alignment - Determined by axle alignment, and is very important.

The range of rolling resistance on a smooth track, from starting blocks to finish line is between .002 and .01 (varying by a factor of 5) wind resistance on the other hand, is a variable much less, considering most racers are relatively streamlined and kept small. The range of effective frontal area is between 135 and 185 sq. in. (varying by a factor of 1.37) and the total drag coefficient between .15 and .27 (varying by a factor of 1.8); multiplying these two factors results in a total factor of 2.43 for the maximum total effect of reducing wind resistance. Effective frontal area is the total of the racer's body, helmet and headrest, axles and axle trees, steering cables, outside stabilizers, wheels and wheel pins.

MORE FROM LESS

The wider range of variation in rolling resistance offers the possibility that for a given racer, better mechanical properties (suspension, dampening, body resiliency, and wheel and axle alignment) can make more difference than air drag reduction, even at speeds for which air drag is somewhat greater than rolling resistance.

With rising speed the relative importance of rolling drag will decline, but not as suddenly as might be expected - the actual energy loss will increase, and the percentage of drag due to rolling resistance will decrease by a ratio only slightly greater than the ratio of increase in the speed itself. Though overshadowed, it doesn't suddenly vanish. Wind resistance reaches 1 1/2 times rolling resistance at 15 mph. So it seems realistic to consider rolling resistance of dominant importance for all derby racers below 15 mph.

The rolling resistance of a soap box derby wheel on a derby track results from the deformation of the rubber tire, and the surface of the track (also slightly to the steel portion of the wheel, bearings, and axles). The deformed areas of the tire and track surface return to their original shapes as the wheel rolls off them. But since no solid material is perfectly elastic, the energy that the deformed areas exert as they recover is less than the energy they exert as they are compressed.

As a result the supporting force for a moving wheel is not centered directly below the axle, but slightly ahead of it (see Figure 2). When combined with the wheel's load, which is centered on the axle, this off-center supporting force exerts a rearward torque which opposes the wheel's motion. When the axle is supported on only one side as is a soap box derby axle, this rearward torque pushes the axle back a few thousands of an inch.

Surface irregularities are important because they cause vertical wheel motions, and thereby dreate a significant retarding force added to the one which results from imprint length. It is this retarding force which is the primary cause of the unpredictability of rolling resistance on derby tracks. The surface of derby tracks vary significantly for the same track. Rough surfaces hardly detectable are often on one side of a lane, and not on the other side. Sometimes the rough side is on the downside of a sloped lane, and it may not be the place to drive.

BUMPS

When a soap box derby wheel goes over a bump, the wheel moves upward, the axle moves upward, the racer itself, and everything in it moves upward. The amount of upward motion of the racer and everything in it can be controlled. Any upward projection (bump) in the track surface will force the wheel up, and the force exerted by the bump will include a component opposite to the direction of travel. Some portion of the wheel', f,rw,rd motion will thereby be lost, or at best converted into vertical motion.

Once the wheel has past beyond the upward side of the bump, gravity will soon convert any upward motion to downward. With luck, this downward motion could then be converted back to forward motion by the descending slope of the bump - but only if the bump were so smooth and round that the wheel actually followed the surface as it descended. If the wheel flew clear of the bump and landed on a level surface beyond it, the vertical momentum could make no contribution to forward motion and would be lost. worse, if the wheel landed on the face of another bump, or was going into a dip, and hits the upward side of the dip, as it is still going downward, its downward speed would actually increase the retarding force. The Fort Wayne hill, in the right lane, looking down the track, has a dip about 100 feet from the top next to the outside edge. Hess, Reinholt, Esque, Smith and others found out about this dip the hard way. In the, case of a downward unevenness, the wheel will accelerate down into the dip, but then would have to climb back out, with the same retarding effect as for the bump. At best, of course, it would lose as much speed as it had gained; and if the bottom of the dip were sharp it would lose much more.

A well developed suspension and dampening system built into the racer will allow the wheels to roll over bumps and dips much smoother. This smoothness enables the tire to stay against the ground over many of the smaller bumps, so it can press against the downhill side of a bump as well as the uphill side. As long as the wheel stays on the ground, each retarding force is followed by a compensating accelerating force. If the tire goes over the bump with enough force, and there is no give in the axles or body, the tire will continue in an upward motion after leaving the bump, and not recover any of the lost energy in getting over the bump. With a good suspension and dampening system, the tire will return sooner to the downhill side of the bump and recover some of this valuable energy. The ideal situation is to prevent "skip" - become airborne and lose the benefit of the downward acceleration.