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Tuesday, January 22, 2008

Observations on the Pinewood Derby

My son's Cub Scout pack held their Pinewood Derby event last Friday night, and I'll note the following:

1. Is it wise to have the wheels titled slightly inward to make the car go faster? An engineering friend of mine suggested it was.

2. Apparently it is wise to have only 3 wheels touching the ground, because there's less friction. I'm not handy enough to make this happen, of course, but many have advised this course of action. If you try it, you'll see that the car goes straight. What has your experience been?

3. It is important to get your car as close to the 5 oz. weight limit as possible, as the weight, properly positioned, helps pull the car down the track. My son's weighed in at 5 ounces precisely, perhaps more out of dumb luck (or a careful application of wood apoxy to attach the 2 oz. weights to the bottom of the car).

4. Is there a specific shape that works? My son's car resembled a Formula 1 car, but apparently there are better shapes that make the car run better, perhaps narrower than the width of the block that they originally give you (you just need to be sure there's enough room for the axels to do their thing). Those that looked more "bullet shaped" seemed to fare better.

5. Does dry graphite powder really help the wheels that do touch the track run better? I'm not sure about this, but I'll take the word of the cognoscenti on it.

6. Does painting the car a dark color somehow make it run slighty faster? This sounded like an old wives' tale to me, but I recall someone's saying it to me a few years ago.

7. Does sanding the axels and smoothing them out make the wheels run faster? Again, I've heard this to be true, but my dexterity with tools is such that I'd probably set the wooden car on fire.

8. Where is the optimal position to put the weights on the car? Many have suggested that you use a router (or a Dremel sander) to carve out a depression in the bottom of the car and glue your weights there. The scoutmaster suggested drilling a hole in the car and inserting the weights, while a scientist friend says that in his troop, they drill the hole and then pour hot lead into it, let it cool, and, voila, you have a finished car. A friend used a Dremel to help sand the bottom, and we used apoxy to affix the weights there.

Of course, the kids are supposed to do as much work as possible, but they aren't supposed to use the power tools. So, our scoutmaster cut the car for us, and a friend helped us make the depression underneath the car to insert the weights. My son sanded, painted and helped glue, and we won both of our heats, but finished in the middle of the contestants overall.

What has your experience been? Please share it, as other readers pull my Pinewood posts up and seek guidance from time to time.


Anonymous Anonymous said...

I'm not an expert on the Pinewood Derby, but I think I can give some background on some of the questions.

2) Running on three wheels as opposed to four shouldn't make any difference at all as far as friction is concerned. Kinetic friction (sliding) is a function of the types of surfaces and the weight of the car -- it is independent of surface area. Now, since the wheels are mostly rolling and not sliding, kinetic friction is probably not the big enemy. When the wheels roll without slipping, all of the friction comes from the axles rotating in the body. As far as I can see, this friction isn't going to be any different when you're running on three wheels than when you're running on four.
The only advantage you could get is if you actually remove the fourth wheel. If you do that, the friction remains the same but the rotational inertia of the wheel-axle system is lower and the car should accelerate faster. It's essentially equivalent to making your wheels lighter. At the end of the day, I don;t know how much difference that's going to make, but it might be worth a try. And, as I discuss below, it is advantageous for other reasons to set up the weights in the car so that running on three wheels will be easy.

4) I don't know much about aerodynamics, but I think the main goal with car shape is to reduce air drag. There are three basic sources of drag on a car: (a) the drag caused by the car cutting through the air (pressure drag), (b) the drag caused by the air moving over the car (friction drag) and (c) the drag caused by the vacuum behind the car as it moves (wake drag). To reduce pressure drag (a), you want to make the perpendicular frontal area of the car as small as possible. Basically, this means a bullet shape, as you noted -- the sharper the better. Friction drag (b) is also pretty simple to minimize. You want to sand down your car as much as possible and apply gloss paint to make it glass-smooth. Wake drag (c) is a little trickier because it's not an intuitive source of drag like (a) and (b), but it's fairly easy to minimize as well. You essentially want another bullet point at the back of the car, again minimizing the perpendicular area. But, as I'll get to below, there are more important reasons why you want the back of the car to be relatively large. All in all, with a moderately streamlined shape and a nice polished surface, I think air resistance is not going to be a major factor. The cars just don't go fast enough.

