Physics & Design of Cub Scout Pinewood Derby C

Quite a few years ago (late-1970s), my grandfather helped me design a car which took 2nd place. The concept and style of the race (heats, lane changes, etc.) sounds the same although I'm not sure if the stock kit is still the same, so take my suggestions with a grain of salt. My grandfather and I whittled away a large chunk of the block of wood and dug a trench into the underside of the car. He filled the trench with solder, but bunched the majority of it very close to the front of the car; with enough through the rest of the trench to provide stability. The result, the car was front heavy so that it picked up speed in the decline and maintained it into the final straightaway.

The only reason I lost is that my car was placed in the dreaded "slow" lane in the finals.

One last thing STL, it's really great to hear how involved you are with your kids. I hope they realize how lucky they are. Good luck to you and both your kids!

This is one of the contests put on by Cub Scouts to see whose father is the least ethical. :-) I helped my son minimally, but lost only to a mechanical engineering professor's son who, as far as I could tell, never touched the car. The secrets are to minimize the weight on the lousy bearings, thereby minimizing normal forces on the nails and wheel bearings, grinding the wheels to a sharp edge, thereby minimizing the rolling friction between the wheels and the track, and either sanding it to an extremely smooth bare wood or painting it with lacquer to minimize wind resistance. None of these factors are significant in the big scheme of things, but added together, along with the things you mentioned, will give a slight advantage.

After many years of racing pinewood derby cars, I'm convinced that the ability to roll straight is a huge part of car performance. If you watch cars that don't perform well, they tend to bounce from one limit to the other on the guide rail. Straighter rolling cars seem to go faster.

This leads one to being very careful with alignment of axles and wheels. I'm assuming that the car is right up to the 5 oz. limit. I've never seen a light car do really well.

Incidentally, in order to encourage the kids to build their own cars, we sometimes have a "Dad's Race," where Dad can build a car and race it. That lets Dad get his competitive urges out while still letting Junior build his own car. Recently, a local BMW drivers club picked up on the whole idea. After coming to us for advice, they have started having their own annual pinewood derby (they borrow our Pack's track).

Disclaimer: My son's cars never did really well, always middle of the pack.

Thanks for the replies, but some of you are missing the point. Conventional wisdom is often wrong. It starts out because someone assumes that something is a major factor when other factors are more critical. The conventional wisdom can sometimes even by completely backwards, when true science is applied.

I cannot understand how a front-weighted car can be faster, unless, as noted by the last poster, the steering/straightness was just so much better than all the others. Physics shows that a higher center of mass will yield a greater final speed. I agree with the other poster that minimizing weight on the wheels reduces friction, that is why I do not understand how increasing weight is supposed to make a car faster, unless of course that weight is all placed to the rear (higher up the incline). There is a point however, where a rear-heavy car allows the front end to "pop up" and bounce around, possibly rubbing its wheels against the center guide strip (there are no side guide rails in Derby racing). The ideal center of mass is supposed to be just slightly forward (about 1/2 inch) of the rear axle.

Also, in our Pack and District (local BSA organization within the regional Council) no modification are allowed to the wheels except to remove the molding projection ("gate" in engineering terms), so trueing of wheels (for roundness) or sanding the profile (to minimize contact) is NOT allowed. We even had a little heated discussion between the Cubmaster and one Dad when the winning cars were examined after-the-fact and found to have modified wheels. The second-place (and third-place) car's wheels were NOT modified. However, the rules stated that any cars that passed inspection before the race must be allowed to compete. Eventually, they decided to allow the boys to keep their medals for placing within their age groups, but NOT to award a Pack trophy this year!

So, back to my original question, all other things being equal, should weight by maximized, minimized, or it makes no difference and why? Please use physics to justify your answer, not empirical observation!

