Pinewood Freak

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Maximum Weight

January 2nd, 2007 · 29 Comments

I constantly hear from dads who remember from high school physics classes that mass doesn’t affect the rate at which something falls. If dropped in a vacuum, a bowling ball and a feather fall at exactly the same speed, so the same should be true of a Pinewood Derby car as well, right? If this logic holds up, a three ounce car should be just as fast as a five ounce car.

The problem with this logic is twofold. We’re not just testing the rate at which something falls; on most tracks, half the track is sloped and half is flat. And we aren’t running in a vacuum; there’s lots of friction involved.

The only propulsion your car gets is the conversion of potential energy to kinetic energy as it rolls down the sloped portion of the track. Once it reaches the flat part of the track the only thing that keeps it going is the energy it already has. The more energy it has when it reaches this point, the faster it will go.

Let’s perform an imaginary experiment. Imagine that bowling ball and that feather both dropped from 3 feet in a vacuum. Both will reach the ground at the same time, but they’ll have very different amounts of energy when they hit. Now, put an egg under both before you drop them. The egg underneath the feather will survive the impact. But when the bowling ball hits the egg — well, let’s just be glad this was an imaginary experiment.

The bowling ball had more energy after its fall because it weighed more. A Pinewood car that weighs more will have more energy after it “falls” down the slope of the track. And more energy is good, beacause that’s what keeps the car speeding along.

Comments

29 comments so far ↓

  • Tod // Jan 12, 2008 at 7:03 pm

    This article is so funny because the physics it purports to be true are simply not so. If you want to understand where weight fits into the grand scheme of pinewood derby, you need to understand the concept of inertial mass versus what we generally refer to as mass. This is very challenging territory. Einstein used this very concept to unravel the secrets of General Relativity. And the person that wrote this page is, quite simply, no Einstein.

    The bottom line, don’t buy the bunk on this page. Weight location in the car is several orders of magnitude more important than the actual weight. Friction is even more important than weight. Done properly, the weight is just about as important as aerodynamics.

  • Adam Kalsey // Jan 14, 2008 at 9:39 pm

    Tod, I smell a troll. I considered simply deleting your comment as not to confuse people, but since other people might hold the same belief as you state in your second paragraph, I thought I’d address it.

    First off, readers, don’t get confused about Tod’s mention of inertial mass and other mass types. Gravitational mass is simply how an object interacts with a gravitational field (what we often refer to as weight). Inertial mass is how an object resists changes in motion (inertia). Unless you’re studying quantum mechanics or very advanced physics, you can assume the two are the same thing. Einstein pointed out that it should be impossible to measure an difference between an object’s gravitational and inertial masses.

    Your car needs to have as much inertia as possible when it reaches the flat part of the track. That’s all that keeps it going. Friction will rob your car of energy, so the more of it you have to start with, the faster you will be.

    Here’s how you can determine the amount of energy your car will have. The formula for calculating potential energy is PE=mgh, where m is the mass of the object, g is gravity, and h is the height of the center of mass. On Earth gravity is constant. So the only ways to increase PE is to increase mass and height. You’ll only be able to raise your mass’s height an inch or two from its default of four feet, an increase of a few scant percent. But you can double your mass from it’s default of around 2.5 ounces.

    So Tod, you build a car weighing an ounce and using ball bearings or whatever. And I’ll build a 5 ounce car using stock kit parts. And I’ll beat you down the track by several feet every time.

