Paul Milenkovic"Behind the dynamometer car-- what do we care what's going on back there? If the engine's drawbar pull is 90000 lb, then it's 90000 lb, . . ." You, sir, get an A in Engineering Mechanics along with a call to teach the class next semester.
You, sir, get an A in Engineering Mechanics along with a call to teach the class next semester.
If that gets an A, then can I teach the phlogiston theory in your school's thermodynamics course for one?
Of course it matters what the train is doing back there. The dynamometer isn't measuring the locomotive's drawbar pull, it's measuring the strain between the tender drawbar and the dynamometer car, probably either electrically or with hydraulics. Now if you get run-in from the train, the effective "drawbar pull" the device is measuring has little to do with what the locomotive is delivering at that moment; likewise, if slack runs out you're going to see a very high reading on the dial and graphs, again nonrepresentative of what the engine is producing.
Meanwhile, when the load on the locomotive is reduced, its power is being used to accelerate only its own mass, so it can reach a higher speed than it would if actually pulling the train. Train resistance will pull that speed down again... but the force measured as the train pulls on the drawbar will create a false impression if you ASSume it's all being generated by the steam rather than yanking the locomotive to a lower speed.
Meanwhile, if my drawbar TE curve has nonlinearities in it (due to shock, slack action, etc.) and I then use a planimeter to integrate under it for relatively short time periods, might I expect to see some resulting figures that... might not exactly reflect the reality of the dbhp actually developed by the locomotive?
Good point-- they couldn't measure grade since they can't separate it from acceleration, but maybe they could get the combined grade-acceleration correction for the drawbar pull?
Your guess as good as mine, and my guess is no such device. They measured speed and calculated accel from that, and got grade from the track charts, which couldn't be perfectly accurate.
Just curious - Does the dynamometer car have some type of level to record the instantaneous grade or do they rely on known grade profiles of the test route?
Thanks
Anthony V.
"We'll need to correct for gravity's pull on the engine, and the engine's acceleration, but that's easy if we're watching speed and grade closely.
Behind the dynamometer car-- what do we care what's going on back there? If the engine's drawbar pull is 90000 lb, then it's 90000 lb, . . ."
If GM "killed the electric car", what am I doing standing next to an EV-1, a half a block from the WSOR tracks?
sgriggsA DB horsepower calculation from a slowing train is not an indication of sustainable horsepower.
In reality, if the train is accelerating, and the dynamometer car shows 90000 lb drawbar pull at 20 mph and then 80000 lb at 25 mph and 70000 lb at 30 mph, that's useful info-- especially if we do it over again. We'll need to correct for gravity's pull on the engine, and the engine's acceleration, but that's easy if we're watching speed and grade closely.
Behind the dynamometer car-- what do we care what's going on back there? If the engine's drawbar pull is 90000 lb, then it's 90000 lb, whether the rest of the train is going uphill or down, or accelerating or slowing.
"Dynamic effects on train resistance"-- if the conductor on the caboose throws out the anchor, how would that invalidate the drawbar pull reading? The train will slow, the engine will continue to pull, the dynamometer will continue to record drawbar pull and speed correctly... what's the problem?
First of all, Merry Christmas!
By dynamic effects, I am referring to changing train resistance because of changes in grade from downhill to uphill. These changes in train resistance cause changes in the balancing speed. If the speed is not constant, the DBHP calculation (speed x pull/375) will not yield a reliable sustained HP value.
Let me explain further. On p 156 of The Allegheny Lima's Finest, Huddleston and Dixon give the following description of the line profile near MP 61:
"Test run No. 104, of August 6 (1943) with 14,075 tons, established an all-time drawbar horsepower record: 'The highest instantaneous drawbar horsepower occurred ... at mile post 61 plus 1400 feet (about ten miles south, or east, of Circleville, Ohio), at which time a maximum of 7,498 drawbar horsepower was developed at a speed of 46 miles per hour.' The profile of the line between mile post 58 and 62 reveals that the train would have built up considerable momentum past mile post 61, along trackage with 'roller coaster' contours: upgrade (.20%) from mile post 58 to 59, then downgrade for a mile and a quarter (mostly .42% with some .21%), then upgrade again for a mile and a quarter (.20% with some .16%). At the point where the highest instantaneous drawbar horsepower was recorded, all of 1608's train would have been out of the dip and on the upgrade."
