DMSBD Tech Tips

Construction Tips for a First-Time Car Builder
Article 5: Weight & Balance - by Ian Carsten

Early in the history of soapbox derby racing it was learned that the speed attained and, therefore, the elapsed time are fairly sensitive to rather small differences in weight. Although each car within a given division is approximately the same, there are still weight differences due to slightly different allowable hardware configurations and variation in the density of the floorboards. However, a much bigger weight variation always exists among drivers. Testing determined that a difference as small as one pound or less resulted in a noticeable difference in elapsed time. A heavier car is faster because it has more energy. Some of your car’s energy is consumed in overcoming the rolling resistance of the tires and bearings. Your car will also spend energy in sharp upward movement caused by hitting bumps. The greatest energy loss is in pushing the air aside as your car moves through it. Whatever is left is available to accelerate your car. It is easy to get an idea of how much extra energy a heavier car has. For example, consider a hill where the center of mass of the car and driver together fall 40 feet from start to finish. At such a track, your 200-pound stock car has 200 pounds multiplied by 40 feet, or 8,000 foot-pounds of energy available to propel it to the finish line. However, suppose your opponent’s car weighed 201 pounds. It would have 1-pound times 40 feet or 40 foot-pounds of additional energy. It would be slightly faster as a result. This wouldn’t be a fair race. The reason ballast is added to achieve a standard weight is to ensure a fair race for as large a weight range of drivers as is practical for each division.

Also, in stock and superstock cars, the fastest posture requires the driver to scoot back against the rear of the cockpit to prevent air from flowing down along the back and then being scooped into the opening, generating drag. However, this posture makes an unballasted car tail heavy. Since a tail-heavy car is usually slower than a balanced one, it is desirable to use ballast for maximum speed. This is another reason why we use it.

Initial Determination of Weight Placement
The first consideration in designing a weight set is, how much does your car plus driver weigh? And, how much must it weigh for racing? As of 2002, the maximum weight for a car plus driver is: stock 200 pounds, superstock 230 pounds, and masters 255 pounds. The car and driver could be lighter. However, under almost all circumstances, that would be a disadvantage. The only way to be really sure of your car and driver’s weight is to weigh them. Unless you have access to an accurate, large-platform commercial scale, you’ll probably have to improvise using one or more bathroom scales. Although not absolutely reliable, you can use the following general values to get a reasonable idea of your car’s weight. With wheels, a stock car weighs about 57 pounds, while a superstock car is approximately 61.5 pounds. Most of the difference is due to the body shells. A stock body weighs roughly 10 pounds, while a superstock body, which is thicker and somewhat larger, weighs about 14.5 pounds. Note: a stock car built on the older and denser particleboard floorboard usually weighs closer to 63 pounds, while a superstock using a particleboard floorboard is about 67.5 pounds.

You should weigh your driver attired for racing. For example, the driver should not wear heavy, thick-soled shoes or a winter coat. Of course, these weights are only preliminary, however, they are useful in getting an idea of approximately how much ballast is required. You simply add the weight of your car and driver and subtract this total from the specified race weight for your division. For example, suppose your stock car weighs 57 pounds and your driver’s weight is 63 pounds, for a total of 120 pounds. Therefore, you need 200 pounds minus 120 pounds, or 80 pounds of ballast. Figure 11.1, in both the stock and superstock plans, shows a full-page diagram of the weight placement for your car. The diagram is a bit misleading in that it seems to imply the seat weight and tail weight are fairly large. They will likely be quite a bit lighter than the other two. Actually, the U-shaped center weight will probably need to be the heaviest and the nose weight will have to be quite a bit heavier than the drawing implies. The center weight and seat weight are considered fixed, non-adjustable weights. They are bolted to the floorboard with 5/16-inch hex head machine screws, washers, and nuts. You are not allowed to change them during the course of a race. Adding or subtracting small weights at the nose and tail fine-tunes total weight. These are your adjustable weights that are placed on the full-threaded 5/16-inch “K1” weight bolts and secured with “Z” wing nuts for quick changes without tools.

