Is there a “simple” formula or rule of thumb for converting a steam loco rated T.E. to horsepower, for comparison with a diesel electric’s rated horsepower?
For example a CPR 4-6-4 Class H-1-b Hudson with 75 in. drivers and a rated T.E. of 45,300 lbs. What horsepower is that and what diesel electric’s today compare?
Horsepower on a steam locomotive is variable and is dependent on boiler capacity, size of the firebox grate, superheating capacity, type of valves on the cylinders, and a host of other items.
As a comparison, the experimental compound 2-8-0’s and 4-8-0 on D&H had a tractive effort comparable to D&H’s 4-6-6-4’s, but the 4-6-6-4’s produced more horsepower and could move the same train at a higher speed than the compounds.
There is a simple formula, Isambard – but like so many things, as Csshegewisch said, it’s very misleading, because steam locomotive ‘horsepower’ is affected by much more than tractive effort. That said, if you know the drawbar pull AND the speed, the formula is: Drawbar pull (lbs) times speed (mph) times 0.0027 equals horsepower. Troubles abound… drawbar pull is rarely the same as tractive effort (and never greater than tractive effort). And it varies with speed… for steam engines, maximum available drawbar pull drops dramatically as speed increases beyond a certain speed, which is dependent on a whole bunch of factors.
Another simple but also complicated factor is that steam locomotives are constant touque machines and so have the same torque at starting as at speed. Same with diesel-hydrolics.
Diesel-electrics, however, are variable torque machines and can start incredible trains with not much HP but can not keep them moving, because, as speed increases, torque decreases.
A steam engine can not even hope to start the trains that a DE can, but that same steam engine can move that same train along right smartly once it gets it started. The DE needs to keep adding units to keep up speed with the steam engine.
Horsepower and tractive effort are indeed related. The confusion occurs at low speeds, where tractive effort is limited by adhesion limits. Getting around adhesion limits is the basis for using slugs in low-speed applications, such as hump pushers and mine runs.
everyone fogot the most important factor with tractive effort, WEIGHT ON DRIVERS. with out adhesion all the horse power is wasted, and there is no tractive effort.
Here is the formula for calculating steam locomotive/ engine horsepower:
H- horsepower
P-steam pressure per square inch of piston
L- length of stroke in feet
A- area of piston in square inches
N- number of WORKING strokes of piston, per minute. (Steam locomotives have 2 working strokes)
H=PxLxAxN divided by 33,000
you will find that the horse power increases the faster the drivers turn, steam locomotive horse power is infinite, they have no governer to limit horsepower.
tractive effort is an entirely different issue
On a diesel locomotive horse power is expressed in kilowatts / main generator volts x amps divided by 700. No place on my EMD charts and graphs does tractive effort factor in and the horse power curve is in no way affected by tractive effort. Tractive effort can be manipulated by changing weight on drivers, driver size, gear ratio( by the way EMD has different settings depending on gear ratio) and on steam locomotives crank pin location.(kind of a steam locomotive gear ratio)
An sd40 will reach max hp / kw in throttle 8 twice, once at about 12 mph before the effect of counter emf in series this will be the current side of the kw curve. It will reach max hp again in parallel at about 50 mph this is the voltage side of the hp curve.
Remember that diesil locomotives are constant kilowatt machines.
Lets compare a GP-40 and an SD-40 , which locomotive is going to pull more? Both engines are 3000 hp, for the sake of arguement the weights are similar. I want to hear
your responses.
btw I have 19 years on the railroad, currently I am roundhouse foreman/electrician.
My recollection was that the biggest 4-8-4s developed between 5000HP and 6000HP at about 50 mph when working very hard. The highest recorded steam horsepower was a Pennsylvania Q-2 4-4-6-4 Duplex on test which produced about 8000 HP, probably also around 50 mph.
So, the maximum power of the largest steam locomotives could be matched by a pair of GE AC4400s, and they would have a higher starting tractive effort.
Anyway, that’s my theory.
