Wednesday, January 28, 2009

Pinewood Derby happy conclusion

Just after submitting a school assignment that had been giving me anxiety for the past week, I rushed to put the wheels on the two cars and get to the race in time. I always think that the next year I will be ahead of schedule but I always end up finishing right before the race.

Shule ended up winning the race with his toad car driven by a pokemon! This is great because this is his last year so he went out with a bang. I was surprised to find that although Shazer's car didn't do too bad, it was not as close as I thought it would be to Shule's. I inspected it after the race and it turns out that there was a problem with one of Shazer's wheels, there was some glue involved in the final preparations and some got on the wheel. When we left the house I checked that the wheel was spinning freely but I guess the glue wasn't totally dry and in transit some must have seeped where it shouldn't have been. Considering this handicap, it did well and Shazer still has 2 more Derbies to look forward to. His sleek design won the "Most Dynamic" award.
You can see here that before painting, I masked the car around where the wheels go. I smooth this area and apply graphite because the back of the wheel rubs here.
Last night I put the weights in and smoothed out the wheels. I didn't have a scale so I used Shule's first car as a standard and I pieced together a balance with a ruler and a jar of paint.
This simple balance turned out to be quite accurate! When we got to the race the cars were right on and no adjustments were made. The race went quickly; there were only 11 cars this year. All the fuss has paid off and Shule will get a trophy next month at the Blue and Gold banquet.
This is a video of the winning race, look at the left side of the screen at the very end of the video, Shule and Shazer give each other a high five. That's the best part and I nearly missed it.

Thursday, January 22, 2009

Physics of the Derby *Bonus*

Here is a bonus post on my thoughts on the physics of a pinewood derby car rolling down the track.

There is really only one thing that makes the car move-gravity.
I drew a simplified diagram of the situation. I simplified the car to just a point mass. There are 3 forces on the car: mg- the force from the gravity of the earth, N- the normal force from contact with the track, and f- the frictional forces acting opposite the direction of travel.

The car only accelerates in the downhill direction of the track, I have designated this direction as the +x direction, which makes the normal force in the +y direction. The only force with a component in the direction of acceleration is mg, we can break it into x and y components to get a better look at what's going on.

Since the car doesn't move in the y direction we know that the magnitude of mg in the -y direction is equal to the magnitude of the normal force in the +y direction and those forces cancel.

We are now left with only x forces:

We want to sum these forces and set it equal to ma, or mass times acceleration by Newton's famous F=ma. So we watch our angles carefully and discover that the magnitude of mg in the x direction is mgsin theta.

The rolling frictional force from the wheels on the axle and wheels on the track can be represented with a constant k multiplied by the magnitude of the normal force which is the same as the y component of mg. If we assume that the race will take place in a vacuum then this is the only friction that we need to consider. This gives us an interesting result:

The acceleration of the car and thus how fast it will go down the track does not depend on the mass of the car! Reducing the friction of the wheels is the only thing you need to do to build a fast car. So why does everyone say that if you add weights to your car it will help you go fast?
Well, it might be that I have neglected important factors in my simplifications. I should put the race back in an air filled environment so the spectators don't have to bring their own oxygen. This will introduce another frictional force from the air but from what I've seen so far in my classes, this force has little effect in many cases and often times is neglected. Either we have in vain been putting weights on our cars for years or conventional wisdom is correct and air drag makes enough difference for us to bother with attaching weights.
It all depends on what the coefficient of friction is, which I believe involves the density of air and the shape and density of the car. This can be found experimentally. With that term added our expression now looks like this:

The force of the drag is proportional to velocity. This makes me very curious now and I want to get that track and do a bunch of tests with varying weights and other things to find out how much effect this really has.
The placement of the weight may have something to do with the stability of the car also, to figure all these things out I'd have to do a more complicated analysis and look at the car as something more than just a point mass. I'm not going to do this, and now that I think of it, the urge to do a bunch of tests is leaving me too. I'm feeling content enough to just get those wheels turning smoothly, put weights on the cars till they are 5 ounces and enjoy the race.
I would like your input on the matter though. If you happen to have any insight on these things please let me know, I'm sure I've missed something.

Tuesday, January 20, 2009

Pinewood Derby part 2, axles and wheels

The nails that make the axles have a few bumps on them out of the box. To smooth them out I mount the pointed side of the nail in the end of a power drill leaving the whole surface that will contact the wheel exposed.
I spin the nail and first use a small file to get the bumps out.

That's just not going to be smooth enough for me though so I will then start using sandpaper, keep doing it over and over with a small strip of increasingly fine sandpaper.

If you look in the paint section of the hardware store you will find some pretty fine sandpaper. What I have is 600 grit wet sandpaper. I've heard of finer sandpaper but Home Depot didn't have any. This will give you a pretty smooth nail. I also like to make sure that the underside of the nail head is smooth, that area will also contact the wheel.

