ACCELERATION and Wheel Weight      ver 1: 9199

Another area that spreadsheets can help clarify is with the effects of acceleration. Rarely can one maintain a steady speed. Frequently one has to decelerate and then accelerate for stop signs, red lights, turning corners, and so forth. Because acceleration is  typically a very short-term effect, higher power levels, can momentarily be endured. [e.g. 0.25 HP (Ref.[1] Marks, 60-year man, plotted down to 30 sec factor of 2 safety)]

Because acceleration typically does occur so often, the total

amount of power integrated over a trip can be quite large. Furthermore the riders ability to recuperate takes more and more time after each peak power demand.

Unlike steady motion, the effect of acceleration is felt even on flat ground. The following is a table to show this effect.

The value of acceleration (mph/sec) has been selected at each speed to reflect what the Average Human would probably use. At low speeds the rate of acceleration can be quite brisk.  But as the speed increases, the rate of acceleration must be reduced to keep the total power manageable.

mph       mph/sec

0 %                5            1.0            .135

0                       7             .7            .145

0                     10              .45           .160

0                       13           .35            .196

WHEEL WEIGHT

A quote taken from the Primer,

“One can see that this expression is independent of the radius r. Consequently, power demand depends only on the wheel mass, not on the wheel radius.  For the ideal hoop model (c = 1), the rotational power is the same as that required to accelerate the wheel mass m in translation.

In practice, small-radius wheels tend to have less mass than large-radius wheels, because they are typically made from the same materials, and the “dynamic mass” is reduced accordingly.  But one can imagine an advanced, low-density wheel of a given radius having the mass of a much smaller wheel.  The same power would be required to accelerate these two wheels to the same rim speed.

It is also useful to keep in perspective the very small fraction of total power used to overcome rotational inertia - typically 1-2% at moderate speeds, slopes, and acceleration values.  Readers can use the power spreadsheet program to determine for themselves just how much attention to wheel mass is warranted.

[1] Mark’s Mechanical Engineers Handbook, 1978 pg 9-162