School is about to start once more (thank God) and my son is already thinking about the Boy Scouts annual Pinewood Derby. He won 3rd place last year and is determined to win Grand Champion. For those who don’t know, the Pinewood Derby is a race. Each boy is given a hunk of wood and four wheels about a month beforehand, which they carve into a car and paint. The maximum weight limit is 5 grams, which is just how much the hunk of wood weighs before anything is done to it. Since the cars run on gravity (they start on a chest-high ramp) obviously you want to get as close to the 5 grams as possible. That, along with a streamlined shape and judicious use of graphite lubricant in the wheels, ensures a fast trip. Most of the boys glue coins or nuts to the cars to get the weight up. My question is, is it better to have the weight on the back of the car, in front, or in the middle, or does it really matter?
I’m pretty sure you mean 5 ounces. 5 grams is the weight of a coupla pennies. Damn metric system…
You can buy lead weights specially made for 'em. It’s more precise than coins. The weight should be evenly distributed. The custom-made lead weights are long and flat to achieve this.
The major speed limiting factor on these tiny cars is probably rolling friction. Thus the lubricated axles. Therefore, you’d want the weight distributed as uniformly as possible over the wheels. Since the vehicle is on an incline and has thickness, you want the weight to be slightly towards the back, so that the force vector goes right between the wheels on an incline. Imagine a car that was 4" thick and only 1" wide. If the weight was in the middle, then at a high incline the front wheels would carry much more load than the back.
I thought a pound was sixteen ounces. Five ounces is also the weight of a few pennies.
I suspect she meant five kilograms, about eleven pounds.
I suspect that the best weight arrangement is where it is evenly distributed between both axles, as dhanson said, but it’s not immediately obvious why:
Friction in an axle is proportional to the weight on that axle.
Imagine one extreme is where all the weight is on one axle and none on the other; call this the one-axle case. The other extreme is where each axle bears the same weight; call this the two-axle case. Obviously, in the two-axle case, the weight on each axle is one half of what it is (on the weighted axle) in the one-axle case.
Now if friction is exactly proportional to the weight, the total friction is the same in the two cases. The one-axle case has twice the friction per weighted axle as the two-axle case, but the overall friction is the same.
BUT, If friction does not rise perfectly linearly with the force, but rather increases faster, then the friction will be less for the two-axle case. I’m not enough of an engineer to know nonlinear friction is, but it wouldn’t surprise me to learn it isn’t perfectly linear.
My premise is that the friction isn’t linear with weight, but I can’t state that with certainty without going back to my old textbooks. It might actually be discontinuous (i.e. linear up the point where there is enough force to strip away the lubrication, at which point it would take a fast jump), but again, I’d better not say for sure. Hopefully, someone a bit more current than I am will jump in here.
For an unpowered race on an incline the most important factors are likely to be friction, and stability. Making the wheels round, and the axles centered and parallel to a very high degree will do a lot to improve performance. At low velocity smoothness of the surfaces is likely to have only minor importance, but still give some performance improvement. Rolling straight and having a low loss of speed from hitting the sides of the roadway (a channel?) could be the most important aspects, though, if the layout is stringent enough to make that the limiting factor.
Tris
I can vouch for this. I tried square wheels once and it really cut into my time.
no, no. These are small cars. I think 5 oz. was correct.
APB, as a former cub scout and vet of the Pinewood Derby, I can testify that five ounces is the correct weight. Also, unless things have changed in the past few years, the wheelbase is standard and unalterable, as axle channels are precut into the block of wood you get.
To the OP, we found a few secrets over the years. Overdo it on the graphite lubricant. Sand the rough spots out of the wheels and make them as perfectly round as possible. Use a thick laquer over whatever paint you apply. (No demonstrable speed effect, but looks darn cool) Remove as much wood as you can and make up the weight by filling a drilled hole with lead solder (pre-weigh the amount of solder you use so you’re not left short.) Some more advice- leave the last bit of the hole open and close it with a cork. Place the weight out at just under five ounces on a postal scale (that’s usually what they use). Carry some lead shot or small fishing weights with you to the event and add just enough to even out at five ounces on their scale. Replace the cork. Wa-la.
Finally, watch a shoddy vehicle that looks like it was constructed by a wolverine with mad cow disease consistently run faster than the masterpiece you spent so much time on. Because as everyone nows, the pinewood is all about having a good time.