Construct your weight set so that your car will be balanced with the driver in racing position, since this is usually the fastest setup. Then you can use the adjustable weights to modify the front/rear weight distribution if needed. Both the stock and superstock rules recommend a minimum10 pounds of your car’s ballast be adjustable weight. You may find it practical to distribute more than 10 pounds of ballast in the adjustable weight positions.

Using the Method Shown in the Plans
Look at figure 8.3 in the stock or superstock plans. If you use this method, you must have the shell and wheels off. Since the weight of the body and wheels is roughly equally distributed from front to rear on the car, the absence of these parts should not alter balance as you determine weight placement. Here is how you might proceed.  You will need some fairly heavy, stand-ins such as barbell weights, bricks, or whatever you can devise for the purpose. Put the floorboard on either a round piece of material such as a dowel, broomstick, pipe, or you can use the edge of a 2 x 4 as in the drawing. It must lie on the floor or up on a strong workbench. Place the floorboard on top of it so it is perpendicular to the piece you use as a balance bar. Also, the bar should be placed at the midpoint between the axles. You should have a scale handy to weigh the test weights. Weigh the test weights and mark each one with its value. You could put on strips of masking tape and write its value on the tape. You need to have the total required weight divided into a number of different pieces. You’ll have to get your driver into racing position. One way to do this is to place the shell on the board without any screws, get the driver into position, and lift the shell off. Now, using figure 11.1 in the plans as a guide, start placing the weights onto the floorboard, centered as best you can over the areas specified in the drawing. When all the weights are distributed onto the board, you’ll probably have to move them until the board is balanced and you have at least 10 pounds distributed into the adjustable weight positions at the nose and tail. Now, make a sketch of the floorboard with the required amount of weight needed at each of the four allowable positions. Now you can start thinking about how to design your weights.

Steel or Lead?
The only practical material to use for ballast is dense metal. Various metals have been used for ballast, typically lead or steel. However, steel is the most practical material and, because it can stiffen the floorboard, it may contribute to speed, as softer materials such as lead cannot. You may have heard that getting your car’s center of mass as low as possible is important for top speed because it gives your car slightly more energy. In absolute terms, this is correct. However, the amount the center of mass can be lowered by using lead, rather than steel, is quite small. The resulting increase in energy is far too small to have any meaningful effect on performance. For example, suppose by using lead instead of steel you could lower your 200-pound stock car’s center of mass by 1/4-inch and you race at a track with a 40-foot drop, launched at 8 degrees from horizontal. That would give your car 8,000 foot-pounds of energy. By lowering the center of mass 1/4-inch, you would gain .008 foot-pounds of energy. It couldn’t possibly make a difference. However, lead cannot appreciably stiffen the floorboard as steel can. And a floorboard stiffened by steel weights, firmly bolted to the board, can make your car slightly faster. Not surprisingly, the majority of fast racers use steel for ballast.

Your Floorboard is a Spring
You may wonder why a floorboard stiffened by steel weights could be faster. If you looked at a derby car and didn’t give it too much thought, you might be led to believe it has no suspension system. That’s not exactly correct. A derby car actually has three suspension elements. The first is the urethane tires. They are a rather poor spring. The second is the cold rolled steel axles. They are a much better spring than the tires. The third element is the floorboard. It may seem perfectly rigid when you handle it. However, it flexes lengthwise under the weight load it carries. It also flexes lengthwise further when both wheels on the same axle strike a bump forcefully at the same time, such as when striking a crosswise crack in the pavement. Further, the floorboard can spring in a twisting fashion if only one wheel on an axle strikes a hole or bump. A spring is a temporary energy storage device. When it is compressed, it stores energy. When it returns to its previous shape, it returns at least some of that stored energy. Some types of springs are much more efficient at returning stored energy than others. In particular, a floorboard stiffened by steel weights firmly bolted in place is a more efficient spring than otherwise. That is why it can make your car slightly faster.


