## Calculating Brake Horsepower

**Calculating Brake Horsepower** is very easy for anyone, If he knows the Exact Formula of BHP.

Here, in this article, we will discuss calculation of Brake horsepower equation in details so that you can calculate BHP Very Fast.

### Formula for calculations of Break horsepower is

1. BHP = (Torque × RPM )/5252,where torque is **lb -ft** and n = revolution per min.

2. BHP = BP /33000,where BP (in watt ) = Torque×2π×RPM (RPM in min. ) Where torque in the formula of BP is in **lb -ft**

3. BHP =BP (in Watt ) / 746 we get it in horse power ,since 1 HP = 746 watt

For calculating Brake Horsepower equation, we need to keep unit of all parameter in mind.

Below you can check also simple formula and derivations in details.

Before knowing how to calculate BHP, first we must know three important terms, what is power, Horsepower and Brake Horsepower ?

## What is Power ?

Power is defined as rate at which work is done or rate at which energy is transferred.

Simply ,Rate of doing work is called power.

Derivations from

other quantities

For Rotary motion, we are finding power so that it is easy for you to understand BHP.

Power = (Force × Distance ) / Time

Power = [Force × Distance (Per Revolution) ] / Time ( in min. )

Distance per revolution = 2π × Radius

Distance per revolution per time = 2 π × Radius × RPM

We know that Torque = Force × Perpendicular Distance ( Radius )

Now, Force = Torque / Radius

As we know Power = [ Force × Distance (Per Revolution ) ] / Time (in min. )

Now, putting the value of force and Distance

We get, Power = {Torque/Radius} × { 2 π × Radius × RPM }

Finally, Power ( in Watt ) = Torque × 2π × RPM. Or,

Power (in watt ) = (Torque × 2π × RPS )/60

For Calculating Brake Horsepower, first we have to understand about horsepower

## What is Horsepower ?

Horsepower (hp) is the unit of measurement of the power or the rate at which the work is performed, usually in regard to the output of the engines or engines.

There are a number of common standards and types of horsepower. Two common definitions used today are mechanical horsepower (or imperial horsepower), which is approximately 745.7 watts, and metric horsepower, which is approximately 735.5 watts.

James Watt, a steam engine pioneer, wanted to measure the performance of his engines against the horse that had previously operated.

Later, this unit is used to measure output of different type of piston engine, turbines, electric motor as well as other machineries.

James Watt described one horsepower as the equivalent of the energy spent by a single horse to lift 33,000 pounds a foot in the air from the Earth’s surface in one minute.

## Horsepower Equation

1 hp (mechanical) = 33,000 ft·lbf/min = 550 ft·lbf/s

1 HP = 550×0.3048×0.4535 = 76.04 kgf/m/s

1 HP = 76.04×9.80 =746 Watts where 1 ft = 0.3048 m and 1 lb = 0.4535 kg

Or, we can say that One horse power is equal to work done by a single horse in lifting the weight of 75 kg to one metre height in one second.

we can say that One horse power is equal to work done by a single horse in lifting the weight of 75 kg to one metre height in one second.

1 HP (Metric Horsepower ) = 75 kgf m/s

1 HP = 75×9.8066 m/s2 . m/s = 735.498 Watt

We understand that horse power is unit of measurements of power.

*HP is defined as *

1 HP = 550 ft-lb per second

1 HP = 550 ft -lb per second × 60

1 HP = 33,000 ft -lb per minute

## How to convert power to HP

To change power into HP, we have to simply divide power by 33000

HP = Power (in ft -lb per minute ) ÷ 33000

We know that indicated power is power developed by engine when it burns.

If Indicated power is in the unit ft -lb per min and we divide that Indicated power by 33,000 then we get Indicated Horse power

IHP = IP (in ft-lb per minute ) /33000

But IP is mainly in watt

Formula for IP for 4 stroke engine is (PLAN x n) / 2

### IHP= ((PLAN x n) / 2) ÷ 4500

(where, P = Mean effective pressure in kg/cm², L = Length of stroke, A = Area of piston in cm², N = RPM of crankshaft, n = Number of cylinders)

Or

If Indicated power is in watt then divide it by 746,

IHP = IP (in watt ) /746

Similar for BHP

Brake Power (lb -ft per min. ) = Torque × 2π × RPM lb -ft per min.

Divide by 33000 on both sides

BHP = (Torque × 2π ×RPM )/33000

BHP = (Torque × RPM )/5252

In both above formula torque unit is ft -lb.

## Other conversion unit of HP

As per the conventions, 1 HP equals to:

- 745.5 watts
- 1.01389 ps
- 33,000 ft lbf/min
- 42.2 BTU/min

## What is Brake Horsepower ?

Brake horsepower is the measurements of the power of the engine at the flywheel or crankshaft after the engine losing power due to the drive train and the resistance of the gearbox.

