rlsteam wrote:Pound for pound, no 4-8-4 equaled the New York Central's S1 Niagaras for horsepower, efficiency and mileage between servicing. With 79" drivers they were definitely a passenger locomotive for level terrain..
here here.............but really wasnt a PRR T1 just a 4-8-4 with some extra parts???
J. Edgar wrote: rlsteam wrote:Pound for pound, no 4-8-4 equaled the New York Central's S1 Niagaras for horsepower, efficiency and mileage between servicing. With 79" drivers they were definitely a passenger locomotive for level terrain.. here here.............but really wasnt a PRR T1 just a 4-8-4 with some extra parts???
No...the T-1 was so much more, and they're starting to get the respect they truly deserved. Their reputation of being slippery has even been called into question in recent years as being an exaggeration. Nothing could have made them the future of motive power they were intended to be, but had they all been equipped with something other than poppet valves they might have fought on for a bit longer.
As for how they matched up with a true 4-8-4, that drama played itself out daily on the speedway south of Englewood, Ill. God only knows what the w/l record was between Niagara and T-1, but I bet they were both about .500 batters.
PS: I like that avatar. Seems I've seen that guy before in the Lost World...
U-2-a/b/c 6100 - 6119 6120 - 6139 6140 - 6159
U-2-d/e/f 6160 - 6164 6165 - 6179 6180 - 6189
U-2-g/h 6200 - 6234 6235 - 6264
U-3-a/b 6300 - 6311 6312 - 6336
U-4-a/b 6400 - 6404 6405 - 6410
The picture below is a model of the streamlined CNR Northern's of the 30's and 40's
There's a big 4-8-4 sitting in the park there in Nashville. Passed through there some months back and stopped to take a few pictures of it. It appears to be in pretty good shape over all. I had heard once a couple years ago that there was talk of restoring it to operation. Any word on that?
I was lucky enough to have ridden both behind T-1's and Niagras, more than once, and I truly treasure the memories. A number of wartime and postwar trips on the Empire State Express with a Niagra between Harmon and Buffalo and then a Hudson to and from Detroit. The Red Arrow and the Trail Blazer between Harrisburg and Crestline behind T-1's, then K-4's for the rest of the trip. Betweem the two, I prefer the Niagra, because riding behind a T-1 at certain speeds one felt a strange subtle oscillation, possibly becuase of lacking of damping in drawbars, either in the PRR passenger equipment or the front or rear of the T-1 tender. I rather think the latter, because I never noticed it with a K-4 or two K-4's at the head end. Anyone else experience this? The superior comfort of the PRR 44-seat Juniata-built long distance coaches more than made up for this annoyance.
I never had the occasion to ride behind an N&W J, although I did see them in operation. By the time I rode the N&W, GP-9's had taken over as passenger power. From what I understand, if one includes quality of workmanship, the J had all other condenders beat. N&W steam power was a close as possible to a Swiss watch as a steam locomotive could possibly be, or at least a North American steam locomotive.
WOW!
I have read this thread from beginning to end, and can no longer refrain from comment. The original question was in regard to quality, and my comments are relative to how I define quality. The very fact that all American 4-8-4s still in existence are at least 58 years old at this writing, is a testament to their quality. That is a long life for any piece of machinery. By it's very design, a reciprocating steam locomotive will eventually tear itself (not to mention a railroad's infrastructure) apart. All were "over designed" as a result. I wish I had a car that I could drive for more than 1 million miles, and own for life.
Is one 4-8-4 of higher quality than another because it can average 15,000 miles a month instead of 10,000 miles? I say that this relates to utilization. All railroads strove to increase utilization of their locomotives. An idle locomotive is making no money for the company. The N&W was better at this than most. The C&O under utilized their motive power due to very conservative tonnage ratings applied system wide, and their 2-6-6-6 was not allowed to really shine until it was used in lake coal service on the Northern Subdivision. C&O never considered using their 4-8-4s in other than mountain passenger service until they were bumped by E-8s, and by then the end was at hand. Both of these roads had a vested interest in maintaining coal as a fuel, yet they both finally dieselized.
