In reading about the Santa Fe Chiefs a question came up in my mind that I have always wondered about. How did railroads decide how much horsepower or number of passenger locos were needed per train? Did they over power the assignment or were there common locos always assigned?
I know for a while the MKT always used the specially painted E7's on the Texas Special between St Louis and Waco TX, where a H3 Pacific took it to San Antonio. When more E8's arrived that changed.
Anybody have more info?
Thanks
SB
They sorta "knew". They sorta "guessed". I think.
Consider the Great Northern Empire Builder--the streamlined one.
It first had 12 cars pulled by two E7's. 4000 HP and 8 traction motors.
Someone "knew""guessed" kinda wrong, because the E's were replaced by three F's--4500 HP and 12 traction motors--a little more HP and 50% more motors.
GN kept that setup for a few years, likely happy with it.
Then they got a new Builder train to replace the other one. 15 cars, now. They stayed with the 3 F's. As I recall.
Then they replaced three coaches in the train with three dome coaches and a full dome lounge. And they weighed more. The full dome needed six-wheel trucks to carry its weight.
16 cars then. That sort of flipped a switch, and GN added another F. Getting up to four. 6 thousand HP and 16 motors.
Then, towards the end of the Builder, GN bought some SDP40's and SDP45's and generally ran two on a train. So that's 6000 HP or maybe 7200 HP, depending. And 12 motors. BUT, the train was shrinking a bit. Maybe. They added maybe a couple of coaches and took off the obs and some sleepers. So the train was shorter.
Anyway, that's a history of one railroad coping with power on one train. It's both typical and one-off, depending.
Ed
Guesstemating, that is what I am beginning to think. The Katy and the Mop tended to underpower the trains where the Santa Fe tended to over power. I have seen pictures of nothing but two PA's on the 13 to 15 car Texas Eagle and pixs of the 14 car Texas Special with no more than two E's. Meanwhile plenty of pics of the 9 to 14 car Texas Chief with three PA's or 4 F7's. An E8m was also common on the three to four car "Dallas Chief".
Add another diesel, why?????
http://www.kansasmemory.org/item/224556/page/1
"One difference between pessimists and optimists is that while pessimists are more often right, optimists have far more fun."
They figure it out......
Here is how.......
Assume a train that weighs 15,000 tons is stopped on a 1% grade. For every ton of train weight on a 1% grade a force of 20 pounds is acting to roll the train down the hill. A 15,000 ton train produces a force of 300,000 lbs. (15,000 tons x 20 lbs per ton = 300,000 lbs).
The level of force required to break the adhesion of your shoes to the ties and thus slide your shoes is dependent upon two things. 1. The coefficient of friction between your shoes and the ties. 2. The weight on your shoes. Increase either one of those parameters and your adhesion to the ties increases enabling you to pull harder before sliding.
For the purpose of this article we will say the factor of adhesion of a steel wheel on a steel rail is about 30%. (Actually it is more like 20%-25% but we will get to that later). A factor of adhesion of 30% means that a wheel will stick to the rail so that a pull equal to 30% of the weight on that wheel is required to break that adhesion and slide the wheel. Locomotives have a lot of weight on their wheels. A typical 4 axle GP40 might weigh 280,000 lbs. Four of them weigh 1,120,000 lbs. Thirty percent of 1.12 million pounds equals 336,000 lbs. In other words, it requires a force greater than 336,000 lbs to slide four GP40s. Therefore these locomotives, with their brakes set, will hold the train on the hill since the weight of that train on the grade is only producing 300,000 lbs of pull.
Tractive Effort is the amount of Pull. You can have pull with no HP. Notice that in the example above we are applying a force, a pull, a Tractive Effort, of 300,000 lbs to that coupler of the first car but we don't need any diesel engines. All we need is at least 1 million pounds of weight on the wheels and a factor of adhesion of 30%. We have Tractive Effort (TE) without any Horsepower (HP).
If I don't need any HP why did I use 4 locomotives. Why not just use one very heavy loco? Because the maximum weight on any single wheel that steel rails can withstand is 35,000 lbs. If we put more weight than that on any wheel it will crush the rail head and create excessive wear or outright failure of the rail. The two wheels on opposite ends of one axle can each carry 35,000 lbs of weight. So the maximum weight on an axle assembly is 70,000 lbs. Since we need a total locomotive weight of at least 1 million pounds that means we need a minimum of 14.3 axles. Three 4 axle locos would only be 12 axles so we must use four which gives us 16 axles.
From this discussion we can see that total locomotive weight determines the maximum amount of tractive effort a locomotive can produce. The number of wheels or the number of traction motors has nothing to do with it. We only add additional wheels to spread the required weight out along the rails to avoid damaging the track. I said that 3 GP40s will not work in this case because they only have 12 axles and each can be weighted no more than 70,000 lbs for total locoweight of 840,000 lbs. At 30% adhesion that only produces 252,000 lbs of TE and we need at least 300,000 lbs. If we take those same 3 GP40s and add two more axles to each unit but DO NOT increase the weight of each unit, then we still only have 840,000 lbs of total weight and 30% of that is still only 252,000 lbs. Adding axles and wheels to locomotives does not increase tractive effort.
