Its definition and relationship to actual horsepower (HP)

The size of early Paxman steam engines, and indeed of other manufacturers' early steam engines (particularly portables and traction engines), was generally quoted in Nominal Horsepower (NHP). This was a standard adopted by the Royal Agricultural Society of England (RASE) in the 1840s to enable farmers to compare the power of a steam engine with that of a horse. There has been, and still is, a great deal of confusion about NHP and its relationship to actual horsepower.

In its 1913 catalogue of portable steam engines Paxman offered this advice to potential customers when comparing different types: "we suggest a careful comparison of the b.h.p. given off, not merely the nominal horse-power, which is an antiquated term and rather misleading". (1) In his book Garretts of Leiston, Robert Whitehead wrote "The nominal horse-power classification was in itself absurd and was held to be so by the Garretts who much preferred purchasers to take account of the brake horse-power of the engines. The nominal horse-power habit in the buying public, however, was too strong for them and they were forced to a compromise … in the published price lists and catalogues". (2)

For some years I searched, without success, for a definition of NHP and an explanation of how to convert NHP to actual horsepower (HP). More recently I came across an extract from John Bourne's book 'A Catechism of the Steam Engine' (1885, London) which sheds a good deal of light on the subject. In one section Bourne discusses the issues of NHP and actual horsepower using a series of questions and answers. Although his comments apply primarily to condensing engines, they help to answer a number of important broader questions and are therefore reproduced below verbatim.

Bourne tells us that nominal power was a commercial unit by which engines were bought and sold, and that it is a quite different measure from actual horsepower. It would appear that the rule for determining NHP was developed by James Watt (1736-1819), the Scottish steam engineer and inventor who substantially improved Newcomen's engine by the introduction of condensing. NHP was calculated by reference to the size of the cylinder bore and the speed of the piston. HP on the other hand is a measure of the actual power produced by an engine, equivalent to 550 foot-pounds per second or 745.7 watts. This being the case it is not possible to convert NHP to HP or vice-versa. However, at the foot of this page there are some notes about calculating approximate equivalent HPs from NHPs.

It is interesting to note from Bourne that even in 1885 there was considerable confusion about NHP and HP. He went on to say "nominal power, even as a commercial standard, is dying out, and need not now be held as of much account". One might question his view on the latter. As late as the mid-1920s the size of some engines entered in Paxman's order book was still being quoted in NHP rather than HP.

__Extract from The Steam Engine, Bourne, 1885 Edition, pages 138-141.__

There were (*therefore*) two standards : the actual power exerted, and the nominal power. This last was a mere expression of size, and so much confusion was introduced that nominal power is now being discarded.

Q. How is the power actually exerted by engines ascertained ?

A. By means of an instrument called the indicator, which is a miniature cylinder and piston attached to the cylinder cover of the main engine, and which indicates, by the pressure exerted on a spring, the amount of pressure or vacuum per square inch existing within the cylinder. Multiply the area of the piston in square inches by this pressure, and by the motion of the piston, in feet per minute, and divide by 33,000 ; the quotient is the actual number of horses power of the engine.

Q. How is the nominal power of an engine ascertained ?

A. Since the nominal power is a mere conventional expression, it is clear that it must be determined by a merely conventional process. The nominal power of ordinary condensing engines may be ascertained by the following rule : Multiply the square of the diameter of the cylinder in inches by the velocity of the piston in feet per minute, and divide the product by 6,000 ; the quotient is the number of nominal horses power. In using this rule, however, it is necessary to adopt the speed of piston prescribed by Mr. Watt, which varies with the length of the stroke. The speed of piston with a 2 feet stroke is, according to his system, 160 ft per minute ; with a 2 feet 6 inch stroke, 170 ; 3 feet, 180 ; 3 feet 6 inches, 189 ; 4 feet, 200 ; 5 feet, 215 ; 6 feet, 228 ; 7 feet 245 ; 8 feet, 256 ft.

Q. Does not the speed of the piston increase with the length of the stroke ?

A. It does : the speed of the piston, according to Watt's standard, varies nearly as the cube root of the length of the stroke.

Q. And may not, therefore, some multiple of the cube root of the length of the stroke be substituted for the velocity of the piston in determining the nominal power ?