Is one 4-8-4 of higher quality than another because it produces a higher cylinder or drawbar horsepower rating? I say this relates to capability, although what seems to be forgotten here is that all horsepower figures both indicated and drawbar are calculated. Dynamometer cars, like stationary dynamometers measure force. PERIOD. The only way to physically measure horse power is with horses. Granted, the mathematical formula for converting force to horsepower has been proven reliable over years of testing, but these numbers can, and have been manipulated. And besides, if you want more power you can put another diesel in the consist without paying for another crew to operate it.
Is one 4-8-4 of higher quality than another because it can haul a given load at a given speed using less fuel? I say this relates to efficiency, and all steam locomotives are terribly inefficient regardless of wheel arrangement and use of modern appliances. The mechanical engineering curriculum of most major universities, as it relates to use of steam for locomotion was not expanded beyond, and in many cases was being phased out, by the end of the great depression. It had been recognized by that time that steam locomotives were on their way out. In 1985 there was much testing of C&O #614 conducted by Ross Rowland and American Coal Enterprises in hope that refinements could again make coal a viable fuel for locomotion. From what I can tell, this effort has been abandoned. Unfortunately the diesel-electric wins the efficiency battle again.
I make no claim here, even though it may seem like it, that diesels are of higher quality than any 4-8-4 extant. Diesels won out based upon economics alone, and to argue that one 4-8-4 is of higher quality than another because of any one of these factors, is to argue that all 4-8-4s were of inferior quality to the diesel electric locomotive.
I think my point has been made. When you consider any of these factors individually, quality can not be determined. When combined with all other factors that made one locomotive different from another, including service life, cost of maintenance, cost and frequency of repairs, and even fit and finish, you would be more able to make such a determination. Quality is not something that can be described easily, but you know it when you see it. For my money, it would be hard to beat Lima...all things considered.
Jim J.
Trace Fork the mathematical formula for converting force to horsepower has been proven reliable over years of testing, but these numbers can, and have been manipulated.
Got an example?
Trace Fork, in fairness to all those who have contributed to this point, and whose work has helped you to put it into some perspective, I believe that we have all attempted to refine the several questions, not just the one you have picked, from the OP's original post. It is perhaps surprising that it has taken us nearly 20 pages and over two years to achieve it, but with asynchronous fora such as this one, I do feel that we have gone a long way towards addressing all of them.
In fact, my own observation, on the first page, was an attempt to have us begin to build a vortex of discussion that would have as its center the salient information and orientation necessary to address the OP's opening remarks.
-Crandell
timz Trace Fork the mathematical formula for converting force to horsepower has been proven reliable over years of testing, but these numbers can, and have been manipulated. Got an example?
I do.
Although not directly related to steam locomotion, in the summer of 2002 I built a class motor for a car that I wanted to campaign in racing events. Upon completion I rented some dyno time from a well respected engine builder here in central Ohio. The first two dyno pulls were to gain a baseline of operating conditions, to set and maintain fuel pressure and water temperature. The next eight pulls were to determine through adjustment of ignition timing only, the optimum timing setting.
All pulls were performed as raw data, and were then corrected to 29.92" of mercury, 60 degree dry air.
A peak corrected horsepower (flywheel) of 527.6 was achieved at 5676 RPM with the ignition firing at 30 degrees before top dead center which was determined by previous pulls to be optimum for this engine. For the eleventh pull the electric fuel pump was removed, and a mechanical pump used as the only fuel supply. (Racing class rules require the use of a mechanical pump). This pull resulted in a peak corrected horsepower of 464 at 4645 RPM and from there on break specific fuel consumption leveled off, and corrected horsepower at 5681 RPM was 421. The formula of peak torque (measured force) X RPM / 5252 still applied on this reading, but it was clear the engine was down 100 HP because it was starving for fuel. This was an unintentional manipulation of the numbers, but a manipulation none the less.
If one were to dig deep enough he would find that the peak drawbar horsepower calculation of 7498 at 46MPH developed by C&O's 2-6-6-6, was achieved with a driver diameter somewhat less than the 67" design diameter. This would affect the machinery RPM at that recorded 46 MPH and thus the final number. Maybe not intentional, but is still a manipulation. I'm confident that other cases could be found with a little research.