HP is the Tractive Effort (pull) times the Speed. Burn that statement into your brain. It is crucial to understanding this essay. While our coal train is just sitting on the grade, held there by the locomotives, there is 300,000 lbs of "pull" on the first car's drawbar. Because the train is not moving there is no HP required. But try to move it at 1 mph up that hill and HP is required. The required HP is the TE needed for the grade (300,000 lbs) times the speed (1 mph or 1.47 ft per second) divided by the definition of a HP (550 lb-ft per second).
The HP required is 801 HP! Yes just 800 hp will move this coal train up the hill. Amazing isn't it? But will one 800 HP 4 or 6 axle unit do it? No! Because that one 800 hp unit must have at least 1 million pounds on its drivers to prevent it from sliding back down the hill. You must have the weight to get the adhesion required. That means each wheel of an 800 hp 6 axle unit would have to have 84,000 lbs on it. (That is 168,000 lbs. per axle). Oh my the crushed and broken rails that would leave behind! Not to mention the overloading of bridges and the track structure itself. As I said above, the minimum number of axles we need to spread out the required weight is 14.3 axles. It doesn't matter whether we have four 200 Hp 4 axle units, or whether we have one 800 Hp 4 axle unit and three 4 axle engineless slugs . It is all the same to the coal train.
One mph is kind of slow. It would take us 24 hours just to get up Parkman hill. We want to go up the hill about 15 mph. 15 mph is a good compromise between taking forever and extreme high power costs. To go up this hill at 15 mph (22 ft per second) requires:
Gee now that sounds familiar doesn't it. That is exactly the Hp of four 3,000 Hp units! So we can use four 3000 Hp GP40s. SD70MACs have 6 axles and weigh 420,000 lbs. Again 70,000 lbs per axle. So three of them give us 18 axles and 1.26 million pounds on the wheels, more than enough to produce our required 300,000 lbs of traction. SD70MACs are rated at 4000 Hp so three of them are 12,000 Hp. Four GP40s or three SD70s, either way you satisfy both the adhesion needed and the HP needed.
Horsepower Alone. Will two 6000 HP units work? No. While you have the required 12,000 hp you can only have 70,000 lbs weight per axle, which times the 12 axles is only 840,000 lbs total. With 30% adhesion and only 840,000 lbs of weight the two 6000 HP units have only 252,000 lbs of adhesion. Not enough to hold or move the coal train. The weight of the train on the grade will slide these two locomotives backwards down the hill. Remember you need at least 300,000 lbs of adhesion (traction).
High HP locomotives on 6 axles create other problems such as traction motor (TM) overheating. Can we pour 1,000 hp into each TM continuously at 10-15 mph without frying them? Low gearing helps. But low gearing lowers the top speed because the TMs will fly apart at high rpms. Here is where AC locos have an advantage over their DC counterparts. AC TM rotors are much more solid than DC TM armatures so they can be geared lower and still have a high top end.
Varying Adhesion. All of the above figures are based on a 30% adhesion factor. IE, the wheels grip the rail with a force equal to 30% of the loco weight. Locomotives of the GP40/SD40 era and their Dash 2 offspring are generally considered to have an adhesion factor of about 25% not 30%. Sand will increase this factor to about 30%. Thus to achieve the 30% adhesion needed for the examples used in this essay so far, these locos may need to be on sanded rail.
Modern locos such as SD70MACs and C44s claim adhesion factors of 36 to 43%! They do this by using sophisticated anti-wheelslip circuits. These circuits allow the wheels to spin slightly faster than the rail speed warrants. It is called creep. Strangely enough, a creeping wheel has a higher factor of adhesion than a stationary or rolling wheel. Thus in theory two 6,000 HP SD90s weighing 420,000 lbs each and achieving an adhesion factor of 36% will produce a TE of 302,400 lbs and should pull the train up the hill at 15 mph.
However, in my experience you cannot count on that 36% adhesion factor in all types of weather and rail conditions. On wet or frosty rail these units slip and you stall. And when you stall you had better set the train airbrakes in a hurry or the train will slide these units back down the hill. On the other hand I have had C44s, SD90s and SD70MACs absolutely astound me with what they are pulling. At times they attain greater than 40% adhesion on dry, sanded, rail. It is that "at times" that concerns me. You cannot count on them to do that reliably time after time.
An Actual Experience with High HP Locos and Adhesion. One night I was running a freight up hill at 7 mph with a Dash 9-44CW on the point. I had previously calculated that we should have gone up the hill at 11 mph, so why were we only doing 7 mph? The rail was slightly frosty. I punched up the loco monitor screen on the computer. It showed that this supposedly 4400 Hp unit was only putting out 2930 HP!!! It had derated to prevent slipping in spite of the sanders being on. So the adhesion factor of this loco at that time was not the touted 36-43% but instead only 22%. The railroad had paid for a 4400 HP locomotive with 36% adhesion but was only getting a 2930 HP locomotive with 22% adhesion. The common SD40-2 would have done as good or better in this situation than the hi-tech wonder. This was not a one time occurrance. I have seen similar performances on many occasions.