  • Redneck Joe // Mar 22, 2008 at 8:47 pm

    Adam,
    You’re putting down Tod and vice versa. You’re both missing the point. Loosely throwing around physical quantities like mass and energy. Come on.
    The heavy car wins for this reason…
    The net force acting upon the car and sending it down the track is the sum of three main components:
    1) Gravity: mg * sin(angle of the track from horizontal)
    2) Friction: mg * (coefficient of friction between wheels and axles) * cos(anle of the track from horizontal)
    3) Air drag
    Yes, there are other frictional forces. They are beyond the scope of the discussion I have read between the two of you.
    The heavy car wins because with increasing mass, #3 becomes a less significant fraction of the sum of the forces. The air drag is the same for the 3 oz car and the 5 oz car at the same speed. Force of gravity and force of friction increase roughly proportionally with increasing mass. But the delta between the two (the NET force on the car due to gravity - friction) becomes greater as a ratio to the retarding force applied by the air.
    Let me know if you want it explained in more detail with deeper math.
    The heavier car doesn’t win because it has “more energy” after the sloped part of the track to carry into the horizontal part. For goodness’ sake, man. You cause me physical pain.
    The 5 oz car would have no advantage in a vacuum.
    It wins because the air drag is a smaller fraction of the difference between the gravity vector and the friction vector.
    I have spoken.

  • Adam Kalsey // Mar 23, 2008 at 6:58 am

    Redneck Joe — In most races, the cars are roughly even when they reach the bottom of the slope. The winning car is always the one that slows down least after this point.

    The way to accomplish that is maximize the energy the car has when it reaches this point, and minimize the energy losses after this point.

    I’ve observed many races in which an significantly underweight car and a car that eventually ended up in the top 5 were within a car length of each other at the bottom of the slope, but the underweight car didn’t even have enough energy to carry it over the finish line.

  • Kevin Butler // Apr 2, 2008 at 8:25 pm

    The cars start out with no kinetic energy (KE), and potential energy
    PE = mass * height*gravity.

    As they roll down the track, that potential energy is converted to kinetic energy - assume no friction, 100% conversion:

    mhg = PE = KE = 1/2 m * v-squared

    If you increase the initial potential energy, you get more kinetic energy.

    You can increase that initial potential energy by:

    1- increasing the mass - more mass, more potential energy, more kinetic energy, but velocity remains constant, because the increased mass is on both sides of the equation. This increased kinetic energy helps you avoid slowing down as much from the forces of friction.

    2- increasing the height (how do you do that? the track is a constant height?). The height that matters is the difference in height between the center of gravity of the car at the top of the track, and the center of gravity at the bottom of the track. Since the car starts out on a slope downwards to the front, putting the center of gravity further back increases the initial height (and thus potential energy, kinetic energy, and more velocity).

    So, increase mass to help the car retain its speed as it travels, position the mass toward the back to give additional velocity from the increased height based on the sloped starting track.

    kb

  • Aaron // Dec 11, 2008 at 6:24 am

    Hey you nerds, help me out with some basic tips, not thoeries. Remember, a large amount of us live in a practical world.

    Respectfully requested.

  • Adam Kalsey // Dec 11, 2008 at 9:13 am

    Aaron, the basic tip is make sure your car weighs as much as it is allowed to under the rules. And on most tracks, putting the weight toward the back is helpful. See http://pinewoodfreak.com/2005/12/14/speed-tip-weight-to-the-back/ for more about weight location.

    Sometimes armchair physicists want to dispute the elementary science behind that by introducing all sorts of theoretical science. But as you’ve pointed out, cars don’t race in a theoretical world.

  • SteveP // Jan 13, 2009 at 2:18 pm

    KB is right. Not an armchair physicist here, multiply degreed Mech Engr. He did leave one thing off his benefit of increased kinetic energy from the increased mass. There’s more energy to combat the F due to aerodynamics which is defined as the cross-sectional area times the drag-coefficient times the square of the velocity. Drag is > zero on these races, its probably more significant than friction.

    The force of friction is a factor in these that has a bell curve. Too little weight, friction from the track will be larger than the directional force of gravity. Too much weight, than friction rears its ugly head again with these little plastic wheels. I’ve not done any testing on the friction of the axles as a function of mass/weight but I doubt anything under 1lb will be significant frictional force change. Just gut feel. ;-)

  • Hypertech Pine // Jan 26, 2009 at 2:04 pm

    You guys can dispute the physics in this, Im not an engineer, Were just 11 time winner.
    The fact remains max weight is the only way to go if you want to win. The air resistance is completely insignificant, its not scale speed its 20 mph or so on a very small surface area. All things being equal, i.e. axel and wheel bore smoothness, alignment, the heavier car wins hands down.