As far as weight goes, P=mv. With P always constant, assuming the high point on all track pairs is equal then a higher mass will yield a higher velocity. With moving bodies through air, the most important parameter is frontal area. The most aerodynamic shape for a vehicle is slighly bowed upward in the center. So the ideal shape should be kind of like a hot dog with the cm centered laterally near the bottom side of the center of the tube tube on the longitudinal axis. If you can fabricate the axle mounting holes so that they are adjustable to allow the wheel base to be identical side to side and that the wheels are all parallel to the center line of the car and that the axles are parallel to each other. Test the rolling resistance of the wheels with the permitted lubricant on as issued fat axles vs. polished skinny axles to see if the lubricant can withstand the added shear stress of a smaller, smoother contact area. If you can design the shape to provide any lift at all it will reduce the drag on the wheels and the center guide rail, an important consideration if the guide rails are not identical or identically lubricated.

Whooaaaa! P=mv, if P is momentum, then it is NOT always constant in this situation. Firstly, original velocity, V(0), is zero! If P is constant, then the mass would have to change for a change in velocity, and we know this cannot happen! No, I think you have to apply the law of conservation of Energy here, not Momentum. PE=KE, potential=kinetic. Please re-read my writeup on this in the original posting.

Yes, I know that aerodynamics are important. Most winning vehicles are very thin, either wedges or "skateboards". You need to have full width at the wheels anyway, so frontal area is the same as your "hot dog", with the benefit that widening the body and spreading the mass makes the vehicle more stable. If you wanted the vehicle to spin around the longitudinal axis, then, yes, a "hot dog" would make more sense, like when a figure skater pulls her arms in to spin faster.

I would be concerned about providing lift with the body. Lift could lighten the load, but at the expense of increasing drag, which would slow the car. You don't get something for nothing!

Also, you may polish the axles, but that does not effectively reduce the diameter, and if it did, that would allow vibration in the "bearing" which would be worse than the minor savings in friction. Also, straight axles and wheels are a primary goal to maintain straight steering. This is well known. I am still looking for justification of the conventional wisdom of maximizing weight, and I just do not see it!

Exactly. So dP/dt=F=f(g)=PE @ t=0,v=0. My thought about lift was that if there is some kind of slipper affair on a guide rail whatever aerodynamic drag you induced to provide lift would be less that any physical sliding contact with the guide rail. Since we're looking for tweaks with very small incremental improvements in speed frictional losses to bearing drag are very important. If the axles extend from the sides of the car so that the wheels are hanging out on stalks, profile the axles to reduce drag.

I would say, also, that another key to having a faster derby car is distributing balast mass to the aft of the car as this has the benefit of increasing the center of gravity of the car when it is on the slope, so that when the car reaches the flat portion, the car's center of gravity has moved further down and transfered as much potential energy to kenetic energy as possible.
Secondly, this method has it's drawbacks(especially the added weight over the rear axle), but reducing shock loads on the aforementioned poor bearing surfaces will keep the load as light as possible for the slope and transition to flat. This is achieved sometimes by elaborate cuts into the bottom half of the car, but usually requires one or two precision cuts a few MM above the belly of the racer on the front and back to have an effective swing arm suspension. This method shows results especially when there is a non-uniform track surface where a small bump would normally send the whole car momentarily off the surface of the track, now only a fraction of the weight is affected.

I am not sure what kind of cuts you need to make to get "swing arm suspension". Don't you run the risk of the car being damaged or broken in handling if you weaken the structure enough to allow it to flex? At least in our Pack and District one is not allowed to ADD any materials (springs, struts, etc.) to create any "independent suspension" effects.

Unfortunately, the car does become more fragile simply due to the fact that it isn't a solid block any longer. However, you don't need to add any materials to the racer. The simplest method is to put the block on a band saw, cutting from the rear bottom, creating a hump over the back axle thick enough to make a sturdy mount for the wheels, but then cut within 1-3 mm of the belly of the racer for anywhere from 25-75mm, creating a somewhat flimsy section that gives some bounce. Additional material can be cut away above the cut to allow for travel but the full thickness of the cut can be used as an effective bump-stop to preserve the flimsy section from breaking under heavy loads. It isn't exactly independant suspension, but can be adapted to be. This simple cut will give a suspended rear axle and can be repeated for the front in the same manner.

