).
It's similar to the question or "Myth" that bigger tyres/wheels means higher velocity due to further rotational distance covered by the larger wheel/tyreAre there any advantages in having 19inch wheels over 18's, or is it purely aesthetic? Seems to me they give a harder ride, tend to transmit more road noise, and are more expensive to replace, I've got 19's on my coupe but still don't get it, who knows?
Did you swallow a maths book tonight. Away and give us peace ! And a set of 20s. Lol.It's similar to the question or "Myth" that bigger tyres/wheels means higher velocity due to further rotational distance covered by the larger wheel/tyre
Mathematically, the question is easily answered, with the equation: length=radius*angle, where we take the derivative to get velocity=radius*angular velocity.
If we held angular velocity constant, and increased the radius, we obviously get a larger straight velocity. But in a scenario with a car where one is deciding on which size tyre to buy, this isn't enough information.
You could, maybe, model this such that you have a single tyre that you just give enough rolling energy such that it rolls exactly 60 miles in 1 hour.
That is, if you have a moment of inertia (cylinder, rotating about the z-axis where the circle of cylinder is drawn in the xy plane) 1/2mr^2, then you need an energy (from the equation Rot.KE=1/2Iw^2 and v=rw) 1/4mv^2 where v = 60mph. m is the mass of our smaller tyre.
Then you "enlarge" the tyre, m becomes the mass of the bigger tyre, and v is now the new rotational velocity.
Equating the two energies, and solving for the larger velocity,
one finds, (ms/ml)vs^2=vl^2
ms = mass of the small tyre,
ml = mass of the large tyre
vs = velocity of small tyre
vl = velocity of the large tyre.
What you find is that the velocity of the larger tyre is smaller because of the accumulated mass.
This is a friction free scenario.
This, of course, doesn't answer the question of "further" but, what we see is that to get it to cover the same distance in the same time it would require more energy then we are given, this would cost MORE fuel.
If we want to keep axel speed the same (rotational velocity), you will not have enough fuel to even cover the 60 miles unless you make the tyre and wheel much lighter, as well as it already being larger.
Note also that larger tyres require more torque to accelerate to the same velocity. Larger tyres on a vehicle usually crushes fuel mileage since higher accelerations are not as efficient on cars. This is maybe why the Prius doesn't have larger tyres, it just doesn't have the output.
Only a disadvantage if fuel economy is your worry but if it isn't then they sure look a lot more fun
:bannana:
It's similar to the question or "Myth" that bigger tyres/wheels means higher velocity due to further rotational distance covered by the larger wheel/tyre
Mathematically, the question is easily answered, with the equation: length=radius*angle, where we take the derivative to get velocity=radius*angular velocity.
If we held angular velocity constant, and increased the radius, we obviously get a larger straight velocity. But in a scenario with a car where one is deciding on which size tyre to buy, this isn't enough information.
You could, maybe, model this such that you have a single tyre that you just give enough rolling energy such that it rolls exactly 60 miles in 1 hour.
That is, if you have a moment of inertia (cylinder, rotating about the z-axis where the circle of cylinder is drawn in the xy plane) 1/2mr^2, then you need an energy (from the equation Rot.KE=1/2Iw^2 and v=rw) 1/4mv^2 where v = 60mph. m is the mass of our smaller tyre.
Then you "enlarge" the tyre, m becomes the mass of the bigger tyre, and v is now the new rotational velocity.
Equating the two energies, and solving for the larger velocity,
one finds, (ms/ml)vs^2=vl^2
ms = mass of the small tyre,
ml = mass of the large tyre
vs = velocity of small tyre
vl = velocity of the large tyre.
What you find is that the velocity of the larger tyre is smaller because of the accumulated mass.
This is a friction free scenario.
This, of course, doesn't answer the question of "further" but, what we see is that to get it to cover the same distance in the same time it would require more energy then we are given, this would cost MORE fuel.
If we want to keep axel speed the same (rotational velocity), you will not have enough fuel to even cover the 60 miles unless you make the tyre and wheel much lighter, as well as it already being larger.
Note also that larger tyres require more torque to accelerate to the same velocity. Larger tyres on a vehicle usually crushes fuel mileage since higher accelerations are not as efficient on cars. This is maybe why the Prius doesn't have larger tyres, it just doesn't have the output.
Only a disadvantage if fuel economy is your worry but if it isn't then they sure look a lot more fun
:bannana:
