Ok semantics but the exact wording is important because it confuses the debate of whether is squared or cubed. My understanding was that drag increases by the square of the speed but the power needed to overcome that drag increases by the cube of the speed.
This ^^^^
For those interested. I copied this off some bloke on the Internet, but I hear that he’s devishly handsome - and that’s important - and he seemed to know what he was talking about so it must be right.
Motive power is a function of running resistance and vehicle speed, and running resistance is a function of the square of vehicle speed, and so motive power is a function of vehicle speed cubed.
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Speed is maintained when the power output of the engine is equal to the running-resistance power (Pw):
Pw = Fw * V
where,
Pw is motive power (kW)
Fw is running resistance (N)
V is vehicle speed (km/h)
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The running resistance is calculated as (Fw):
Fw = Fro + Fl + Fst
where,
Fw is running resistance (N)
Fro is rolling resistance (N)
Fl is aerodynamic drag (N)
Fst is climbing resitance (N)
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The rolling resistance (Fro) is the product of deformation processes which occur at the contact patch between the tyre and the road surface:
Fro = F * M * G
where,
Fro is rolling resistance (N)
F is coefficient of rolling resistance [0.025 for preumatic tyre on tarmac]
M is vehicle mass (weight) (kg)
G is gravitational acceleration [9.81m/(s*s)]
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Aerodynamic drag (Fl) is calculated as:
Fl = 0.5 * Ro * Cw * A * (V + Vo) * (V + Vo)
where,
Fl is aerodynamic drag (N)
Ro is air density [at 200m altitude: 1.202 kg/(m*m*m)]
Cw is drag coefficient (also commonly referred to as Cd)
A is maximum vehicle cross section (m*m)
V is vehicle speed (km/h)
Vo is headwind speed (km/h)
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The climbing resistance (Fst), or downgrade force (Fst), are calculated as:
Fst = M * G * sin(Alpha)
where,
Fst = Fst is climbing resitance (N)
M is vehicle mass (weight) (kg)
G is gravitational acceleration [9.81m/(s*s)]
Alpha is gradient angle (degrees)
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