why weight your Derby car?

January 18, 2006 10:36 AM

The physics behind the Pinewood Derby...

OK, my little Tiger Cub and I will race our first Pinewood Derby tonight. I had quite a time building the little wooden car. Every PD website I went to recomended adding extra weight to the car, right up to the 5 oz limit, as the wood alone usually weighs about 2.5 oz. This required quite a bit of extra work to get the weights in.

So it got me thinking - since the wheels and axels of all competing cars must be the same (as required by the Derby rules), how could a 5oz derby car go faster along the same track then a 2.5 oz car? What would Galileo say ?

posted by shino-boy to sports, hobbies, & recreation (38 comments total)

Aerodynamics.

You're dealing with only a few forces. Gravity, the friction of the wheels against the axles, and the drag.

I think there are certain requirements, right? The car has to have a maximum and minimum height and width, it has to weigh no more than 5 oz., etc.

I think your best strategy is to go for something that's as thin as possible and which has the center of mass towards the front of the car. Also, a smooth finish will add an additional fraction of a percentage of performance.
posted by bshort at 10:40 AM on January 18, 2006

It's all about friction. Greater mass equals greater downwards force (downwards force = mass * acceleration, where acceleration is earth's gravity, 9.8m/s^2). Friction increases marginally with the weight also, but not as much as downward force, is my guess.

Keep in mind that the same is actually true of falling objects also -- things fall at the same rate only in a vacuum. In the air, a bowling ball falls faster than a feather due to friction with the atmosphere.
posted by RustyBrooks at 10:46 AM on January 18, 2006

I think your best strategy is to go for something that's as thin as possible and which has the center of mass towards the front of the car. Also, a smooth finish will add an additional fraction of a percentage of performance.

and through anecdotal experience, I can say that these are the ones that usually won. If you're not going for "Best Appearance", the flat bars with the weights right in the front usually seem to finish well.

The first year I raced, my dad just help me cut out the standard recommended pinebox shape (and we drilled a couple holes in the bottom and stuffed them with weights) and that did pretty well, but i don't recall it placing. I think the next time I did it I tried to do it myself and I designed a monstrosity that lost to the eventual winner of "Most Creative" or whatever (which was somewhat of a disappointment, as he had lost to everyone else but me.)
posted by fishfucker at 10:51 AM on January 18, 2006

The race will be won or lost based almost entirely on one factor: Friction.

Where is this friction?
Between the wheels and the axles
Between the side of the wheels and the side of the car
Between the bottom of the car and the raised part of the track
Between the wheels and the track.

What is the solution?
Make the wheels as smooth as possible. But, don't make them smaller -- the bigger the wheels, the less contact there will be between the car and the raised part of the track. In fact, if the rules allow it, make the wheels bigger somehow.

Make sure the wheels are not tight against the car.

Use tons of graphite or other friction reducing stuff on the wheels, axles, the bottom of the car, and the sides of the car. Yes, it will make the car ugly -- and fast. If you can find something better than graphite, use it.

Aerodynamics are a small factor. Don't have a block of wood racing down the track. But don't stress it too much, either.
posted by JekPorkins at 10:52 AM on January 18, 2006

By putting the center of mass at the back of the car, you position the center of mass higher at the start, resulting in higher potential energy. The mass has slightly more time to accelerate since it's higher. I wonder if gains from mass placement really outweigh losses from wheel friction and wobbling. Seems losses from air drag would be almost negligible except for the most degenerate of designs.

I loved Pinewood Derby as a kid though, even though my car sucked.
posted by ldenneau at 10:58 AM on January 18, 2006

Where is this friction?
Between the wheels and the axles
Between the side of the wheels and the side of the car
Between the bottom of the car and the raised part of the track
Between the wheels and the track.

Unless your car is skidding the entire way there is no friction between the wheels and the track. There will be friction between the side of the wheels and the side of the raised part of the track and between the wheels and the axels, but that's it.
posted by bshort at 10:59 AM on January 18, 2006

Unless your car is skidding the entire way there is no friction between the wheels and the track.

Not so sure about that. Any time you have contact between two surfaces, you'll have friction.
posted by Witty at 11:01 AM on January 18, 2006

The winningest car I ever saw looked like a missle with axles (it was my brother's - I always went for the 'most creative'). All the weight was perfectly centered, it had very little drag, and, because it wasn't a wedge, there was no lift (think airplane wing). We spent hours polishing the axles and the wheels with fine liquid abrasives.
posted by jmgorman at 11:03 AM on January 18, 2006

Not so sure about that. Any time you have contact between two surfaces, you'll have friction.

