# Inside tires Vs Outside tires:

sonhouse
Posers and Puzzles 03 Apr '08 15:30
1. sonhouse
Fast and Curious
03 Apr '08 15:303 edits
There is a race track with a straight section, then a 180 degree bend ending with a straight again and of course at the other end the same. The track is 10 meters wide.
The inside radius is 100 meters. There is a car coming down the track, it first travels next to the inside of the lane (smallest radius) and around the oval but the second time it goes around the outside of the lane. The car has a 1.5 meter wheelbase, 1.5 meters center to center of the tires. It goes around the bend with 0.25G of side thrust, nowhere near enough to make the tires skid. but at a constant velocity.
How fast is the car going on the inside curve and how fast is it going when it makes the second trip around the outside of the lane, also hitting 0.25 G. Each tire is independently suspended, so each tire can rotate at the rate established by the road. The tires are all 650 mm in diameter. When they go into the turn, they each have a marking visible on the outside of the tire at top dead center of the tire. That establishes the zero degree point. How many degrees do the tires get out of sync, left front V right front and of course the back tires would be the same. Where are the marks as they just enter the straightaway? And the same for the second trip on the outer edge of the roadway.
2. uzless
The So Fist
03 Apr '08 17:25
Originally posted by sonhouse
There is a race track with a straight section, then a 180 degree bend ending with a straight again and of course at the other end the same. The track is 10 meters wide.
The inside radius is 100 meters. There is a car coming down the track, it first travels next to the inside of the lane (smallest radius) and around the oval but the second time it goes aro ...[text shortened]... just enter the straightaway? And the same for the second trip on the outer edge of the roadway.
how heavy is the car? how far does the sidewall of the tire extend horizontally as the car is in the turn?
3. sonhouse
Fast and Curious
03 Apr '08 19:49
Originally posted by uzless
how heavy is the car? how far does the sidewall of the tire extend horizontally as the car is in the turn?
You don't need that information to solve this problem. When you specify a G force outwards around a curve, that is a parameter independent of the weight, would be the same velocity if it was one Kg or 1000 Kg. The tires can wobble left and right on the rim, if the tire isn't skidding, the relative places of the markers won't change either.
There would be a certain amount of strain on the tires but it won't effect the relative change in position of the markers. Say a tire is, oh, just to pick a number purely at random π, 318.3098862 mm in diameter, well what do you know, it just happens to be 1000 mm in circumferance. So every meter forward it goes around the curve, the inside tire goes a bit less so the markers change position relative to each other. Whether the tires are wiggling back and forth, they are specified not to be skidding so that part is out of the equation.
4. 03 Apr '08 20:11
Originally posted by sonhouse
There is a race track with a straight section, then a 180 degree bend ending with a straight again and of course at the other end the same. The track is 10 meters wide.
The inside radius is 100 meters. There is a car coming down the track, it first travels next to the inside of the lane (smallest radius) and around the oval but the second time it goes aro ...[text shortened]... just enter the straightaway? And the same for the second trip on the outer edge of the roadway.
I recognize this problem from a totally another problem.
If I say that there is a lot of unneccesary information given, and only the weelbase and 2 times pi is involved, am I at the right track?
5. joe shmo
Strange Egg
04 Apr '08 03:051 edit
Originally posted by sonhouse
You don't need that information to solve this problem. When you specify a G force outwards around a curve, that is a parameter independent of the weight, would be the same velocity if it was one Kg or 1000 Kg. The tires can wobble left and right on the rim, if the tire isn't skidding, the relative places of the markers won't change either.
There would be a g back and forth, they are specified not to be skidding so that part is out of the equation.
you are good at picking numbers at random...you must be some kind of mathematical genius π² are you sure you sure you didn't just divide 1000 by Pi to get that diameter.π
6. sonhouse
Fast and Curious
04 Apr '08 11:04
Originally posted by joe shmo
you are good at picking numbers at random...you must be some kind of mathematical genius π² are you sure you sure you didn't just divide 1000 by Pi to get that diameter.π
Nah, not meπ Just had a dartboard and threw it from 15 metersπ
7. joe shmo
Strange Egg
04 Apr '08 13:52
Originally posted by sonhouse
Nah, not meπ Just had a dartboard and threw it from 15 metersπ
huh...amazing!!!π
8. sonhouse
Fast and Curious
04 Apr '08 15:11
Originally posted by FabianFnas
I recognize this problem from a totally another problem.
If I say that there is a lot of unneccesary information given, and only the weelbase and 2 times pi is involved, am I at the right track?
whatever the weelbase isπ
9. 10 Apr '08 01:33
All this is very interesting, but as you know the wheelbase and the angle of the turn are all that matters. But did you know that this is the reason railroad wheels are made with a slight taper in the wheel tread. The axles are fixed to each wheel so uneven rolling causes torsion in the axle. But when the train enters a curve, the fat portion of the outside tire touches the rail, and the thinner portion of the inner tire rides on the inside rail to compensate for the shorter travel of the inside tire.
10. sonhouse
Fast and Curious
10 Apr '08 01:44
Originally posted by dinosaurus
All this is very interesting, but as you know the wheelbase and the angle of the turn are all that matters. But did you know that this is the reason railroad wheels are made with a slight taper in the wheel tread. The axles are fixed to each wheel so uneven rolling causes torsion in the axle. But when the train enters a curve, the fat portion of the ou ...[text shortened]... the inner tire rides on the inside rail to compensate for the shorter travel of the inside tire.
Wonder if they could make it with a strong spring between the wheels where the connecting rod is, so when it goes in a turn, the spring winds up and then unwinds when it gets out of the turn.