reciprocating mass / spun weight, torque, top end

[HarryMann]

If overall weight stays the same, will the fact that the new tire has a larger circumfrence cause you to be slower off the line?

There are a few separte issues here, some have been dealt with (grip) but the one that hasn't been quantified is MoI of the wheel/tyre/disc assembly (the driveshafts can be pretty well  ignored)

Moment of Inertia (MoI) of the wheel/tyre is the rotational equivalent to mass, so when accelerating a slug of iron from 10 ft/s to 20 ft/s it puts up a resistance based on its mass, and a when speeding a wheel up from 10 rpm to 20 rpm, it puts up a resistance based on its MoI..

MoI is proportional to the radius or diameter squared.. so for a 'similar' wheel tyre combo, but a larger one, a rough estimate of change (in torque required to accelerate it) would be D^2/d^2 or 17*17/13*13 for a 13 being changed for a 17.. that is 71% increase.

Because MoI takes a bit of work to calculate exactly for a mixed up thing like a wheel/tyre combo, relative ratios are useful. In the above, we took the wheel size, whereas in reality the tyre is a predominant mass being further out, so that increase would be even more, possibly 2 or more...

Now, how is this increased torque requirement compared to that available  for accelerating the linear mass of the car?

This is where these very rule-of-thumb figures come in... such as every pound of mass in the wheel/tyre driveline assembly is equivalent to three on the vehicle... That rule is really too rough for me to give much credence, but when I came across it once before did do some sums which showed it was somewhere near for typical cars and wheel sizes, but honestly its pretty meaningless - you can have a heavy large wheel and light low aspect ratio tyre on it, or a large lightwieght wheel with a heavyish tyre - would be quite a difference.

But one thing not mentioned, is that one reason larger brakes are fitted by manufacturers on the same car but when larger wheels are fitted is the need to slow them down rotationally, as well as the car's mass.  It makes a difference in both directions, of course, and when larger changes are made, more than an inch or so, then its likely to afect something.

On the grip issue, there's the  contact patch effect, as well as  larger wheels and tyres having a restraining effect on wheelspin and breakaway, due to this increased MoI. Conversely, once its spinning, it could take longer to slow back down again when reganing adhesion, but the overall effect is probably worthwhile. [One very positive effect from left-foot braking a FWD car, is to minimise front wheel adhesion loss under acceleration, to counter this effect]

Unsprung mass is as described, the mass that the spring-damper system has to control, being the wheel/tyre/brake/stub axle mass and a contribution from the pivoting control arms (derived using their MoI again!)

So these are not things that can be calculated in 5 minutes, though the general rules are as above...

In conclusion, if getting off the line is what matters, significantly larger wheels and tyres may help, but if acceleration through a speed range where grip is not an issue matters, they will slow you down, and quite a bit more than many realise!

[burn_your_money]

Thank you for teh in depth write up

What if MPG matters though?

[HarryMann]

Smaller wheels and tyres, as every time you accelerate more energy is being used to increase their rotational speed...

by smaller, of course smaller MoI.

The proper way to calculate this is to {Sum} the Product of every minute mass and the square of its radius from the point of rotation. To make this feasible in reality requires calculus which simplifies the job by giving equations for regular shapes, that look like this:

Cylinder rotating about its axis:  ˝mr^2

Ring rotating about its centre point (bicycle wheel): ˝PI* rho*h * (ro^4-ri^4)

Spoke rotating about its endpoint:  1/3 ml^2


where:
PI = 3.14159
m = mass (kg)
r = radius (m)
rho = density (kg/m3)
ro = outer radius of ring (m)
ri = inner radius of ring (m)
l = length of spoke


==============================

Another (empirical) way to compare MoI of assmeblies is to actually time their acceleration to a given speed. Something that takes twice as long to accelerate from 0 rpm to say, 5 rpm, with the same applied torque, would have an MoI two times the original one... just as an object that takes twice as long to accelerate linearly from 0 to 10 mph would have a Mass twice as much - that's ther beauty of the MoI concept , it is an exact equivalent of mass's inertia, but rotationally.

Another idea you might hear of is Radius of Gyration - this derives from the equations above, and is the radius at which ALL the mass of a rotational object can be said to be acting, so if a wheel has a RoG of 12 ", and weighs 30 lbs, its MoI can be calculated as 12" x 12" x 30lbs, just as if its a infinitely small blob of mass (30lb) being rotated on a 12"  arm or radius.
===================

So yes, for mpg, smaller wheels, but what you really need to know is whether realistic differences could be measured against the common sizes of wheels and tyres in use...

I'd say, yes and no, at extremes possibly yes, otherwsie possibly no

[burn_your_money]

I just put my bigger, heavier steel 14" summer tires on compared to my steel 13" tires. The 14s are also wider yet I am seeing about or slighty better mileage and I drive 10km/h faster on the highway

[xud9te]

Nice going harry!!  

    I think you got it ALL!!!

Pour example.  If we were to assume a simple disc for the wheel and tyre combo, and gave this a nominal mass of say 12kg and a radius of 280mm (14" wheel with 185/55 tyre), then the force required to accelerate it through 1Km/h in 1 second would be :

.5*12*(.280^2) = .4704

I omega = Torque;

.4704*(.277/(PI(.56)))*2PI = Required torque at wheel = .465 Nm

Adding one kilo equally to the wheel gives required torque at wheel of .504, ie an 8% increase in required torque, this is for one wheel only.

