Soapbox racer - heavier is better?

[DaveC426913]

If you are starting on a ramp, place as much weight to the rear as possible. This gives the cart more "energy of position" (potential energy) as the centre of mass is higher up the ramp and you'll get a better start.

I am not at all convinced of this. Can you demonstrate why it might be true?

It is not enough to presume that, because one object is higher than another that means it translates into more useable energy. A rigid body of mass m is going to accelerate at the same velocity regardless of how that mass is distributed, ignoring frictional forces on air or axles.

 

[mender]

I am not at all convinced of this. Can you demonstrate why it might be true?

I can only demonstrate with results:

Two kids, total of 9 years of soap box derby events between them, 7 Grand Championships and 9 class wins.

However, in response to this:

It is not enough to presume that, because one object is higher than another that means it translates into more useable energy. A rigid body of mass m is going to accelerate at the same velocity regardless of how that mass is distributed, ignoring frictional forces on air or axles.

When an object is being accelerated by gravity, and the centre of gravity is higher off the ground (more potential energy), the object will accelerate for a longer period of time before reaching the flatter part of the course and get to a higher speed. No presumption needed; if an object has more potential energy and that gets converted to kinetic energy, the object will end up with more kinetic energy, i.e. speed.

 

[DaveC426913]

I can only demonstrate with results:

'fraid that doesn't cut it.

You are certainly skilled, and have surely applied your skill in countless ways to get wins. But even you can't be sure that that adjustment is what is causing your wins indepedent of the other 50 things you've improved.

However, in response to this:

When an object is being accelerated by gravity, and the centre of gravity is higher off the ground (more potential energy), the object will accelerate for a longer period of time before reaching the flatter part of the course and get to a higher speed. No presumption needed; if an object has more potential energy and that gets converted to kinetic energy, the object will end up with more kinetic energy, i.e. speed.

OK, I see, so you're not suggesting that the cart gets a faster start at the top of the hill, you're suggesting that, at the bottom of the hill, it has an extra few feet of downhill roll under full mass before hitting the flat, as opposed to one with weight on the front, whose centre of mass levels out sooner.

How fast do carts move? We can calculate how much that would gain. 25mph over 3 feet? I'm going to guess it's on the order of an inch over the competition.

 

[mender]

OK, I see, so you're not suggesting that the cart gets a faster start at the top of the hill, you're suggesting that, at the bottom of the hill, it has an extra few feet of downhill roll under full mass before hitting the flat, as opposed to one with weight on the front, whose centre of mass levels out sooner.

Uh, no, Dave; as I said right at the start:

If you are starting on a ramp,

As in this video:
http://www.youtube.com/watch?v=O8L78uKnyW8&NR=1
That means that I'm talking about the top of the hill.

Having the centre of mass farther back on the car means that it is also higher off the ground on the starting ramp.

Pause the video when they show the two cars about to start. Make a WAG as to the angle of the ramp and the C of G height of one of the carts (assume 50% of the wheel base), then calculate the difference in speed that would result if the centre of mass was located 10 inches further back on the other cart. Now check to see how much time the rest of the run takes (about 50 seconds on our runs), then multiply the speed difference in inches/second by the number of seconds that the run took and you'll have a pretty good indication of the difference.

Any advantage gained at the start adds all the way down the track. Even the crown of the road is useful. You'll notice that the drivers of the carts are well aware of that; they start fairly close to the crown and move to the side right off the start, again making use of the extra potential energy as soon as possible to maximize the effect, only steering back at the finish line. Only a few inches in height but many inches difference by the bottom of the hill.

How fast do carts move? We can calculate how much that would gain. 25mph over 3 feet? I'm going to guess it's on the order of an inch over the competition.

Nope.

 

[DaveC426913]

Uh, no, Dave; as I said right at the start:

As in this video:
http://www.youtube.com/watch?v=O8L78uKnyW8&NR=1
That means that I'm talking about the top of the hill.

Having the centre of mass farther back on the car means that it is also higher off the ground on the starting ramp.

My mistake. I did not know they now use starting ramps. I'll rephrase:


OK, I see, so you're not suggesting that the cart gets a faster start at the top of the ramp, you're suggesting that, at the bottom of the ramp, it has an extra foot or two of downhill roll under full mass before hitting the flat, as opposed to one with weight on the front, whose centre of mass levels out sooner.

And you're right. Now that I see this all occurs right at the start, it will make a big difference.


My error was in not realizing that they now use starting ramps.

 

[mender]

My kids almost always ended up racing each other for the Grand Championship at the end of the day, along with two other carts (four wide!). The first cart I built was quite sleek, made from wood with foam overlays for shaping but used the steering and axle kit that was available; it required meticulous setting of the wheel alignment and was prone to "realignment" from the rough loading of the carts onto the trailer for the trip back uphill; several easy wins came down to driver technique when they should have been run-aways because of damage.

