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Automotive & Engines

What makes cars go: horsepower, torque, compression, gearing, fuel economy and braking

Power from Torque & RPM

NEWIntermediate
P=τ×N9549P = \frac{\tau \times N}{9549}

Engine power in kW from torque and rotational speed.

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Horsepower from Torque (Imperial)

NEWBasic
HP=τ×N5252HP = \frac{\tau \times N}{5252}

Horsepower from torque (lb-ft) and engine rpm.

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Compression Ratio

NEWIntermediate
CR=Vd+VcVcCR = \frac{V_d + V_c}{V_c}

Ratio of cylinder volume at bottom vs top of the stroke.

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Engine Displacement

NEWBasic
V=π4b2snV = \frac{\pi}{4} b^2 s\, n

Total swept volume of all cylinders.

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Gear Ratio

NEWBasic
GR=NoutNinGR = \frac{N_{out}}{N_{in}}

Ratio of driven to driving gear teeth.

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Vehicle Speed from RPM

NEWIntermediate
v=πdNGRGfv = \frac{\pi d N}{GR \cdot G_f}

Road speed from engine rpm, gearing and tyre diameter.

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Fuel Economy (L/100km)

NEWBasic
E=100FdE = \frac{100\, F}{d}

Litres of fuel used per 100 km travelled.

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Miles Per Gallon

NEWBasic
MPG=dFMPG = \frac{d}{F}

Distance in miles per gallon of fuel.

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Braking Distance

NEWIntermediate
d=v22μgd = \frac{v^2}{2 \mu g}

Distance to stop from speed v with friction μ.

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Power-to-Weight Ratio

NEWIntermediate
PWR=PmPWR = \frac{P}{m}

Engine power divided by vehicle mass — the key to acceleration.

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Aerodynamic Drag

NEWAdvanced
Fd=12ρv2CdAF_d = \tfrac{1}{2}\rho v^2 C_d A

Air resistance a car must overcome, rising with speed squared.

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Kinetic Energy of Vehicle

NEWBasic
KE=12mv2KE = \tfrac{1}{2} m v^2

Energy that brakes must dissipate to stop a moving car.

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Torque from Force

NEWBasic
τ=F×r\tau = F \times r

Turning effect of a force applied at radius r.

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EV Range

NEWIntermediate
R=EcR = \frac{E}{c}

Electric-vehicle range from battery capacity and consumption.

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EV Charging Time

NEWBasic
t=EPt = \frac{E}{P}

Hours to charge a battery at a given power.

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Tyre Rolling Circumference

NEWBasic
C=πdC = \pi d

Distance covered in one wheel revolution.

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