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Big Wheels or Small Wheels

  1. May 31, 2010 #1
    This questions does my head in, someone asked me it a while ago and I don't feel like it was answered right.

    If you have a car, travelling at 60mph and it used its full tank of fuel. This means on a very long straight road it would cover 60miles on the hour with no fuel left. Now, providing everything stayed the same, gears, speed the axel is spinning, and the time of an hour, the car would surely travel further if the wheels we swapped for a larger size. Say tractor wheels. Much larger wheels means further to go before it completes one rotation, so it would cover more ground on the same amount of fuel.?

    Why aren't we driving around with tractor wheels and saving fuel? would kick *** in winter.
  2. jcsd
  3. May 31, 2010 #2
    im not sure but at first guess i would say they would remain the same..

    although they would cover a greater distance per turn of the wheel it would need more energy to turn the wheel than for the smaller wheel.

    Not sure though that was just a quess =]
  4. May 31, 2010 #3


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    Instead of bigger wheels, you could just use taller gearing, which is why cars have overdrive. There's a point of diminishing returns, as engines generally are not that efficient at very low rpms.
  5. May 31, 2010 #4
    A big problem with any vehicle is keeping the tires in contact with the road when the vehicle hits a bump. To do this, the vehicle suspension system requires a large vehicle mass to tire mass ratio. A heavy tire will bounce, and a light tire will not. If the tire loses contact with the road, the driver loses steering control. and static friction gives way to sliding friction.

    Larger tires have a larger moment of inertia, but they rotate slower at a given vehicle speed, so the net result is that the rotational energy stored in the spinning tires is independent of tire size, for a given tire width.

    For any given tire size, the gearing should be changed so that the engine is operating at the optimum (most efficient) point in the BSFC (brake specific fuel consumption) map. See


    The vehicle with bigger tires would have a larger frontal cross section, so the air drag would be more, and because air drag is the major power loss at highway speeds, the vehicle would travel a shorter distance on a full tank of fuel.

    Bob S
  6. May 31, 2010 #5
    I find this to be an interesting question.
    Though we can not, of course, get "something for nothing", nor was it implied, I wonder if perhaps there is some "optimum" wheel radius for specific vehicle conditions.

    In other words, I wonder if there have been studies of 2 identical vehicles, except for their tire radius/width to determine optimal fuel economy.
  7. May 31, 2010 #6
    Well of course there is, that's why the engineers specify the gear ratios in the transmission and in the differential. It used to be that the manufacturers offered various differential ratios, and the drag racers picked one for more acceleration off the line, where the traveling salesmen picked the highest ratio for more top speed and/or better fuel mileage. Trucks find it economical to pay for an overdrive to get better than 1:1 out of the transmission. Everything works together - the engine characteristics, the transmission ratios (in the lower gears), the axle ratio and the wheel/tire size. The only question is, how do you define "optimum?" Your post said "fuel economy" but there are plenty of choices as to what any given user might consider optimum.
  8. May 31, 2010 #7
    A 2x larger wheel is at least 2x harder to turn, because you'd be attempting to make the car go 2x faster. It's just like 2x steeper stairs are 2x harder to climb. Yes, if your legs are moving the same speed for the same time, you will climb twice as high. But, the point is that your legs will probably NOT be moving the same speed for the same time :)

    So...based on your constraints (providing everything stayed the same, gears, speed the axel is spinning, and the time of an hour), yes the car would travel further. The flaw is that in the real world, the speed the axle is spinning would NOT be the same unless more energy was put into it.

    Again, attempting to spin a 2x larger wheel at the same speed would be attempting to move the car 2x faster. Since energy is force x distance, traveling 2x faster for 1 hour necessarily requires at least 2x more energy (since you covered 2x more distance). You would run out of gas after at most half an hour.

    Even more bad news is that in the real world, air resistance is actually a square function! (2x more speed means 4x more air resistance!). This means you would actually probably need at least 4x more energy...so you would run out of gas after 15 minutes.
  9. May 31, 2010 #8

    jack action

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    Like Lsos said, everything else being the same a larger tire diameter means a faster speed.

    Just think about it: if with one tire diameter you cover 60 miles in an hour, your average speed is 60 mph. If with a larger tire diameter (say twice as big) you cover 120 miles in an hour, then your average speed will be 120 mph.

    You will need to accelerate to that speed (acceleration = fuel consumption) and you will need to fight aerodynamic drag at that higher speed (which means more fuel consumption).

