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### Conversion of non-SI units

• Foot = 0.3048 m
• Mile = 1.61 km
• Pound, lbs, lb = 0.453 kg
• Ounce, oz = 28.35 g
• Lbs / sf = 4.88 kg/m2
• HP (horsepower) = 735.5 W
• 1 tesla [T] = 104 gauss [G]

### Definitions

• m = mass [kg]
• n = revolutions per minute [rpm]
• v = velocity [m/s]
• ω = angular velocity [rad/s]
• e = back electromotive force [V]
• F = force [N]
• T = torque [Nm]
• P = power [W]
• E = energy [Ws]
• Tf = friction torque [Nm]
• Cr  = Rolling resistance [m]
• ρ = Air density [kg/m3]
• Cw = Drag coefficient [ ]
• A = Reference area [m2]

### Physics

• 1 kg = 9.81 N
• 1 calorie = 4.1868 joule
• v [m/s] = [km/h] / 3.6
• ω = 2 * π * n / 60 = 0.1047 * n
• ω = v / r = kmh / (1.8 * diameter)
• F = m * a
• P = E / t [W] or [Nm/s]
• E = 0.5 * m * v2

### Required bicycle power

• Proll = Cr * m * g * v
• Pdrag = 0,5 * ρ * Cw * A * v3
• Pslope = m * g * v * slope[%] / 100

### Bicycle speed calculation

• kmh = n * wheel circumference * 0.06

### Motor torque and power

• P = T * ω [Nm/s]

### The two linear relationships of an PM motor

• Kv = rpm/V
• k = 30/(π * Kv) [V/rad/s]
• k = e / ω [V/rad/s]
• k = T / i [Nm/A]