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Wheel Horsepower Calculator

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What is wheel horsepower? | Bhp to whp calculationDrivetrain loss calculation — Horsepower loss calculationEfficiency of different drivetrain componentsHow do you calculate horsepower delivered to the wheels?How to use this wheel horsepower calculatorFAQs

Our wheel horsepower calculator will help you determine the horsepower available on the car's drive wheels. The power generated by a car's engine is transmitted to its wheels by the drivetrain. Some energy is lost during this transmission, so the wheel horsepower is always lesser than the engine or crank horsepower.

Automotive manufacturers usually specify engine horsepower simply because the number is higher. In this article, we shall learn how to calculate wheel horsepower from crank horsepower by calculating drivetrain loss. We shall also look at the drivetrain components resulting in horsepower loss.

What is wheel horsepower? | Bhp to whp calculation

To propel a vehicle, it requires power (and torque). The vehicle's engine (or electric motor, in the case of an EV) generates this power, and its drivetrain delivers this power to its wheels.

Wheel horsepower is the amount of power available on the driving wheels of an automobile.

The wheels to which the drivetrain transmits the power are called driving wheels. The formula for the wheel horsepower is given by:

WHP=ηdvtr⋅EHP\text{WHP} = \eta_{\rm dvtr} \cdot \text{EHP}

where:

  • WHP\text{WHP} — Wheel horsepower;
  • ηdvtr\eta_{\rm dvtr} — Efficiency of power transmission of the drivetrain; and
  • EHP\text{EHP} — Engine horsepower.

💡 Note that the engine horsepower is the same as the crank horsepower or brake horsepower (bhp). Not sure what is your engine horsepower? You should be able to find the information in the car manual or on the manufacturer's website. Alternatively, you can use our cool tool to estimate your vehicle's horsepower — head to our horsepower calculator.

We can classify drivetrain systems based on which wheels are driving wheels:

  1. Front-wheel drive (FWD), where the front wheels are driving wheels;
  2. Rear-wheel drive (RWD), where the rear wheels are driving wheels; and
  3. All-wheel drive (AWD) or Four-wheel drive (4WD), where all four wheels are driving wheels.

In the following section, we shall learn to calculate the horsepower loss through each drivetrain system.

Drivetrain loss calculation — Horsepower loss calculation

The different components in the drivetrain introduce losses while transmitting power. This loss depends on the efficiency of the parts used. The more components involved in the power transmission, the more the power loss.

The formula for the efficiency of the front-wheel drivetrain is given by:

ηFWD=ηgbx⋅ηdif⋅ηfdrs\eta_{\rm FWD} = \eta_{\rm gbx} \cdot \eta_{\rm dif} \cdot \eta_{\rm fdrs}

where:

  • ηFWD\eta_{\rm FWD} — Efficiency of front-wheel drive system;
  • ηgbx\eta_{\rm gbx} — Efficiency of gearbox;
  • ηdif\eta_{\rm dif} — Efficiency of differential; and
  • ηfdrs\eta_{\rm fdrs} — Efficiency of front drive shaft.

Similarly, the efficiency of the rear-wheel drive system is given by:

ηRWD=ηgbx⋅ηprs⋅ηdif⋅ηrdrs\eta_{\rm RWD} = \eta_{\rm gbx} \cdot \eta_{\rm prs}\cdot \eta_{\rm dif} \cdot \eta_{\rm rdrs}

where:

  • ηRWD\eta_{\rm RWD} — Efficiency of rear-wheel drive system; and
  • ηprs\eta_{\rm prs} — Efficiency of propeller shaft.

Once we've determined the efficiency, drivetrain loss calculation is simple:

Drivetrain loss=1−ηdvtr\footnotesize \text{Drivetrain loss} = 1-\eta_{\rm dvtr}

To calculate the horsepower loss, we multiply by the crank horsepower:

Drivetrain hp loss=(1−ηdvtr)⋅EHP=EHP−WHP\footnotesize \begin{align*} \text{Drivetrain hp loss} &= (1-\eta_{\rm dvtr}) \cdot \text{EHP}\\ &= \text{EHP} - \text{WHP} \end{align*}

Can you use this wheel horsepower to determine the torque on your wheels? Our torque to hp calculator says you can!

Efficiency of different drivetrain components

Now let's learn to calculate the horsepower loss through the drivetrain by calculating the efficiency of different components involved in power transmission.

Gearbox efficiency

The efficiency of the gearbox depends on the bearings used and the gear meshing. The gearbox must have at least two shafts (one each for input and output), with two bearings for each shaft to support it at each end. Also, at least one gear mesh occurs between these two shafts for each gear engagement.

The efficiency of the gearbox is given by:

ηgbx=ηbrgNbrg⋅ηgrmNgrm\eta_{\rm gbx} = \eta_{\rm brg}^{N_{\rm brg}} \cdot \eta_{\rm grm}^{N_{\rm grm}}

where:

  • ηgbx\eta_{\rm gbx} — Gearbox efficiency;
  • ηbrg\eta_{\rm brg} — Bearing efficiency;
  • NbrgN_{\rm brg} — Number of bearings;
  • ηgrm\eta_{\rm grm} — Gear mesh efficiency; and
  • Ngrm{N_{\rm grm}} — Number of gear meshes.