Maybe all the parents should take a step back and see what the real point of this race is. What does WINNING really get you, especially if mostly the parent did the work. Look at the children who have won previously, are they better or worse off than the kids who had fun with their father figure and built a cool car that made it down the track. We try to emphasize that winning isn't everything, but how will kids ever know that unless winning REALLY isn't everything. Be a good role model. Teach THEM to think, not just to win.

NOOOOOOOO.......the point of my question was physics, not philosophy. And I do not build the kid's cars by myself. The creative concepts are their own ideas, with some guidance in the excecution of those ideas. I involve them in every step of the process, to the point where something might be beyond their skill or comprehension. Perhaps they will even learn a little bit of engineering and physics, not just woodworking!

As an engineer, I show them how the car is designed FIRST, on paper in this case, before any wood is cut. Then I show them how to mark the measurements on the block, what will be cut away, and what will be left.

I also try to explain why some cars may be faster than others, so they learn some physics. Which brings me back to my main point, is it better to maximize or minimize weight and why?

By all means keep the weight at max. As a veteran of soapbox derby, I have given much thought to this problem and the determinants of overall speed are: max weight, minimum effective cross section, aerodynamic flow (parting flow in front and departing flow in the rear, absolute roundness of wheels, absolute centricity of axle, absolute perpendicularity of the axle to the plane of rotation of the wheel, perfect geometry of axles and direction, and (in your case) an aerodynamic vane(rudder)in the rear to maintain direction. You could also experiment with dimpling to induce good turbulence to reduce drag (like on a golf ball. Good luck and enjoy!

"By all means keep the weight at max." Why? What law of physics justifies this statement in this situation? If you read my original posting, I think you will see that I made a pretty good case for increased mass being a neutral, or even negative factor. Location of the CENTER of mass, however, would give different results, theoretically, all other factors being the same.

I do like two of your ideas. The rudder (which I was thinking about already) and the dimpling effect. Dimpling could be revolutionary, if effective. I have not seen this implemented in any Derby cars. I wounder how large and what geometry the dimples would have to be. What is "good turbulence" versus "reduced turbulence" (from a streamlined rear)? Does golf ball dimpling actually increase speed for greater distance or simply reduce spin, and therefore reduce curving (like when a baseball pitcher throws a curve ball or a sinker by spinning it at release) yielding a straighter, and therefore farther, flight?

Hmmm...I googled the dimpling effect of golf balls and found that it would not apply here:

'The secret of dimples: The golf ball gets tremendous back spin from a drive shot, spinning as fast as eight thousand revolutions per minute. As the ball spins, the dimpled surface traps a layer of air that rotates with the ball, like a small whirlwind around the ball's surface.

Since the ball is traveling forward, the layer of air spinning on the top of the ball is moving "with the wind." And the layer of trapped air along the bottom of ball is moving "against the wind", so it is slowed by this wind resistance. As a result, air pressure builds up at the bottom of the ball, and the ball rises, much like an airplane wing.

The importance of the turbulence caused by the dimples is quite surprising. Without dimples, the ball would travel only about three-fourths as far. But there is a down side to dimpling--the ball has a greater tendency to hook or slice.'