  • Dave Taylor // Jan 26, 2009 at 7:21 pm

    Hypertech pine is correct. all other things being equal, heavy wins. Aerodynamics in a 30 foot track don’t mean squat.

  • Handsoff // Apr 2, 2009 at 9:09 am

    Two questions:

    1. Did your kids really build the cars?

    2. Are the trophy’s you’ve won because of all your technical expertise displayed in your kids bedroom…or in your offices?

  • ridin' the pine // Apr 12, 2009 at 1:55 am

    so if weight is the only thing that matters, and you race two cars that weigh exactly the same, with the same kit parts and the same graphite lubricant etc; which car wins? Is it the smoother finish? the lower profile? the wedge, the tank, the cop car, the pencil? Shape’s gotta count for somethin, right?

  • Rukkian // Apr 15, 2009 at 9:45 am

    I do not think anybody would try to claim that size, shape, etc do not matter, just not as much as weight.

    Typically you see alot of the Tiger cubs (at least in our pack) come in well under weight, with no way to adjust it, and they get smoked, no matter what else they did with the car. This causes a big difference in finishes for Tiger cubs than for the older kids.

    With the older dens that have done it a few times, they all weigh pretty close to the max, and then other things come into play, but usually the cars are pretty close to the same for speed.

  • Rookie // May 5, 2009 at 6:15 pm

    So, my 4-year old son ran his car in the Awana Grand Prix a few weeks ago (Awana version of Pinewood Derby)…first time for both of us. We built his car on a Sunday before I had to go out of town and it seemed pretty quick. When we finished, it was well balanced, ran straight, minimal friction, slick and smooth. We thought not bad for a bunch of rookies. Might not take it all, but we were curious to see how we’d do against the the field. I went out of town for a work trip and left instructions for my son (and wife) to leave the car alone until race day. We even built it a shoebox garage to keep it safe while i was gone. I came home on Wednesday night (race night) and discovered only two of the four wheels still turned. Not good. Someone had been playing with his car on the carpet and someone else let him. In the process of pulling the carpet lint from the wheels, I deceided an emergency axle change was in order…1 hour before the race. In the process, I broke one axle and then broke one wheel. Hmmm, two wheeled cars probably aren’t fast. We piled into the minivan and off to the race we went. I told my son we had to shift focus from putting out a winning car to putting out a surviving car, like the guys in NASCAR who put a wreck back together and go for as many points as they could get. He got it and he was with me. Race Comittee spotted us two new wheels, I had two spare axles. Whe hammered them home and got three out of four wheels working again, lots of friction, pulled right, wobbled. Grrrr. Weighed in, measured in, ran slow…BIG victory. We not only survived one run, the car ran all four of its heats and didn’t lose any of them (3,3,2,2). Great job, son, great job. Thats what I call a comeback. Lots of lessons for all. First, tweak the car and sweeten it up with all ther tricks you all are discussing here, put in the work with your son and make a sweet, fast car. Second. leave the car alone until race day (duh). Third, don’t freak out at your wife and kid (like I did) if they unknowingly trash the car before the race, but do ensure they learn the lesson of why not to do it again. Fourth, never give up. Fifth, have some popcorn and lemonade and be thankful broken plastic wheels are the biggest problem you faced today. We’ll get ‘em next year, and I’ll vault the car before the race. Not bad for a bunch of rookies.

  • Troy // Dec 7, 2009 at 3:50 pm

    THE DEFINITIVE (and simple) ANSWER to maximum weight…

    1 gram means about 1/8″ difference at the finish line - and race timers measure 10 times closer than this. All else being equal, a 4 oz car would be over ½ car length or 4″ behind a 5 oz car at the finish line.

    To properly manage your car weight, realize:

    A) It is about the same importance as friction control (lubrication)

    B) It is about the same importance as air drag control (streamlining) - the statements above disputing this are not accurate.