    You could reduce the wheel rpm by 2 to get the same average speed of 60 mph. Then your fuel consumption would be the same with the only advantage of a tire that wears slower. But the bigger tire will probably have more inertia, increasing fuel consumption under acceleration.
  10. May 31, 2010 #9
    Up to a point, larger diameter wheels have less rolling friction, and better advantage. There's a reason bicylce tires are not two inches across.

    We might ask why the Prius designers didn't opt for wheels somewhat larger in diameter than usual.
  11. May 31, 2010 #10
    Mathematically, your 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 tire to buy, this isn't enough information.

    You could, maybe, model this such that you have a single tire 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 tire.

    Then you "enlarge" the tire, m becomes the mass of the bigger tire, 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 tire,
    ml = mass of the large tire
    vs = velocity of small tire
    vl = velocity of the large tire.

    What you find is that the velocity of the larger tire 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.

    You mention that you want to keep axel speed the same (rotational velocity), which means that you now do not have enough gas to even cover the 60 miles unless you make the tire lighter, as well as larger.

    Note also that larger tires require more torque to accelerate to the same velocity. Larger tires on a vehicle usually crushes gas mileage since higher accelerations are not as efficient on cars. This is maybe why the Prius doesn't have larger tires, it just doesn't have the output.
  12. Jan 1, 2012 #11
    So, what if we were to look at this question a different way: let say the only difference between two wheels was the diameter. To clarify the conditions; the width of both wheels would be the same, the contact material to the ground the same, the weight of the wheel would be the same, axles the same....etc., so the only difference between the two were the diameters.
    The test environment would be as follows; lets say for the sake of argument there were two sets of four wheels; one set (big wheel) to be two inches in diameter and the small set one inch in diameter. The weight of the vehicle, with either set of wheels attached, to be the same (Cub Scout Derby Car would work). And the surface the car would roll on is smooth; lets say a finished hard wood floor at a 5 degree decline.
    Assuming the car goes straight with out the aid of a track slot, which set of wheels would be faster; the two inch diameter wheels or the one inch?
    Now, what ever the results, is there a math equation that explains the reason why one set of wheels rolls faster than the other, or perhaps why they roll at the same rate?
  13. Jan 2, 2012 #12
    Under perfect conditions (no friction), I can't see why both cars wouldn't be equally fast (assuming also that the moments of inertia of the different sized wheels are the same). What makes the difference comes down to friction. A larger wheel would probably have more air resistance, but perhaps less rolling resistance. It would also spin slower, so the frictional losses in the bearings would be smaller. There are probably some other frictional variables, some of which go up and some down depending on diameter/ speed/ etc, making the question hard to answer. There's probably a perfect sized wheel for each set of conditions.
  14. Jan 2, 2012 #13
    Whether friction the size of the wheels won't matter because the car won't move :P
    The wheels turn because the axle applies a torque, for the wheel to not move there would have to be a torque of equal magnitude, since the force required to produce a torque is inversely proportional to the distance from the center of the wheel there must be a much smaller force at the circumference of a larger wheel than a smaller one and since the rotation of the wheels produces motion from the force they apply to the road a larger wheel would produce less force so the angular momentum would (or could depending on the conditions) be lower than with a lower circumference wheel.
  15. Jan 2, 2012 #14
    For a given car the design of the engine, transmission, drive-line, suspension, wheels, and body are all designed to work together to achieve a good balance between fuel economy, ride quality, handling, performance, cost of manufacture, etc. In recent years EPA standards have forced manufacturers to weight fuel economy very heavily in that balance. Any change you make to the vehicle will probably hurt fuel economy. Basically, if there was anything you could change that would have improved fuel economy without drastically hurting some other desirable trait the engineers would have already spec'd it that way.
  16. Jan 2, 2012 #15
    Big wheels = long effective gear ratio.

    Have you ever tried setting off in 5th gear?

    Also at 60mph, you'll need to be doing very low hundreds of RPM in top gear (below the stall speed for most engines).
  17. Jan 2, 2012 #16
    I don't think wheel size is dictated by torque/power etc but by more practical considerations. The front wheel size can't be huge because the vehicle has to turn corners. Given that the front wheel size is limited then, on most cars, that will set the rear wheel size as well. Who wants to carry two spares around? Large wheels also reduce passenger and load space, which is why mini type cars have very small wheels. Very small wheels have their own disadvantages, for example they wear out proportionally quickly. The very high fuel efficiency vehicles now appearing achieve this by having narrow tyres with a higher pressure to reduce the contact area.
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