What the Rules Say
It is important to understand the rules and believe they mean what they say. Read your rulebook carefully regarding ballast weights. In the 2002 stock rules, you must read sections s3, s6, stock division adjustments 2, 3, 4, step 8 with figures 8.1 and 8.2, figure 11.1, and the stock checklist under “Weights”. In the 2002 superstock plans, you must read Step 1 #2, step8 and figures 8.1, 8.2, and 8.3, figure 11.1, superstock checklist under “weights”, ss3, superstock division adjustments 2,3,4, and ss6.

Your main weights, in the seat and center positions, may be no higher above the floorboard than 1.5-inch. There is no limit on the height of the adjustable weights in the nose and tail. However, all weights are restricted to flat shapes. No angles, channels, tees and so forth are allowed. Also, no weight or stack of weights may be longer than 12-inches lengthwise in the car. Further, no weight is allowed to touch the body shell. Figure 11.1 specifies minimum 1/8-inch weight-to-weight clearance. The nose and tail weights must clear the axles a minimum 1-inch. Too, the tail weight in a stock car must clear the radius rods by 1-inch. Also, observe the weight-free zone from the pre-drilled mounting holes for the brake and footrest to the floor-mounted steering pulleys. Also, all weights must be removable without removing any other components except the screws and nuts fastening the weights to the floorboard. Additionally, all weights must be painted and each piece must be marked with its weight in pounds.

Calculating the Weight of Each Piece
As you plan each major piece, you’ll want to know its weight before your make it. If your calculations show it will be too far off your requirements, you may want to give it a different thickness and/or “footprint”. It’s easy to do. Once you have selected a size and shape (as viewed from above), you should be able to resolve it into one or more simple shapes, such as rectangles, triangles, or trapezoids, each of which has a simple formula for calculating its area.  Here is an example of calculating the required shape and thickness of a center weight for a stock car. Suppose you have used the method given to determine what weights are necessary for your 57-pound stock car with 63-pound driver. 200 pounds – (57 pounds + 63 pounds) = 80 pounds. Further, suppose stand-in weights determined the following distribution: nose 12.5 pounds, center 42.5 pounds, seat 10 pounds, and tail 15 pounds. Then you made a rectangular template 12 x 13 inches with a 3.25 x 8.5 inch cutout for the pulley, cable, and keeper block. You plan on making it of steel and you need to know how thick it must be. For solid objects, weight (w) = area (a) times height (h) times density of steel (d). In symbols, w = ahd. To find the required height, we must solve for height. So h = w/(ad). The density of steel is .2835-pounds/cubic inch. The area of a rectangle  = length times width, so the area of the weight should equal the area of the 12 x 13 rectangle minus the area of the 3.25 x 8.5 rectangular cutout. Therefore, a = (12)(13) – (3.25)(8.5) = 128.4 square inch. Then using the above formula for height, h = 42.5/(128.4)(.2835) = 1.16 inch. Since steel plate is only available in standard thickness, such as 3/4-inch, 1-inch, 1.25-inch, and so forth, you will probably have to use 1-inch as the closest size available and add a thin weight on top to compensate. Or, you could use the next thicker size and reduce the other weights to compensate. Lets suppose you want to know how much heavier it would be using the next available thickness, 1.25-inch. Then w = 128.4(1.25)(.2835) = 45.5-pounds, or 3 pounds heavier than you planned on. That should work. Just remember to write down the new weight of the centerpiece, since you will have to make the other weights 3 pounds lighter in total to compensate. Now lets consider the other alternative. Instead, choose to use 1-inch thick steel. Its weight is w = 128.4(1)(.2835) = 36.4 pounds, or 6.1 pounds too light. You could make an additional center weight with the same footprint out of sheet steel. It could be stacked either on top or under of the main weight. One of the advantages of using sheet steel is that it is usually available in large sizes so it’s easy to get a piece big enough for a derby weight. A likely thickness would be 1/8 = .125 inch. Its weight is w = 128.4(.125) .2835 = 4.6 pounds. The 1-inch weight plus the 1/8-inch weight together weigh 40.9 pounds, or only 1.5 pounds lighter than planned. Don’t worry if the weights end up being a little different than you originally planned. This is a cut-and-try process and you should be able to adjust total weight with either your adjustable weights and/or small additional weights added to the permanent weight stack at the center. In view of this, it may be a good idea to make a piece slightly lighter rather than heavier than the planned value if you can’t get it exact because you can easily add weight if your ballast is not heavy enough. On the other hand, if they total too much, you’ll have to do some cutting, which is generally more difficult.
 

