[math-fun] Square-wheeled trike essay
The essay is now live, at https://mathenchant.wordpress.com/2015/07/15/the-lessons-of-a-square-wheeled... . (I removed the calculations that initially gave me trouble; I eventually got them to come out right, but I couldn't muster much enthusiasm for them, so I figured my readers wouldn't either.) Comments are welcome, especially those that I might be able to apply in future columns. The intended audience is the sort of people who read Martin Gardner's column. Jim Propp
On 2015-07-17 09:05, James Propp wrote:
The essay is now live, at https://mathenchant.wordpress.com/2015/07/15/the-lessons-of-a-square-wheeled... .
(I removed the calculations that initially gave me trouble; I eventually got them to come out right, but I couldn't muster much enthusiasm for them, so I figured my readers wouldn't either.)
Comments are welcome, especially those that I might be able to apply in future columns. The intended audience is the sort of people who read Martin Gardner's column.
Jim Propp ___________ Couldn't you make a trike with a square front wheel, and respectively three-cornered (convex?) and five-cornered (concave?) rear wheels with curved sides? Maybe all the corners could be right angles. --rwg
You can make wheels of different shapes and compensating tracks so that the axle height remains constant, but the wheels don't turn with constant angular velocity when the axle move with constant speed. Since the wheels have rotational inertia the vehicle will experience oscillating forward motion. Brent Meeker On 7/17/2015 5:46 PM, rwg wrote:
On 2015-07-17 09:05, James Propp wrote:
The essay is now live, at https://mathenchant.wordpress.com/2015/07/15/the-lessons-of-a-square-wheeled... .
(I removed the calculations that initially gave me trouble; I eventually got them to come out right, but I couldn't muster much enthusiasm for them, so I figured my readers wouldn't either.)
Comments are welcome, especially those that I might be able to apply in future columns. The intended audience is the sort of people who read Martin Gardner's column.
Jim Propp ___________ Couldn't you make a trike with a square front wheel, and respectively three-cornered (convex?) and five-cornered (concave?) rear wheels with curved sides? Maybe all the corners could be right angles. --rwg
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On 2015-07-17 19:25, meekerdb wrote:
You can make wheels of different shapes and compensating tracks so that the axle height remains constant, but the wheels don't turn with constant angular velocity when the axle move with constant speed. Since the wheels have rotational inertia the vehicle will experience oscillating forward motion.
Brent Meeker You ought to be able to pretty nearly null that out with a wheelbase that keeps the front and rear wheels out of phase. Conceivably dog-leg the rear axle a bit for additional fudging.
Dark matter matters. --rwg Clearly NHTSC needs to regulate the unsprung weight of polygonal tricycle wheels.
On 7/17/2015 5:46 PM, rwg wrote:
On 2015-07-17 09:05, James Propp wrote:
The essay is now live, at https://mathenchant.wordpress.com/2015/07/15/the-lessons-of-a-square-wheeled... .
(I removed the calculations that initially gave me trouble; I eventually got them to come out right, but I couldn't muster much enthusiasm for them, so I figured my readers wouldn't either.)
Comments are welcome, especially those that I might be able to apply in future columns. The intended audience is the sort of people who read Martin Gardner's column.
Jim Propp ___________ Couldn't you make a trike with a square front wheel, and respectively three-cornered (convex?) and five-cornered (concave?) rear wheels with curved sides? Maybe all the corners could be right angles. --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 7/17/2015 9:28 PM, rwg wrote:
On 2015-07-17 19:25, meekerdb wrote:
You can make wheels of different shapes and compensating tracks so that the axle height remains constant, but the wheels don't turn with constant angular velocity when the axle move with constant speed. Since the wheels have rotational inertia the vehicle will experience oscillating forward motion.
Brent Meeker You ought to be able to pretty nearly null that out with a wheelbase that keeps the front and rear wheels out of phase.
If the front and rear are out of phase with respect to the forward motion oscillation then one or both will have to slip some rather that rolling without slipping.
Conceivably dog-leg the rear axle a bit for additional fudging.
Yes, if you allow a little variation in wheelbase they could both roll without slipping and move relative to the vehicle. Brent
Dark matter matters. --rwg
Clearly NHTSC needs to regulate the unsprung weight of polygonal tricycle wheels.
On 7/17/2015 5:46 PM, rwg wrote:
On 2015-07-17 09:05, James Propp wrote:
The essay is now live, at https://mathenchant.wordpress.com/2015/07/15/the-lessons-of-a-square-wheeled... .
(I removed the calculations that initially gave me trouble; I eventually got them to come out right, but I couldn't muster much enthusiasm for them, so I figured my readers wouldn't either.)
Comments are welcome, especially those that I might be able to apply in future columns. The intended audience is the sort of people who read Martin Gardner's column.
Jim Propp ___________ Couldn't you make a trike with a square front wheel, and respectively three-cornered (convex?) and five-cornered (concave?) rear wheels with curved sides? Maybe all the corners could be right angles. --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (3)
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James Propp -
meekerdb -
rwg