I would have expected those running the test to use figures for speed and tractive effort derived from the dyno car, not from the engine...and thus not from the drivers. Still, I do agree with you that non-standardized dimensions in running and in leveraged surfaces would very possibly yield slightly skewed results. That would also be as true for the dyno car as for the engine.
selector I would have expected those running the test to use figures for speed and tractive effort derived from the dyno car, not from the engine...and thus not from the drivers. Still, I do agree with you that non-standardized dimensions in running and in leveraged surfaces would very possibly yield slightly skewed results. That would also be as true for the dyno car as for the engine.
You are correct that the measurements are derived from dyno car instruments. The force measurement however would be greatly impacted by the operation of the locomotives revolving assembly. A 67" drive wheel revolves 301.01 times per mile. A drive wheel worn (or turned) to 65" will revolve 310.28 times per mile. That would equate to nine additional piston cycles per mile, and in turn affects steam admission requirements to the cylinders. Basic physics dictate that the locomotive work at slightly different capacity under these conditions.
I am in no way saying that the Alleghany could not produce 7498 DBHP while in "as new" condition. It likely could. It was a fine locomotive and VERY well engineered. But it is widely understood that tractive effort increases as drive wheel diameter decreases. And my point is that any one variable in an equasion will result in a different solution, and that horsepower being a calculated value, may not be the best indicator of capability.
C&Os 1943 dynamometer tests of #1608 on the allegheny sub measered an instantaneous drawbar pull of 113,790 pounds, over 3% greater than Lima's calculated value of 110,200. This test was conducted 2 years after the locomotive arrived on the property, and I don't know if class repairs had been made on #1608 prior to testing, It had probably not been re-tired as this test was one month prior to the record setting test of #1608 on the Northern sub. But it is likely #1608 was only working at about 90% capacity in this test given another 2-6-6-6 was pushing the 11,623 ton train. In practice, two locomotives working together can only achieve about 90% of their true drawbar exertion due to lack of perfect coordination between the two. None the less, these numbers speak volumes as to the capability of the 2-6-6-6.
With a factor of adhesion of roughly 4.6 the Allegheny had much room to grow. It would be interesting to see the effect of an increase in boiler pressure. Just enough to force a factor of adhesion of 4.00 so the locomotive wouldn't become slippery. I can only speculate to the increase in power that would result.....But wait, this is a discussion of 4-8-4s
Trace ForkThis was an unintentional manipulation of the numbers, but a manipulation none the less.
So by "manipulation" you just mean "a change to the engine that affects its output"?
Trace Forkit is widely understood that tractive effort increases as drive wheel diameter decreases.
But you'd agree that a 2-6+6-6 with 33-inch drivers wouldn't be twice as powerful?
I believe both drawbar pull and speed are read from dynamometer car instrumentation, not the locomotive. Therefore, driver size would not affect the 7498 DBHP @ 46 mph figure, if the drawbar pull reading ifrom the dynamometer was correct. For the 1943 tests 1608 had a driver diameter worn to 65.25" (pg 7 of the test report), about 2.5% less than spec.
However, the track profile where the reading was taken would have an effect. If speed and grade were not constant (and they weren't), then adjustments would have to be made to the drawbar pull figure. However, the DBHP figure would be arithmetically linked to DB pull and not adjusted:
(drawbar pull x speed)/375=DBHP
The first two terms are read in the dyno car. The constant term 375 is neither empirical nor variable, but rather a combination of about six constants from subparts of the horsepower equation. They aren't fudge factors, so I don't see how the dbhp calculation by itself could be manipulated. DB pull can be adjusted for grade, curves and acceleration/deceleration.
timz Trace ForkThis was an unintentional manipulation of the numbers, but a manipulation none the less. So by "manipulation" you just mean "a change to the engine that affects its output"?
By manipulation I mean any variable introduced (from the locomotive, the instrumentation, or the atmospheric corrections etc.) into the equation that alters the solution. This applies to any value that is calculated from other measurements, and not measured physically.
timz Trace Forkit is widely understood that tractive effort increases as drive wheel diameter decreases. But you'd agree that a 2-6+6-6 with 33-inch drivers wouldn't be twice as powerful?
I'm not sure this question even deserves an answer. I did not state that a reduction of driver diameter by one half doubled tractive force. There is however a proportional correlation. If one were to install 33" drivers on an Allegheny it wouldn't pull a dynamometer car...The locomotive frame would be sitting on the roadbed between the rails.
Trace Fork I did not state that a reduction of driver diameter by one half doubled tractive force. There is however a proportional correlation.