Well, trivially, yes, but in the case of a wheel you don't have enough force to overcome the static friction, which is good, so you'll never need to talk about kinetic friction.

The last thing you want to do is to put graphite on the "tire" part of the wheels.
posted by bshort at 11:08 AM on January 18, 2006

There will be friction between the side of the wheels and the side of the raised part of the track

Um, that's the wheels and the track. And if you just use the wheels straight out of the box without any sanding/smoothing, they're bumpy and will have uneven traction and tracking, which leads to friction problems.

If the wheels are turning on the track, that's because of friction. You either want the wheels to have even, smooth friction with the track that allows them to turn at maximum efficiency, or you want zero friction, which means they'd be skidding all the way down the track.

Bottom line: smooth wheels, well-lubricated axles. Make sure the inside edge of the wheel is smooth, too.

If you want to be super badass:

mount the axles so that the wheels are not very close to the car, then put a tiny bead of solder on each axle between the wheel and the car (maybe put the solder there after putting the weel on, but before putting it all on the car) Apply lube liberally. This will make sure that the wheel has no contact with the car, thus eliminating a major source of friction.

The only reason a feather falls measurably slower than a bowling ball is friction. The same is true of a pinewood derby car. Eliminate as much friction as possible, and nothing can go faster than your car.
posted by JekPorkins at 11:09 AM on January 18, 2006

Um, that's the wheels and the track.

Yeah, I was talking about the "tire" part of the wheel and the track.
posted by bshort at 11:11 AM on January 18, 2006

Do the wheel bearings have to be the same as everybody else's? If not, buy some small precision ball bearings, wash the oil out with kerosene, and dry them. Then adapt the wheels to accept the bearings. (If you dry them with compressed air, don't let them spin while you do it; that galls the races.)

Or put a small matter-transfer device on the car, to remove air from in front and insert it behind the car.
posted by Kirth Gerson at 11:17 AM on January 18, 2006

Since a pinewood derby car doesn't have any engine driving the wheels, and since the track has no curves that would require the wheels to have grip, there's no good reason that the wheels need to maintain traction on the track, except, possibly, to transfer the friction issues to the axles, which are smoother than the track. I wouldn't worry about whether you get lube on the "tire" part of the wheel or not, since skidding isn't going to affect the speed of the car unless the skidding is caused by the wheels not turning on the axles freely.
posted by JekPorkins at 11:17 AM on January 18, 2006

Okay, here's the science:

The standard soapbox racer is powered entirely by gravity. Gravity pulls the car down the hill. If the car has a greater mass then the component of the weight acting parallel to the 'course' is greater. Take a look at these images.

The force labelled mgsinθ is what is pulling your car down the hill. If you increase m, you increase that force. As Newton once said: F=ma; therefore larger force = larger acceleration = quicker gain in speed.

It's worth noting that the frictional force acting opposing the motion of the car is F=μN, where N is the normal reaction force, in this case mgcosθ. Therefore, increasing the mass of the car will also increase the frictional force. Without knowing the details it's impossible to say which of these factors will be most important "on the day".

Good racing! I want follow-up!
posted by alby at 11:18 AM on January 18, 2006

bshort writes "Unless your car is skidding the entire way there is no friction between the wheels and the track."

Rolling friction.

I agree with JekPorkins: it's all about friction. And there's a (possible unethical; I'm not sure about the rules) way to cut your friction by 25%. File down one of the wheels such that it doesn't come into contact with the track. The car has to be properly balanced so that it will roll on three wheel, but if you manage this, you've got it made.
posted by mr_roboto at 11:20 AM on January 18, 2006

I'm a former "PWD" Champion... seriously. I know it sounds silly, but I have assembled multiple cars with my father using professional tools in our basement.

Some key factors to remember:

Distribution of weight - spread it out evenly over the car. Putting all the weight on the back does not give you a "boost"... it give you drag.

"Smoothness" - PWD is a game not of inches... but centimeters. When you have shaped the block to your liking, sand it, then paint it, then wait for the paint to dry... then repeat the sand/paint/dry two more times.

Oil the wheels - You should never hear anything when you roll your car. Lightly oil the wheels prior to weigh-in... lightly wrap the blanket in a thin towel and keep the car away from other competitors.