Propeller shaft efficiency

The propeller shaft transmits the power from the gearbox (or transfer case) to the rear differential (or front differential). A propeller shaft has universal joints (minimum two) to allow for relative movement between the gearbox and the driving axle. Hence the propeller shaft's efficiency largely depends on these universal joints and any support bearings.

The propeller shaft efficiency is given by:

ηprs=ηujNuj⋅ηbrgNbrg\eta_{\rm prs} = \eta_{\rm uj}^{N_{\rm uj}} \cdot \eta_{\rm brg}^{N_{\rm brg}}

where:

  • ηprs\eta_{\rm prs} — Propeller shaft efficiency;
  • ηuj\eta_{\rm uj} — Universal joint efficiency; and
  • Nuj{N_{\rm uj}} — Number of universal joints.

Differential efficiency

A differential is used at the drive axle to turn the power by 90° and deliver the torque to the wheels. It also lets the wheels rotate at different speeds when the vehicle turns left or right while allowing them to rotate at the same speed on straight paths. Its efficiency depends on the gear meshing and bearings used.

On a straight path, only one gear mesh (between the input pinion and ring) comes into play in the differential. Its efficiency is given by:

ηdif=ηbrgNbrg⋅ηgrm\eta_{\rm dif} = \eta_{\rm brg}^{N_{\rm brg}} \cdot \eta_{\rm grm}

where:

  • ηdif\eta_{\rm dif} — Differential efficiency;
  • ηbrg\eta_{\rm brg} — Bearing efficiency;
  • NbrgN_{\rm brg} — Number of bearings; and
  • ηgrm\eta_{\rm grm} — Gear mesh efficiency.

Drive shaft efficiency

The drive shaft delivers power from the differential to the drive wheel. It has two constant velocity joints at each end to allow for relative motion between the differential and the wheel. Usually, a tripod joint is used at the differential end, and a Rzeppa joint is used at the wheel. The efficiency of the drive shaft is given by:

ηdrs=ηtrp⋅ηrzp\eta_{\rm drs} = \eta_{\rm trp} \cdot \eta_{\rm rzp}

where:

  • ηdrs\eta_{\rm drs} — Drive shaft efficiency;
  • ηtrp\eta_{\rm trp} — Tripod joint efficiency; and
  • ηrzp\eta_{\rm rzp} — Rzeppa join efficiency.

How do you calculate horsepower delivered to the wheels?

You can calculate the wheel horsepower by following these steps:

  1. Determine the drivetrain efficiency. Our wheel horsepower calculator can help with this.
  2. Multiply the drivetrain efficiency with the engine horsepower to get the wheel horsepower.
  3. Verify your result with our wheel horsepower calculator.

How to use this wheel horsepower calculator

This bhp to whp calculator allows you to calculate crank-to-wheel hp from the drivetrain's efficiency. The following instructions are to help you make the best use of this tool:

  1. Select the drive type of the vehicle between:

    • Rear-wheel drive; or

    • Front-wheel drive.

  2. Enter your vehicle's engine horsepower or brake horsepower.

  3. Each major component of the drivetrain has its section:

    • Gearbox efficiency — Enter the overall efficiency of the gearbox. Alternatively, click on the Gearbox parameters and enter the efficiencies of bearings and gear meshes individually.

    • Propeller shaft efficiency — Enter the overall efficiency of the propeller shaft. Alternatively, click on the Propeller shaft parameters and enter the efficiencies of bearings and joints individually.

    • Differential efficiency — Enter the overall efficiency of the differential. Alternatively, click on the Differential parameters and enter the efficiencies of bearings and gear mesh individually.

    • Drive shaft efficiency — Enter the overall efficiency of the drive shaft. Alternatively, click on the Drive shaft parameters and enter the efficiencies of bearings and joints individually.

  4. This tool will automatically calculate the horsepower lost through the drivetrain and provide you with the calculated wheel horsepower.

🔎 The three most common numbers you'll hear about a car are its engine displacement, horsepower, and the time it takes to accelerate from 0-60 mph. Determine how fast your car can zoom from 0-60 with our 0-60 calculator.

FAQs

What is the wheel horsepower of a 660 bhp rear-wheel drive vehicle?

The wheel horsepower (whp) of a 660 bhp rear-wheel drive vehicle is 539.4 hp. To calculate whp from bhp, follow these steps:

  1. Assume a drivetrain efficiency of 0.8173, typical of a rear-wheel drive vehicle.
  2. Multiply this with the brake horsepower to get 660 × 0.8173 = 539.4 hp.
  3. Verify this result with our wheel horsepower calculator.

What is the drivetrain loss of a 118 bhp car if the wheel horsepower is 95 hp?

There is a 23 hp loss of power through the drivetrain. To verify this yourself, follow these steps:

  1. Subtract the wheel horsepower from the brake horsepower to get 118 - 95 = 23.
  2. Double-check with our wheel horsepower calculator.

Which drivetrain system has maximum drivetrain efficiency?

Front-wheel drive systems have the maximum drivetrain efficiency. This is due to the lack of components like a propeller shaft that you would have in rear-wheel or four-wheel drive systems, reducing the amount of power lost in transmission.

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