The Physics of Pinewood Derby Cars
by
Clifford W. Lazar
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My first car design came in second place. Then I learned the shape of the racetrack. My second car design finished first. The competing fathers were aerospace engineers and mathematicians. My opponents’ cars were tested in TRW’s wind tunnels.
Operating Environment
The Pinewood Derby Cars travel downhill, initially at about a 45-degree angle, through ambient air, not in a vacuum. The track is composed of two parallel runways, each with a raised center median. The wheels of each car are placed straddling the median of their runway.
The cars are held in place, before the start, by a two-tanged vertical fork that is pivoted forward and away from the front of the cars, until the fork tangs are below the respective medians. The tangs move through two slots in the respective medians.
Air Drag is a Minor Factor
There is a small air resistance that means a 5.0 oz. car will travel faster than a 4.5 oz. car, ceteris paribus. At the same time, since the cars don’t exceed 15 to 20 mph, the relative air drag resistance between two cars is a minor factor, contributing little to speed. Wind tunnel testing, at hundreds of miles per hour, is meaningless.
Major Factors: Rolling resistance and Angular Momentum
I have tested, motor oil, graphite, and 3-in-1® oil. Motor oil is too viscous, graphite is the second most viscous. 3-in-1® has the least viscosity. It also won’t last from one heat to another. The pinewood derby car manufacturer recommends against using 3-in-1® because it allegedly deteriorates the plastic in the wheels. We don’t care if the wheels only last 12 hours. Actually, they last for years. If you don’t oil the wheels before each race, they will slow down.
Axles
An often-ignored factor is the drag caused by the axles, which are four cheap nails. I spun the nails in a hand drill bit and used emery cloth to eliminate longitudinal ridges and replaced them with parallel V-shaped ridges (WWWWW). This reduced the surface area of contact between the axle and the wheel to nearly nothing. The wheel rides on 3-in-1® oil. It doesn’t touch the axle.
You want to have the wheels as close to the body as possible to avoid wobble. If the wheel hub rubs against the car body, it will lose energy to friction. Polishing the body as smooth as glass and lubricating the body with 3-in-1® Oil can minimize this.
Angular Momentum
A major factor for the travel time of the car is the angular momentum. If the car doesn’t go straight, the wheels will ride up on the median strip, converting forward speed to chattering increased height. You can hear the losing cars chattering their way down the track. The car manufacturer incorrectly recommends that the extra weight be placed in the center of the car. This is like putting a mid-engine roadster in a drag race. Drag racers are long. They try to maximize their angular momentum. Mid-engine sports cars try to minimize the effort required to turn.
I placed the fish weights evenly in two pairs of holes drilled in the front and back of the car. This created a barbell effect, maximizing the angular momentum. My car wanted to go straight.
Winning the Race Before It Started
Most of the hotshot fathers shaped their cars to look like formula one racers, low slung, aerodynamic. When the fork tangs were pivoted forward and down by the Starter, the low slung cars stood still until the tangs were nearly rotated 90 degrees.
My car was shaped like a landing barge, a funny sight to see: A landing barge beating the formula one racers.
Back ....................................................Front .................Back.......................................Front
The landing barge shape meant that when the tang of the starting fork had moved 10 degrees my car was already moving and ahead of the low slung car, next to it. At 45 degrees my car was already .75 inches ahead of the opponent. Some of the heats were only won by .75 inches. The other guy must have done a good job with his wheels and angular momentum. Still, he lost because the beast will beat the beauty ... if the physics is right.
If you use this design or improve upon it, please email me. Tell me how you did.
Sites: http://www.pinewoodcup.com/ http://pinewoodextreme.com/
Using Superglue on the Axles
Ted Johansen wrote:
My son and I came up with an ugly little car that won all the heats for first place. I stuck to the rules and didn't help my son build his car. I gave him some suggestions that seemed unimportant to him. I had done a little research and decided that rolling resistance was the most important function. I chucked the axles in a drill and polished them with emery cloth. I also removed any burrs from the tread part of the wheels and sanded them making for very narrow tread-track contact. I left the wheels off the car in order to let my son paint and finish the car before final assembly. Final assembly was performed a few minutes before the race. The den leader built a fixture to hold the axle perpendicular to the body during installation (pounding with a hammer). No weight was added to the car and it was very light.
After the races, my son and I were playing with the car on the floor, pushing back and forth across a 10 foot length. I noticed that the car went very straight. I concluded that polishing the axles and sanding the wheels helped, but not as much as having very straight wheel alignment. The car never lost much time rubbing against the side or middle rails. The last few heats were very close. I'm sure the dad's that built sleek cars for their sons didn't like the drubbing they got from a very plain looking car.
I just saw your pinewood derby info. Very informative. I had a few other ideas that helped us win most years -
- angle the nails (axles) so that the wheels were "toe out". Less wheel wobble, and less wheel contact with the track.
- sand the wheels so that the surface was also "angled". Less contact with the track. Also make sure the inner parts of the wheel are sanded and polished (those parts that touch the track guide, and the part that touches the body of the car).
- put graphite on the inside surface of the wheels as well, where they would touch the center "guide" track
- use round stickers as "hubcaps". Before you put these stickers on, fill the center portion of the wheel with graphite. The hubcap "stickers" will keep the graphite in for many, many races. Make sure these stickers aren't sticky at the center, and don't touch the nail axle.
- if you can get away with it ;-), also shape the front of the car so that it is (looking down from the top), a long, inverse "V" shape - that is, exactly the opposite of a "pointed" car. That way, when the car is sitting at the top of the track ready to go, the tang of the starting fork is in the middle of the car (the inside point of the "V"). The outside "points" are maybe 2" farther down the track, already giving you a 2" advantage at the finish line.
Just my two cents - thanks!
On our track you gain a half an inch on every other car. Just be careful of the fragile front!
Good luck next year!
Hi Cliff. Here is a quick variation on a recommendation I read several places on your site. You, and others, mention polishing and/or lubricating the car itself where the inner hub of the wheels may make contact. I agree. My tip is to apply an old piano repair persons tip to this application. Mix a little bit of graphite with isopropyl alcohol. Using a cotton swab, apply just a drop of this mixture to the side of the car where each wheel would rub. The key is to do this after lightly sanding, but before painting the car. Also, cover these spots so they do not get painted. (They should be hidden by the wheels.) The alcohol will wick into the pores of the wood (capillary action) pulling graphite in with it. In one minute or less the alcohol evaporates and you have a wooden surface which is graphite impregnated, and stays slippery for a long time. This is not a liquid lubricant - the alcohol is merely a mechanism used to help apply dry graphite, and it does not remain on or in the car. I haven't tried this with wheels yet. The plastic is certainly not as porous as wood, but like everything else, it is somewhat porous. The alcohol may eat away at the plastic and do more harm than good. If you try, please let us know! JimC.
Brian Kronberg, MCSE: Messaging
Microsoft Consultant
I just wanted to let you know about the Pinewood Cup, The Official Pinewood World Championship. Please visit our site at www.pinewoodcup.com.
Oil Reservoirs
Thanks for your insight. I'm not sure I follow how you replace the ridges on the nails w/ parallel V-shaped ridges (WWWWW). I can eliminate the existing ridges, but how do you add the V-shaped ridges, and why is this an improvement from a completely smooth axle? Also, we are not permitted to oil the wheels before each race. What's your recommendation on a lubricant presuming we can't add anything once the racing begins? Thanks.
Webb Campbell
4/8/03
Here's my response:
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