The second (all metal) used straight axles front and rear to prevent that damage, but without the fine adjustments of the first one it has slightly more drag; not as aerodynamic either. I took full advantage of the rearward weight bias to get a better start to compensate, and it does, barely. The first cart though slower at the top of the hill gradually matches speed then steadily gains on the second cart all the way down and the winner is the one who made the fewest corrections and the smoothest steering at the top of the hill; after 50 seconds, it's a matter of inches either way.

They loved the competition (and the trophies) but they're "retired" now to let other kids have a shot at winning.

 

[flyingferret]

Apologies for resurecting this topic, but I've been thinking about this again recently and have come up with a slightly different equation to BobS's (although not changing the overall conclusion). I've probably made some stupid mistake, although I can't see it myself.

So here goes. The force F acting on the cartie (NE Scots word for a soapbox) is m g sin(θ). This has to overcome drag, rolling friction and wheel inertia, and whatever is left over accelerates the cartie. So;

m g sin(θ) = F$_{t}$ + F$_{r}$ + F$_{d}$ + F$_{R}$

Where;

F$_{t}$ = Translational Force (i.e. moving the whole machine down the hill)
F$_{w}$ = Force rotating the wheels
F$_{d}$ = Drag force
F$_{R}$ = Rolling friction

The last two terms we can dispense of quite quickly - they are exactly the same as BobS's terms.

F$_{t}$ is pretty straightforward - for a cartie of mass m accelerating at a;

F$_{t}$ = m a

The F$_{w}$ term is a little more fiddly; the angular acceleration ω of the wheel with moment of inertia I is caused by the torque T

T = I ω

I for a hoop of mass m$_{w}$ is m$_{w}$ r$^{2}$, and ω is given by a / r, so the above equation becomes;

T = m$_{w}$ r$^{2}$ (a / r)
T = m$_{w}$ r a

T also equals F$_{w}$ r, so

F$_{w}$ r = m$_{w}$ r a
F$_{w}$ = m$_{w}$ a

Substituting these two terms back into the initial equation we now have;

m g sin(θ) = m a + m$_{w}$ a + F$_{d}$ + F$_{R}$
m g sin(θ) = (m + m$_{w}$) a + F$_{d}$ + F$_{R}$

which can be rearranged for a as;

a = (m g sin(θ) - F$_{d}$ - F$_{R}$) / (m + m$_{w}$)

Or, in full;

a = (m g sin(θ) - (1/2)ρAC$_{d}$v$^{2}$ - C$_{R}$mg cos(θ)) / (m + m$_{w}$)


This produces results that are very close to BobS's, but just very slightly greater acceleration

So - am I right, or have I got something horribly wrong here?

 

[morgan349]

I love this thread.

I'm looking to take part in a race with a pushed start (2 people pushing for a max of 10m at the srat of the race, at the top of the hill)

in everyone's opinions, does this affect the assumptions and suggestions mentioned in this post?

Also very interested into the science behind wheel selection (diameter and tyre width)

great reading though...thanks all!

 

[flyingferret]

Hi Morgan,

The simple answer to your question is ... it depends.

There is a trade off between the mass of the racer in terms of your pushers' ability to accelerate it and the overall speed reached. Any braking for corners also needs to be considered.

All other things being equal, a lighter cart will be accelerated quicker at the start line, but will have a lower top speed further down the course. If your course is short and straight you might benefit from being lighter, but on the longer course a heavier cart will claw back that advantage.

If there is lot of braking required for corners, a lighter cart might be quicker overall as it could brake later.

There are other considerations too. If you are racing head-to-head, for instance, there might be an advantage to getting an early lead and controlling the race from the front.

Using the equations above I actually developed some software to model all the variables and help you optimize for mass etc. Check out http://scottishcarties.org.uk/cartiesim/download.

 

[juanverde]

Hello all, I'm reviving an old topic as I just competed in a coffin race over the weekend.
Basically, it is fashioned after a soapbox derby. The only 3 rules are: 6" wheel max diameter, some sort of brake and steering. There is a 10 foot push section where the cars can be shoved down the hill.

I haven't taken a physics course in over 20 years. After reading through this thread, I'm getting the gist of it. A heavier car, if able to be pushed to an advantage at the start, will likely keep the advantage over a lighter car. Bigger wheels will roll faster.

At some point (above my intelligence level) the weight will have an effect on the wheels/bearings - creating friction/drag and slowing it down.

I ended up using some 5" diameter scooter wheels with the standard abec 5 bearings that came with them. We did well, but did not win. To my layman's eyes, it seemed like the starting push almost always won the race if the cars had similar type wheels. (nobody had any car that had any sort of aerodynamic advantage)

After the race, I was thinking that if I added more wheels it would spread the weight out more and therefore be able to roll easier with more weight. I was thinking of in-line skates. Maybe have a row of 3-4 wheels on each side of the rear of the car. Any validity to my thinking ?

Would I need to add more wheels to the front as well ?

 

[flyingferret]

Sadly that won't work. Each individual wheel will have lower rolling resistance, but this will be offset by there being more wheels. The net change is likely to be negligible.