Horsepower is Speed. Up to now we have assumed that a locomotive has enough power to slip its wheels. That is true only at low speeds. Note that Hp is TE times speed. If the speed remains the same and the TE (pull) increases then the Hp requirement increases. If the TE remains the same and the speed increases then the Hp requirement increases. If you have a fixed maximum Hp, such as a loco has, then as speed increases the TE must come down. The product of the two must remain a constant and is directly related to the HP rating of the loco. On the 12,000 Hp coal train above why can't we go faster than 15 mph on the 1% grade? Because 15 mph times the required 300,000 lb of drawbar pull divided by 550 lb-ft per second (the definition of a HP) equals the total locomotive Hp. If the train went faster the product of the speed times the pull would be higher and thus the required Hp would be higher. But we are limited to 12,000 hp on this consist so it trudges along at 15 mph. Similarly if we throttle down a notch or two, reducing the HP, then the speed is going to drop because there is now less than 12,000 HP available. The drawbar pull account of the grade remains the same at 300,000 lbs and the lower HP means a lower pull x speed figure so the speed must drop until the product is proportional to the new lower HP. This why I like to say Hp is speed.
Steeper Grades. We are proceeding at 15 mph up the 1% grade with our 15,000 ton train powered by four 4 axle GP40s. What happens when we encounter a steeper grade with this train? The drawbar pull needed to hold or move a train on a grade is 20 lbs per ton per grade percent. That is where the 300,000 lb figure came from for the 1% grade of the example above. If this train were to roll onto a 1.5% grade what happens? The drawbar pull needed now is 450,000 lbs.
We still have only 12,000 hp available. Since HP equals pull times speed, if the pull goes up then the speed must come down. The train speed will drop to 10 mph, the point where the product of the new 450,000 pounds pull and the speed divided by 550 (HP definition) equals the available HP. But we are in real serious trouble here folks. Our four 4 axle locos can only deliver 336,000 lbs of pull because of their 1.12 million lbs of weight on drivers and the 30% adhesion factor. So our locos are going to slip and stall on the hill. Although we have enough Hp to pull this train up the 1.5% grade at 10 mph we do not have enough traction to do so. And, again, you had better set the train air brakes as you stall or the train will drag you back down the hill.
Slugs, and SDs. So how do we proceed? Well we can't increase the weight on drivers by adding weight to our existing four 4 axle locos because they are already weighted to the max for the rail. The only other way to increase traction, weight on drivers, is to increase the number of drivers. Add more units. We will need to add two more units (8 more axles) to get the weight up to at least 1.5 million lbs so the 30% adhesion factor gives us 450,000 lbs of adhesion. We do not need the added HP of those two units however, they could be just engineless slugs. Without additional Hp the train will go up the hill at 10 mph. At this point I would like to point out that if we simply add two 4 axle slugs, which get the power for their traction motors through electrical cables from the original 4 locos, that we can do the same thing by switching from GP models to SD models. From 4 axle units to 6 axle units. An SD40 is simply a GP40 with two more axles (with traction motors) and 50% more weight. In other words we've added "half a slug" to each of the 4 units. In this manner we once again have the required weight on drivers by using just four SD40s. These are the same weight and number of drivers as 4 four axle units plus two 4 axle slugs. If we want to go up the hill at 15 mph instead of 10 mph however, we must add the Hp. Slugs or converting to SDs will not do. If the additional units added are 3000 hp like the rest then we will again go up the hill at 15 mph. Hp is speed.
Helpers. In either case we will not go up the hill very far, probably not at all! Why not? The figures say we will. The one word is Kapow! You are going to break in two. We are now trying to put 450,000 lbs of pull into a coupler rated at 390,000 lbs, it is going to break. So what can we do? Well we could double the hill. Take half the train up to the top and leave it there then come back with the engines and get the second half. When you get both halves to the top, recouple them, make an air test, and proceed. By taking half the train up the hill at a time the required coupler pull is only half that of the entire train or only 225,000 lbs. Well under the 390,000 lb strength of our couplers. This method also requires no more slugs, SDs, or other units. The original 4 GP40s have enough traction to haul half the train up at a time. Unfortunately doubling the hill requires a lot of time. The line is blocked while it is being done and this train and others are delayed for the duration.
Alternatively we could put the added two units on the rear of the train to PUSH. We would need another engineer (a helper engineer) or a distributed power set-up (radio controlled slaves). The physics are the same, the coal train and grade could care less where you apply the power just so you have the right amount to move it. But the couplers do care where you put all that power. If you try to put it all thru one coupler, the first one, it is going to say "Screw you, I ain't gonna take this abuse" and it will break to prove its point. (You never knew couplers were so animated did you.)
