1 Northlander March 2013 - North Country Region

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Notice that the width of the wheel is not explicitly contained in the formula but is instead
accounted for in the mass term (wider wheels being heavier than narrow wheels). Notice also that
is squared which means that the tire can contribute more to the rotational inertia than the wheel
on which it is mounted. This is especially true in the case of lightweight track wheels, which in
many cases are lighter than the tire. On the other hand the rotor is generally about half the
diameter of the tire and weighs slightly less than either the wheel or the tire and is therefore the
least important of the three, albeit not insignificant.
Although professional race teams may care greatly about the exact values of these moments in
order to generate computer simulations we need not know them to determine the relative
advantage of lightweight assemblies. To show this we ask what equivalent amount of inertial mass
moving at the speed of the vehicle would result in the same kinetic energy as that produced
by a rotating wheel assembly with moment of inertia
energy formulas in Table 1)
. This is equivalent to writing (see kinetic
Now the angular velocity is related to the tangential velocity at the outermost edge of the tire
by
Note that is also the velocity of the vehicle by virtue of the fact that the tire is in contact with the
ground, i.e., no slippage. Using this together with Equation (1) in Equation (2) yields
Thus, the equivalent mass of a rotating wheel assembly is equal to half the inertial mass of the
assembly (to within the approximations for ). It is important to realize that is not a true
inertial mass in the sense of adding mass to the vehicle for the wheels need to be “angularly”
accelerated to realize their rotational inertia. This implies, for example, that there are no benefits
from in reducing the lateral in a constant speed turn, although it will help in decelerating
and accelerating the vehicle in and out of a turn, respectively.
To the previous equation must be added the actual weight of the assembly plus the fact that there
are four such assemblies so that the total real-plus-equivalent mass is
(In general, the front wheels are lighter than the rears but this is somewhat mitigated by the fact
that the front rotors are generally heavier than the rears.) If we now lighten the assemblies by an
amount we obtain for the total effective inertial mass change
In order to find the gain in equivalent horsepower we can insert this expression into Equation (3) of
Article 1. We first note, however, that the appearance of mass ratios in that equation allows us to
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March 2013
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47 Northlander