let say you have two wheels one is a 15" wheel and one is a 16" wheel they both weight exactly the same weight lets say about 20 lbs. Would the car be quicker with the 15" wheel or would it not matter since they are both the same weight.

Assume the wheels weigh the same. And assume the tires that go on them weigh the same (perhaps not a good assumption, but it's the question you asked).

It's actually not the weight that matters directly. It's the polar moment of intertia of the wheel/tire combination.

Skipping all the math: The more mass you put out near the *perimeter* of the wheel/tire the larger the moment will become.

You can feel this yourself which a simple experiment. Pick up a hammer. Flip over 180 while holding the end of the handle. Then flip it over holding the head of the hammer. Same weight in each case. One is harder on the wrist than the other. That's polar moment of intertia.

So, all other things being equal the 16" wheel/tires will slow the car down more than the 15" under acceleration. Because the 16" ones have more metal (heavy) out near the perimeter of the wheel/tire.

Now in real life, the larger sidewall tires that go on the 15" wheels weight more than the ones on the 16" wheels (unless you also went with wider tires in the upgrade). And in any case, the effect will be very small and hard to notice.

But the physics say: more spinning mass out near the perimeter of the disk = higher polar moment of intertia = harder to accelerate.

polar moment of wheel/tire combinations.

Make a cradle from three thin cables (1/16 dia works) to hold the tire/wheel horizontally, then suspend it 8 feet or so on a single strand of that cable from the ceiling joists. Rotate the tire to wind up the cable a few turns. Accurately measure the period for a few turns of wind up and wind down. Direct comparisons are easy, and with some math you can calculate the actual polar moment.

A 24 inch dia. circle of 5/16 thick steel plate, about 40 lbs. and easily calc'd I.

That's not easy to get so how about eight 24 in. dia. circles cut from a 4' x 8' sheet of 3/4 in. MDF available from your home center and glued together. That should be about 36-37 lbs, and make a good calibrator.

I'll find the math if anyone wants it.

It think it's next to the NIST traceable mass standards and under the calibrated radiometers.

Sorry, couldn't resist.

;)

SCC did a test on 16-18 inch wheels. They found that going from 17 to 18 inch rims, even with equivalent weights, had the same effect on acceleration as having an extra 50lbs in the car.

you won't see my bot. Got eliminated in round one. (They make all the rookies and un-seeded bots fight to get on TV and take on the ranked bots).

We'll see about next time. It's pretty hard to win at this thing. And I wanted to make an interesting bot. But the rules & combat realities really favor simple boring bots, so you end up with lots of fights as "polygons bumping into on another for 3 minutes."

But "Alcoholic Stepfather" will be back. And more drunk and beligerent than last time!

An effect, but a pretty small one.

I have always had an idea for a killer bot, but I don't think I'll even have the time to get serious about it. I'll email you my idea.

need weighing ;-)

Regards,

James R.

I=(W*R^2/L)/(2*pi*f)^2

I = polar mass moment, slug*in^2
W = weight (wheel, or wheel+tire, or flywheel ..)
R = radius out to string
L = length of string (make 4 or 5 times R)
f = freq, cycles per sec

I had to derive it ... no specific formula I could find. Small angle assumptions, bla, bla ..

Tested on a 7" od x 1.125" steel disc, and agreed with exact solution within 3%. Should be very accurate for comparisons. Time 20-30 full cycles, and do several times to check consistency. No swaying allowed. Use small angles ... for tire, just rotate od an inch or so.

For tires/wheels, 3 quality strings tied together, knot at bottom, and vertical legs above tire evenly spaced ... plant hanger technology. Place 3 small wood block spacers under the string, at tire face center, to give clean pivot points for string. Match this spacing at rafter area supports, adjust tire/wheel to be level so string effective lengths are the same.

I had another offset method I used on flywheels and clutches, but this method is more direct. Again, good thinking smallTTs! ... check my physics :o

specify polar moment on wheels instead of weight. Oh hang on, they don't even really tell us weight.

Long way to go...

- Z

That's just how it's usually done.

Thanks for detailing the technique. I was too lazy.

A tire & wheel weighs about 4X what your test piece does and with a much higher 'I' your accuracy would probably be closer than the 3%. Agree?

Ain't physics fun?

While we're all geeking out on high-school physics experiments...

If you wind the wires up too much the objuct under test will lift up (as the wires coil and the net gets shorter). This ends up storing energy in potential energy as height change, and can distory results. Because the object is pretty heavy.

The real error source will be in measurment of the period. Slow moving sinusoidal motion where the object slowly comes to rest before turning around, and somebody is trying to stop a stopwatch at the right time result in poor results. And the heavier (higher polar momet) wheel unter test will do this - have a lower period of oscillation. Need to measure lots of cycles/period and counted them up and divide total time by number of cycles.

It's always a bummer to tell people how to calculate the thing, then do the experiment, and have it not match. Kids stop believing in physics and stuff.

- Z

a toothpick stuck in the tread (and colored black with a Sharpie) which passes over a white paper with lines on it (tablet paper?) gives a pretty accurate visual clue for end-of-period.

How about timing with a stopwatch with a lap feature? You can then play back each 'lap' to see how the periods repeated. None of this is expensive, and perhaps it helps teach/reinforce that accurate data gathering is VERY important.

"Design it with a computer, measure it with a micrometer, mark it with chalk and cut it with an axe" is all too prevalent, IMO.

Teacher/engineer or ?? I'm curious. M.E. here.

Now a VP of Engineering who imagines cashing out and teaching high-school p/t in retirement.

A quick check of 245-45-16 kuhmo track tires on 16 lb rims, with similar less accurate method I considered, indicated about 1 cycle/sec, which is easily counted. Remember .. very small displacements, and mabe 20-30 cycles counted with stop watch ...

Any automotive engrg?

Semiconductor mfg monioring equipment. Lasers, microscopes, optical physics, sensors, supercomputing. That sort of thing.

Servo robotics EE/MechE degree from MIT.

Hey Zain, do you know BJ in San Mateo? I was his roommate for a while, and I think I met you at "Survivor and Sushi" or at a bar sometime.

Good post on wheel weight.

-Ian

Don't think I've ever been to anything called "survivor and sushi" and don't recall a BJ. But then I'm about the second worse person on the planet for names and faces. So...

- Z