APB9999
The pinewood derby cars are limited to 5 ounces (141.75 grams), which in pennies would be 57 cents (A penny weighs 2.5 grams.)
stolichnaya
The wheel base is not standard and unalterable, unless they’ve changed the rules recently. The precut blocks do have wheel grooves, but they are not mandatory. The only requirements as far as that goes is that the entire car be able to fit in a box 7 inches long and 2.75 inches wide, and clearance has to be 3/8 inch (the cars are guided by placing them on an inclined track with a raised strip betweeen the wheels).
dhanson
Weight should not be evenly distributed. Although minimizing friction is important, and you should be careful to not overbalance the car, the weight should be as far back as possible. The farther you can move the rear wheel axles back the better, and then the center of gravity should be about half an inch in front of that axle.
The car starts on an angle and is powered entirely by gravity. Once the car hits the bottom of the track, it runs only on its momemtum. So, you want to maximize the potential energy at the top of the track, which will be converted to kinetic energy along most of the length of the track. Moving the center of gravity back from the center of the car to one inch from the rear can mean the difference of a couple car lengths at the end of the track.
One consequence of this is that the car should be as low as possible. A high center of gravity would not only tend to destabilize the car, it actually causes a slight negative shift in effective potential energy. (Imagine the weight at the top of a leaning flagpole at the top of the track, then the flagpole vertical at the bottom of the track. The top of the flagpole could actually be higher at the bottom.)
That’s why you see a lot of the winning cars that look like thin flat pieces of wood–they’re actually almost solid lead in the back. They achieve this by drilling holes into the wood and slipping lengths of solid core solder into the holes. Pretty boring. So let 'em go crazy with the paint.
Maybe it was a local rule, but I have a clear memory of a friend being disqualified for making his own axle holes. You could change the relative wheelbase by lopping off the front and/or back of the original block of wood you get- but the wheels had to be that standard distance apart.
I’m not saying here that RM is wrong, just that you might want to check the rules in your local race before altering the axle guides. It sucks to be disqualified.
In my troop, the prize with the most prestige was always the “best decorated”, anyway. I still have my “Batmobile” which took the prize in 1985 or thereabouts. It is important to note that the “Batmobile” placed dead last in the first two heats. I think that may have had something to do with the drag characteristics of the plastic flames belching menacingly from its afterburner.
Pack 53 of Black Hills, SD
http://www.rapidnet.com/~ethor/pack53/pinewood.html
“The wheelbase (distance between front and rear axles) may not be changed from the body kit distance of 4-1/4”."
And pack 258, location unknown:
http://www.3n.net/people/jjenkin/pwdrules.htm
“Wheelbase may not be modified, it must be the same as the official kit.”
Pack 49, of Austin, TX
http://www.main.org/boyscout/drbyrule.htm
says, “If desired, you may change the wheelbase (distance between front and rear axles).”
RM’s characterization describes the official BSA rules, but the wheelbase alteration seems to be a fairly common local proscription. Check your local rules.
Here’s how I won a pinewood derby as a wee lad:
(1) Low profile body design to reduce drag, smooth all edges
(2) Wheels were slightly milled by a machinist friend
(This insured perfect roundness)
(3) Polished wheels on the insides where they touch the track rail, plus the hole and surface where they touch the axel
(4) Axels were polished, including the nail head surface that rubs against the wheel
(5) Lead weight, distributed mostly towards the back
(6) Generous use of graphite on wheels and axels
(7) Nice glossy paint job to make it look good and possibly reduce drag
When I weighted the car, I made it slightly heavy. My thinking was:
(1) My scale might be a little off
(2) The race scale might be a little off
(3) The judge might not check that accurately
The lead was accessible from the rear of the car and I brought a tiny jewler’s screwdriver to dig out any excess lead if my car was too heavy. As luck would have it, the car passed with no need to dig (I’m pretty sure it was over the limit, but who am I to argue)
One of the most important steps was fine tuning the alignment. Once the car is completely done, run it down a smooth board (I drew lines the width of the track). Watch to see which way the car pulls and adjust the axels to compensate. When I was done, my car could roll about 10 feet down my board without veering outside the lines. Once I was happy with my alignment I was careful to never put undue stress on the wheels (always handle the car by the body).
Remember, even with a great car, the track can be a big factor. Sometimes the track undermines your alignment and causes you car to drag. Watch carefully and if you see your car pulling too much in a particular lane you may be able to appeal the results of a heat and rerun in a different lane. I never had to do this, but I’ve heard of it being done.