6) Color has no effect on speed unless for some reason darker pigments typically provide smoother finishes. For all I know they might. And darker colors look cooler, anyway ;)

7) My recollection of Pinewood Derby axles is that they're already pretty smooth to begin with (they're polished steel, right?). I wouldn't try to do anything to the axles. It could be very helpful, however, to aggressively sand the grooves where the axles rest in the body. I vaguely remember that these were typically pretty rough and that roughness could create quite a bit of friction as the axle spins. You might also want to consider painting the grooves with a gloss paint (As long as it's smooth) to make things even slicker. If you did that, you'd definitely want to put some sort of lubrication, but I would lean toward wet lube (like white lithium grease or even 3-in-1 oil) as opposed to dry stuff like graphite. Finally, if you're really ambitious, you could reshape the axle grooves to minimize contact between the axles and the racer body. I'd imagine something like a an inverted-V shape would do pretty well. Not sure if that's worth the effort, though.

8) Weight placement is, I think, where you can get the biggest competitive advantage. The basic idea in the Pinewood Derby is that you're converting gravitational potential energy (henceforth, P) into kinetic energy (K, which is just motion). By conservation of energy, P = K + (Energy lost to friction). To increase K for a given P, then, you want to decrease energy loss (various methods for which I've touched on above). This is the obvious approach and it's about as far as most people get. You can also increase P, however. Note that P = mgh, where m is the mass of the car (which you can increase, but hold that thought for a moment), h is the car's height above the ground (actually its center of gravity) and g is the force of gravity (which you probably can't change). So you have to focus on m and h:
m - the obvious choice here is to make the car heavier. That increases m, which is what you want. I should note that in theory this shouldn't matter, because K = (1/2)mv^2, so the m terms drop out. In practice, heavier cars cut through the air better, so you want to bu right up at the 5 oz. limit.
h - you can actually increase h if you're clever with your weight placement. h is measured from the center of mass of the car to the ground. Therefore, a car with its center of mass all the way at the tail will be in some sense higher when its lined up than a car with its center of mass in the center or at the front will be. In fact, if you get the center of mass all the way at the back, you can effectively gain a 3.5" head start. SO definitely put your weights as far back on the car as possible. As for whether you put them on the high or low, it shouldn't make any significant difference. Do whatever works best with your design.

Putting the center of gravity back farther also makes it easier to balance the car with three wheels. You can take off one of the front wheels and have the car pretty well balanced.

6:01 PM  
Anonymous Anonymous said...

Running on 3 wheels does indeed make a difference but the difficulty in achieving this makes this route moot. The car bouncing against the center strip is the larger issue and unless the wheels are aligned you will not notice any advantage. The same can be applied for tilting the wheels. If it is misaligned then you encounter the bumping.

Aerodynamics have little effect on the race. The length of track and the speed of the cars render the resistance small.

Weight is a huge issue and this is where you gain the advantage. There have been arguments for weight in the back but I've seen an evenly weighted car (front, middle and rear close to evenly weighted) lead a race (it eventually was damaged).

12:39 PM  
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Anonymous Anonymous said...

Don't over analyze it with math. The one floating wheel definitely makes a difference, and cars with the weight all the way to the back are very prone to jumping track about halfway down track when it hit the bottom of the decline and the track then flattens out. The axels have ridges that like to be polished out as does the wheel surface, and yes graphite makes a major difference. When you think it's ready, spin the wheels as fast as you can with the car in your hand and each wheel should spin around 20 seconds, if not work on it more. One more thing, if you glue your axels, be extremely carful not to get any near the wheels and keep the wheels just a little looser from the body than you would think. Good Luck, see you at the races!

8:29 PM  

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