There is a theory that if less area of the axle comes in contact with the wheel it will spin faster so some people make grooves in the nail, reducing the area of the wheel in contact with the nail. I'm not convinced this does anything because friction depends on the mass of the car and the coeffecient of friction of the materials which are rubbing and it does not depend on the ammount of area in contact. If you reduce the area in contact, you also increase the load per unit area so it all evens out. Another "myth" that I've seen searching the internet and heard a few fathers talking about last year is that if you raise one wheel up so it doesn't touch the track it will make your car faster. By the same reasoning I say this is false and while I've witnessed fast cars that only have 3 wheels touching, I think it could make your car a little more shaky. So I'm going to stick with what I've learned from Newton.

After getting super smooth axles you should think about the back part of the wheel that will rub against the car, smooth this out and apply graphite here. Also put graphite on the part of the car that touches the wheel here. One more thing that I just thought of this year is the rubbing of the inside of the wheel on the raised part of the track that keeps the car in the lane. I'm going to make sure that part is smooth as well.

Wow, do I sound obsessed or what?
Hope this is helpful to someone out there.

Thursday, January 15, 2009

Pinewood Derby 1 of 4

The pinewood derby is a model car race for scouts age 8-10. It's a simple wooden car with plastic wheels held on with nails as axles. They roll down a sloped track accelerated only by the force of gravity. The key is to make the wheel movement on the axles as frictionless as possible by smoothing out all surfaces that the wheels may rub against.
This will be my third pinewood derby as a scout leader. The race is two weeks away and the last two years my son Shule has been in the program so we made cars together. The first year he made the "Mammal Mobile".
He decided to make it brown and green camouflage with yellow eyes in front. The pink sticker is just for identification purposes during the race and wasn't part of the design. It wasn't a bad car but we got to the race as it was starting and didn't have time to apply any graphite. This was a disastrous move and I'm pretty sure his was the slowest car that year. Each time it went down the track you could hear the squeaking of the un-lubricated wheels. His was the only car that sounded like that! I felt so awful but he won the "best paint job" award and went home not totally devastated.

With lesson learned about how important graphite on the wheels is the next year was much better. He made the "Titan" which was to resemble a ship. He placed 4th out of about 18 and it was really very close. This is his car on the right just coming in short of the second place winner in red. You can imagine how close he was to the third place car.

The derby is the biggest and potentially the funnest event of the whole Cub Scout year, it doesn't come without stress though. The biggest issue I have with the race is that building a suitable car is not a job that most 8-10 year olds can practically do. It is almost totally necessary to have help from family and scout leaders which is fine but because of the competitive aspect (trophies are awarded to top 3 places) it just gets a little weird knowing that the boys don't all get equal ammounts of adult help. In order to combat the potential injustice, our troop devotes 3 January meetings to working on the cars together so kids without access to tools and help at home can have a chance for adult leaders to help. Seems like a good idea but what we can do is still limited and we mostly just get the cars shaped and sanded which has a neglidgible effect on how fast the car is. Getting the wheels straight, spinning smoothly and the cars weighted up to 5 ounces is what makes most of the difference and these are the last things you do.

When I was a kid I remember participating in 2 derbys, I vaguely remember a red car and a blue car. I remember working on my back porch with the block of pine and a hand saw. I made a cut that looked fine from my angle but it turns out that it was croocked and the cut on the other end of the block went partway through where the axle was supposed to go. I was very upset and felt that I ruined my car. Tears were shed. Later I did get help to salvage it and we were able to make it so the wheel would stay on and I could race it, but I never had one of the fast cars. It was ok that I never placed, I would have liked to but looking back on it I'm glad I even knew how to use a saw by myself even if I couldn't cut straight. My boys aren't good with a saw, I think most 8 year olds who aren't raised on a farm or in a woodshop or something won't have the muscle to properly use a hand saw and heaven knows we won't let them get their hands on power tools. I don't even know how to use a power saw.

So I let my boys design the car, I cut it with the hand saw and they help with sanding and painting. I have them help a little as I spin the nails in a drill and smooth and polish them. I try to explain about reducing friction and why we do these things but until the race is actually happening, they pretty much only care about making their car look cool.

This will be Shule's 3rd and final race, but I now have Shazer in the program so we are doing 2 cars this year and we have brother against brother which adds a whole new level of competetion. So far we have the cars cut and have started to do some sanding. Shule's toad car is to the right and Shazer's rocket style car to the left (facing away from the camera to show off the fancy rear).I will do 3 more posts about the derby, one next week all about getting the wheels and axles ready for speed, I'll post some photos and share what tips I know. Then I'll do a short post just before the race to show how the cars turned out and another just after the race with the results of course.