How Fast Can a Car Go in Reverse?

Many drivers have wondered how fast their car can go in reverse, either out of curiosity or necessity. The answer depends on several factors, such as the type of transmission, the gear ratio, the engine power, and the aerodynamics of the car.

In this article, we will explain how these factors affect the reverse speed of a car and how to calculate it.

Transmission Type

The type of transmission determines how the engine power is transferred to the wheels. There are two main types of transmission: manual and automatic. Manual transmission allows the driver to select the gear ratio by shifting a lever, while automatic transmission does it automatically based on the speed and load of the car.

Manual transmission usually has a fixed gear ratio for reverse, which is usually lower than the first gear. This means that the engine has to rotate more times to turn the wheels once in reverse than in first gear. For example, a typical manual transmission has a reverse gear ratio of 3.2:1, which means that for every 3.2 revolutions of the engine, the wheels make one revolution. A lower gear ratio provides more torque (or pulling power) but less speed.

Automatic transmission, on the other hand, usually has a variable gear ratio for reverse, which can change depending on the speed and load of the car. This means that the engine can rotate less times to turn the wheels once in reverse at higher speeds, resulting in more speed but less torque. For example, a typical automatic transmission has a reverse gear ratio range of 2.6:1 to 0.7:1, which means that for every 2.6 to 0.7 revolutions of the engine, the wheels make one revolution.

Therefore, automatic transmission usually allows a higher reverse speed than manual transmission, as long as the engine power is sufficient.

Gear Ratio

The gear ratio is the ratio of the number of teeth on the input gear (or cog) to the number of teeth on the output gear. The input gear is connected to the engine side and the output gear is connected to the wheel side. The gear ratio determines how fast the wheels rotate relative to the engine.

A higher gear ratio means that the input gear is smaller than the output gear and that the output gear rotates slower than the input gear. This provides more torque but less speed. A lower gear ratio means that the input gear is larger than the output gear and that the output gear rotates faster than the input gear. This provides less torque but more speed.

The reverse gear ratio is usually higher than any forward gear ratio, which means that it provides more torque but less speed than any forward gear. This is because reversing requires more torque to overcome inertia and friction than moving forward.

Engine Power

The engine power is the amount of mechanical energy produced by the engine per unit time. It is measured in watts (W), kilowatts (kW), or horsepower (hp). One horsepower is equal to about 746 W or 0.746 kW.

The engine power determines how much force can be applied to turn the wheels and overcome resistance from air drag, rolling friction, and gravity. The more power an engine has, the faster it can accelerate and reach higher speeds.

The engine power also affects how fast a car can go in reverse, as it determines how much torque can be delivered to the wheels at different speeds. The torque is the rotational force that causes an object to spin. It is measured in newton meters (Nm) or pound-feet (lb-ft).

The torque is calculated by multiplying the engine power by a constant and dividing by the rotational speed of the engine (measured in revolutions per minute or rpm). The constant depends on the unit of measurement used for power and torque. For example, if power is measured in kW and torque is measured in Nm, then

Torque (Nm) = Power (kW) x 9549 / Speed (rpm)

If power is measured in hp and torque is measured in lb-ft, then

Torque (lb-ft) = Power (hp) x 5252 / Speed (rpm)

The torque times the rotational speed of the wheel gives the power output at the wheel, which is also called brake horsepower (bhp). For example, if torque is measured in Nm and speed is measured in rpm, then

Power output (bhp) = Torque (Nm) x Speed (rpm) / 7121

If torque is measured in lb-ft and speed is measured in rpm, then

Power output (bhp) = Torque (lb-ft) x Speed (rpm) / 5252

The power output at the wheel determines how fast a car can go in reverse, as it has to overcome the resistance from air drag, rolling friction, and gravity.

Aerodynamics

The aerodynamics of a car refers to how well it passes through the surrounding air. The air exerts a force on the car that opposes its motion, which is called air drag or air resistance. The air drag depends on the shape, size, and speed of the car.

The shape of the car affects how smoothly the air flows around it. A more streamlined shape reduces the air drag by minimizing the turbulence and pressure difference behind the car. A more boxy shape increases the air drag by creating more turbulence and pressure difference behind the car.

The size of the car affects how much air it has to push out of its way while traveling. The larger the frontal area of the car, the more air drag it creates. The frontal area is the projected area of the car as seen from the front.

The speed of the car affects how much force the air exerts on it. The faster the car moves, the more air drag it creates. The air drag increases with the square of speed, which means that doubling the speed quadruples the air drag.

The aerodynamics of a car is measured by a dimensionless number called the drag coefficient, which denotes how much an object resists movement through a fluid such as air. The drag coefficient is usually denoted by C D or C w . The lower the drag coefficient, the less air drag the car creates.

The drag coefficient depends on the shape and orientation of the car. For example, a typical sedan has a drag coefficient of about 0.3 when moving forward, but it can increase to about 0.5 when moving backward, as the rear end of the car is less streamlined than the front end.

The drag coefficient times the frontal area gives an index of total drag, which is called drag area. The drag area is usually denoted by A D or A w . The lower the drag area, the less air drag the car creates.

The air drag times the speed gives the power required to overcome it, which is called aerodynamic power. The aerodynamic power is usually denoted by P D or P w . The higher the aerodynamic power, the more engine power is needed to maintain a certain speed.