First, I have to say that your participation in your sons'activities is both selfless and in the best practice of fatherhood. You are an icon. Regardless of the outcome of the race, the greatest outcome is the relationship you are building with your sons. I based my recommendation to keep the weight at max based on the experience of soapbox derby participants. The experience is that if the car is too light, the difference between the air resistance vector and rolling friction vector(drag)and the vector producing forward force (thrust produced by weight--mass in a gravitational field)is smaller than the vector produced by a heavier (more weight) car. If one were to run the cars in a vacuum, on a frictionless track, then the weight would not matter. A feather would accelerate as fast as a cannonball. In fact, this is a popular physics demonstration using a feather and a ball in a long tube under vacuum. To comment on dimpling and other laminar flow turbulence inducers: the effect of inducing small amounts of turbulence is that it breaks up boundary layer formation on areas of the object. The boundary layers are "stickier" than the micro-turbulent areas. The catch to this is that to see and adjust the effect some sophisticated measures are needed--like a wind tunnel. Reflecting on the max speed of the pinewood cars, dimpling or surface roughening may be a very small factor. The greater factor might be the reduction of the reduced air pressure area forming on the rear of the car as it gains speed. Ideally, the air that is parted at the front could be redirected to fill in the little vacuum caused by the end of the car leaving the space. The practical effect is that a squared off car end will drag more than a tapered end. The squared off end creates more vacuum drag and bad turbulence. I hope this clears up the previous post.

Ok, so from a seasoned veteran of the pinewood derby (I won two years in a row) I can vouch for the fact that the weight does matter, although I don't know why...the cars that I won with were shaped like a formula one car with all of the extra weight hidden on the under side. I also concur that keeping it straight was HUGE, and it may rank the highest in importance. Second would be decreasing wind resistance, and third would be polishing and painting. Also, just for the record, I did do my own design work (I told my dad that I wanted it to look like a race car) and all he did was do the cutting, I had to do the rest. Even though I was fortunate enough to win a little bit, I would not say that it was a big deal in the long run (although it was at the time), my father worked out of town and I only got to see him every other weekend, so giving us the time to work on something together was very, very important to me both at the time and now. Sooo in conclusion, a.) if you want to go fast, make it heavy and aerodynamic and b.) everyone wins when fathers and sons work together

OK, here's why. Force = d(mv)/dt. Heavy cars have more "mv" even though their velocities are the same as they approach the straightaway. Retarding forces that do not depend on weight such as aerodynamic drag will have a greater percentage effect of changing "mv" and thus "v" on lighter cars. So heavy gets the nod. You can express the change in velocity (from max) as being equal to Retarding Force times delta t divided by mass. Delta t is roughly the overall race time.

So a 5lb car and a 5oz car with the center of mass in exactly the same location would cross the finish line at the same time, all other factors being the same?

At the start of the run both cars (same c.g.) accelerate with a "component" of gravity. If the track is 45 degrees the acceleration rate of both cars is .707 times g. Absent friction, at the beginning of the horiz. run both cars have accelerated to same speed. Again, absent friction both cars cross the finish line at the same time (Newton's First Law) However, from the starting point both cars are retarded by friction which causes them to lose speed (from what they would have had if zero friction)as they progress along the track. Aerodynamic drag is a function of shape and velocity, not mass. So shapes being equal result in equal drag forces. The heavier car will slow down less. Axle friction is proportional to weight (thus mass) so the heavier car will experience proportionately greater retarding force than the lighter car. The result is that given equal coefficient of friction the speed changes will be the same. RESULT: shape-equal and coefficient of friction -equal ...... heavy car wins.

My son is doing a science project on this. We are planning on running a test where we use the same wheel base and two different body shapes that can be connected to the wheel base. The design of the wheel base will also permit addition of weights.

I am not an engineer but I like the logic of your post. Some questions though:

1) when you say "the heavier car will slow down less" is this because higher mass is less affected by drag forces, all other factors being equal (i.e. - same body shape)?

2) as weight or mass changes it seems unlikely that the coefficient of friction will remain equal. The coefficient of friction i would imagine will increase as weight/mass increases, so this will reduce the speed of the heavier car.

1) and 2) above are countervailing forces, so unclear to me which will prevail as weight is increased, "all other factors being equal".

