Well, I have not taken the time to calculate that, but I did back up my assertions as to the effect on torque, and do understand the physics very clearly. And the effect is definitely quantifiable as well as noticeable.

The supporting calculations for the moment of inertia increase of a larger, heavier wheel can be a little more comples to buzz through The moment of inertia is both proportional to the mass as well as the square of the radius. The trouble with figuring this for wheels is that you do not have an evenly distributed weight, and further more, the distribution (along the radius) will be different for various wheel designs.


So we have three main effects of a larger and heavier wheel (supposing both are in fact the case): A larger moment of inertia, a negative effect on force applied to the ground as a result of torque at the axle and a positive effect on rolling resistance. Again, as all of this points to (and the last time I will go through explaining this), the effect depends on the type of driving you are looking at. As far as acceleration is concerned, both the moment of inertia and effect on transmitted force is going to be detrimental. After that, the improved rolling resistance is going to come into play much more. The total effect of the moment of inertia is more difficult to quantify given the unknowns. However, the effect on transmitted force to the ground is DIRECTLY proportional to the change in diameter size.

I have worked with off road vehicles as well as street vehicles, and I can tell you that wheel and tire diameter play a DEFINITE role in launch and hard acceleration, especially when you are not dealing with tons of HP to begin with. So I can say that I understand this from both my educational background as well as practical application. So there is the last of my .02 for this thread I'll leave it to you guys to argue more if you like.

 

OK, you've avoided the issue by making it sound very complex, but a worst case scenario isn't that hard to work with. Let's say that we add 2kg of mass to the very outside circumference of each wheel/tire combination. The radius of the wheel is 0.30m and the circumference is 1.88m. At 90km/h (25m/s) the wheel is rotating at 13.3 revolutions per second or 83.6 radians per second.

The moment of inertia of the added mass is found using I=mr^2:

I=2(0.3)^2 = 0.18kg-m^2

The rotational kinetic energy is found using KE=0.5I[omega]^2:
0.5(0.18 )(83.6)^2=630J

There are four wheels, so the total rotational KE of the added mass is 4*630=2520J

So, what is the KE of the rest of the car? Assuming the car has a mass of 1100kg:

KE=0.5mv^2

KE=0.5(1100)(25)^2= 344,000J

So the heavier wheels absorb an additional 2520/344000 =.00733 or 0.733% of the original kinetic energy in getting up to speed.

Less than one percent and this was a worst case situation, so the actual number will be lower! This might be significant if you are trying for .01second better ET at the dragstrip, but it's not something that you can feel with the seat of your pants.

Therefore, any difference that the driver could feel would be the result of a change in wheel diameter. Even this would be minor unless the driver uses WOT for every acceleration. With larger wheels the acceleration will be lower for a given throttle setting, so the driver will simply open the throttle a bit more and adjust his shift points to achieve the desired acceleration. More throttle means more fuel use per engine revolution, but of course the engine is not turning as many revolutions so the net effect is a wash.

Racing paradigms don't always work well in street situations.

 

Back to Basics Please.....

I switched from the stock 185-60-15s to 185-65-15s -- front only.

The tire calculator says there is a 2.95% difference (larger) in diameter.
And, 3.034 too low a speedo reading.

This is why I should have paid more attention in class ;
Can I just add 3.034% to my mileage calculation after doing the mpg/gals?
Or should I add 3.034% to the miles indicated before doing the mpg/gals calculation?

I've done it both ways here with the same result. Am I forgetting something? Again, lets keep it simple. I only want the nominal number - not the torque vs aero vs compound vs top off vs brand vs fresh wax job vs etc numbers.

 

Both calcs are mathematically the same so either will do.

However, did you also take into account that the stock odometer is about 4% low with stock tires? Check it out over 100 miles against a GPS and you'll see what I mean.

George

 

I think we can agree on the bottom line:

Even after taking effective gearing into account, larger diameter tires will significantly reduce mileage due to the fact that rotational inertia increases exponentially with increase in diameter.