Another thing... if possible, place the weights inside the car. We have a machine used for just that... if you go through the phonebook you should be able to find a carpenter to help.
posted by bamassippi at 11:22 AM on January 18, 2006

Expanding on mr_roboto's idea:

Will the rules permit you to modify the car so that it has two wheels in back and one wheel in the center of the front, so that the front wheel rides on the raised center part of the track? If so, that would both eliminate one wheel's worth of friction, and eliminate car-against-track friction entirely.
posted by JekPorkins at 11:23 AM on January 18, 2006

mr_roboto writes "cut your friction by 25%. "

OK; it's not 25%, since you're redistributing the same weight amoung the remaining three wheels, but it'll still be a significant reduction.
posted by mr_roboto at 11:24 AM on January 18, 2006

Another piece of advice: don't let one of your son's friends run the car for him while you go to a basketball game. Amazingly enough, little kids *will* do shit like put superglue instead of graphite in your bearings.

As for weight, I made something like an airfoil to keep the weight off the wheels, but made sure it was the regulation 5 oz. As an eight year old, i *thought* it helped, but that was also the year of the superglue incident.
posted by notsnot at 11:30 AM on January 18, 2006

As I recall, the "axle" is actually a finish nail pounded into a slot in the car blank. I could be wrong though.

I saw a few good methods of weight inserting when I did this back in the day.

The first was to buy cylindrical weights, and drill holes in the car, and epoxy the weights in. The second was to create a cavity however and fill with molten lead.
posted by RustyBrooks at 11:35 AM on January 18, 2006

Static and kinetic frictional forces are simultaneously acting on the car for all but the first instant of its descent. Static friction acts between each of the four wheels and the track and prevents them from skidding, while kinetic friction acts between the axles and the wheels and reduces their maximum rate of rotation.

As far as the wheels go, you don't want them to lose traction (i.e. static friction) with the track. In addition to losing energy to heat from kinetic friction between the wheel surface and the track, you'd also be losing angular momentum that builds up in the wheels as they spin faster and faster.

My advice would be to lubricate the crap out of the axles and try to reduce any wobble from their spin as possible. The more times the car bounces off the side of the track, the more speed you'll lose.
posted by pmbuko at 11:40 AM on January 18, 2006

pmbuko has a great point about why you wouldn't want the car to skid.

Also, before you go messing with molten lead, think about whether you really want to be exposing yourself to that.
posted by JekPorkins at 11:47 AM on January 18, 2006

Or your Tiger Cub... I mean, he IS building this car, right? :^)
posted by Witty at 11:49 AM on January 18, 2006

On one hand, it would be theoretically good if the kid did it all themselves. OTOH, it was way cooler to "help" my dad, since he did stuff like melting the lead sinkers with the blowtorch, and shaping the car with a full-size drum sander. Stuff that I wouldn't have been allowed to do on my own, and I woulda been stuck with a hacksaw.
posted by smackfu at 11:57 AM on January 18, 2006

Witty:
My Tiger is "supervising" the project... Way to put me one the spot! :)
posted by shino-boy at 11:58 AM on January 18, 2006

The winningest car I ever saw looked like a missile with axles

Same here. Kind of a teardrop shape, actually.
posted by frogan at 12:22 PM on January 18, 2006

I woulda been stuck with a hacksaw.

I was stuck with a hacksaw, and while my car probably would have never beat yours in a race. In a dark alley, it would have been another story.
posted by dial-tone at 12:23 PM on January 18, 2006

I didn't have any tools, nor a father-figure to help me. I had a hammer, chisel, and paint. I chisled out a vaguely car-shaped chunk, hammered in the wheels and painted it blue and yellow.

Oh, and I glued some scavenged washers to the bottom because I saw that everyone else had added weight to it too.

Mine finished dead last. I don't know that it completely made it down the track. I hated those kids who obviously had their father make it for them. Good times!
posted by unixrat at 12:23 PM on January 18, 2006

some college should really run one of these for their undergrad or grad students.

looks like we'd have some good competition just with the people in this thread.
posted by fishfucker at 12:39 PM on January 18, 2006

The Pinewood Derby has very specific rules, which eliminate a whole lot of the tactics already discussed here.

I think these (geocities, sorry) are the BSA's most recent official rulings. At least they were the last time my brother did it.

