by Ollie Brower

The KEY to winning a soap box derby or gravity type race is ENERGY.

The four factors of energy are:

- Amount available to propel the car to the finish line.
- When energy is available to propel the racer.
- Amount of energy lost.
- When this energy is lost.

All four of these factors are different for different racers.

**AMOUNT OF ENERGY AVAILABLE **

The amount of energy available to propel the racer to the finish line comes from two sources. - Wind and Gravity

**WIND **

If you are racing under conditions with a wind blowing, no matter how slight, or from any direction, it will have an affect on the racers. This wind is energy, and can help speed your racer up, or slow it down more than it will the other racers. At the top of the hill, a perpendicular crosswind will slow some racers down, and speed others up. After the racer has attained a speed of 80% of the cross wind, this cross wind will no longer help propel racers. Although it will slow some down more than others.

A sail on a sail boat is nothing other than an airfoil, designed to propel the boat forward against a headwind, crosswind, or with a tailwind.

**GRAVITY **

Energy is available from the gravitational pull of the earth. Because the racer is going to fall (roll) a certain vertical distance, from the start- ing ramp to the finish line, and because the racer and driver weigh a specific amount, these two factors together equal an amount of energy available to propel the racer. This amount of energy is called Potential Energy (PE).

Lets take the Akron hill for example. The starting plates are 47.8 feet above the finish line (straight up). See Figure 1.

The center of gravity (CG) for a balanced racer with a short wheelbase, and the rear axle is as far back as possible, and the racer as long as possible will be 49 feet above the finish line.

Specifically: PE - H x W Potential Energy (PE) is equal to the height (H) times the weight (v4) of the racer. Potential Energy is expressed in foot pounds (ft/lbs).

The energy available (PE) to propel this Senior Division racer to the finish line at Akron is 49 feet times 236 pounds (Z-glas wheels), which is 11,564 ft/lbs of energy. For a Junior Division racer it is 48.7 feet (shorter car, and longer wheelbase) times 206 pounds, which is 10,032 ft/lbs of energy.

The amount of energy gained by having a short wheelbase over a long wheel base at Akron is 25.15 ft/lbs of energy.

A racer with a long wheelbase (Figure 2, Racer A) and balanced weight will have its CG at 42 inches from the nose. With a short wheelbase (Racer B) the CG will be at 50 inches from the nose. With the racer on a 16% slope, the CG is raced vertically by 1.28 inches, which converts into .1066 times 236, or 25.15 ft/lbs of energy.

Through tests on a hill similar to Akron's, using steel wheels, we have determined that one ft/lb of energy is equal to .39 inches at the finish line. Therefore racer B is 9.81 inches faster than racer A. These figures are for a balanced racer in both cases.

At Akron, if you were to be 30 pounds tail heavy, with a short wheelbase racer, you would move your CG back 6.32 inches from the nose. Your CG would rise vertically 1.01 inches, which converts into .0842 times 236, or 19.87 more ft/lbs of energy, which is equivalent to 7.75 inches. But for each pound being unbalanced, you loose .51 inches due to increased tire compression friction. Being 30 pounds tail heavy converts into a loss of 30 times .51, or 15.3 in6hes, or for a combined loss of 15.3 minus 7.75, which equals a 7.55 inch loss. This is why the you should run the Akron hill exactly balanced.

It is very important to have a short wheelbase, with the rear axle back exactly to the legal limit, and the racer's length to the exact legal maximum limit. The CG will be higher up the hill, with the same tire compression losses. Every 1/16" you give up on length, rear axle to the rear, or minimum wheelbase, is costing you speed. This is because you will have less energy available to get you to the finish line, than does the top competitors.

Energy from the sun can not be directly converted into propelling energy. The only way energy from the sun can increase the speed of your racer, is indirectly, by heating of the wheels, axles, and construction components, which will increase their resilient qualities. Better resilient qualities will reduce the energy loss when these items are deflected during the normal run down the hill.

**WHEN ENERGY IS AVAILABLE TO PROPEL RACER **

Propelling energy is to be taken advantage of, as soon as possible. The quicker you can get your racer to accelerate, the quicker you will get to the finish line. (Figure 3 and 4) If you have a ramp affect, (see Derby News: March 1977, page 68; Summer 1983, pages 1 & 2. Gravity Drags Racing Report, May 1983, page 12) you must take advantage of these situations. If the race course has a crown or a valley, you must use it to best advantage as soon as you can. If the track has a crown or a dip (from top to bottom) , you must set your racer up, weight-wise and wheelbase-wise to get acceleration as soon as possible. You want to be on the steepest part of the course as quickly as you can.

PROPELLING FORCE: F = W sin SS

ACCELERATION: F = M x a

Which breaks down into:

- F (W sin SS)
- M (W/g)
- a (g sin SS)

WHERE:

- a = Acceleration
- g = Gravitational Constant
- CG = Center of Gravity
- D =Drag Forces (wind and wheels)
- F =Propelling Force
- M =Mass (W/g)
- N =Normal Force
- W =Weight of Racer
- SS =Angle of Hill

**CONCLUSION: **

1. Acceleration is independent of racer weight (disregarding D), but is proportional to the slope of the hill.

2. A short wheelbase car rests on a steeper angle of the hill, if the hill is convex.

**AMOUNT OF ENERGY LOST**

On the Akron hill we have 11,564 ft/lbs of energy available. Part of this energy is lost or dissipated through friction of the wheels, tires, and all component parts that move or flex due to track surface conditions, and aerodynamic drag. Different racers lose different amounts depending upon their elasticity efficiency. See "Efficiency of a Derby Racer" in the next issue of Derby Tech.

THE RACER THAT LOSES THE LEAST AMOUNT OF ENERGY WILL GET TO THE FINISH LINE FIRST! (Assuming PE is the same for each) This is the KEY to derby racing. Always keep this in mind.

**WHEN ENERGY IS LOST**

At the start of a race, with the racers in the starting ramp, the racer has 11,564 ft/lbs of PE, but has absolutely no Kinetic Energy (energy in motion) (KE). This KE builds gradually as the racer gains speed. If the driver makes steering corrections while moving on the ramps, or driving to the high side of his lane with almost no KE, and loses valuable energy because of steering. He must start the process of building up KE over again. By now he has lost valuable time which is hard to make up. If you are going to take advantage of a crown in the track, set your racer on that angle to eliminate a steering maneuver. The steering correction that is necessary to straighten the racer must be done gradually. After taking advantage of a slope, do not come back to the center of your lane unless the center is lower or smoother than your present lane position.

*ENERGY LOST SHOULD NOT BE AT LOW SPEEDS.*