Bike Speed from Power

$P = (1/2)*C_D rho A (v+v_w)^3 + (mu m g cos theta + m g sin theta) (v+v_w)$

$(P) "Power exerted"$

$(M_r) "Rider mass"$

$(M_b) "Bike mass"$

$(G) "Grade: positive = upslope"$

$(A) "Projected rider surface area"$

$(v_w) "Wind speed"$

$(mu) "Rolling friction coefficient"$

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Bike Speed from Power calculates the speed of a bicycle from the maximum power output that the rider can supply. The forces are:

Gravity "drag": the weight experienced pulling a bike either backwards or forwards, due to the grade;
Friction: due to the weight of the bike and rider, and the rolling friction coefficient; and
Drag: the force due to wind and the motion of the bike through the air.

The inputs for the calculator are:

Power (P): Maximum output power the rider can supply. Default is 100 W.
Road grade (G): enter in percent. Default is 0 % grade. Positive is upslope, negative is downslope. If you enter too high a negative value, you'll get a nonsenical answer.
Wind speed (v_w): positive is a head wind, negative a tail wind. Default is 0 mph
Friction coefficient (μ): Used in calculating friction force. Default is 0.008, which is for narrow, high pressure tires. Use a larger value for lower pressure or wider tires
Rider mass (m_r): Mass of the rider. Default value is 70 kg (about 155 lbs)
Bike mass (m_b): Mass of the bike. Default value is 14 kg (about 30 lbs) (Yes, this is high for modern bikes.)
Rider area (A): Projected frontal area of rider. Default is 0.4 square meters. (For those with technical knowledge, I'm assuming a drag coefficient of 1.)

The output is v_m, the. maxiumum bike speed given these parameters. Default units are mph.