Is it really ok to just say "all other factors equal"? Would the test show the same results with respect to added weight if we are comparing a really poor body shape design to a really good one (aerodynamically speaking)? Are there diminishing returns for weight offsetting drag forces as aerodynamic drag forces get lower? In other words, does the benefit of higher weight in reducing drag forces have a better chance of prevailing over an increase in the coefficient of friction if drag forces are kept low? If I understand correctly, if there are no aerodynamic drag forces at all weight wouldn't matter at all - other than its impact on the coefficient of friction, so it almost seems to me that the more aerodynamic a car, the less helpful added weight will be.

Here are the tests we are thinking about running:

1) Using the same wheel base, test speed of each body type with total weight for each body type equal to A.

2) Using the same wheel base, test speed of each body type with total weight for each equal to B (where weight B is substantially higher than A)

3) Increase weight in less efficient body type until it produces equal speed compared to more efficient body type (perhaps diminishing returns will make this an impossible goal?).

Instead of testing speed, would it be equivalent to test total distance travelled for each test run?

It seems to me the trickiest thing in this test will be to keep the "straightness" of each body type the same. Any suggestions on 2 simple but very different body shape designs in terms of aerodynamic efficiency that will be roughly equal in terms of "straightness"?

Will post results

"By all means keep the weight at max." Why? What law of physics justifies this statement in this situation? Namely, Newton's Law of Universal Gravitation. The attractive force between two bodies (in this case the car and the Earth) is proportional to the product of their masses and inversely proportional to the square of the distance between them. Both cars start at the same height and assumed to have same center of gravity. Mass of Earth is obviously constant during the few seconds of the race. Big G is obviously a constant. This means there is more attractive force (i.e., gravity) between a heavier object and the Earth than a lighter object and the Earth. In equation form, F = G(m1*m2)/r^2. m1 is the only variable in a pinewood derby race in this equation at the start of the race. If a lighter car having less starting energy wins the race, it certainly isn't because it weighed lighter. It's because the heavier car had enough drag due to wind resistance and friction from axle-wheel interaction that it dropped the heavier car's energy level to below that of the lighter car. Ergo, heavy, aerodynamic, and polish the heck out of the axles and use lots of graphite. (And my own opinion here, don't put the weight entirely in the back and you want to consider the handling stability of the car by centering weight slightly rear of center of the car).

My grandson (with help) followed your formula here "to a tee" and placed second in a field of 32 and will be in the division races May 13. The cg of his car is about 1 inch offset back from the car's geometrical center. His dad polished standard axles and attached the wheels. I added a lot of graphite on race day. I will post final results in May.

Please do post how your grandson does, I'm interested to see if the offset give any advantage in real time.

I posted the above reply. My son just placed 2nd in the district pinewood derby race out of a field of 83 cars. The car that beat him was, imagine that, aerodynamic, 5oz exactly, covered in graphite and was balanced 1.5 inches behind center of car. The other car won by what looked like less than an inch. I'll be using this approach above again when my younger son starts in cub scouting.

Well, congrats to your son! Interesting. It seems that second order effects will finally determine the order of finish. My grandson is still waiting for May 13. I'll post results.

PE never equals KE, otherwise you could have a perpetual motion machine. PE minus losses due to friction, air resistance, heating, etc. = KE. Because you don't have mass terms in the losses part of the equation means you can't cancel out the mass term from PE and KE. You have to think of the Pinewood Derby problem in terms of energy and how mass affects the energy state of the car. Just my .02 worth.

Four wheel car running as fast as can down track, all weigh the same. Alter one axle so that wheel does not touch track, counter weight to keep that wheel from touching. three wheels touching less rolling resistance. I will let you figure out which wheel!

The energy lost to friction would be proportional for light cars and heavy cars.

It takes some energy to spin the wheels. For a lighter car, this is a higher proportion of its initial energy than it is for a heavy car.

The bigger effect, though, is due to air resistance. Air resistance depends on the surface area of the cross section of the car. Heavier cars go faster not because they are *heavier* but because they are denser. They increase the weight without increasing the cross section much. If you made your car heavier by adding a bunch more pine wood, that would not help (much)