 

Another physics thread rises from the dead!

If your theory were correct, then racing bicycles would come with small diameter wheels! Those guys worship at the alter of energy efficiency.

Rotational inertia does increase with the square of the radius, but the increased inertia will only have an effect (and a small one) during the period in which the wheel and tire are actually being accelerated. There is no inertial effect at constant speed.

Mileage is more affected by rolling resistance (worse on grippy high-performance tires), aerodynamic drag (worse on wider tires with deeply dished wheels) and non-optimized gearing than it is by increased rotational inertia.

 

Wow! An old one dredged up.

Yes there is inertia to account for when accelerating the rotation of a wheel, and that is matched by the momentum of the wheel when not trying to accelerate it.

As soon as one goes to neutral throttle the momentum of the wheel - it's tendency to keep turning at the same rate of speed unless acted on by an outside force - comes into play. The extra energy used in spinning the wheel up is returned directly as it is slowed down.

The only losses in that formula are the losses to friction.

====

BTW, with the 185/65R15 BFG Traction T/A's on my box - stock tire size on the bB, oversize for the xB - my speedo is currently right on at 60MPH and my odometer reads 6.1% short.

To provide a nearly correct MPG figure, I multiply the MPG I obtain from the usual gallons vs miles traveled calc by 1.06...

 

How often do those guys come to a stop then accelerate back up to speed?

 

Exactly

Overall inertial effects are not the issue, since any negative impact upon acceleration is mitigated by the positive impact of them being harder to decelerate.

Again (as I stated over and over in my original posts here) the largest detrimental effect is the fact that it takes more work to accelerate the larger diameter (even if you take weight out of the equation) at the same rate, period. And this is a nice, simple proportion as I mentioned previously. So if you are running a constant speed all the time, then you could say that the rolling resistance had more weight in this scenario. Seeing as how the rest of the real world drives on roads with stop signs, slower traffic, etc, then that is not the case. The fact is that unless you are on very long road trips, this effect IS important (effect of diameter alone).

I had this discussion recently with my friend who went to larger profile tires on his truck. And, just like predicted, his mileage decreased, especially in city driving where he has to accelerate from a stop more often ;)

 

Uh-huh.

On my box the tires I went to are .4 inch taller, so they should require about 3% more effort to accelerate to speed, but at speed my engine is turning 3% slower than "normal" so depending on one's expected driving patterns it could go either way.

(For the most part I tend to drive with long, gradual changes in speed. My only 'extravagance' in my driving is not necessarily slowing down as much as most folks for corners...)

The taller tires I'm running now have lower rolling resistance than the stock tires, and the contact patch is about the same (same tread width, likely same patch length due to running increased pressure*).

Overall, city mileage has remained the same with the aftermarket tires, highway mileage has increased noticeably, due to the slightly more relaxed cruise at legal speeds.

So many small things affect the results that one has to know what one is after, and how to change which parameters to gain small advantages.

* Higher tire pressures are easily allowed without reducing ride quality because of the slightly taller sidewalls offering better flex when needed and aftermarket shocks with variable-valving over their range of motion. In fact, ride quality has improved noticeably.

 

For those who think that the rotational inertia is significant, consider the equations that determine the rotational kinetic energy (the energy stored in the rotating wheels).

The moment of inertia of any part of the wheel is determined by I = mr^2
Where m is the mass of the wheel and r is the radius.

This equation makes it seem that a small change in radius will have a large change in rotational inertia, and that idea is correct.

However, rotational kinetic energy is determined by I _and_ by [omega], the angular rate of rotation of the wheel. The formula is:

RKE = 1/2 I [omega]^2

Now, the [omega] is interesting because it is dependent upon circumferential speed of the tire (the vehicle's speed) and the inverse of the diameter.

v = r [omega] so [omega] = v/r

Put the these formulas together and you get:

RKE = (1/2) (m r ^ 2) ( v / r ) ^ 2

Which rearranges to:

RKE = (1/2) m (v^2) (r^2) /(r^2)

Note that the radius drops out of the equation, leaving the familiar

RKE = 1/2 m v ^2

Yes, if speed and mass remain constant the RKE is the same no matter what the wheel diameter!