A. The substitution is quite practicable, and will accomplish some simplification, as the speed of piston proper for the different lengths of stroke cannot always be remembered. The rule for the nominal power of condensing engines when thus considered will be as follows : Multiply the square of the diameter of the cylinder in inches by the cube root of the stroke in feet, and divide the product by 47 ; the quotient is the number of nominal horses power of the engine, supposing it to be of the ordinary condensing description. This rule assumes the existence of a uniform effective pressure upon the piston of 7 lbs. per square inch. Mr. Watt estimated the effective pressure upon the piston of his 4 horse-power engines at 6.8 lbs. per square inch, and the pressure increased slightly with the power, and became 6.94 lbs. per square inch in engines of 100 horse-power ; but it appears to be more convenient to take a uniform pressure of 7 lbs. for all powers. Small engines, indeed, are somewhat less effective in proportion than large ones, but the difference can be made up by slightly increasing the pressure in the boiler ; and small boilers will bear such an increase without inconvenience.

Q. How do you ascertain the power of high-pressure engines ?

A. The actual power is readily ascertained by the indicator, by the same process as that by which the actual power of low-pressure engines is ascertained.

Q. But how do you ascertain the nominal horse-power of high-pressure engines ?

A. The nominal horse-power of a high-pressure engine has never been defined, and it is better that it should not be, as to do this would only be to multiply confusion. The speed of Watt's engine was about 128 times the cube root of the stroke.

Q. Is 128 times the cube root of the stroke in feet per minute the ordinary speed of all engines ?

A. Locomotive engines travel at a far quicker speed - an innovation brought about not by any process of scientific deduction but by the accidents and exigencies of railway transit. Most land condensing engines, however, travel at about the speed of 128 times the cube root of the stroke in feet ; but many marine condensing engines of recent construction travel at as high a rate as 700 feet per minute. To mitigate the shock of the air pump valves in cases in which a high speed has been desirable, as in the case of marine engines employed to drive the screw propeller without intermediate gearing, india-rubber discs, resting on a perforated metal plate, are now generally adopted ; but the india-rubber should be very thick, and the guards employed to keep the discs down should be of the same diameter as the discs themselves, and should permit but little lift.

Q. Can you suggest any eligible method of enabling condensing engines to work satisfactorily at a high rate of speed ?

A. One most effective way of enabling condensing or other engines to work satisfactorily at a high speed, lies in the application of balance weights to the engine, so as to balance the momentum of its moving parts, and the engine must also be made very strong and rigid. In the case of engines condensing by jet, it appears to be advisable to perform the condensation partly in the air pump, instead of altogether in the condenser, as a better vacuum and a superior action of the air-pump valves will thus be obtained. Engines constructed upon this plan may be driven at four times the speed of common engines, whereby an engine of large power may be purchased for a very moderate price, and be capable of being put into a very small compass ; while the motion, from being more equable, will be better adapted for most purposes for which a rotary motion is required.

Q. Then, if by this modification of the engine you enable it to work at four times the speed, you also enable it to exert four times the power ?

A. Yes ; always supposing it to be fully supplied with steam.

Q. The high speed engine does not require so heavy a fly wheel as common engines ?

A. No ; the fly wheel will be lighter, both by virtue of its greater velocity of rotation, and because the impulse communicated by the piston is less in amount and more frequently repeated, so as to approach more nearly to the condition of a uniform pressure.

Q. Can nominal be transformed into actual horse-power ?

A. No ; that is not possible in the case of common condensing engines. The actual power exerted by an engine cannot be deduced from its nominal power, neither can the nominal power be deduced from the power actually exerted, or from anything else than the dimensions of the cylinder. The actual horse-power being a dynamical unit, and the nominal horse-power a measure of capacity of the cylinder, are obviously incomparable things.

Q. That is, the *nominal* power is a commercial unit by which engines were bought and sold, and the *actual* power a scientific unit by which the quality of their performance was determined ?

A. Yes ; the nominal power is as much a commercial measure as a yard or a bushel, and is not a thing to be ascertained by any process of science, but to be fixed by authority in the same manner as other measures. The actual power, on the contrary, is a mechanical force or dynamical effort capable of raising a given weight through a given distance in a given time, and of which the amount is ascertainable by scientific investigation. But nominal power, even as a commercial standard, is dying out, and need not now be held as of much account.

Q. Is there any other measure of an actual horse-power than 33,000 lbs. raised one foot high in the minute ?

A. There cannot be any *different* measure, but there are several equivalent measures. Thus the evaporation of a cubic foot of water in the hour, or the expenditure of 33 cubic feet of low-pressure steam per minute, was reckoned equivalent to an actual horse-power in Watt's engines, though in modern engines the evaporation of a cubic foot of water in the hour will generate three times that power. 528 cubic feet of water raised one foot high in the minute involves the same result.

