Calculations of EDBHP in steam hauled locomotive performances

[GreensandsParticipant @greensands]

Hi all – Reading around the record performances of steam hauled trains back in the “good old days” several writers give values for EDBHP which would have been required in order for them to achieve their task with the given loads and controlling gradients. Nowhere however have I been able to discover just how these calculations would have been made and some illustrative examples of the required calculations would be most interesting to study. I am sure that there are several members of the forum who could provide answers to these questions.

[GreensandsParticipant @greensands]

[roy entwistleParticipant @royentwistle24699]

Explain what EDBHP is please

Roy

[Nigel Graham 2Participant @nigelgraham2]

The "ED" abbreviation is new to me, but generally, it is a sort of reverse process, starting with purpose first.

Describing in detail would need a book. And whole books were written on designing steam-engines generally! To summarise though from some of these books:

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First calculate the power needed to accelerate the required loads from rest and maintain them at fair minimum speeds on the steepest gradients. This is a matter of fairly basic Theoretical Mechanics, a branch of Physics; but it does mean having to assess the retarding forces, not just the "ideal" in which the only retarding is that of gravity up a hill. These forces are proportionally a lot lower on a railway than they would be for road vehicles – an observation noted in effect though probably not numerically, on horse-drawn quarry tramways well before the first steam locomotives.

Normally, in British steam-locomotive practice at least, the aim was not to use HP but TE – Tractive Effort, in lbs force. A reciprocating steam-engine's HP and speed in rpm are interlinked; but its mean effective torque (hence a locomotive's pulling-power) is more or less constant for a given admission-pressure and cut-off irrespective of speed.

"Mean Effective" because the torque varies harmonically from 0 at dead-centre to maximum when the crank and connecting-rod are perpendicular to each other, approaching mid-revolution (not mid-stroke). Once the train is well under way the cut-off may have been brought back so early the steam-pressure on the piston is already well below its admission-pressure, at this maximum torque point.

At dead-centres the connecting-rod is simply trying to compress or stretch the crank-arm, and the engine on that side of the locomotive is relying on its companion(s) at other angles, to help it past this stasis. (Single-cylinder traction-engines sometimes need the driver to pull the flywheel round a touch to get them to start.)

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Now design the engine itself (the cylinders and motion) – largely from calculating the theoretical Indicated Horse-Power by the cylinder dimensions and cut-off values to match the specified power and TE as far as possible.

The basic formula for the cylinder alone, in Imperial units, is ePLAN/33000 HP:

P = the Mean Effective Pressure (not boiler or even steam-chest pressure. It is the mean of the pressure-range, of admission pressure to cut-off plus then, that of the hyperbolic expansion to release),

L = Stroke in feet,

A = Area of Piston (square inches)

N= Strokes per minute, which for a double-acting engine is rpm X 2, per cylinder.

and e is a rather empirical decimal fraction called the "Diagram Factor", an efficiency allowance reducing the PLAN product somewhat. It accounts for the internal losses difficult to quantify accurately. They are mainly by temperature cycling, clearance volume and the compression due to the exhaust cut-off / lead-steam cushioning.

That lot gives the result in ft/lb/minute that the 33000 divisor converts to HP. This is the work done only within the cylinder, not that actually between wheel and rail, affected by the intervening frictional losses and the mean torque inherent in a crank-driven transmission.

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From this, derive the steam-raising rate needed, to design the boiler.

This means knowing the thermodynamics: the specific heat and latent heat of water, the calorific value of the coal in BTU / lb, the heat transfer rate from fire to water, superheater variables, steam "losses" to the injector and ejector, and for passenger services, the train heating…

On top of these are conditions such as the low overall thermal efficiency of a steam-locomotive, and the railway's loading-gauge, maximum axle-loadings and minimum curve radii, etc.

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I don't know to what extent the auxiliaries did need considering. On main-line working the small ejector is on continuously, and the injector on at least for much of the journey. The larger BR Standards and similar also have exhaust-steam injectors that lessen their boiler-steam draw a bit though still need an auxiliary live-steam feed: a steam-relay valve brings in more from the boiler when the driver closes the regulator. In full size the injectors were designed to meet steady mean water demand though; unlike the intermittent use more familiar to most of our miniatures with injectors matched to boiler size more than steam use. In Winter the train-heating would have been on continually. However. by far the greatest drain on efficiency is the loss of heat directly up the chimney, followed by radiation despite the cladding.

It is worth bearing in mind though what the official training-manuals issued to railwaymen said about steam-demand and firing rate: that these average to be fairly constant throughout most of the journey.

Edited By Nigel Graham 2 on 24/05/2023 11:10:20

[GreensandsParticipant @greensands]

I understand EDBHP to stand for Estimated Drawbar Horse Power i.e. that the horse power available for hauling the load attached at the rear of the tender.

[Nigel Graham 2Participant @nigelgraham2]

Were steam-locomotives rated by HP?

I have very rarely seen HP, only Tractive Effort, figures quoted for them, though presumably dynamometer-car trials could produce horse-power readings as well, by a function of TE and speed?

Horse-power only was used in marine and plant applications, sometimes both the Indicated HP and Shaft HP, the latter by dynamometer. For a full marine engine system a goodly amount of cylinder power would be absorbed by the pumps driven from the motion. The larger engines were also designed so the crank-end (lower) half of the cylinder end gave the same output power as the cover end, by compensating for the piston-rod volume and the mass of the moving iron. I don't know if locomotive cylinders were also power-balanced for their relatively thick piston-rods, by adjusting the ports or valve dimensions.