Now, the next argument is that larger wheels are heavier and will create higher RKE.
This is true, but the effect is only linear. If the larger wheels and tires are 10 pounds heavier they will have exactly the same effect as adding 10 pounds anywhere on the vehicle.

Isn't physics fun!

George <-- who is considering 195/65R15s for the next tire change.

 

We are not talking about kinetic energy. Again, you are assuming cars travel at a constant speed indefinitely. The last time I drove a car there was a traffic light at every intersection.

And saying that adding mass to a rotating object is the same as adding mass to a static object is plain wrong. I don't know where you learned your physics from.

 

(Actually my aftermarket alloy wheels and slightly taller, same width tires are lighter than stock wheels/tires...)

 

There is more in effect than inertial changes.. which is what I have been saying all along.. but apparently it keeps getting fixated on rotational inertia... but oh well

When you increase diameter, you proportionally require more tq to accelerate at the same rate.

 

It's not THAT fierce a change - my one-size-taller tires (10mm or 0.4 inch) are the equivalent of changing the final drive ratio on my auto box from 4.15:1 to 4.03:1 (and the final ratio in a stick box from 4:31:1 to 4.18:1).

A 3% reduction in mechanical leverage advantage in acceleration, but also a 3% reduction in engine RPM at speed...

 

That is true Tomas.. which is why we have discussed that it greatly depends on how you drive your car the most. My friends case shows this since he drives primarilly in the city areas and takes their other car on road trips. His larger diameter tires have cost him mileage since he put them on.

But you are also very conscious of how you accelerate from an efficiency standpoint if my memory serves me (the old throttle cable trick with the wife if I remember correctly ) . The average driver will tend to want to get up to speed at the same rate no matter what.

 

Just a little bit on a tangent, here, but I was just thinking about the variable mechanical advantage of an automatic transmission - it's torque converter really is a variable ratio energy transfer device.

I strongly suspect that the minor change in advantage I'm seeing with my taller tires is for the most part accommodated by the auto transmission compensating nearly the same amount in the opposite direction during acceleration.

That MIGHT mean that is why I don't really see a difference in city mileage...

On the other hand, the top two gears in this transmission are locking, so even with an automatic transmission I see the actual 3% reduction in RPM at cruise.

I suspect that the minor 3% effective change in final drive ratio all but disappears in acceleration with this transmission, but becomes real once the transmission locks.

:D

 

I suspect that the fact we are analyzing such a miniscule change to such a degree makes us utter geeks.... but I can live with that I also enjoyed making force diagrams and solving multivariable statics problems in college.. something about solving equations that should always equal zero that I find enjoyable

 

Yeah, "back in the day" I had four different sorts of slide rule, and the ubiquitous CRC Math Tables book...

We ARE geeks... Engineers are like that.

 

Actually, I teach physics. It's a second career after fifteen years as a mechanical engineer. I'm pretty well-versed in the subject.

You may not wish to talk about kinetic energy, but if we're going to talk about mileage, we have to talk about about how energy is used, hence the discussion of rotational kinetic energy stored in the wheels. In a stop-and-go cycle with a given top speed the energy stored in large diameter wheels will be the same as that in small diameter wheels of the same weight. I did not assume that "cars travel at a constant speed indefinitely." The fact remains (as shown above) that wheels of equal mass and circumferential velocity have the same rotational kinetic energy and that the kinetic energy is proportional to the mass of the wheel.

If you think that I'm wrong about the effect of adding mass to a rotating wheel then show where I went astray in my reasoning. The equations are there for your examination and correction. Just saying "you're wrong" and questioning my education doesn't prove your point.

Yes, we're getting quite geeky now! I have a few slide rules (including a 6-foot-long Pickett!), and an entire drawer-full of expensive calculators of various abilities.