    C) It’s easy to get maximum weight, compared to optimizing a) or b), so effort-wise its almost free if you have a good scale.

    For those who want the data to back this up, read the Dr. Jobe’s lectures at
    http://www.pinewoodderbyphysics.com/lectures.shtml
    For those who are not convineced, by his book!

  • Hyper-Tech Pine // Dec 14, 2009 at 9:40 am

    Aerodynamics of a pinewood car are soo insignificant (unless your hanging parachutes off the car) your time would be much better utilized on wheel and axle preparation
    alignment, proper weighting and location, lubrication and break in are all about a 1000 fold more important. Our computerized timer testing of multiple body designs with maximum allowable frontal areas vs minimal wedge frontal designs determined NO significant differences in real world application.
    Read what you like, but like everything on the internet its not reviewed by editors or piers verifying the information to be accurate

  • arlington // Jan 18, 2010 at 6:21 pm

    Kevin Bulter has it right.

    Potential and kentic energy are not theoretic phyics or even advanced physcis, they are taught in basic high school physics and have application in every day life…. like pine wood derbys.

  • Andy // Feb 17, 2010 at 8:58 am

    When me and my kids have built their cars, we alway get the weight to 4.9 oz; we leave .1 oz leeway just in case the scales at the Pack/District read differently. How much difference does .1 oz make? Is it worth it for me to get it to 5.0 oz? I’ve been doing this for 3 years now and have always wondered that.

  • reddog83 // Feb 23, 2010 at 12:52 pm

    We are having an unlimited wheels/weight race just for bragging rights. i would think too heavy might hurt in the flat section? EX: hollowed out derby kit full of lead - max weight for size

  • David H // Feb 27, 2010 at 12:38 pm

    The maximum kinetic energy will be associated with the biggest difference in the center of gravity from top to bottom. If your weights are in a fixed position, you can optimize the shape and weight placement by knowing the angle of the ramp.

    One dynamic way to do this is to have a shifting center of gravity, one that is high at the top and low at the bottom. This can be accomplished with a hinge-based design. The hinge allows the weight to be positioned at the highest possible point, which could actually be above the track starting point. As you reach the bottom, the hinge allows the weight to flip to the lowest possible point just above the track base. This will give you the largest delta in your center of gravity.

    Part of the design challenge will be designing a damper to minimize wheel bounce as the hinge flips down.

    If someone can pull off, he’ll have the most mechanically advanced pinewood derby car ever.

  • reddog83 // Mar 15, 2010 at 5:44 pm

    Results from the outlaw race are as follows. 69 ounce solid steel “pinewood” derby car with steel ball bearing wheels. ran 2.78 seconds. it actually ran the average speed of the regulation cars. Turns out the friction in the wheels was just too much with the extra weight. Oh well should have done more testing before the race. At the very least it looked cool and was indestructable. PS: My son won fastest car out of 75 cars in the pack - 5oz on the nose.

  • mark // Mar 22, 2010 at 5:06 pm

    Theoretical physicist. Much nonsense here. Keep your kids in school and have them design the car for themselves.

  • Jason // Mar 28, 2010 at 11:33 am

    Anyone know a good size and weight for a gravity car?

  • Hypertech Pine // Sep 23, 2010 at 12:49 pm

    reddog83
    should have used high quality needle bearing wheels like really good in line skates do!

  • Rob // Dec 29, 2010 at 1:38 pm

    Your all a bunch of tools..let the kids build them, so what if they lose at least they learned something

  • Blackhawk // Apr 23, 2011 at 5:49 pm

    Handsoff,

    Doesn’t the Dad need to teach the children how to build cars? We don’t throw kids a math book and tell them to learn it. Dads who don’t care much about learning how to build fast cars, cannot teach their kids how to build them. My kids build their car and I teach them. Isn’t that what Scouts is suppose to be? Who are you to say anything?

