Energy consumption with different size of tire in a general vehicle (combustion engine)

[AndreaBianchi1984]

Hi everybody,
I'm an electronic engineer and i thinking about this issue:
In a vehicle you can select different kind of tire/wheel rime. Most of the time people say that if the overall diameter is reduced...the consumption increaseas...let's phisycally analyze the situation:
Here below, when speaking about BEFORE i refere to the situation where the original tire/wheel were mounted.

1) If the overall diameter is reduced, the rolling circunferenc is reduced as well.

2) Since the rolling circunference is reduced, for each single revolution of the wheel hub the car will travel for a reduced value of meter than before.

3) to travel the same distance, the wheel (and consequently the wheel hub) will have to perform more revolution than before.

4) perform more revolution than before does not mean necessary to have more fuel(energy) consumption, that's because for each revolution the distance performed (hence the energy needed) will be lower than before. In the end, theorically, the work performed should be the same as before, since L=force*space is not changed in any way.

5) Finally, the speedmeter value will not be real since it will measure a speed higher than the real one of the wheel.

6) From my point of view, there is no doubt up to now...but....Considering the point 5, to mantain the same speed as before, i will have to press deeper the accelerator, that's why it may seems that I should have to keep the engine RPM higher, and consequently the consumption should be higher...

For sure there is something wrong in the point here above, since the 2 conclusions (4 and 6) are completely in contradiction.
Obviously, i am not taking into consideraiton the possible differences between the type of wheel...let's suppose everything is the same...

May somebody explain to me where the error (or maybe errorS) is/are?

Thanks to everybody.

Andrea

 

[zekeman]

In a simplistic world, if the car manufacturer assumes that the maximum efficiency occurs at a highway speed of say 55mph ( wind tunnel or calculated drag is known), then at the engine maximum power efficiency point , the "gear ratio" is determined to give 55mph.
Any deviation of the total "gear ratio" that includes the tires would reduce that efficiency.

So, under this assumption, changing tires larger or smaller would REDUCE the overall efficiency.

With a few ( perhaps dubious) assumptions

GPH= fo(e,power)
power is constant =V*drag estimated
GPH minimum at e=e* from basic engine data for the known power
GPH minimum=fo(e*,power)
Mpg=V/GPH
GPH =gallons of fuel per hour
fo is a function of engine speed and power
V= velocity 55mph=e*n*r*60/5280
r tire radius, feet
e engine RPM
n overall gear ratio including tires
If you change r then e changes and fo gets larger and MPg goes down
I know I made a number of assumptions but....I believe the conclusion is true for an already designed automobile.

 

[Cockroach]

Most of the energy generated by the consumption of a conbustable goes out the tail pipe as heat and lower grades in fuel oxidation, improper burns. Some of it is also consumed by internal frictions which impart retarding forces on mechanical motion of the vehicle. But a very large proportion of energy consumption goes into the mechanical deformation in the walls of the tire.

You can easily see this if you ride your vehicle with very low inflated tires verses solid steel tires for example. The rolling resistance is less with a solid, non deformable tire. This is why I run tubes internal to my radial truck tires and then inflate above the recommended tire pressure from the manufacturer. My 2009 Ford X150 FX4 has a 100L tank with 20L reserve, I can get 800 km in the city on a single tank of gas. Mind you, this is summer time. In the winter, this drops to about 625 km with the trade-off being handling on snow and ice. And of course the ride gets a little more bumpy with solid tires, so the suspension takes a bit of a beating since it is the stiffer, off road variety.

In the end, no matter what happens it tends to cost the same. You pay at the pump or at the garage with Bob the Mechanic.

Regards,
Cockroach

 

[bigTomHanks]

As others have noted the engine has different power/fuel economy curves based on engine rpm. Your engine may actually use less fuel at a higher RPM due to increased efficiency. Lets say 55 mph, if the smaller tires that you put on you car increase engine RPM to a location where fuel consumption is smaller then you will reduce fuel consumption while maintaining the same MPH. Doing a google search for fuel consumption vs RPM will bring up many graphs that illustrate this.

 

[Tmoose]

Fairly typical BSFC map.

http://img208.imageshack.us/img208/1358/19210mrmopartorque.png

If I need 20 or 30 kW to go down the road, lower revs are where the better BSFC is going to be, unless the cam timing,etc is biased heavily to high rpm "performance". The larger the engine the more likely this is to be true, since it won;t be "working as hard" and the throttle will be more closed (lower torque/BMEP).

My experience with a few cars with instantaneous MPG displays is Non highway Driving will generally reveal tiny throttle openings = higher mpg.
That is not a measure of the BSFC, because the HP is also severely reduced, along with the speed, so the miles travelled per time increment is chopped too. The desire or even need for "more acceleration" for safety in traffic or just to get where I want to go makes that kind of driving unattainable

The peak torque rpm is generally where best BSFC lies, but unless a car has a truly tiny engine it will not be cruising over half throttle at that rpm. The high BSFC islands extend up and down the rpm scale a bit, but they are ALWAYS at the upper end of the BMEP/torque/big throttle opening scale.