If so, will the proportional correlation continue until the engine's frame reaches the rails?
feltonhill I believe both drawbar pull and speed are read from dynamometer car instrumentation, not the locomotive. Therefore, driver size would not affect the 7498 DBHP @ 46 mph figure, if the drawbar pull reading ifrom the dynamometer was correct. For the 1943 tests 1608 had a driver diameter worn to 65.25" (pg 7 of the test report), about 2.5% less than spec. However, the track profile where the reading was taken would have an effect. If speed and grade were not constant (and they weren't), then adjustments would have to be made to the drawbar pull figure. However, the DBHP figure would be arithmetically linked to DB pull and not adjusted: (drawbar pull x speed)/375=DBHP The first two terms are read in the dyno car. The constant term 375 is neither empirical nor variable, but rather a combination of about six constants from subparts of the horsepower equation. They aren't fudge factors, so I don't see how the dbhp calculation by itself could be manipulated. DB pull can be adjusted for grade, curves and acceleration/deceleration.
What I am inferring is that all other factors being identical, the drawbar pull exerted with 67" drivers would be less than that with 65.25" drivers. The output of the locomotive would be less, so the dynamometer reading would reflect the reduction in measured drawbar force. As a result the final horsepower calculation would be lower. The readings were drawbar measurements regardless of where the instrumentation was located. The force exerted is purely a function of locomotive output, and I don't know if those recording the measurements had an agenda, so I will assume their procedures met all engineering standards of the time.
Perhaps I should not have used the term manipulation as it implies wrong-doing at some level. I do not deny that the locomotive produced these readings, but firmly believe the readings would have been lower on 67" drivers.
timz Trace Fork I did not state that a reduction of driver diameter by one half doubled tractive force. There is however a proportional correlation. I think you suggested an engine with 65-inch drivers would be more powerful than the same engine with 67-inch drivers. Would the same engine with 63-inch drivers be more powerful still? And even more powerful with 61-inch? If so, will the proportional correlation continue until the engine's frame reaches the rails?
I think you suggested an engine with 65-inch drivers would be more powerful than the same engine with 67-inch drivers. Would the same engine with 63-inch drivers be more powerful still? And even more powerful with 61-inch?
In a nutshell, yes. As the diameter of the drivers is reduced the tractive output increases proportionally. That tractive output though, will be produced at a lower speed. This would result in diminishing returns and would eventually run counter to the very principals that gave rise to the "Super Power" concept of steam locomotives.
This concept was to build steam power plants capable of not necessarily hauling more tonnage, but equal tonnage at higher sustained speed. Speed which would be lost as the diameter of drivers decreased. You will find remarks earlier in this thread that C&O used Super Power locomotives with a drag era mentality of operation, and this is largely true with regard to the 2-6-6-6. You will also find my comments that the 2-6-6-6 wasn't able to really perform until used on the Northern sub-division. These locomotives were originally put into service hauling 11,500 ton trains through the mountains in pairs at drag era speeds. After the last order of locomotives arrived in 1948, some started to stray onto the flatter Northern and Toledo sub-divisions where they actually out performed the T-1 2-10-4 locomotives (also built to Super Power concept) on the standard 13,500 ton trains. This however, only lasted until diesels took over in 1952.
So to sum it up without being overly technical, if the 2-6-6-6 were built on 57" drivers, they would be substantually more powerful than the 2-8-8-2s that they replaced. They would not however be capable of moving equal tonnage much faster, so there would be little point in building it.
Trace ForkAs the diameter of the drivers is reduced the tractive output increases proportionally. That tractive output though, will be produced at a lower speed.
If by "tractive output" you mean force (in pounds)-- then sure, at the same driver RPM drawbar pull will increase. If it increases (inversely) proportionally to driver diameter, then horsepower will remain constant.
If by "tractive output" you mean horsepower, then we have no way of knowing whether it goes up or down as we shrink the drivers. With 33-inch drivers it won't produce 15000 dbhp, even if we can circumvent the practical difficulties.
timz Trace ForkAs the diameter of the drivers is reduced the tractive output increases proportionally. That tractive output though, will be produced at a lower speed. If by "tractive output" you mean force (in pounds)-- then sure, at the same driver RPM drawbar pull will increase. If it increases (inversely) proportionally to driver diameter, then horsepower will remain constant. If by "tractive output" you mean horsepower, then we have no way of knowing whether it goes up or down as we shrink the drivers. With 33-inch drivers it won't produce 15000 dbhp, even if we can circumvent the practical difficulties.