Heavy Haul vs High Speed. You may have noticed that most railroads tend to use 6 axle power on heavy trains such as coal and grain while they use 4 axle power on their high speed lighter weight intermodal trains. 1. If a particular railroad has a good mix of high speed and heavy haul trains its locomotive roster will be a mixed bag of 4 axle and 6 axle power. 2. If a railroad, such as BN, has a preponderance of coal and grain trains and/or operates its trains in mountainous territory where grades are steep and speeds are low its roster will be dominated by heavy 6 axle power. 3. If a railroad, such as ATSF, has a majority of lighter weight high speed intermodal trains and a lot of relatively flat territory its roster will reflect that with lots of high Hp 4 axle power and/or lighter weight 6 axle power.
Lets look at the difference between 6 axle SD40s and 4 axle GP40s. Suppose we want to run a 5200 ton priority manifest train up a 1% grade at 30 mph. This requires 8320 HP. TE is not a consideration because even three 280,000 lb GP40s will have 252,000 lbs of adhesion. Our train only requires 104,000 lbs of adhesion on this grade. Three GP40s weigh a total of 840,000 lbs or 420 tons. These locos require 672 Hp just to move themselves up the grade at 30 mph. So our 5200 tons of train requires 8320 Hp and the 420 tons of locos require 672 Hp to go up this grade at 30 mph, total 8,992 Hp. The three GP40s produce 9,000 Hp. What happens if we use three SD40s instead of GP40s. Same Hp at 3000 each but the SDs weigh much more. Ours are ballasted for lots of TE needed on coal & grain trains. Our SD40s weigh 420,000 lbs each. Three of them weigh 630 tons! To move these SDs up the grade at 30 mph requires 1008 HP. This means we only have 7992 HP left for the train. That means we can only haul 4995 tons at 30 mph instead of the original 5200 that the GP40s hauled. While this may not seem like much difference it is over 4% and a 4% efficiency improvement is a big deal when you are burning 1.6 billion gallons of fuel per year. Trains that run at high speeds don't need heavy locos with lots of Tractive Effort. What they need are light weight high horsepower locos.
Here is a table showing the theoretical Tractive Effort a 3000 Hp loco produces at various speeds.
A loco that cannot use full throttle below 30 mph without slipping would be rather restricted in its service. So railroads tend to compromise. If instead of 280,000 lb locos or 125,000 lb locos we use a loco weighing 250,000 lbs we still get some of the fuel savings and the loco becomes much more versatile since it can now operate as low as 15 mph in full throttle without slipping.
It is in high speed freight service where locos with high Hp to weight ratios shine. This why the ATSF had 3800 Hp 4 axle GP60s and 4,000 Hp 4 axle B40-8s. Since BN had a preponderance of heavy coal & grain trains and even its freights had to contend with steep grades it had 3,800 Hp heavy SD60s and 4,000 Hp heavy SD70MACs instead of the GP60s and B-40-8s that the ATSF had.
Lets look at this Hp to loco weight ratio from another angle. The following chart shows the maximum Tractive Effort of various loco models and the speed at which that maximum TE is achieved. All units are 3,000 Hp and we assume a 30 % adhesion factor.
Those Superpower units. If you haven't been paying attention you might think that the new 6000 HP single unit locos are destined for heavy haul service. True they are all heavy 6 axle units. But that is because the weight is needed to put that 6,000 HP to the rail without slipping. A 6,000 Hp unit that weighs 420,000 lbs and can attain a 43% adhesion factor has an adhesion of 180,600 lbs. The 6,000 Hp diesel engine can deliver that 180,600 lbs of Tractive Effort at a speed of 13 mph. Below that speed you cannot use full throttle on these locos because they will slip. That was for an astounding adhesion factor of 43%. What if they cannot maintain that extreme level of adhesion? What if they "only" get 36%? 36% of 420,000 lbs is 151,200 lbs of TE. The 6000 hp diesel can deliver that TE at 15 mph so the loco cannot operate below 15 mph in full throttle without slipping. At an adhesion factor of 30% the lowest full throttle speed is 18 mph. If the rail is wet or frosty can these modern marvels maintain even a 30% adhesion factor? My experience with 4400 Hp units is a definite no. The C44s often have trouble maintaining 22% adhesion with bad rail conditions. If a 6,000 Hp unit gets down to 22% adhesion it can only operate at full throttle above 24 mph! Thus if you want these behemoths to reliably move your trains over the hills in all kinds of weather you had better dispatch them with trains light enough that they can maintain 24 mph or greater on your steepest hills. That means they are only useful for trains such as intermodals which get a high Hp to tonnage ratio. When it is frosty they won't work on heavy freights or coal or grain trains which routinely pull up the hills at 10-12mph.