As explained above, strictly speaking it is not possible to convert NHP to HP or vice-versa. However Alex Walford tells me that, for a single cylinder steam traction engine, one NHP is broadly equivalent to between 6 and 7 BHP, but generally closer to 6 BHP. For a compound engine the figure may be closer to 7 BHP. In practice the actual output of an engine is also dependent on working steam pressure and engine speed. Traction engines were relatively highly rated as the power to weight ratio was an important consideration. Stationary engines were much more conservatively rated. Alex has a Handbook of the Steam Engine, dated 1920, which provides information on steam engines of most manufacturers, including Paxman. In this a 16 NHP Paxman stationary engine is said to produce 40 IHP or 35 BHP. Thus with this stationary engine one NHP is equivalent to a little over 2 HP compared with the more than 6 HP applicable in the case of a traction engine.

Some examples of NHP and BHP ratings (given below as normal load / max load) of Paxman stationary engines taken from early 20th century catalogues are as follows:

Class B single cylinder with working steam pressure of 90 psi: 4 NHP, 8/10 BHP; 10 NHP, 20/30 BHP; 20 NHP, 45/66 BHP.

Undertype single cylinder with working steam pressure of 100 psi: 4 NHP, 8/10½ BHP; 10 NHP, 20/27 BHP; 12 NHP, 24/32 BHP.

Class B coupled and tandem compounds, Undertype compounds, 'Colchester' compounds, all with working steam pressure of 140 psi: 8 NHP, 19/23 BHP; 10 NHP, 26/30 BHP; 20 NHP, 50/60 BHP.

Kempe's 'Engineer's Year-Book', 1898 edition, says of Nominal Horsepower "This may be taken as 1/6 of the Indicated Horsepower".

David Macloy of Australia emailed in October 2005 with information about horsepower and NHP he has found in other sources:

According to 'An Elementary Manual on Steam and the Steam Engine' by Professor Jamieson (1908), Watt found that the average horse, working at a steady rate, could lift 22,000 pounds one foot in one hour (or 366 foot-pounds per second) but he added half as much again "to ensure his customers received value for money". According to another source Watt exaggerated the pulling power of a horse by 50% to cover the additional work done by the more efficient steam engine. Whatever his reasons for the 50% addition, Watt created the unit of a horsepower which equates to 550 foot-pounds per second, or 745.7 watts, which is more than a horse is capable of producing.

According to Reed's Engineers Hand-Book (circa 1900), Watt's formula for calculating Nominal Horsepower, with it's cube root of the piston speed etc, was too complicated so generally the steam pressure was taken as 7 psi, the piston speed was taken as 220 feet per minute and it was simplified to NHP = diameter (of the piston in inches) squared, divided by 28, but that only works for condensing beam engines.

David Macloy himself calculates Nominal Horsepower as follows: NHP = the diameter of the piston squared, divided by 12.3. This formula is taken from 'The Engineman's Master Key' by L F R Schnabel (c. 1920). So for a portable steam engine with, say, a 10" piston the NHP is 10 x 10 / 12.3 = 8.13. For compounds David simply calculates the NHP of the high pressure piston and doubles it.

Mike Dyson also emailed in October to say that in 'A Century of Traction Engines' by W J Hughes, published by Percival Marshall (1959), there is reference to the definition of NHP as used by most steam engine manufacturers. According to this formula, which Mike believes was that used by the RASE in one of their early trials - 1856 or 1861, one nominal horsepower is equal to 10 circular inches (*I've not come across one of those before !*) of piston area. Thus NHP is calculated by finding the square of the cylinder diameter in inches and dividing by ten. So for an engine with 9" bore cylinder NHP = 9 x 9 / 10 = 8; and for one of 6¼" bore NHP = 6¼ x 6¼ / 10 = nearly 4 nhp. Pressure is assumed to be 45 psi which was fairly common in the early days although actual pressure and stroke do not come into the equation.

**In conclusion**, it will be seen from the above that the one constant in all the different formulae used for calculating NHP is the square of the diameter in inches of the piston. Other parts of the equation seemed to constantly change with the development of the steam engine as new types emerged, and steam pressures and engine speeds increased.

1. Paxman Portable Steam Engines, &c., Paxman publication No 700A, December 1913. (page describing Log-Burning Portable Engines.)

2. Garretts of Leiston, R A Whitehead, Percival Marshall & Co Ltd, London 1964. p 147

**Acknowledgement:** My thanks to Alex Walford for the information and guidance he has provided in the course of many discussions. Alex is an acknowledged authority on early steam engines, oil engines, diesels, engine governing, and a host of other engineering topics. Possessing a remarkable breadth of technical knowledge and practical skills, he clocked up nearly fifty years service with Paxman and its associated business Regulateurs Europa before retiring.

© Richard Carr 2005

Page updated: 17 AUG 2008