Good point. Some competitions insist upon an official kit, and you cannot add wood to the kit. Sometimes the wheelbase is set to 4.25 inches, sometimes it is 4.5, sometimes there is a range. Sometimes you can cut wood off the back, and glue it to the front–which wouldn’t change the wheelbase, but you could move the back wheels back that way. You’d want some car body behind the wheels anyway, just to hold the lead weights.
I didn’t think to try it back in my Pinewood days, but now I wonder if you could make a three-wheeler. Cut an oblong hole straight down through the wood and cross drill a small hole for the axle, then hold the wheel in the right place and insert the axle from the side. And since it would be riding on the raised center of the track (3/8"?), you’d probably want that axle 3/8" higher. I hope you can all picture what I mean.
The advantages are lower rolling friction and (minimally) less drag. But there might also be an interesting stability question. The only way the cars stay on their tracks is when the wheels brush against the raised center. With the single wheel in front, the rear wheels might wedge against the raised part of the track, or you might get increasing left-right oscillations. And with the single wheel in the back, I’m not sure how that would fit in with the balanced weight/rearward c.g. debate.
I understand the argument in favor of a rearward center of gravity, and I like it. I’m not sure I know the theoretical basis for wanting the maximum weight allowed (and I have studied a fair amount of Physics). A heavier car has more potential energy at the start, and more kinetic energy at the finish, but it needs more kinetic energy for a given speed. Think Galileo here. My best idea is that the energy loss to friction and such isn’t strictly proportional to weight. For example, if energy loss was constant for every car, that would correspond to a greater speed loss for a lighter car. Can anybody confirm that theoretically or experimentally?
I wonder about three-wheelers too. Even if there is a rule against modifying the axles, maybe there’s no rule against eliminating the right front wheel and putting a weight on the rear left side of the car. Might be tricky to get it to run straight, but it would cut down on the rolling resistance. You also don’t waste energy spinning up the 4th wheel.
By the way, are you allowed to modify the wheels? Reducing the weight of the wheel by making it thinner and/or drilling holes should help. Also narrower wheels (smaller contact patch) have less rolling resistance, I think.
Quoth RM Mentock:
Depends-- In my pack, the entire track was sloped, and it just ended when it reached floor level. In this case, the net vertical change for the weights is the same for weights in front or back, so the potential energy argument doesn’t apply. Also, I’m pretty sure that air resistance is more significant than rolling friction, but I can’t back that up. In any event, you ideally want to make your car as flat as possible, and possibly narrow (think a cylinder with streamlined wing-like pieces holding the wheels), so as to reduce the cross-sectional area (the major consideration for drag). Another thing you can try is to buy extra kits and make a couple of cars, and test them at home and enter the fastest. I did that one year, and got my best time that year.
One other tip that has nothing to do with physics: If a person is acting overly secretive about their car, mention it to the officials sooner, rather than later. One year when I was racing, there was a boy who used an illegal axle, and was ultimately disqualified for it in the semifinal round, but by that time he had already eliminated many of the other racers, myself included. I had earlier in the race asked him some minor question about his car, and he quickly hid it and protested his innocence.
As Chronos said, the rolling friction–given that you use sufficient lubrication and take care with the wheels–is less significant than the air resistance. A heavier car will overcome the drag easier, but I’m not so sure it’s as critical as you’d have to eke out the last milligram.
One year, my son’s car had an adjustable weight, and he ran it on another pack’s electronic track as part of his science experiment. Moving the weight back made a lot of difference–but of course it wouldn’t make any difference on a track built like Chronos’s. The only tracks I’ve seen, at district and state competitions have had a steep section at the beginning to get the cars up to speed quickly.
Chronos only said the whole track was sloped, not that the slope was constant along the entire length. A rearward c.g. will give the car a boost anytime the slope decreases, even if it doesn’t go to zero.
Is there anything in the rules about movable weights in the cars? Imagine a Pinewood Derby car with a lead weight inside it that could slide front-to-back. Now put a spring in to press the weight backwards, and compress the spring by squeezing the weight to the front. You need some sort of catch to hold it in place and release it during the race. When the spring moves the weight backwards, the car will accelerate forwards. Once the weight reaches the end of its travel, the speed will drop back to what it would have been anyway, but it might be worth a few carlengths.
Of course, once we start looking for loopholes the sky’s the limit. How about a car with a tiny compressed air cannister that could give a little bit of thrust during a race.
Can you add your weight to the wheels? I’m thinking that this would reduce the friction load on the axles, and the weighted wheels would store energy as angular momentum, much like a flywheel. I can see the argument for putting the weight at the back, so what about having heavy rear wheels and light front wheels?