I hope so too, as I am not an engineer.
It doesn't have to be. The radius is the distance between the centre of the object and a point on the perimeter (circumference). In our case, the point closest to the centre.
20P and 50P coins have a constant diameter despite not being circular.I did, but am always learning.
There isn't actually and the total number who have commented isn't high enough for what correlation you claim to see to be significant either.
You've lost that bet too.
I think you would have to be going some though for that to me any use ITRW. ;-)
I'm sure he's swung the lead a few times. ;-)
Cheers, T i m
That was in a rooundwheel case, in which case the two are absolutely related by the formula 2*PI*R = C.
My point is that once te tyre is on and deforming, that relationship has no validity or meaning. I applies to circle only. And the flatter the tyre is the less circular it is.
YOU and your ilk are claiming that this means that the thing that is most important is the radius, even though a non circular object has no constant radius. It DOES however have a circumference. That doesn't change.
It is.
No, it is not.
No, they do not.
No, you are not.
Radius between centre of wheel and point of contact to the road surface. That is the only relevant part as regards how far the car travels per rotation of the wheel. Not any theoretical amount.
They do for the normal meaning of "diameter" (which is not confined circles, spheres or other n-spheres)
I must admit, I would tend to confine the word "diameter" to circular (or spherical) objects. But let's leave semantics aside.
I had never realised that the flats on a 20p or 50p coin were arranged so the distance between one edge and the other, for any line that goes through the centre, was always the same, irrespective of which part of the flat or point the line happened to go through and even though the middle of that line may not always coincide with the centre of the coin.
Do all polygons with an odd number of sides have the property, or is it unique to heptagons (7 sides)?
I think the only important thing is the the distance between the axle and the point which touches the ground ("the effective radius", as some people have called it) is constant as the tyre rotates - as indeed it must be, otherwise you'd have a very bumpy ride :-) The radius at all other points on the tyre which are not touching the ground is not important.
Its still the distance that determines the rotation rate of the wheel.
Yes, I can see that your line about the circumference of the tyre that determines the rotation rate of the tyre, but given that it is so easy to determine whether it is the circumference or the distance between the axle and the road that determines the rotation rate experimentally, IMO there isnt any point in proclaiming which it actually is, time to actually measure it.
No one said anything about any constant radius.
And yet the system that uses the ABS rotation rate does work for a lot more than just a flat tyre.
At first I thought that it would be the minimum radius, measured to the centre of the contact patch, which would be important. But having seen the diagrams that were referred to earlier in the thread, I now wonder whether the effective radius is somewhere between the minimum and the no-load radius, to take into account the fact that the radius varies depending on whereabouts on the contact patch you measure it.
Part of the problem with all this discussion is that we are talking about a very small variation between loaded radius and no-load radius, which makes it difficult to measure in the real world with a crude tyre-on-a-road-surface measurement. The chances are that if you measure how far a tyre travels for a given number of revolutions, firstly with negligible load and/or pumped-up tyre, and secondly with a loaded and/or half-way flat tyre, you would find it difficult to see any difference that was larger than experimental error. This assumes that you measure a fairly small number of rotations to keep the total distance travelled down to a length that can easily be measured.
I don't really have a feel for how much of a difference there is for a typical tyre, and therefore how many revolutions you'd need to measure before you observed a difference that was noticeable.
All you can do is to try to make the difference as large as possible (deep, high-profile tyre; significantly under-inflated - to maximise the amount of flat on the contact side of the tyre) in order to demonstrate that there
*is* a difference in distance travelled per revolution compared with a truly circular tyre.
Yes, but you also have a problem with explaining why it isn't the circumference of the tyre which doesn?t change much isnt what determines the rotation rate of the wheel.
Fair enough - but the general meaning of "diameter" does apply more widely. And "diameter" is a lot shorter than eg "the distance between one edge and the other for a line that goes through the centre" :)
I'm old enough to have "done" the design of the original 50p coin at school before it was in circulation :(
I _think_ it's possible to achieve it with any odd number of corners but couldn't tell you the parameters that can be fiddled with.
the usual phrase is 'curves of constant width', but in real terms (e.g. a coin mechanism measuring coins) they do have a constant diameter, but a varying radius.
Never play with multiple 50ps and two rulers at school?
No, its a class of Reuleaux prisms, even 'better' are solids of constant width
No. I must have missed out on that bit of geometry. Tell me more: I'm intrigued. I've lived with decimal coins for 47 years and never knew that
20p and 50p coins had constant diameter. I realised that the sides are slightly curved rather than being flat, but not that the curves were so arranged as to create a constant width object.It's just the sort of thing that my old maths teacher (who taught me from from 1974-77) would have revelled in, so I wonder why he never mentioned it.
Yes, "the concept that something could roll but not be round totally messes with your head" :-)
I hadn't realised that the rotor of a Wankel engine was a constant width shape, only that it was an equilateral triangle with curved sides. Indeed I thought that the sides were only curved to make the corners slightly less sharp and so reduce the stress on each corner.
Hmm. Wonder if drivers in Milton Keynes have problems with over-zealous triggering of TPMS?
An interesting thing related to this: if you have a DSG-equipped VAG car, and it starts refusing to change up gears (but will do it if you use the lever to tell it to change up), it's an ABS sensor failing. It generally won't trigger an fault code for a while. It's done that way so it won't auto-change up half way around a corner, apparently.
I'm on my second such car, but have not experienced that issue, the reason for the last one going was that the gearbox was getting "fussy" ...
Interesting. Just got a car with a similar box which they call PDK (twin clutch) And it is superb. At low speeds (as in round town) it just seems to get into as high a gear as possible very quickly. Regardless if the road is straight or not.
I'll have to take note when driving at higher speeds - although I'd expect an ABS sensor throwing up irregular pulses to generate a fault code
Did wonder what the expected life of these boxes is compared to a conventional auto.
Was on a London single decker bus the other day that appeared to have an SMG type auto, and that crunched when changing up into what I think was third gear. Like you get with worn synchromesh.
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