Please re-read some of my earlier posts. I for one think that using a calculated value (Horsepower) is to use a flawed indicator of performance potential. Instead of using the term tractive output, which is more indicative of force on the rail, I should have said drawbar force, which is physically measured. I apologize for the confusion. Increased tractive force does relate to increased drawbar force, but I should not have mixed the terms.
The practical difficulties you mention would include the fact that the Allegheny's piston stroke was 33". That would be very difficult with 33" drivers. And no...15,000 DBHP would not be achieved.
What's baffling me is... you said
Trace Forkall other factors being identical, the drawbar pull exerted with 67" drivers would be less than that with 65.25" drivers. The output of the locomotive would be less, so the dynamometer reading would reflect the reduction in measured drawbar force. As a result the final horsepower calculation would be lower.
And then you said
Trace ForkAs the diameter of the drivers is reduced the tractive output [in pounds] increases proportionally. That tractive output though, will be produced at a lower speed.
which implies the "final horsepower calculation" will remain constant. Wouldn't you say the latter makes more sense?
Horsepower is a calculation of force over time. The accepted formula to calculate horsepower of objects in linear motion is:
HP= (F X V) / 33000
Where F= Force (lbs) V=Velocity (ft/min)
Thus if an increased force is recorded at a lower velocity the calculated horsepower will be different, not necessarily constant.
So let's assume we are in the dyno car behind C&O #1608 on its record breaking trip. A measured drawbar force of 61,125lbs has been measured at 46mph. 46mph=4048ft/min.
61125 X 4048 = 247434000 247434000 / 33000 = 7498.00dbhp
Now lets assume that we are on another trip behind #1608 and the drivers are now 64" instead of 65.25". We will assume a 2% increase in drawbar force or 62350lbs, but this was recorded at 44mph. 44mph = 3872 ft/min.
62350 X 3872 = 241419200 241419200 / 33000 = 7315.73dbhp
Now for an example of how flawed this formula is, please read the following:
Even more interesting is how the formula came to be. It was originated by James Watt, (1736-1819) the inventor of the steam engine and the man whose name has been immortalized by the definition of Watt as a unit of power. ...
...To help sell his steam engines, Watt needed a way of rating their capabilities. The engines were replacing horses, the usual source of industrial power of the day. The typical horse, attached to a mill that ground corn or cut wood, walked a 24 foot diameter (about 75.4 feet circumference) circle. Watt calculated that the horse pulled with a force of 180 pounds, although how he came up with the figure is not known. Watt observed that a horse typically made 144 trips around the circle in an hour, or about 2.4 per minute. This meant that the horse traveled at a speed of 180.96 feet per minute. Watt rounded off the speed to 181 feet per minute and multiplied that by the 180 pounds of force the horse pulled (181 x 180) and came up with 32,580 ft.-lbs./minute. That was rounded off to 33,000 ft.-lbs./minute, the figure we use today.
Given the assumption that a horse can pull with a sustained force of 180lbs for one hour, and the arbitrary rounding to the closest whole number (or next even thousand), I'd say we need to get away from this fixation with horsepower. Dynamometer cars are equipped with instruments that measure and record force, horsepower is calculated using the above formula. Even though this formula is the accepted standard for horsepower calculation, I question it's accuracy.
I don't see the point. If everyone uses 33,000 ft-lbs/min, comparisons at any speed are equivalent if purportedly "inaccurate". So everyone using the English system of units is wrong. What should the correct unit be if 33,000 is incorrect? Must we throw out all the diesel and electric HP ratings? Should we use a different size horse?
Is the metric system of units any less flawed or arbitrary?
If TE is increased 2% because of a reduction in driver size, why does speed fall exactly 2 mph?
Sorry to ask so many questions, but there a several parts of this I don't understand.
feltonhill I don't see the point. If everyone uses 33,000 ft-lbs/min, comparisons at any speed are equivalent if purportedly "inaccurate". So everyone using the English system of units is wrong. What should the correct unit be if 33,000 is incorrect? Must we throw out all the diesel and electric HP ratings? Should we use a different size horse? Is the metric system of units any less flawed or arbitrary? Sorry to ask so many questions, but there a several parts of this I don't understand.
