Expert: Abe Mantell - 8/12/2011

Question
QUESTION: Dear Abe

Invention of the Wheel
----------------------

There are Two Wheelers, Three Wheelers and Four Wheelers running on the Road.
Trains run on Roads driven by electricity.
Aeroplanes require tyres for Landing and Take-off.

What is common in all is the Wheel made of rubber, in trains wheels metals shape, aeroplanes
rubber shape. But common to all is the Geometrical Shape "Circle" where radius is same.


Reference
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http://wiki.answers.com/Q/Why_are_tyres_always_circular

There could be several advantages of using a Circual Shape for the wheels viz
1. Less Energy to Drive
2. for all Types of roads viz smooth, bumpy, hills, slopes, curvy the circular shape may be tested
with all automobiles.



Question
--------

Other than the circular shape for the automobiles which Geometrical Shapes perhaps could have been useful
for tyre rubber manufacturing tested for all automobiles running on roads i.e Two Wheelers, Three Wheelers, Four wheelers,
Trains and Aeroplanes ?

Can Oval, Ellipse, Parabola and Hyperbola Geometrical Shapes be used for those Tyres (Rubber, Metal Forms)  Manufacturing ?


Awaiting your Reply,


Thanks & Regards,
Prashant S Akerkar

ANSWER: Not likely that non-circular tires were ever seriously used.
Sure, figured with a constant height could work, but the troble is that the
axle/center oscillates and would not provide a smooth (or safe) ride - esp.
at high speeds!

Abe


---------- FOLLOW-UP ----------

QUESTION: Dear Prof Abe

Thank you.

Can Oval, Ellipse, Sphere Geometrical Shapes be used for those Tyres (Rubber, Metal Forms)  Manufacturing ?.

Looks like Oval (Egg Shaped - Horizontal, Vertical Orientation), Ellipse,Sphere Shapes can be tried out for experimentation with trial runs on Bicycle, Motorcycles, Cars.

As you mention we will try with these shapes with High Speeds and experience the Ride (i.e User Experience).

Those with straight lines viz Square, Triangle, Hexagon may cause a problem over flat roads. But the geometrical curves viz Oval (Egg Shaped - Horizontal, Vertical Orientation), Ellipse and Sphere Shapes might work, but we have to test. Rubber (Two wheeler, Three wheeler and Four Wheelers) and Metals (Trains) can be molded and given shape to any other form than a Circle.

Prof Vijilant, AllExperts told me to try "Equilateral Curve Heptagon" for Design.


http://www.allexperts.com/ep/2079-63939/Number-Theory/Vijilant.htm

The web url is given below :

http://www.mathopenref.com/heptagon.html

Check Heptagonal coins section "50 pence coin".

What is your opinion about these shape ?

Thanks & Regards,
Prashant S Akerkar

ANSWER: My response is pretty much the same as before.  For flat roads, circular tires are best.

We can certainly devise "special roads" so that non-circular tires will be best.
For example, take a look at this square-wheeled tricycle on a "bumpy" track!
http://www.youtube.com/watch?v=LgbWu8zJubo

Abe


---------- FOLLOW-UP ----------

QUESTION: Dear Prof Abe

Thank you.

Looks like Oval (Egg Shaped - Horizontal (Roll the egg in Flat Roads), Vertical Orientation), Ellipse,Sphere Shapes can be tried out for experimentation with trial runs on Bicycle, Motorcycles, Cars.

We will test the newly designed vehicles viz bicycles, motorcycles and cars on Flat Roads, bumpy roads, Hills, Slopes etc.

We will try with these shapes with High Speeds and experience the Ride (i.e User Experience) with these Automobiles. The Automobile Overall Design will also change as the tyre shape is a non circular one.

Also we can try "Equilateral Curved Heptagon" as explained by Prof Vijilant for Tyre Design.

We can provide inputs to Bicycle, Motorcycles, Car Manufacturers - Research and Development Department viz
Ford, General Motors, Bajaj Auto, Mitsubishi, Honda, Mahindra and Mahindra etc

http://www.mathopenref.com/heptagon.html

What is your opinion ?

Can we give inputs to Automobile manufacturers - R & D Department for experimentation of these newly designed vehicles with different tyres shapes viz non circular and their feedback after trail runs ?

Thanks & Regards,
Prashant S Akerkar

Answer
My opinion about using non-circular wheels?

I think circular wheels are the best all-purpose wheel design.

If our roads and passageways where some special (uniformly designed) non-flat
surface, then perhaps we would benefit from some other wheel design.

Abe