Allow me to "clean up" the expression (expression - not equation) for power required to propel a mc at speed, and correct an inadvertent typo error.
First, I slipped in the symbol V to represent speed. We aerodynamicists use V (velocity) to express speed. Velocity is numerically equal to speed, but has the additional property of direction.
Second, since I cannot type with superscripts or subscripts, let us define ^ as the symbol to raise a number to an exponent. Then V^2 is speed raised to 2 power or squared.
As Dances notes, air resistance is referred to as Drag, and is a force. Drag = Cd x 1/2 (Rho)V^2 . Cd is the coefficient of drag, and Rho is the density of air. Aerodynamicists use a "standard" density of air for calculations; sea level barometric pressure and temperature = 59 deg F - why 59 F? It is the mean global air temp. between the temperate latitudes.
From the above, the Drag force can be precisely calculated, if one knows precisely the value Cd, which for a mc is not easily estimated. It also show how and why air temp and baro. pressure affect the result.
Now, let's define the mechanical power transmission loss as "tr" and express it as a decimal fraction, that is, if the loss is 15%, then express it as 0.15 (not say'n that is the value, it is only an example). Then the power that must come out of the engine's crankshaft is (1 + tr) x necessary rear wheel power.
The necessary rear wheel force equals the sum of Drag + Rolling Resistance + Spindle (front) torque. Let's call rolling resistance RR, and spindle torque Ts.
and power being force x distance/time, or power = V x force
Then, necessary power at rear wheel = (1 + tr) x V x (Drag + RR + Ts) ...... my inadvertent typo put the V inside the quantity brackets!!!
Expressed as a function (f) of speed or V,
Prw ~ (1 + tr) x V x [ (f)V^2 + (f)V^y + Ts] ............ here I substituted 'y' for the rolling resistance exponent since I do not know with any conviction what value is has. Surely, engineers have done tons of research on this and it should be available if anyone cares to research it. Those who are going for speed records should do so, as it is the second most important component limiting maximum speed. Any light airplane pilot will tell you that the airplane seems to leap forward as soon as the wheels clear the ground.
At the risk of being overly pedantic, note that the V outside the brackets [ ] raises the exponent of the terms inside the [ ] by a factor of 1.0 when the multiplication is carried thru.
Slick