Similarly for adding 1kg to a car of 1000kg, we see an increase in required torque of only .0103146% compared to the car without the extra 1kg.  However, the torque required to accelerate the cars total mass by 1Km/h in 1 second is 77.56 Nm, and to accelerate all four wheels only 1.86 Nm.

Therefore we can say that the mass on the wheels may give a bigger proportional change, but in comparison to the mass of the body it is not so substantial.  

This is why the best way to make a car go fast is to increase torque and decrease wieght, wheels and tyres make it handle!!  

When was the last time you saw a tyre manufacturer selling a tyre under the fact that it was of light weight?

You also touched on the handling point, if you have a wheel spinning on an axis, it does not want to turn in any direction (self centering).  The gyroscopic effect.  The less Inertial mass, the easier it is to turn, another point of having light wheels and tyres, but nowhere near as important as grip (within reason).

Also, remember smaller wheels (diameter) will mean you have higher gearing and will be possibly putting the engine out of efficiency range to stay at the right speed.  

At the end of the day, light is good.  No detrimental effects in this application at all.  Just wheels getting weaker as they get lighter.  Also light materials (magnesium etc) have a tendency to corrode.

[HarryMann]

I just put my bigger, heavier steel 14" summer tires on compared to my steel 13" tires. The 14s are also wider yet I am seeing about or slighty better mileage and I drive 10km/h faster on the highway

1) Winter to spring/summer mpg trends on all vehicles tend to be of the order of 5~10% (improvement)
 a) Warmer air, less wind resistance (large effect actually, lower air density + less wind)
 b) Less rain, less snow, less slush (lower rolling resistance)
 c) Less choke, cold-start enrichening
 d) Others (less nightime driving with lights/heater; freer flowing traffic etc.)

2) If you read my conclusion you'd see that I was answering a point of theory, that it's probably a smaller effect than some think, that other factors are in the field of play too (tyre pressures/tread patterns for instance, skip grip etc.), and that the final word was that only for large changes in wheel/tyre sizes would the effect be measurable in any way at all, even then small on economy, depending on your cruise ~ stop/start traffic ratio, so as you quote a difference in speed, presume it's mainly cruise - no effect whatsover from inertial considerations)..

3) As you say 'just' changed: I take it you haven't got the figures to hand plotted for 1,000 miles before and after the change... when I see them and plot them out for myself, with an arrow pointing to the odo reading when the wheels were changed, would then be interesting to discuss the trends (cars cannot be fuelled accurately enough to see much of a genuine difference within one or two fills)...

[HarryMann]

Nice going harry!!

Thanks, just a bit of fun really...

I'd have to check that working   Engineers are a right pessimisic bunch and take little at face value without checking :wink:
But that's the idea, yes..

A good comparison is to rig up a wheel hub quite high up, to take your wheels and wind a string around tyre with a weight on the tyre's outer edge. Let go and stopwatch it till it reaches a given rotational speed (difficult to measure) and then calculate, with an allowance for bearing drag... would give a fair idea though of comparative Moments of Inertias.

Therefore we can say that the mass on the wheels may give a bigger proportional change, but in comparison to the mass of the body it is not so substantial.

Yup, not so substantial compared to accelerating a ton and half of car, and a lot of larger wheels might have lighter rims (out where it counts, and why its done!) and lighter, lower AR tyres)
But can be noticeable on the brakes for large heavy off-road wheels and tyres (something we do a lot with Vanagon Syncros, swap 13" road tyres and wheels with 15 or 16" off-road ones)

When was the last time you saw a tyre manufacturer selling a tyre under the fact that it was of light weight?

Can't say I've noticed them shouting about it :wink: but in fact they have obviously put a lot of development into reducing AR which also has that effect..

Also, remember smaller wheels (diameter) will mean you have higher gearing and will be possibly putting the engine out of efficiency range to stay at the right speed.

Yup, but with heavier vehciles with limited power, its also far too easy to overgear, for motorway gradients and into-wind conditions... I hate both overgheared and undergeared cars/trucks :wink:  :wink:

[subsonic]

Wow :!:   OK I think I will need to dig out the calculator for this stuff.

[HarryMann]

I'm sure the theory and practice is well understood - and the really fast boys know where to draw the line:

Heat absorption at the tyre/road interface ( >> larger tyres)
Absolute Grip (>> larger tyres)
Resistance to spinning ( >> larger tyres)
Resistance to tramping and hopping (>> smaller? but very dependent on how the wheel is lcoated, sprung and damped)
Linear acceleration/deceleration (>> smaller tyres)
Rotational acceleration/deceleration (>> smaller tyres)
Aerodynamic drag (>> smaller tyres)
Structural strength at high speeds (>> smaller tyres, but maybe mildly)


Quite a complex package to optimise... depending very much on the main aim... (like how much does acceleration matter in a speed record attempt? Ans: more than you'd think if trying to hit Mach 1 without running out of room at Black Rock!)

Looking at dragsters and comparing to speed record vehicles, we move from mayb 3~4ft diameter up to 4 ~5 ft and beyond (Thrust SS1 had tyres (but undriven) about 5 ft diameter at a guess, some of the old 300~400 mph powered cars (Bluebird) even larger I think (but much eralier technology and driven wheels, 400 being about the limit for that)