Note that the authors describe this section of the line as having "roller coaster" contours. Keep in mind also that the train does not in reality behave as a point mass, but each car is affected by the grade on which it is running. Assuming the coupled length of each car is 45 feet, a 160 car train would be 7200 feet long (about 1 1/3 mile in length). Therefore, as the train transitions from negative grade to positive grade, the resistance would be constantly changing as more cars went from a negative effect on the aggregate resistance to a positive effect. Straightforward physics (not Davis approximation) shows that a 14,075 ton train exerts 28,150 lbs of grade resistance for every 0.1% of grade. Going from the -.42% grade around MP 60 to a +.20% grade around MP 61 means the grade resistance alone would swing from -118,230lbs to +56,300lbs in a track distance of less than 2 miles! That doesn't even take into account the locomotive weight (a not insignificant 500+ tons), which similarly shifts its effect on measured DB pull from positive to negative. The transition from -.42% grade to +.20% grade would also mean a slowing train as more cars move onto the positive grade. A DB horsepower calculation from a slowing train is not an indication of sustainable horsepower.
It was these dynamic effects on train resistance that lead me to question the meaningfulness of DB horsepower calculations on such a grade profile.
sgriggsrolling terrain makes it darn near impossible to reliably determine DBHP or DB pull curves.
You seem to imagine when the train runs from +0.2% onto -0.4% the dynamometer car's drawbar pull reading is thrown way off-- too many "dynamic effects". What effects?
I don't have access to the test report or the grade profile chart for the C&O Northern Subdivision, but I assumed there was a favorable downhill grade somewhere before MP61 that allowed the test train to carry 45-50mph mph into the grade where the 7498 measurement was made. By my calculations, the Davis resistance formulas would have to overpredict by well over 20,000lbs for a single H-8 to be able to haul a train that heavy at 46mph on level track (even if the loco was making 7500hp). If the Davis prediction is reasonably accurate, I don't know how the train could even reach that high of a speed without a suitable downhill stretch prior to MP61 or a second locomotive in the consist (a la NYC practice). I calculated that a 14075 ton train would have to be on a 0.09% downgrade to produce approximately 61,000 lbs resistance at 46mph which corresponds to ~7500 DBHP uncorrected for engine weight. As far as I know, there is no mention of a second locomotive in the test train (although IIRC Huddleston talks of other testing in the mountains to establish coal train tonnage ratings where a second engine was in the consist but not doing much work).
The biggest takeaway for me is that rolling terrain makes it darn near impossible to reliably determine DBHP or DB pull curves. There are just too many dynamic effects to measure power with any degree of precision. Add to that the inherent characteristic of reciprocating steam locomotion to produce a peaky, parabolic power curve and the task of accurate measurement on the road becomes all that much more difficult. Of course, railroads had very little use for knowing peak horsepower of their locomotives (other than possibly to evaluate equipment modification effectiveness on an apples to apples basis). At the end of the day, I think the railroads cared about such things as gross ton-miles per hour over the run and efficiency in terms of fuel and water consumption per ton-mile.
As everyone knows, C&O said its 2-6+6-6 reached a momentary maximum drawbar horsepower of 7498 at 46 mph. I never noticed until seeing the other thread that, near as we can make out, they meant the engine reached 46 mph northward in Ohio with 13000+ tons. At Milepost 61 plus 1400 ft, which suggests it was on test 104, with 162 cars and 14075 tons, rather than test 106 that didn't run that far north.It turns out we have to cut Davis train resistance in half to give the engine a reasonable chance of reaching 46 mph at MP 61 plus 1400 ft; details follow.The Davis formula says at speed V (in miles/hour) on level track a 162-car, 648-axle, 14075-ton train requires 37089.5 pounds, plus (633.375 times V) pounds, plus (7.0875 times V squared) pounds of drawbar pull:At 20 mph 52592 lb25 mph 57354 lb30 mph 62470 lb etcWe'll assume the engine's drawbar-pull-vs-speed curve is a sequence of straight lines connecting the points below:At 20 mph 95000 lb25 mph 8600030 mph 7700035 mph 6900040 mph 6200045 mph 5600050 mph 51000From MP 42.2 to MP 54.9 a northward train gains 89 feet of elevation; average compensated grade is +0.15%. The last three miles of that averages +0.18% compensated. Then 3.8 miles averaging level compensated, then 1-1/4 miles averaging 0.38% down, then 1.3 miles averaging 0.2% up.
We'll say the engine and tender weigh 500 tons. We'll say it takes 93 lb/ton to accelerate the train at 1 mph/second, a lower-than-usual allowance for rotational inertia.Total resistance on +0.15% at 20 mph is 96000 lb, so we'll say the engine passes MP 54.9 at 20 mph. (We could take the length of the train into account, but I'm too lazy to do that, so from here on the train is a point mass, and it starts accelerating as soon as the engine passes MP 54.9.) After 3.8 miles of level it's up to 30.1 mph and it passes MP 61 + 1400 ft at 34.6 mph.Halve each of the Davis coefficients and leave everything else the same-- then we'll figure the engine passes MP 54.9 at 31 mph. Speed at MP 61 +1400 ft then comes out 46.2 mph.
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