The railroad I work for uses 12,000 Hp on their coal trains through here and we go up the hills at about 12-13 mph. Note that you can replace the 12,000 Hp of 3 SD70MACs, or the 12,000 Hp of 4 SD40-2s, with the 12,000 Hp of just two SD90s. You have the same Hp so you should go up the hills at the same 12-13 mph. But it will be awfully iffy. That is because the minimum speed these 6,000 Hp units can operate at full throttle is 13 mph even with an adhesion factor of 43%. If anything causes the train speed to fall below 13 mph even momentarily, you will never regain the lost speed. The train might be temporarily slowed for various reasons. Perhaps the SD90s temporarily lost that 43% adhesion factor and slipped or reduced Hp to prevent slipping. Perhaps a wind came up and increased train restance. At 12 mph the 6,000 Hp locos cannot operate in full throttle even if they regain that 43% factor of adhesion. They will slip. Operating at reduced throttle the locos are not producing the 12,000 Hp this train needs to travel up the hill at 13 mph. So the train will never accelerate back up to 13 mph where it could again operate at full throttle. Four SD40s or 3 SD70MACs would have no difficulty re-accellerating the train back up to 13 mph. That is because they are not operating at the limit of their adhesion as the SD90s are. The 4 SD40s have 12,000 Hp just like the two SD90s but the SD40s have a total weight of 1,680,000 lbs and even at a 30% factor of adhesion can operate in full throttle down to 9mph! The 3 SD70MACs weigh 1,260,000 lbs and with only a 30% factor adhesion they can operate at full throttle down to 11.9 mph. If they achieve a 36% factor of adhesion they can operate at full throttle down to 9.9 mph. So either the SD40s or the SD70s have enough reserve adhesion they can operate at full throttle after being temporarily slowed. That allows them to accellerate the train back up to the 13 mph.
Thus on an equal total Hp basis these high Hp units are not equal to their lower Hp cousins when used in heavy haul service. And heaven help you (more like helpers help you) if the factor of adhesion on these brutes ever falls below 36% because you won't have enough adhesion to pull that 15,000 ton train up that 1% grade, period. You had better hope that it does not rain, frost, or snow.
Keep the high Hp units in high speed freight service where they do the most good. You are trading 8 axles of weight on two 3000 HP GP40s or 12 axles of weight on two SD40s for the 6 axles of the new units and you have 25-50% less Hp-wasting weight with the two high Hp units. Remember that TE decreases as speed increases, so as long as they keep the Hp per ton ratio of the trains high enough to maintain high speeds then the TE will be low enough that these high Hp single units won't slip. But try to use them in low speed drag service and they will slip as noted in the coal train discussion above. The slower the train goes up a hill the closer these high powered 6,000 Hp wonders perform like the good old 3,000 Hp SD40.
The calculated Hp required is 9563 Hp. Since our locos are only about 80% efficient this means we need a Hp rating of 12,000 to actually deliver the required 9563 Hp.
Put the train on a 2000 ft long 3 degree curve and you get:
Using a loco efficiency of 80% the required 9985 Hp becomes 12,481 Hp. The 12,000 Hp of four SD40s is not going to be able to pull this train up the hill and around the curve at 10 mph. The speed will drop until the rolling resistance and grade Hp drops enough that the actual Hp required equals 80% of 12,000 Hp (9600 Hp). That speed is 9.6 mph.
At 9.6 mph we get the following values:
Lets say we want to accelerate a 15,000 ton train at a rate of 1 mph per minute. In other words we want to be going 1 mph faster at the end of one minute than we are going now. To accellerate at that rate requires a steady force of 23,450 lbs. Note that it doesn't matter whether we are going up hill or on the level. We need to supply an additional 23,450 LBs of drawbar pull to accellerate at 1 mph per minute. Horsepower is pull times speed. Since the force to accellerate this train at 1mph/min is a constant, the HP required to accelerate the train varies according to speed. At 10 mph the HP needed is 625 Hp, at 40 mph the Hp needed is 2500 Hp.
An accelleration of 1 mph/minute is slow. It would take a train 60 minutes to go from 0 to 60 mph. But if we want to accelerate at 10 mph per minute it requires 10 times the force and 10 times the Hp at each speed. At an accelleration rate of 10 mph per minute the drawbar force needed is 234,520 lbs. At 10 mph that requires 6,250 Hp. At 20 mph it requires 12,500 Hp. At 40 mph it requires a whopping 25,000 Hp. Note that if we have only 12,000 Hp then we run out of Hp before we reach 20 mph. We can no longer accelerate at 10 mph per minute and will fall back to lower and lower acceleration rate as speed increases.
Keep in mind that these values of drawbar pull and Hp are ONLY for acceleration. You still need to supply the normal pull and Hp for any grade and rolling resistance. Lets look at that. A 15,000 ton train on a 1% grade going 8 mph requires 357,104 lbs of pull and 7617 Hp. If we have 4 SD40-2s we have 12,000 Hp times 80% efficiency = 9600 Hp available. 7620 Hp is what you get in throttle 7. We have one more throttle notch and 1980 Hp (9600-7620) remaining that we can use for acceleration. At the stated 8 mph that equates to 97,345 lbs of additional drawbar pull available. This additional force will accelerate the train at a rate of almost 4 mph per minute. Yeehaw! Put 'em in number 8 throttle and we'll be doing 12 mph at the end of the next minute.
