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One mechanism is energy loss from mechanical flex. At higher speeds, the tires suffer increased flexing that steals energy and increases the energy loss.

Heinz Heisler MSc., BSc., F.I.M.I., M.S.O.E., M.I.R.T.E., M.C.I.T., M.I.L.T., in Advanced Vehicle Technology (Second Edition), 2002
8.1.5 Rolling resistance (Figs 8.10 and 8.11)

When a loaded wheel and tyre is compelled to roll in a given direction, the tyre carcass at the ground interface will be deflected due to a combination of the vertical load and the forward rolling effect on the tyre carcass (Fig. 8.10). The vertical load tends to flatten the tyre's circular profile at ground level, whereas the forward rolling movement of the wheel will compress and spread the leading contact edge and wall in the region of the tread. At the same time, the trailing edge will tend to reduce its contact pressure and expand as it is progressively freed from the ground reaction.

The consequences of the continuous distortion and recovery of the tyre carcass at ground level means that energy is being used in rolling the tyre over the ground and it is not all returned as strain energy as the tyre takes up its original shape. (Note that this has nothing to do with a tractive force being applied to the wheel to propel it forward.) Unfortunately when the carcass is stressed, the strain produced is a function of the stress. On releasing the stress, because the tyre material is not perfectly elastic, the strain lags behind so that the strain for a given value of stress is greater when the stress is decreasing than when it is increasing. Therefore, on removing the stress completely, a residual strain remains. This is known as hysteresis and it is the primary cause of the rolling resistance of the tyre.

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Fig. 8.10. Illustration of side wall distortion at ground level

The secondary causes of rolling resistance are air circulation inside the tyre, fan effect of the rotating tyre by the air on the outside and the friction between the tyre and road caused by tread slippage. A typical analysis of tyre rolling resistance losses at high speed can be taken as 90–95% due to internal hysteresis, 2–10% due to friction between the tread and ground, and 1.5–3.5% due to air resistance.

Rolling resistance is influenced by a number of factors as follows:
a) cross-ply tyres have higher rolling resistance than radial ply (Fig. 8.11),

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Fig. 8.11. Effect of tyre construction on rolling resistance

b) the number of carcass plies and tread thickness increase the rolling resistance due to increased hysteresis,
c) natural rubber tyres tend to have lower rolling resistance than those made from synthetic rubber,
d) hard smooth dry surfaces have lower rolling resistances than rough or worn out surfaces,
e) the inflation pressure decreases the rolling resistance on hard surfaces,
f) higher driving speed increases the rolling resistance due to the increase in work being done in deforming the tyre over a given time (Fig. 8.11),
g) increasing the wheel and tyre diameter reduces the rolling resistance only slightly on hard surfaces but it has a pronounced effect on soft ground,
h) increasing the tractive effort also raises the rolling resistance due to the increased deformation of the tyre carcass and the extra work needed to be done.

Not identified in this source, another paper pointed out that tires can have a circumferential vibration mode, a circular resonance. When tires "sing", they are also losing energy by flexing the tire tread.

Bob Wilson