Making Templates for the Weights
You have to look at figure 11.1 to get an idea of the size and shape of your weights. There is no point trying to design the weights until you have finalized the position of the controls, cables, and pulleys. Probably the most difficult weight to make is the center weight, especially if you make it in one piece. It must have clearance for the brake pulley, brake cable, and the wood cable-retainer block. The awning pulley option requires the least amount of metal to be removed for clearance. Remember, under 2002 rules, you have to mount the retainer block even if you use the awning pulley option.

Here’s a good way to make a weight template from 1/4-inch plywood, Masonite, or an old piece of scrap paneling. First remove the bolt, nut, washers, (and bushing if you use the awning pulley) and remove the pulley and place it and the cable aside. You can probably loop it over the steering wheel to get it out of the way. Once you have the template cut to size and shape, you can clamp it in position with two c-clamps. Use some pieces of wood on the bottom of your floorboard to prevent damage from the clamps. Be certain that it is centered from left to right and cannot touch the body shell. The largest practical size for the center weight is 12-inches lengthwise in the car by 13 inches wide. This will enable you to make the largest legal footprint for the center weight. Consequently, it will be as short vertically as possible for a given amount of weight. This helps to achieve a low center of mass, which most experienced builders prefer. Now place the board bottom-up on the horses. Transfer the bolt locations by drilling through the mounting holes in the board and through the template with a 5/16-inch drill for the weight bolts. Use a 1/4-inch drill to transfer the location of the brake pulley. Be careful to observe the clearance requirements in the rules. Turn the floorboard back upright and remove the clamps. From the top, put 5/16-inch bolts into the mounting holes through both the template and the floorboard. You don’t have to put any nuts onto the screws, since you are only using them to locate the template to the floorboard. Due to the additional thickness of the template, you will have to place a 1/4-inch screw, longer than the original, from the bottom and reinstall the pulley and cable with all the original washers, nuts, (and bushing if using the awning pulley). Then place the mandatory cable-keeper block in position. There is no need to screw the keeper block down. Now it’s easy to see how much clearance is needed for the cable, pulley, and block. If you use the awning pulley, you won’t need to cut away nearly as much material as with the floor-mounted roller. And that means your weight can be heavier since less metal will have to be removed. This is another argument for the use of the awning pulley. Now use a carpenter’s or number 2 pencil to lay out at least 1/8-inch clearance in each direction from the cable, pulley, and keeper block. Remove the template and carefully saw it to the layout line. This is best done with a woodcutting band saw. Afterwards, you may wish to use a file to smooth out the saw cuts on the template.

Now you can transfer the shape of the template to the steel with a scriber. The steel should first be coated with layout ink so the scribed line will be sharply defined and easy to see. Now use a scriber to trace the outline of the template onto the steel. The most likely and economical source of flat steel is a scrap yard. New steel from a steel supply firm will likely cost quite a bit more per pound. Steel can be cut to the required shape with a steel-cutting band saw or an oxygen-acetylene torch. If you live near a high school or community college with an industrial arts program, you might be able to contact the instructor and have your steel cut to shape and drilled by students for a nominal fee. You will have to provide the template and steel along with adequate instructions to the person who will do the work. If you choose to drill the steel yourself, you should use the method used to transfer the holes into the template. However, it is better to drill only shallow starting holes through the floorboard and into the steel. Then remove the steel from the board and finish drilling through the weight with a drill press. Regardless of who drills them, the clearance holes in the steel should probably be 3/8-inch diameter to ensure the screws will fit through without any interference.