Well not quite. A few problems crop up with that assumption. One is that as the train speed increases so does the horsepower required for both the grade and the rolling resistance. So as the speed begins to increase we have less "left over HP" for acceleration. The rate of acceleration will drop, we cannot maintain that 4 mph / minute rate we started with. In fact when we reach 10 mph all of the loco's HP is being used to pull the train and none is left over for acceleration. The speed will level out at 10 mph and stay there. Ain't physics neat?
The second problem is that you just broke the train in two so you are actually stopped. Why? Because the train traveling at 8 mph required 357,104 lbs of drawbar pull to maintain that speed on this grade. When you opened the throttle from notch 7 to notch 8 to accelerate you just put the additional 92,602 lbs of available loco tractive effort into that same drawbar. 357,104 lbs + 92,602 lbs equals a total of 449,706 lbs. Since drawbars are only good for about 390,000 lbs you just pulled one in two. Moral: When you are moving slowly you'd better handle that throttle gently if you want the train to remain in one piece. Acceleration can break trains in two.
Now for the purists, those 4 SD40-2s are not going to develope that 454,449 lbs of TE. That would mean an adhesion factor of 27% and SD40-2s can rarely if ever achieve that. They would most likely slip. But they can develope the 390,00 lb rating of the drawbars either continuously or by slipping and jerking. So either way the train is going to be in two pieces.
Note that the above train theoretically can go up this hill at 10 mph based upon Hp, efficiency, grade, and drawbar strength. Whether it actually can or not is in doubt. If we rolled onto this hill at a speed higher than 10 mph then all would be OK. As the train rolled onto the grade in number 8 throttle it would simply slow down to 10 mph and proceed up the hill. The drawbar force would be that 357,104 lb figure. Well within the rating of the drawbars. But if the train had stopped on this grade or had started from a stop on a lesser grade and was not yet up to 10 mph then we may be in trouble. Under these circumstance we may find ourselves in the situation above where we are only going 8 mph when the entire train is on the hill. We cannot go from notch 7 to notch 8 because the drawbar force will exceed their rating. Thus we cannot get to 10 mph. The only recourse is to slug it out all the way up the hill in the lower throttle position and a lower speed. It is very annoying to know you have the HP to go faster but you can't use it. If you are a real good engineer and really know what you are doing you can get around this obsticle in some cases. How? By applying some independent brakes to the locomotives drivers. Those brakes will absorb some of the extra Hp you get when you go from #7 to #8. Therefore that amount of the extra Hp and its attendent TE never reaches the train's drawbars. In that manner you can keep the total drawbar force lower than the drawbar rating. As the speed increases you feather off more and more of the independent brake until finally you are at the 10 mph physical limit and the brake is fully released. But make one mistake during that process, fail to coordinate the independent brake just right with the increasing Hp as the locos rev up and increase their load....or feather it off too quickly.......and Kapow! You are in two pieces. You have let enough extra TE reach the drawbars that their rating was exceded. Going 10 mph in #8 vs 8 mph in #7 saves you 15 minutes on the hour. But if you break it in two attempting to reach 10 mph then you are delayed 2 hours while you chain up a car and set it out and double the hill. If you are not sure of your expertise maybe it is better to just go up the hill at 8 mph in number 7 instead of trying for 10 mph in number 8.
The main point of all this is to hopefully dispell the myth that high HP means lots of pull. It does not. Higher HP means higher pull at higher speeds but the total maximum pull is strictly related to weight on drivers. No HP required. None! Therefore a switch engine which only operates at low speeds does not need, nor can it use, high HP. It needs to be heavy. (but not too heavy that it breaks or turns over light industrial or yard rails). Life is a compromise.
Whew!
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Created 06-06-2001 Updated 09-25-2002
This is really frustrating! Three times I have come close to the conclusion of a fairly lengthy explanation of the practices of the major Eastern trunk lines, and all three times the text has vanished without a trace before I could send it. I will try again, but will send a partial text so that it doesn't get lost, then add to it with edits. I'll start with B&O.
B&O was the first Eastern trunk line to dieselize their through passenger service. They started by assigning AB sets of EA units to the Capitol Limited and National Limited, but soon bought additional AB sets of E6's with a somewhat higher horsepower rating of 4000 horsepower. These were followed by AA sets of E7's with a comparable rating of 4000 horsepower. By about 1950, the premiere Washington to Chicago trains operated behind E6 AB combos, and the premiere Washington to St. Louis trains operated behind E7AA combos. The EA's generally operated on Royal Blue trains between Washington and Jersey City. The road bought some passenger F3's in AB sets, but found that their 3000 horsepower rating wasn't enough, so they usually ran them as 4500 horsepower ABA or ABB sets, or with an E unit for some extra oomph. Originally, the F3's were usually assigned to the Capitol Limited to Chicago or the Ambassador to Detroit. All of these trains invariably did all right east of Cumberland and west of Grafton or Sand Patch, but they always needed helpers in the mountains. Assignments were often adjusted, so the scenarios above are general rules and not to be taken as hard and fast rules. When the E8A's started to arrive, they filled in as necessary, making assignments less predictable. In general, passenger sets for most B&O through trains in this era were about 4000-4500 horsepower.