Before this all began. If I were to have asked you, "WHAT IS HORSEPOWER? What would have been your response?
Force in puonds is a direct measurement, and as such reveals the amount of energy applied to an object. Force measurements are used to calculate diesel horsepower as well. The formula is a little different though, because the force is measured at a rotating shaft:
HP = (T X N) / 5252
Where: T = Torque (lb/ft) N = Speed (rpm) 5252 = (33000 / Pi) / 2
Torque = F X R
Where: F = Force (lbs) R = Radius (ft)
So you see the same value of 33,000 is used in this calculation. My question is why? What does knowing this value tell you? And no...metric units of calculation in no way make the calculation more accurate, and / or useful.
Railroads used dynamometer readings mainly to develop tonage ratings for their locomotives (steam and diesel). Railroad motive power, and operating department officials did not need to know how many horses could be replaced by a locomotive. They needed to know how much force is applied at the drawbar, and if that force was sufficient to overcome the forces of gravity and friction involved in moving a train from point A to point B. By the turn of the 20th century the steam engine, and the internal combustion engine, had all but rendered the horse obsolete for industrial use. As creative as man kind is, a century later they have yet to develop a better indicator of a machine's capability than to compare it to horses. Or have they? Force and torque, both direct measurements.
feltonhill If TE is increased 2% because of a reduction in driver size, why does speed fall exactly 2 mph? Sorry to ask so many questions, but there a several parts of this I don't understand.
I used 2% (actually 2.249%), and 2mph because I did not have actual measured values. These values are assumed. This is not the correct forum to discuss the advanced physics and mathematics involved in calculating the energy applied to a rail by a certain diameter wheel, and how that translates to the force applied to a linear object like a locomotive drawbar. There are people who teach this for a living, and I am not one of them. My training is in geodesy. The speed will decrease (albeit at varying values) due simply to the fact that a smaller diameter wheel is also smaller in circumference, and will not travel as great a distance as a larger wheel given the same application of energy.
Don't apologize for asking questions, that is how knowledge is gained. There is an abundance of text available that will better answer your questions than available band width will allow me to answer them here. Libraries are a good first source. Seek them out.
Trace ForkI used 2% (actually 2.249%), and 2mph because I did not have actual measured values. These values are assumed.
You first said larger drivers produced lower power-- "What I am inferring is that all other factors being identical, the drawbar pull exerted with 67" drivers would be less than that with 65.25" drivers. The output of the locomotive would be less, so the dynamometer reading would reflect the reduction in measured drawbar force. As a result the final horsepower calculation would be lower."
Now you're assuming it's smaller drivers that produce lower power. You must have gotten careless with one of your assumptions?
Trace ForkThis is not the correct forum to discuss the advanced physics and mathematics involved in calculating the energy applied to a rail by a certain diameter wheel, and how that translates to the force applied to a linear object like a locomotive drawbar.
If in 1943 we wanted to know a 2-6+6-6's maximum drawbar horsepower at 46 mph with 65.5-inch drivers, would advanced physics and mathematics have told us? If so, they still will-- math and physics are just as advanced now as they were in 1943. So how about it-- think their 7498 dbhp measurement was correct?
Trace Fork There is an abundance of text available that will better answer your questions than available band width will allow me to answer them here. Libraries are a good first source.
Trace ForkNow for an example of how flawed this formula is...
Trace ForkEven though this formula is the accepted standard for horsepower calculation, I question it's accuracy.
Everyone agrees that a 7000 dbhp locomotive won't equal exactly 7000 flesh-and-blood horses. (You remember there's also something called a metric horsepower, and 7000 of them won't be "right" either.)
But "this formula is the accepted standard" in the same sense that 12 inches = 1 foot is "the accepted standard". This unit of power has been defined as 550 ft-pounds per second, or 33000 foot-pounds per minute, or 375 mile-pounds per hour-- and it has no independent existence beyond the various forms of the definition. It's still called a "horsepower", but its definition won't change even if somebody breeds a horse that's good for 10 dbhp.
timz You first said larger drivers produced lower power-- "What I am inferring is that all other factors being identical, the drawbar pull exerted with 67" drivers would be less than that with 65.25" drivers. The output of the locomotive would be less, so the dynamometer reading would reflect the reduction in measured drawbar force. As a result the final horsepower calculation would be lower." Now you're assuming it's smaller drivers that produce lower power. You must have gotten careless with one of your assumptions?