Peter
I’d be glad to send any one copies of the EMD charts & graphs for just about any locomotive EMD built, in fact I have one in front of me right now for an sd-45. I still don’t see any thing about tractive effort, how ever you are correct in that a wheel slip correction will affect main generator exitation , but when the HP is calibrated on a locomotive, tractive effort is not an issue, the wheel slip system is calibrated by itself. Locomotive horsepower is kilowatts Period.
It is correct to say the GP-40 has it’s motors wired in parallel, it does not make transition. The AR-10 main alternator has it’s limitations therfore with the addition of 2 more traction motors the capacity of the AR10 is exeeded, the locomotive starts in series to reduce current demands on the AR10. You are correct, the GP-40 should kick the SD’s butt, however since the kilowatt out put of the AR10 is divided over 4 motors, not 6 ,the horsepower per traction motor is greater causing wheel slip/ lower tractive effort, the GP40 will accelerate very quickly. The comparison I use when I’m holding training classes is to compare the GP and the SD to a corvette and a Jeep.
Answer this, suppose you went out to the service tracks ,to a locomotive you were entirely unfamilier with, suppose the locomotive" would not pull" , your job is to repair this engine. Where would you start? Remember you are not familier with the engine, HP , TE is all unknown , all you have is a wiring schematic.
The formula for calculating steam locomotive HP is correct, it is well known that steam loco hp is limited only by mechanical technology, had the steam locomotive continued developement we would have seen how limitless they really are, just the developement of poppet valves made a big difference in the valve efficiency. The formula does not lie. take a calculator and try it.
It is true that a diesel locomotive HP is infinite you can increase RPM, increas the fuel etc in fact EMD did just that on the DD 40X , they took a regular 16 645 e3 and r
All very interesting. I don’t know if Isambard’s ever got the answer he was looking for. I think the answer is, there is no simple formula because both TE and power (HP, watts, etc.) change with speed. The only way to find them is to measure them in most cases. TE can theoretically be calculated for steam engines from things like steam pressure, piston area, driver diameter, etc. for startup only. After that, you have to measure it and special test equipment is required.
The simple equations are:
TE is a force (F) measured in lbs, etc.
Force x Distance = work or energy (ft lbs, etc.)
Energy/Time = power (HP, watts)
We can calculate output power from a generator or alternator, but there are losses, so the only way to get HP at the drawbar is to measure it and you have to do it with the train moving.
Hope this helps somebody.
Oh, any two variables can be plotted on a chart. However, that does not imply causation. If we look at the equation above, power = f x d / t and we know that
distance/time = speed so TE x speed = power
EMD plots power vs. speed because that makes a useful chart for RR engineers, etc.
Also, while it may be possible theoretical to increase power out of a system without bound, in reality something will break before you can get to infinity. We call that a non-linearity.
jerry
Alright guys, you’ve given more to think about than I ever expected. As a supplementary question: It’s great to have lots of horsepower and /or tractive effort, but what about the limits on the drawbars between the locomotive and the first car behind. What is the “do not exceed” tonnage that I can haul on a zero percent grade without pulling the drawbars out?
while i haven’t the experience to speak to the drawbar durability question . . .
(though with a few minutes with my materials text and a calculator i could give an upper limit on that number, if anyone is really all that interested in what would be an entirely theoretical answer. )
the following occurs to me:
Horse power is the rate at which a machine does work, (work x time) and work, as someone has already pointed out, is force x distance, so power is therefore force x distance x time.
two locomotives that make the same drawbar pull at the same speed are producing the same amount of useful work, and by extention, the same ‘train’ horsepower.
things get then confusing fast, because the numbers most often bandied about for steam are for starting TE, while Diesels are rated in prime mover HP.
And THOSE numbers don’t translate to ‘TRAIN’ horsepower at all. The confusion happens because we talk about a prime-mover producing so many horsepower, when we really only mean it can generate x,xxx,xxx watts . . . train speed doesn’t enter it.