Note :- If we know power at the flywheel or crankshaft of the engine in ft -lb per min. ( this is called brake power ). To get Brake Horse power, we should only divide with 33,000 i.e. BHP = BP (in ft -lb per min. ) /33000

Other wise BHP = (Torque × RPM ) /5252, unit of torque is ft -lb

Or simply, BHP = BP (in Watt ) / 746

## How Brake horse power is measured ?

BHP is measured by applying a resistance torque as a brake on the Shaft .Due to friction, heat is generated which is remove by circulating cooling medium like water.

**Brake Horse Power formula**

**1. **BHP = (2πnFR ) / 33000,where 2πnFR = Power in lb -ft per min.

( n =No. Of Revolution per minute,F = Break Resisting Force ,R = Radius at which force is applied)

**2.** Break Horse Power for Shaft in torque form

Power = Torque x 2π x Revolutions / Minute

A ) BHP = (2πnT ) /33000 ,2πnT = Power in lb-ft per min.

n =no. of revolution per minute of the engine , T = Torque applied on shaft.

B )BHP = (Torque × RPM ) /5252

**3.** BHP = BP in watt / 746

## How Brake horsepower calculated

Brake Power (Power at the shaft )= 2πnT watt

As we know that 1 H.P. = 33,000 lb-ft. / min.

Divide both side by above value we get,

Bhp = (Torque × n )/5252

Remark :-Here’s what we’ve got for the equation

33,000 lb-ft / min = lb-ft. x 2π x revolutions/min

Dividing each side by 2π (6.28315) and we get 5,252 lb-ft / min = lb-ft. x revolutions / min.

Next,we divide each side by 5252,we get final equations :-

1 Horsepower = Torque x R.P.M. / 5252

**Note :-** Due to this math, lb-ft of torque and horsepower will always be the same at 5,252 RPM.

Finally We have ,

**1.** BP = 2πnFR in Watt

2π =6.2831853,n = No.of revolution per minute

F=Resisting force

R= Radius at which force is applied

**2. **BP = 2πnT in lb -ft per min.

2π =6.2831853

n = No.of revolution per minute

T=Torque Applied on shaft

**3.** BHP = Power (in lb -ft per min ) /33000

**4. **BHP = (torque x RPM) ÷ 5,252

Remember, Unit of torque is ft-lbs in Imperial system.

Let us know How this formula came,

Brake horse power is the difference between Indicated power and friction loss.This is the actual power delivered to the power.

The power supplied to the propeller for useful operation is known as the brake horsepower (bhp).

**Also Read :** Crankcase Explosion

The difference between the indicated and the brake horsepower is known as friction horsepower, which is the horsepower needed to overcome mechanical losses, such as the pumping action of the pistons, the friction of the pistons and the friction of all other moving parts.

## Units in calculation of brake horsepower

The measurement of the bhp of the engine involves the measurement of a quantity known as a torque or a twisting moment. Torque is the product of the force and the distance of the force from the axis on which it is acting.

As we know BHP = (Torque ×n ) /5252, where Torque is **lb -ft** and n = revolution per min.

Torque = Force × Displacement

### Torque

Torque is a measure of force or load that cause rotation of the shaft around axis.

### How Torque is Expressed

Generally, Torque is Expressed in pound-feet (lb-ft) or pound-inches (lb-in).

Note:- Torque should not be Confused with work ,Which is expressed in inch-pounds (in-lb) or foot-pounds (ft-lb).

### How to measure Torque

For measuring torque, there are so many devices like dynamometer or a torque meter.

Prony Brake is one of the very simple type of device which is used for calculations in torque.

Also Read : Difference between 2 stroke and 4 stroke engine

## Relation of BHP in Other unit system

## Relationship of BHP for Calculating Brake Horsepower with other unit system

### The relation between the BHP, Ps & kW is:

### 1 Hp = 1.01 PS = 0.70 kW

### 1kW = 1.34 Hp = 1.4 PS

### 1 PS = 0.98 Hp = 0.70 kW

**Brake-Horse-Power** (bhp), **Pferdestärke** (PS) which is the German translation of horsepower. Metric system uses **kilowatt** (kW) unit of measurement while in the case of the imperial/British system, it is ‘**feet-pound-force-per-second**‘ (fps).

## Calculating Brake Horse power for positive Displacement Pump

**BHP = Q × P / (1714 × n)**

BHP = Brake Horsepower in Horsepower

Q = Flow Rate in gallons per minute

P = Pressure in pounds per square inch

n = Efficiency expressed as a decimal value*

Many positive displacement pumps are assumed to work at 90 percent efficiency. A value of 0.9 is sometimes used for this measurement. For more precision, refer to the test sheets of your pump manufacturer.

**Brake Horsepower [HP] = Flow Rate [GPM] × Pressure [PSI] / (1714 × Efficiency)**

Brake Horse Power calculation for pump

To convert MGD to GPM, use the following:

Wikipedia :- Horse power

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