I see what your driving at here. I was mistaken in stating that "the final horsepower calculation would be lower" I should have said it would differ. Without a physical measurement on 67" drivers, my assumption that horsepower would be reduced was erroneous.
Furthermore, I am not now assuming that the smaller drivers produce less power. In fact the 64" driver was assumed to result in a 2.249% greater drawbar force than that of the 65.25" driver. 62350lbs vs. 61125lbs. The end result here is that the smaller driver, due to it's inability to travel as great a distance, given equal application of energy, as the larger driver, produces lower power OVER TIME. Force is not measured over time, it is measured at a specific point. Horsepower is a calculation of the application of measured force over time. Thus the reason for a speedometer on the dynamometer car, to determine as accurately as possible, velocity at the specific time force was measured. I think the confusion here is from our differing definitions of power. To clarify, when I speak of power I am referring to force and/or torque. Each a measurable value. I don't want to get into a pi$$ing match here, so from this point forward I will concede that the formula to calculate horsepower, being the accepted one, is absolute. But I must still respectfully disagree that horsepower is the best indicator of locomotive performance.
timz If in 1943 we wanted to know a 2-6+6-6's maximum drawbar horsepower at 46 mph with 65.5-inch drivers, would advanced physics and mathematics have told us? If so, it still will-- math and physics are just as advanced now as they were in 1943. So how about it-- think their 7498 dbhp measurement was correct?
If in 1943 we wanted to know a 2-6+6-6's maximum drawbar horsepower at 46 mph with 65.5-inch drivers, would advanced physics and mathematics have told us? If so, it still will-- math and physics are just as advanced now as they were in 1943. So how about it-- think their 7498 dbhp measurement was correct?
I don't profess that math and physics would produce the same number. And as I stated in a previous post, I don't dispute the Allegheny was capable of producing 7498 instantaneous dbhp. In fact I have the numbers in published form. And at last, an absolute formula to verify it from the measured values. As to it's correctness? Since it was not a measurement, but a calculation, I must assume the accepted formula was applied correctly using the measured values of force and velocity.
timz Lotsa luck finding a book that tells you how to calculate a locomotive's drawbar horsepower from first principles. They'll tell you how to guess at it, but if you want to know what it actually is you'll have to measure it, and you won't be astonished if the calculated guess is wrong.
Lotsa luck finding a book that tells you how to calculate a locomotive's drawbar horsepower from first principles. They'll tell you how to guess at it, but if you want to know what it actually is you'll have to measure it, and you won't be astonished if the calculated guess is wrong.
This is the point I am trying to make.....there exists no accurate method to measure horsepower, It is a calculated value only. And as you state above, math and physics would indeed only render an approximation of the drawbar horsepower (or drawbar force for that matter) that the Allegheny (or any locomotive) could exert. That is perhaps one reason the engineering staff at Lima assigned starting tractive effort values to the 2-6-6-6 at 85% of boiler capacity. A tractive effort which was determined inaccurate by subsequent dynamometer testing. Engineers had to estimate energy losses between the boiler and the rail, and those losses were based on many factors. The same calculations they used will allow the estimation of the differing effects of driver size in application of force at the railhead. But you're right. It is an educated guess. An accurate measurement would need to be taken at the rail and / or wheel tread to determine an actual value. Although the texts to which I elude will not specifically provide formulas to calculate drawbar horsepower of any locomotive, they will discuss the application of principles that will allow it's estimation through calculation. And if given the availability of accurate values to calculate from, these estimates should be quite close.
It's true, fans do overemphasize horsepower as a measure of locomotive performance-- a more useful statistic would be total work done at the drawbar per dollar of operating cost. But we don't know that.
(And the 7498-dbhp figure is particularly useless, since we don't know how long a given engine could maintain it, or how close the average engine in average condition with average coal and average water could come to matching it.)
As to whether we can "measure" horsepower, that's a semantic argument. Can we "measure" the area of a rectangle drawn on a plane? We measure the sides, and confirm the corners are 90 degrees, then we calculate the area. You're saying we haven't measured the area-- I'd say we have, but I'm no expert on the definition of "measure".
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