Tom
Wow, .... just wow...
Wow, I guess, so this was even supposed to be a longer post?
Mike.
My You Tube
Atlantic Central, that is exactly what I have been looking for. Thanks, I now have some idea as to why the Texas roads assigned power like they did. It also seems that the age of the loco my have affected asssignments in later years. The Katy in the last years of passenger service tended to use three or more F's or combinations of E's and F's. Probably in case of breakdowns. I also have pix of the Texas Chief in the late sixties with 5 or more F's pulling fewer cars.
Yes, there's more. The Pennsylvania Railroad wanted to avoid the helper problem that the B&O experienced, so they specified 6000 horsepower sets in ABA combos. These were E7's, PA's, Baldwin BP20's, and FM Erie Builts. The high horsepower Centipedes were used in comparable two unit sets, but were soon removed from passenger service. Most of these trains were about 12 to sixteen cars long (roughly comparable to the B&O's). Eventually, the road decided that this wasn't working too well. The third unit was irrelevant east of Altoona and west of Pittsburgh; and it often wasn't enough to avoid the use of a helper in the mountains anyway. So around the middle of 1948, most of the three unit sets were broken up into 4000 horsepower AA and AB sets, and helpers were routinely used in the mountains. A few 4500 horsepower FP7A-F7B-FP7A sets were purchased for dual service utility work, but all other subsequent purchases of passenger cab units were E7A's and E8A's, usually operated in two unit sets. Later, some trains became longer due to their consolidation with other trains, and the aging units became less reliable, so more than two units were often seen in the latter years on the PRR and B&O.
NYC and Erie operated through the same general region, but neither of them had mainline grades to compare with those of the B&O and PRR.
Erie's needs were the most modest. They started passenger dieselization with 4500 horsepower F3 ABA sets, but soon reassigned those units to freight and replaced them with back to back E8A sets in two unit 4500 horsepower sets, supplemented by PA's of roughly equivalent horsepower.
New York Central operated over territory roughly similatr to Erie's, but their passenger operation was much more extensive and many of the trains were longer. For the most part, they dieselized with E7's, PA's and Erie Builts in ABA combos, but soon settled on A units only for passenger service. Some trains continued to use three units, but many were handled adequately by two unit sets.
Bottom line: Two units totalling about 4000-4500 horsepower were adequate for most trains on moderately level ground, if the engines were in good shape and the consist not unusually large. Extremely high speeds, unusually long trains (City of Everywhere, for example), or steep grades, might take a toll on the engines, so extra units might be needed. And once the units got a little long in the tooth, an extra engine might be added for insurance against road failures.
My SP Employee Timetable includes a page with the weight of each type of passenger car, so using Mr. Krug's, or similar, equations; the engine assignments could be made. I would imagine most ETs had similar information.
I imagine for most routine runs, they knew from experience what engines would be needed, but the table would come in handy for special movements or unusual consists.
The locomotive engineer would also calculate his train weight so he'd know what to expect over the route.
Ray
blabride Atlantic Central, that is exactly what I have been looking for. Thanks, I now have some idea as to why the Texas roads assigned power like they did. It also seems that the age of the loco my have affected asssignments in later years. The Katy in the last years of passenger service tended to use three or more F's or combinations of E's and F's. Probably in case of breakdowns. I also have pix of the Texas Chief in the late sixties with 5 or more F's pulling fewer cars. SB
The controlling factors are:
Weight of train
Ruling grade/curve resistance
Desired average and top speeds
Passenger trains need lots of HP relative to weight to accelerate reasonably fast and to maintain speed on grades. As speed goes up, tractive effort goes down, when the tractive effort dips below that required for the train weight....the train slows down.....or needs a helper on a grade.
Railroad personnel assigning power power have learned the requirements of their section of the railroad. Given a train weight and desired speed, they have a good idea of the needed power, freight or passenger.
Some of it learned through the math I posted above, some learned by experiance.....
Sheldon
Thanks for posting that Al Krug dissertation on tractive effort versus horsepower, Sheldon. I hadn't noticed the accreditation at first, but recognised its source immediately when I began to read.
I had saved it, and one on braking, too, but lost both when my old computer died late last year.
Wayne
Another consideration was how rural or populated the area way. The Santa Fe liked to over-power their passenger trains so that a loss of a single engine wouldn't strand the train in the middle of the desert somewhere.
Compare that to 2018 Amtrak, who uses single engine trains, but runs them through populated areas where they can get another engine in under an hour if something happens.