The aerodynamic power is calculated by multiplying the air density, the drag coefficient, the frontal area, and half of the square of speed. For example, if air density is measured in kilograms per cubic meter (kg/m3), drag coefficient and frontal area are dimensionless, and speed is measured in meters per second (m/s), then

Aerodynamic power (W) = Air density (kg/m3) x Drag coefficient x Frontal area (m2) x 0.5 x Speed2 (m2/s2)

If air density is measured in slugs per cubic foot (slug/ft3), drag coefficient and frontal area are dimensionless, and speed is measured in feet per second (ft/s), then

Aerodynamic power (hp) = Air density (slug/ft3) x Drag coefficient x Frontal area (ft2) x 0.5 x Speed2 (ft2/s2) / 550

The aerodynamics of a car affects how fast it can go in reverse, as it has to overcome more air drag than when moving forward.

How to Calculate Reverse Speed

To calculate how fast a car can go in reverse, we need to know its engine power, reverse gear ratio, wheel diameter, and drag coefficient. We also need to assume a constant air density and neglect rolling friction and gravity.

We can use these formulas to calculate the reverse speed:

Torque (Nm) = Power (kW) x 9549 / Speed (rpm)

Power output (bhp) = Torque (Nm) x Speed (rpm) / 7121

Aerodynamic power (W) = Air density (kg/m3) x Drag coefficient x Frontal area (m2) x 0.5 x Speed2 (m2/s2)

Wheel speed (rpm) = Engine speed (rpm) / Reverse gear ratio

Wheel circumference (m) = Wheel diameter (m) x pi

Speed (m/s) = Wheel speed (rpm) x Wheel circumference (m) / 60

We can use these formulas to find the maximum reverse speed by equating the power output at the wheel to the aerodynamic power required to overcome air drag:

Torque (Nm) x Wheel speed (rpm) / 7121 = Air density (kg/m3) x Drag coefficient x Frontal area (m2) x 0.5 x Speed2 (m2/s2)

We can then solve for speed using algebra or a numerical method.

Alternatively, we can use these formulas to find the reverse speed at a given engine speed by substituting it into the wheel speed formula:

Wheel speed (rpm) = Engine speed (rpm) / Reverse gear ratio

Speed (m/s) = Wheel speed (rpm) x Wheel circumference (m) / 60

We can then compare this speed to the maximum reverse speed to see if it is feasible or not.

Example

Let us take an example of a car with the following specifications:

• Engine power: 150 kW (201 hp)
• Reverse gear ratio: 3.2:1 (manual transmission)
• Wheel diameter: 0.6 m (24 in)
• Drag coefficient: 0.5 (backward)
• Frontal area: 2.4 m2 (25.8 ft2)
• Air density: 1.2 kg/m3 (0.075 lb/ft3)

Using the formulas above, we can calculate the maximum reverse speed by equating the power output at the wheel to the aerodynamic power:

Torque (Nm) x Wheel speed (rpm) / 7121 = Air density (kg/m3) x Drag coefficient x Frontal area (m2) x 0.5 x Speed2 (m2/s2)

Solving for speed, we get:

Speed (m/s) = sqrt(Torque (Nm) x Wheel speed (rpm) x 7121 / (Air density (kg/m3) x Drag coefficient x Frontal area (m2) x 0.5))

Substituting the values, we get:

Speed (m/s) = sqrt(150 x 9549 / 3.2 x 7121 / (1.2 x 0.5 x 2.4 x 0.5))

Speed (m/s) = sqrt(133,387 / 864)

Speed (m/s) = sqrt(154)

Speed (m/s) = 12.4

Converting to kilometers per hour, we get:

Speed (km/h) = Speed (m/s) x 3.6

Speed (km/h) = 12.4 x 3.6

Speed (km/h) = 44.6

Therefore, the maximum reverse speed of this car is about 44.6 km/h or 27.7 mph.

Using the formulas above, we can also calculate the reverse speed at a given engine speed by substituting it into the wheel speed formula:

Wheel speed (rpm) = Engine speed (rpm) / Reverse gear ratio

Speed (m/s) = Wheel speed (rpm) x Wheel circumference (m) / 60

For example, if the engine speed is 3000 rpm, then:

Converting to kilometers per hour, we get:

Speed (km/h) = Speed (m/s) x 3.6

Speed (km/h) = 29.4 x 3.6

Speed (km/h) = 105.8

Therefore, the reverse speed of this car at an engine speed of 3000 rpm is about 105.8 km/h or 65.7 mph.

However, this speed is higher than the maximum reverse speed calculated earlier, which means that it is not feasible or realistic. The engine power would not be enough to overcome the air drag at this speed, and the car would likely lose control and damage its transmission.

Conclusion

In conclusion, the reverse speed of a car depends on several factors, such as the type of transmission, the gear ratio, the engine power, and the aerodynamics of the car. The reverse speed can be calculated using some formulas that relate these factors to the torque, power output, and aerodynamic power of the car.

The maximum reverse speed of a car is limited by its engine power and drag coefficient, while the reverse speed at a given engine speed is determined by its reverse gear ratio and wheel diameter.

The reverse speed of a car is usually lower than its forward speed, as reversing requires more torque and creates more air drag than moving forward.

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