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# convert DHP to BHP

## convert DHP to BHP

(OP)
Many years ago I was taught that steam power (measured in dynamic horsepower) was basically the same as electric motor power. This had to do with the fact that the torque curve of both was basically flat. Either had as much power at 1 rpm as at 1,000 rpm.
I was also taught that dynamic horsepower was "more powerful" than Brake Horsepower because BHP has a very steep torque curve. For example an internal combustion engine has virtually no power until it reaches at least 2,000 rpm.
And I was given the following formula to convert DHP into BHP.
BHP = 1.59 x torque in inch pounds x rpm ÷ 100,000
1.59 is a constant
550 foot pounds = 6600 inch pounds
100,000 is a constant
As an example: a Chevy 350 V8 = 412 foot pounds of torque at 4600 rpm (this is the maximum power output for this engine)
So, 1.59 x 4944 in.lbs. x 4600 ÷ 100,000 = 361.6 BHP
However a 1 HP electric motor has 550 ft. lbs. of torque
So, 1.59 x 6600 in.lbs. x 4600 ÷ 100,000 = 482.7 BHP
If what I was taught was correct, this means that a 1 HP electric motor has more power than a Chevy 350 V8.
It seems counterintuitive but if the formula is correct, it is true.
Can anyone help me confirm or deny this formula ?

### RE: convert DHP to BHP

https://en.wikipedia.org/wiki/Horsepower

"Brake horsepower (bhp)
Brake horsepower (bhp) is the power measured at the crankshaft just outside the engine, before the losses of power caused by the gearbox and drive train.

In Europe, the DIN standard tested the engine fitted with all ancillaries and exhaust system as used in the car. The older American standard (SAE gross horsepower, referred to as bhp) used an engine without alternator, water pump, and other auxiliary components such as power steering pump, muffled exhaust system, etc., so the figures were higher than the European figures for the same engine. The newer American standard (referred to as SAE net horsepower, not as bhp) tests an engine with all the auxiliary components (see "Engine power test standards" below).

Electrical horsepower
The horsepower used for electrical machines is defined as exactly 746 W.[21] In the US, nameplates on electrical motors show their power output in hp, not their power input. Outside the United States watts or kilowatts are generally used for electric motor ratings and in such usage it is the output power that is stated."

"Engineering is achieving function while avoiding failure." - Henry Petroski

### RE: convert DHP to BHP

(OP)
Thank you for that information. But, does the formula I am using make sense to you ?

### RE: convert DHP to BHP

Power = Torque x Speed (measured in radians / second)

If you work in metric units, it's simple, you don't need any "conversion constants", but you need to remember that there are 2 x pi radians per revolution, and 60 seconds in a minute (if you're using rpm).

412 foot-pounds @ 4600 rpm gives 269 kW or 361 hp (as per your calculataion).

I suspect your 1 hp electric motor only gives that much torque after a geared reducer, and there is no way to get that much torque at 4600 rpm on the output shaft. According to this link http://www.engineeringtoolbox.com/electrical-motor... a 1 hp electric motor only has about 18 in-lbf of torque (or 1.5 ft-lbf) @ 3450 rpm. You need something like a 400 hp electric motor to be generating the sort of torque that you are talking about.

### RE: convert DHP to BHP

(OP)
1 horsepower = 745.7 Watts.
1 watt ≈ 44.25372896 ft·lbf/min = 0.737562149333 ft·lbf/s
1 horsepower (mechanical) = 33,000 ft·lbf/min = 550 ft·lbf/s
According to this, whether you calculate by horsepower or Watts a 1 HP motor has 550 Ft. Lbs. of torque per second, 6600 in. lbs. per second.
If you plug 550 into the formula BHP = 1.59 x torque in inch pounds x rpm ÷ 100,000 The Brake HP of a 1 HP electric motor should be 482.7.
Thanks to inertia the high speed of 4600 rpm should actually create more torque.

### RE: convert DHP to BHP

"Foot-pounds of torque per second" doesn't mean anything in this context. Think about it - it is a rate of change of torque.