You are most welcome Wayne.
A few more thoughts.
Tom has posted some great insights into the operations of several roads, particulary here in the east.
I model the B&O, and pull my B&O premier trains with a pair E units......and models of those passenger F3's Tom spoke of. And while typically used as Tom described in ABB or ABA sets, I do have several pictures of them ABBA.
And my freelanced ATLANTIC CENTRAL has E units, PA's and FP7's.
It should be noted, that several western roads ended up prefering F units on passenger trains, ATSF, NP and GN were all very commited to F unit passenger power - they pulled long trains through very demanding routes.
7500 or 9000 HP worth of F units on an ATSF passenger train was pretty common.
Time to go,
Calculating how much horsepower was needed to pull X amount of weight was well established by the time diesels came along. However, there were other factors than brute force.
Great Northern bought E-7 diesels for the Empire Builder in 1945, apparently largely because subsidiary CB&Q had been using E units successfully for some time. However, the Burlington's lines were pretty flat. The GN's E-units worked fine on the relative flatlands of Minnesota, North Dakota, and eastern Montana, but had problems in the mountains with motors overheating due to the engine's A-1-A trucks (i.e. a nonpowered center axle). They fairly quickly switched to F-units, which worked much better.
Northern Pacific learned from GN, and bought A-B-B sets of F-units when it streamlined the North Coast Limited. However, they soon switched to A-B-A sets to make it easier to back onto a train on a curve in St.Paul (and I believe Seattle) since the set could be run from either end.
NP found that in the mountains they needed more power, so generally added another A-unit in their mountainous areas.
The problem NP and the Canadian railroads faced was that even if they had enough power to pull the train, they often were running short of steam from the engine's steam generators, which was used to heat the cars in cold weather. A big part of the reason NP bought FP-7s was that these engines had more capacity than a regular F-7A for water and a steam generator. (Even so, NP also equipped some baggage cars with extra water tanks that could be connected to the engines.)
The need to heat cars still is a limiting factor today with Amtrak and HEP. I believe Amtrak figures a ratio of something like 6 cars per engine is needed during winter to heat and power the passenger cars, so for example the Empire Builder during winter often uses 3 engines even though it's pulling fewer cars than two engines pull during the summer.
I saw in a video I was watching four Alcos (2 PAs, 2 PBs) pulling a SP Daylight at the heyday of the service... then later same era I saw three Alcos (2 PAs, 1 PB) on another Daylight... the first was on flat lands as it appeared, the second was either on the Donner or Siskiyou line...
Steve
If everything seems under control, you're not going fast enough!
Stix,
I went back and looked at my Texas Chief pics and most that had 4 or 5 F's were shot in colder weather. Those in the Summer had fewer so maybe the boiler issue for steam heat was the reason. I need to research what A/C system they used.
That might make for some interesting operation. Passenger loco assignment would depend on the time of year.
This is all great information!
Many roads in the day ran on timetable with extras. They had to get X amount of trailing tonnage, plus motive tonnage, over distance in a specified time-frame. Originally, the term 'ruling grade' meant that a timetabled typical consist, with typical head-end power, had to be able to maintain the requisite speed over the ruling grade unassisted in order to adhere to schedule to the extent possible under changing road conditions. A ruling grade was not necessarily the steepest or longest grade in a district, but it might have been. If help was a must, then the district became a helper district, and this was the practice in the Selkirks and Monashees in the Canadian Rockies, and in the east, as an example, on the Blue Ridge. Head end power was exchanged to heftier pullers, such as the CPR 5000 "Selkirk" 2-10-4s, or pushers were added/cut off on the fly by roads such as the Norfolk and Western, in latter years with their superb Y6 series Mallets.
You can be absolutely certain that investors would have insisted, vociferously, that the roads in which they cast their money would be scrupulous calculators of all operations that helped the company generate revenue for them. Included would be delivery of needed parts and materials to sustain operations, hiring, training, and deployment of personnel, and also the proper assignment of available power to keep revenue freight and passengers moving smoothly on the track system. In the latter case, assignment of just enough power to do the job meant that the enginemen and trainmasters knew what it would take to do the job for each manifest on the path it would take to the next destination or district. This was only possible using empirical data and engineering principles. IOW, they had the facts, and they used them on penalty. Nobody who liked their jobs could afford to 'guess'.
In bad weather extra locomotives were added because locomotives lose more traction on wet rails. Also snow drifts can cause friction when cars have to be pulled through them. I have an old Charles Smiley video that has footage of passenger trains going over Donner Pass that specifically says that extra helpers were added that day because of the drag caused by the cars rubbing up against the snow banks and you can clearly see the cars were rubbing the sides of the snow banks caused by using rotary snow plows which cut a channel through the snow instead of pushing it out of the way. Since then the Southern Pacific (now Union Pacific) modified their rotary plows to cut a wider path through the snow to reduce the problem and tries to only use rotary plows when the snow is too high for Jordan spreaders to deal with.