[GreensandsParticipant @greensands]

I think that EDBHP figures would have been as a result of observations made in the dynamometer car and then corrected for the given gradient to give a figure equivalent for running on level ground.

[Clive Brown 1Participant @clivebrown1]

Apart from dynamometer car testing, there were "rolling road" test plants at Swindon and Rugby. These methods would allow direct calculation of horse-power at the drawbar or the wheels. Other calculations presumably made assumptions on friction, gradient etc.

I don't know much about the stationary test plants, but there is some footage here.

The GWR tested their locos over quite a long period, including experimental work on draughting improvements, the benefits were seen in their general loco performance.

Edited By Clive Brown 1 on 24/05/2023 15:33:42

[duncan webster 1Participant @duncanwebster1]

Estimated means what it says, you reckon the tractive effort from train mass, rolling resistance, windage, curvature and gradient, multiply by speed to get horsepower. I can't see it being terribly accurate.

If you've got a dyno car or a rolling road you can measure tractive effort accurately, no need for estimates. 

Edited By duncan webster on 24/05/2023 16:43:03

[SillyOldDufferModerator @sillyoldduffer]

DBHP is Drawbar Horse Power, and it's the power actually available at the enginecoupling. (The tender is part of the engine.)  A dynamometer car is towed for some distance behind the engine to provide a load, and it measures speed, distance travelled, and the pull on the coupling. Sums are done on the results to calculate the actual power consumed.

An Indicator on the cylinder gives time/pressure graphs from which the power available at the piston can be calculated – Indicated Horse Power. DBHP/IHP gives the mechanical efficiency of the engine, which is low on a steam locomotive because a great deal of power is wasted between piston and coupling hook due to friction, spinning the wheels, turning crankshafts, lifting the coupling rods, and driving the valve-gear. Slide-valves require a a lot of power to run,

Also possible to calculate the power of the fire box and the fuel. When the fuel value is compared with DBHP, the best steam locos are only about 5% efficient, and most locos are worse.

There are several flavours of Horse Power, but only Brake HP, Shaft HP and Draw Bar HP are meaningful in terms of how an engine will perform in the real world. The E in EDBHP is worrying. It must be a caveat. Your guess is as good as mine: Efficient, Effective, Economical, Estimated, Equivalent etc. Economical DBHP might be legit – the power output at peak efficiency, say when a goods engine is cruising with a 1000 ton load at 40mph, when the same loco performs poorly pulling light passenger carriages at 70mph.

Nigel mentions Tractive Force, which also comes in at least 3 flavours. There's Indicated Tractive Force, Rated Tractive Force and Drawbar Pull. Just a guess, but maybe engine drivers probably only worry about drawbar pull, because it's needed to get a train moving. Planners take a deeper interest – they have to provide engines with enough drawbar pull to restart the train if it happens to stop on the steepest incline on a route. A smaller engine can move empty wagons (Tare). If the wagons are full (Gross Weight), more tractive force is needed. DBHP is potentially useful to schedulers, in that enough power is needed to accelerate engines fast enough between stops to keep to the timetable. In that case, Greensand's Estimated DBHP suggestion makes sense – when planning a train, the number of wagons needed to haul a load of given weight at an average, result in an estimate that defines which engine or engines are needed to work the train.

I suspect ITF, RTF, IHP, Fuel efficiency and DBHP are valuable to designers and planners rather than drivers. They're engineering measures useful to the folk who improve machines rather than those who work them.

Dave

Edited By SillyOldDuffer on 24/05/2023 19:07:44

Edited By SillyOldDuffer on 24/05/2023 19:09:25

[John HinkleyParticipant @johnhinkley26699]

As will become clear, I have little knowledge of and even less interest in, Steam engines, though I can and do appreciate the engineering that goes into them, full size and scale.

My late father was presented with a copy of D. A. Law's "Pocket-Book for Mechanical Engineers" in 1933 when he won first prize in the H.M. Dockyard School, Hong Kong as a 4th year fitter apprentice Christmas Examinations.

It is to this publication that I reach when a question such as this is posed. Often, I garner little from it, but on this occasion, I think there might be a bit of interesting reading within its hallowed pages. I present, for your delectation, a scan of two pages which may or may not be relevant.

If nothing else, it gives me pleasure to know my father read and hopefully absorbed some of its contents.

John

(In contemplative mood)

[Niels AbildgaardParticipant @nielsabildgaard33719]

Eqvivalent Draw Bar Horse Power (EDBHP) maybe.

It was ,I think,the measured draw bar horsepower between tender and train (DBHP) plus the calculated horsepower for taking locomotive and tender up the gradient.

It was safer to measure potential full power of locomotive going up rather than down or level.

Britania going uphill Seetle Carisle

Max  2300 EDBHP measured/calculated  at a speed of 45 mph going uphill

 

 

Edited By Niels Abildgaard on 24/05/2023 20:17:28

[duncan webster 1Participant @duncanwebster1]

I'm wrong, Niels is right, it's equivalent, not estimated. The likes of OSNock used to conjure up figures for horespower based on number of coaches, gradient, speed etc which is what pushed be down the wrong road.

This goes into it in some detail

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