  • Bill Klingler // Feb 11, 2012 at 9:26 am

    Mr. Troy, you’ve been reading Hodges Hobby House and Dr. Jobe and you are absolutely correct. I’ve been building cars for 27 years and still host our local Pack race using my track. I have read Dr. Jobe’s book many times and still do. Each year I offer the 1st place winner of each grade of our Cub Scout Pack $5.00 to race my car, win or lose. I have never lost a race. The Pinewood Derby is relatively easy to win because I sense many times it is a nuisance for parents to begin with. In my Clinics I start with telling the scouts that the Pinewood Derby is a lesson in Physics and I have many visuals, especially explaining the “Front End Extension” effect and increased velocity. Why you cut off the back of the car and move it to the front. Why you use the long end of the car for the Front. Why you place the weight where it needs to be placed. Why you save Rotational Energy, not friction, by running the car on 3 wheels. Why “Rail Riders” are cheating under our BSA rules and don’t do it because I inspect the cars. I Love the Pinewood Derby and do it year around using Assisted Living facilities for my students. Yes, I’m Retired. Follow all the Laws of Physics and you’ll be fine.

  • Danny // Apr 4, 2013 at 4:30 pm

    Rob, your comment reflects the type of parent who doesn’t really want to be bothered with something their kid is involved in.

    Throwing a block of wood at a 9 year old and saying “here, go learn something” defeats the entire purpose of the derby.

    It’s easy as parents to become pre-occupied with adult and work related issues - and the derby creates an opportunity for a parent and child to spend time together achieving something that requires interaction and instruction.

    This is my 8-year-old daughter’s first Girl Scout derby. I’m not going to turn her loose with saws or drills. She picks out the design and colors and helps with sanding and painting. That’s pretty much the limit she’s able to handle right now. She’s not even strong enough to swing a hammer yet.

    At the conclusion of the race, she’ll see what all the fuss is about and have a far better understanding why we did some things the way we did.

    Next year she’ll play a larger role in building her car - because she has learned more and is physically capable of doing more.

    This is how children learn, not just throwing a block of wood at a kid and telling them “do their best.”

    Coaches don’t teach a sport by throwing a ball at a young player and saying “here, go learn something.”

    Also, there is nothing wrong with aspiring your kids to succeed and showing them the dilligence that is required to make something perform better.

    Kids aren’t born with this knowledge. They learn dilligence by seeing what it leads to and the difference it makes.

    You want a world where there are no winners or losers. Kids float through school like jellyfish, learning how to show up. Not show up and succeed at something.

  • Bill Klingler // May 18, 2013 at 3:17 am

    I’d like to answer “ridin’ the pine’s” question. Shape does count but not because of aerodynamics. Aerodynamics will be automatic. The car should weigh no more than 10 grams at the beginning. How do you accomplish this? Get rid of the wood. Your “car” will resemble a Hershey bar but a lot of it will be gone. This will enable you to place 2 rows of twelve 1/4″ tungsten cubes behind the rear axle and 2 rows of 1/4″ tungsten cubes in front of the rear axle while striving for a 5/8″ to 3/4″ COM for the car. This is recommended for an extended wheelbase car. The remaining work of polishing axles and bore preparation is super important. For wheel bores, Novus 2, Q-tips, wax, Hob-E-Lube graphite, etc. A 3 wheel rail rider, rear axles negative canting , front DFW Positive canting with tow-in, and then tuning on a track. Find out what track you will be racing on. Is it a wood track? Is it a smooth track? Is it an aluminum “Best” track with incline in stead of curve? Is it a circular arc track? The drift is different for different tracks. There, of course, is more detail than what I have said but that can be found on the internet. I described what is the ultimate car. If everyone did this it would be very boring. If your scout wants to build a car this way then that’s the way it should be built. If he wants a different design then he should get the design he wants. Wheel prep and axle prep should be done properly and the very best you can do. Above all else, make sure it’s your scout’s car, not yours. If you want the car to be yours, join a league and enjoy racing other adults. There’s something for everyone.

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