Built on Facts

Crow for Tuesday Breakfast

Sunday night I was thinking about what to write for Monday morning and settled on the moment of inertia of the tires on a vehicle. If I may say so, it’s a pretty good illustration for an interesting topic. Friction was a possible hitch for my proposed experiment, but I figured that cars were specifically designed to minimize friction, and both cars and tires are pretty heavy. Surely friction can be ignored safely. I wrote up the post in about half an hour and went to bed feeling pleased with myself.

Well. I know from experience that physics Ph.D. holders are not infallible even when talking about their areas of expertise. I’m not a Ph.D, and cars aren’t my area of expertise. The readers of ScienceBlogs are brilliant and widely skilled, and they set to work on correcting me immediately.

Let me give you a few numbers, and I’ll skip writing the equations since we went over them in the last post. A Ford F150 sitting on an incline of 10 degrees will experience a forward gravitational force of about 3400 newtons. The combined mass of all the tires – even assuming they are thin shells in terms of moments of inertia – only adds an additional effective mass of less than 1% of the truck’s total mass. Thus the 3400 newtons is only going to need another 34 newtons or so added to produce the same acceleration that would be produced if there were no rotational inertia in the tires at all.

How does this compare to the force of friction? While you have to take Wikipedia with a grain of salt, the rolling resistance article says 300 newtons is typical for a 1000kg car. My example Ford F150 is twice that heavy, so the friction should be correspondingly greater. Either way it’s a lot more than the 34 newtons worth of effective mass added by the tires.

That will teach me not to run the numbers first. Thank you all for keeping me honest!


  1. #1 Chris P
    August 12, 2008

    When I asked my daughter about her studying special relativity (Which seemed an impressive title for a class) she said “Oh it’s pretty straightforward”

    Possibly more so than vehicle rolling resistance.

    Chris P

  2. #2 Carl Brannen
    August 12, 2008

    If someone asked me to estimate the ratio of rolling friction to KE stored in rotational mass on my Miata, I’d look for a smooth (parabolic maybe) road, start the car at a fixed place, and let it roll back and forth, measuring the period and marking the points at which it comes to rest before reversing.

    The idea is to eliminate the frictional component by looking at the period averaged over a full cycle. Then the period should correlate with the depth and shape of the road.

  3. #3 efrique
    August 12, 2008

    Yeah, I figured out that friction was way more important than you indicated – as anyone who has coasted along in neutral at slow speeds (slow enough that you don’t have to attribute most of it to air resistance) will attest.

    As recent political discussions have reiterated, just inflating tires up can save a few percent in fuel, which is basically just a way of somewhat reducing friction.

    The fact that you ignored it didn’t worry me all that much – but I am happy that you came back and addressed the fact that it’s an issue.

  4. #4 Paul Murray
    August 12, 2008

    “I’d look for a smooth (parabolic maybe) road .. measuring the period”

    Well, measuring the period won’t help. If the road is catenary shaped, then the period is the same no matter where you start – so period depends on shape in odd ways. You’d want to measure the height that the car reaches, and its velocity at the bottom of the arc.

  5. #5 Dunc
    August 13, 2008

    This is exactly why mechanical engineers tend to start sniggering whenever a physicist says “ignoring the effects of friction for the moment…”

  6. #6 Chris P
    August 13, 2008

    What is ironic, from this sniggering mechanical engineer, is that I really liked physics and it is the backbone of everything we do as engineers.

    Everytime some nutcase inventor comes out with an overunity generator we can quite confidently say – bullshit.

    Like yesterday when somebody posted an article on the human powered vehicle group about an Indian who had invented (yet another) bicycle crank that would extend at certain points of the stroke to “double the power output”. Total and utter BS. He even won an award for it and was working on his “tenth” prototype (right) trying to perfect it.


    Chris P

  7. #7 CCPhysicist
    August 13, 2008

    Good for you.

    Tough to admit an error in an open forum, but it will serve you well in the future. There is nothing worse than watching a student (either giving a seminar or, worse, defending) insist that everyone else is wrong.

    You only learn from your mistakes when you realize it was a mistake!

    I remember one particular story where the shop foreman (not an engineer, but the guy who ran the machine shop) pointing to something and saying “it will break there”. The physicist carried on, insisting he had worked it out and it was just fine. It broke. Right there. An engineer would have known it was not a static situation, just as an engineer knows that every bridge is flexing when you drive over it – whether you know it or not. The shop foreman had learned the same thing the same way engineers did: seeing things break. (What you see happen to the ice on Ice Road Truckers also happens on concrete pavement on dirt. There is a “wave” in there as well.)

    PS to Chris P:
    I watched in horror as some engineering students presented a design that would amplify their power output with gear ratios. They didn’t even get it when asked a question about energy flow. (See my second paragraph up above.) I was just glad that none of them had taken physics from me….

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