An Easy Alternative to Sawing
If you find cutting steel to shape to fit your car too much trouble, it is possible to locate pre-cut squares and rectangles of flat steel that can be drilled for mounting holes and stacked to form your ballast. That can eliminate the need to do any cutting. In the southeast Michigan area we can obtain pre-cut steel plates from the Ideal Steel Company. Also, structural steel fabricating firms may be able to supply you with flat plates for main weights or shims of an appropriate size for adjustable weights. They need only be drilled for mounting holes.
 

Should the Car be Balanced or Tail Heavy?
Front/rear weight distribution is a balancing act. We’ve done some testing to find out what effects various loads have on the tires and bearings of z-glass wheels. We found that the greater the load, the harder the tires and bearings roll. Of course, this is something we have all experienced with carts, wagons, and bicycles. By running your car tail heavy, the rear wheels turn harder than the front. We found that a balanced car rolled with about 30% less rolling resistance than one run 15 pounds tail heavy. Pretty much the same type of reduction can be achieved by eliminating a bad case of crossbind. With a tail heavy car, the steeper the slope, the less you will notice a difference. Also, the shallower the slope, the slower your car will be when run tail heavy. The reason for this is, on a steep slope, your car is spending its energy rapidly enough by dropping quickly to overcome most of the additional rolling resistance generated by being tail heavy, so you may not notice much of a difference in performance. In contrast, on a sufficiently shallow slope, the additional rolling resistance of your more heavily weighted rear wheels in a tail heavy car may slow you down enough to loose your race. Since most derby hills have been built or selected for a modest enough slope for safe racing, being balanced or close to balanced is usually the best policy.

To understand this, consider a race where the track is a continuous shallow angle like a long, straight ramp of, say, 1000 feet at 2 degrees from horizontal all the way from the start to the finish line. Drive it with your car balanced and suppose someone is timing your run with a stopwatch. Since you are running balanced, the wheels on the rear axles are producing the same amount of resistance as the front. Perhaps it takes 60 seconds. Now set your car 15 pounds tail heavy and run it again. You may think that since the front wheels are now less heavily loaded, they will roll with sufficiently less resistance to compensate for the excess drag imposed by the rear wheels. Our testing indicates that the excess drag from the more heavily weighted rear is considerably greater than the decreased drag from the front. It wouldn’t be surprising to find that the tail heavy run takes a few seconds longer. You’ll probably never see such a track but this is useful in trying to understand how weight distribution works. Some tracks, particularly temporary street courses, sometimes have a fairly steep starting ramp feed onto a shallower track. In this situation, the race is often won or lost on the ramp. Here’s how it works. By running tail heavy, your car will experience a greater initial acceleration while it is on a sufficiently steep ramp and as it makes its transition to the shallower track surface. You will now be moving at a greater speed just off the starting ramp than you would if you had run your car balanced. This is due to moving the center of mass further up the ramp in a tail-heavy car. Admittedly, your car will experience more rolling resistance from the more heavily weighted rear wheels but, if the starting ramp was sufficiently steeper than the track, your greater initial acceleration off of the ramp will more than make up for it. Therefore, you will get to the finish line a bit quicker. In general, your front/rear weight distribution should be at least balanced. It should almost never be nose heavy. Optimum weight distribution for your car at a particular track can most easily be determined by actual testing when there is no significant wind to influence the results. You must record the elapsed time for each weight distribution. Obviously, you are looking for the setup that gives you the shortest elapsed time. To do so would probably require the use of a stopwatch operated at the finish line by an assistant who received the signal to start the timer from someone at the starting ramp with a radio. The general rule for weight balance is: the greater the angular difference between a steeper starting ramp and a shallower angled track, the more tail heavy you should be. The optimum amount can only be determined by experimentation. If the ramp is nearly the same angle as the slope of the track, and the ramp and track have a modest slope such as at Flint or Akron, then you should run balanced or approximately so.

This Concludes Article 5.

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