1 hp = 550 ft.lbf/s means that the motor can deliver a torque of 550 ft.lbf at a rotational speed of 1 rad/s = 1 / (2 pi) revolutions per second = 9.55 rpm. The faster you gear the output shaft, the less torque you will get.

http://julianh72.blogspot.com

### RE: convert DHP to BHP

(OP)
"Foot-pounds of torque per second" doesn't mean anything in this context. Think about it - it is a rate of change of torque."
First, I disagree that Ft. Lbs. of torque per second is a Rate Of Change of torque. It is simply an increment of power within a given time period. 6600 In. Lbs. equals 550 Ft. Pounds. Nothing has changed. It's just a different way of saying the same thing.
Also, I never said anything about gearing the output shaft. The output shaft of the motor is turning at 4600 Rpm just like the crankshaft of the Chevy 350.
If you are thinking of an automotive application, the motor output shaft would be connected to the torque converter in exactly the same way as the crankshaft of the internal combustion engine.

### RE: convert DHP to BHP

JCB369,

Let's take your formula: Power[HP] = 1.59 * Torque[Inch-Pounds] * RPM / 100000

Consequently Torque[Inch-Pounds] = Power[HP] * 100000 / (1.59 * RPM), so when Power = 1HP and RPM = 4600

Torque[Inch-Pounds] = 1 * 100000 / (1.59 * 4600) = 13.7 (approximately)

That is the torque of your motor according to your own formula.

"For every expert there is an equal and opposite expert"
Arthur C. Clarke Profiles of the future

### RE: convert DHP to BHP

"Also, I never said anything about gearing the output shaft. The output shaft of the motor is turning at 4600 Rpm just like the crankshaft of the Chevy 350."

Awfully special motor to turn at that rpm. Where did you buy it, and is the shop still there?

### RE: convert DHP to BHP

#### Quote (btrueblood)

Awfully special motor to turn at that rpm. Where did you buy it, and is the shop still there?
I scanned through and didn't see where it said the motor was AC, might be a DC motor and then that speed becomes somewhat less unlikely.

### RE: convert DHP to BHP

@JCB369:

There are two possibilities here:

a) I'm right, and your 1 hp motor will only put out around 15 in-lbf of torque when it is geared to drive an output shaft at around 3500 - 4000 rpm.

b) You're right, and your 1 hp motor really DOES deliver 550 ft-lbf of torque at 4600 rpm (and it really is generating around 480 hp).

I'm pretty sure your'e wrong - but if you have faith in your calculations, you should patent that motor design, because you're gonna make billions of dollars!

### RE: convert DHP to BHP

I think you are making the mistake of equating Work / Energy with Torque, because both of them have the same dimensions (Force x Distance] - but they are NOT the same thing!

Similarly, Power has dimensions of Energy / Time (or Force x Distance / Time), but that doesn't mean that a motor with 1 hp output (550 ft-lbf / sec) will generate 550 ft-lbf of torque. A 1 hp motor can do 550 ft-lbf of work in 1 second.

### RE: convert DHP to BHP

The very first line is completely false and as noted above there are many unit errors in the following lines.

Quote: "Many years ago I was taught that steam power (measured in dynamic horsepower) was basically the same as electric motor power. This had to do with the fact that the torque curve of both was basically flat. Either had as much power at 1 rpm as at 1,000 rpm."

This is patently false as power is the product of torque and speed. Torque may be nearly flat but power will increase linearly with speed. Neither a steam engine nor an electric motor produce any horsepower at zero RPM. The only difference with an internal combustion engine is that it dies at zero rpm so it must be decoupled from the system via a clutch or gearbox. Many internal combustion engines have nearly flat torque curves within their operating range.

Horsepower is horsepower, it's a rate do doing work, it does not matter what the source is. Certainly different prime movers have different torque curves, this is why most electric cars can eliminate the clutch and gearbox and get away with just a simple reduction gear.

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