Shino-boy, your pack or den may also have more specific rules. Be sure to check these out. It's not really helpful to talk about "fastest Pinewood Derby car" if the car's going to be eliminated before the race begins.
posted by booksandlibretti at 1:06 PM on January 18, 2006

Having *assisted* with four PWD cars with my son years ago I can advise you to centrally MAX the weight (Hobby Lobby and Michaels craft stores sell weight kits) SMOOTH the axle with wet emory cloth, stick as much graphite in as possible and make one front wheel not touch the track. Wedge shape seems to usually win.
My son came in second three years in a row (his first car was mostly art). The thing is, really, I spent HOURS with him at Derby Time and now that he's 20 I have a wonderful warm feeling when I look at those cars, displayed proudly in my den.

Win or Lose... YOU win
posted by dkippe at 1:27 PM on January 18, 2006

Back in the day, the winning cars in our area were as flat as possible (usually a slight wegde to allow some weight in the back) and weighed exactly 5 ounces.

Here's a tip to help on the wheels/axles that makes a huge difference in performance from car to car (but does not directly address the mass difference):

Chuck the axle into a drill and start it spinning and lock it running. Then with progressively finer grades of emery cloth, polish them until smooth. Then, if you have a buffing wheel, polish them further. If not, you can probably use rubbing compound on a soft cloth (think cloth diaper).

As far as mass difference, it has to do with drag. At the mass of these vehicles, two cars with identical design will have identical drag and the drag can be significant. Which car will be affected more by drag? The one with less momentum. Which car has less momentum? The one with more mass (f = ma).
posted by plinth at 1:41 PM on January 18, 2006

I was glad to see boksandlibetti point out that there are very specifics do's and don'ts among the PWD requirements. I'm still scarred by having my car disqualified AFTER being presented the championship, even though it was built according to the rules (which were amended the following year to make my winning car illegal). This was around 1971. Thanks for building a winner anyway, dad. (Yes, he did a lot of work on the car, as I would gamble is the case on many of the fastest and best-looking cars).

Incidentally, I recall that way back then a lot of the cars were plugged with lead in the bottom. At race time the cars were weighed in using a very accurate scale, and an electric drill was used to drill out small amounts of lead to bring the weight down to the maximum legal weight. My car looked like a soap box racer, nothing fancy but aerodynamic. Dad made spacers for the axels to keep the wheels from wobbling so the car ran a little more smoothly. Still, you shouldn't give a kid a big trophy and then take it back.
posted by JamesMessick at 1:50 PM on January 18, 2006

plinth writes "As far as mass difference, it has to do with drag. At the mass of these vehicles, two cars with identical design will have identical drag and the drag can be significant. Which car will be affected more by drag? The one with less momentum. Which car has less momentum? The one with more mass (f = ma)."

Whoa, there, big guy. First of all, I'm sure you meant "Which car has less momentum? The one with less mass (p=mv)". Right?

The force calculation you're interested in is F_n=F_g-F_d, where F_n is the net force on the car, F_g is the force on the car from gravity, and F_d is the force on the car from air drag. I'm neglecting friction and treating force as a scalar (direction is figured in with the negative sign in that equation). Let's also neglect the fact that drag is a function of velocity, since I'm not in the mood for calculus right now.

F_d is the same for cars with identical shape; let's call it the constant D=F_d. F_g=mg, where m is the car's mass and g is gravitational acceleration (9.8 m/s/s). Then we have F_n=mg-D. Since F_n=ma, we can calculate the rate of acceleration of the car as it speeds down the track: a=g-D/m. So the heavier the car, the greater the acceleration.
posted by mr_roboto at 1:57 PM on January 18, 2006

Lots of good stuff here, bringing back great memories. From a family that won a few spots in the PWD back in the 60's and 70's, I'll add a few things:
- Use a dry lubricant (like graphite powder). Liquid lubes will gum up.
- Sand/buff/smooth down the nails that the wheels sit on.
- Make the shape as aerodynamic as possible.

Good luck! And enjoy!!!
posted by ObscureReferenceMan at 4:36 PM on January 18, 2006

The one with less mass (p=mv)
Geez, yes that's what I meant. Damn fingres typed the wrong thing.
posted by plinth at 8:38 PM on January 18, 2006

Follow-up:

Dead last (third out of three) after 4 heats.

That's the way the racer...rolls!
posted by shino-boy at 10:50 PM on January 18, 2006

If you get a chance, please post a picture of your PWD car!
posted by bshort at 6:59 AM on January 19, 2006