And steam TE is ONLY cylinder pressure dependant. Firing rate (watts) doesn’t enter into it except when steam consumption becomes a factor. . . a situation that arises once you’re moving. . . at which point the starting TE number is largely meaningless.
so steam TE vs diesel horsepower is an apples-oranges question.[banghead]
try comparing Starting TE to Sustained TE vs locomotive weight. that’s as close a comparison as you’re likely to get. . . . and without looking at the numbers, i’ll bet diesels probably win because every axle is driven vs pilot and trailing trucks, tenders, etc.
in the real world, we’re really interested in bananas. . .[}:)]
the real question, i think, boils down to how much fuel energy is consumed per ton-mile-hour of cargo moved, and how many manhours were spent maintaining the equipment that did the work. I think we all
Electric traction motors have always been able to out pull steam angines at low and starting speeds, even lower hp electrics. That is why the diesel ELECTRIC out performs the steam engine on heavy freight and heavy grades.
Even if you calculate that a particular steam engine has so much hp a small diesel electric can pull a longer cut of cars more easily.
Steam engines often had that dramatic wheel slip trying to start even passenger trains, once moving they would be in good shape.
When I was much younger, my uncles worked as engineers for CNRR in Nova Scotia. Their job was to load passenger cars on the ferry from tha mainland to Cape Breton Island. When the tide was in, pushing cars up the ramp onto the ferry was a challenge, especially in inclement weather. I learned quite a vocabulary while while there during summer vacations, enough to make a sailor blush. I remember being told that the size of the drivers or physical size of the engine had nothing to do with its “power.” It was the weight on the track plus the boiler pressure which could pu***hose *@!! cars up the ramp! I’m a steam lover, but I bet the diesels would have more consistent success and a lot less colorful language.
May we regress to the theoretical laboratory of high school physics? “Tractive Effort” is force. It has no dimension in time, it has no dimension in distance. Suppose you stand on your own two feet and push against a boxcar. You’re devceloping a force (tractive effort). If the boxcar doesn’t move, that’s all you’ve done. But your tired muscles and aching feet tell you that you’ve developed tractive effort. If the boxcar moves, there is force (your pushing), the distance the car moved and the time it took you to move the boxcar. These are the three factors which constitute power.
SO – the “laboratory” answer is that tractive effort is independent of power, but power is composed of force (tractive effort), distance and time.
There’s another usage for these terms in the railroad business. “Tractive Effort” is a term from some 100 years ago. It told management how many cars (tonnage) a steam locomotive could “bust loose”, drag out of the yard and haul down the track. Time and speed didn’t matter. One hundred miles was the day’s pay for the crew. If the crew averaged only 8 mph they’d still get over the road before the hog law caught them. Each additional car was more profit for the railroad. And “horsepower” was something for the “slide rule buys” to play with.
Today the railroads make money by moving “stuff”, frequently at “track speed”. Speed takes “Horsepower”. Today’s trains are dispatched with a very rigid ratio of lcomotive horsepower to train weight. And only the railfans pay much attention to tractive effort.
Very nice explanation of why the emphasis on horsepower today rather than tractive effort. My education has been advanced thanks to all who responded to this topic.
I found my way back to this thread after some time away. I take ptt100’s points about the PRR Q-2. If that class had performed up to its potential they would have remained in service a bit longer!
During the weekend before last, I was able to follow and photograph NSWR 4-6-2 3801 running a passenger train. On one of the steeper grades, I noticed how much the train slowed down, despite in this case having an 875HP light roadswitcher pushing at the back of the train. It brought to mind the fact that steam horsepower is completely dependent on speed, while the diesel was capable of providing its contribution at any speed, as long as the motors didn’t overheat.
While most trains slow on that grade, the effect is not as pronounced with adequate diesel power.
Peter
The above last statement is contradicted by the very existance of slugs, which show that someone does consider tractive effort to be important, still, in certain applications.
What’s the difference betweent tractive effort and drawbar pull?
Visit http://www.vcn.com/~alkrug/rrfacts/hp_te.htm
That is the best explanation i have ever read.
Adrianspeeder