One thing that's seldom mentioned when considering the T.E. equation is that you get the maximum tractive effort when the cylinders are bored out almost to the condemning limit (3/4-inch oversize for a PM Berkshire) and the driver tires are likewise almost at the tread worn too thin limit (4 inches under nominal for that same PM Berkshire). This can add a surprising amount to T.E., but also makes the engine more slippery.
@@Hybris51129 The trouble with a worn-out engine is that K = 0.85 is probably lower on account of the mean effective pressure in the cylinders through one stroke being lower on account of deferred maintainance.
One of the sounds I shall never forget is a drawbar breaking. Another is a trio of 10,000 amp fuses blowing from a bolted dead short. One was a huge very loud ka-blam, and the other was little plinking sounds. Both were really expensive.
Layman´s terms: 1) Tractive effort: the maximum weight of your car that your engine can power without choking and dying 2) Adhesion: are you able to use that power without spinning the wheels? 3) Drivers´ size: final gear -> big = more revolutions, needs more torque 4) Piston stroke, surface, pressure: torque Lesson: 1) If you want to tow a cargo ship, your super ultra tuned, high tractive effort semi truck may not be enough if it has only one powered axle (and low weight), as it would overcome the adhesion limit of its tires and produce only wheelspin. 2) Converting your cheap little grocery-getter car into all wheel drive won´t increase its tractive effort. In fact it may decrease it a little bit (due to increased inner friction). But it may help on a slippery surface. 3) Higher gear (bigger wheels) is only good if you have enough tractive effort and adhesion, and just want to go faster.
@@kornaros96 Ferry is surely nothing like a cargo ship. Anyway, if the car has enough torque and adhesion to overcome the resistance of the water, then why not?
I instantly recalled the Drivers video you did some months back on the 4th myth, and recalled you saying "Generally, medium to large wheels were used for passenger service, and smaller to medium were generally used for freight service, but this isn't always the case." Nice to see a bit more train mythbusting
Since you mentioned diesel, I thought I'd do my own nerding out, lol. In diesel locomotives, (I'll only mention those with DC traction because I'm not remotely qualified to talk about the minutia of AC traction) your tractive effort is related to your traction motor amperage. (I think you actually mentioned the approximation EMD uses in your other video. The equation that uses horsepower, a constant, and divides that by the speed) As such, you get the most tractive effort with the motors at (or near) stall. The nerdy part and nuance comes into play when you consider low speeds and how the excitation system works. Starting simple, diesels have a spec called "minimum speed for full horsepower" (which depends on the gear ratio selected by the railroad) Above that speed, the approximation of tractive effort based off horsepower works pretty well, but below that speed the actual tractive effort will be less than the equation says. This is where the complexity (and my nerding out) begins. So as the motors slow down, they draw more and more current, which means we get more torque out of the motors. But, it also means that the motors and main have to pass more current, which causes things to heat up. As such, the excitation system is designed to limit the current from the main to help avoid overheating issues. Above the "minimum speed for full horsepower," the load regulator and excitation system will work to keep the engine running at full horsepower (or a constant horsepower based on what throttle notch you're in). However, below that line the excitation system is designed to "override" (sort of) the load regulator to (try to) keep the current in the main at a relatively safe level. The excitation system does a similar thing at high speeds, except it's limiting voltage instead of amperage. So, (ignoring transition) if you were to watch the load regulator on a locomotive in 8th notch at a high speed as it pulled up a hill to a stall, you see the load regulator start out at "full field" because the excitation system is limiting the voltage from the main and the engine isn't producing full horsepower. Then, as things started to slow down, the excitation system would allow for more horsepower and eventually the engine would reach full horsepower, at which point the load regulator would start to back off a bit to keep the engine at full horsepower. As you continued to slow down, eventually the load regulator would start to move back to "full field" position as the excitation system starts limiting current from the main. Once you reach the "minimum speed for full horsepower" the load regulator would hit "full field" and then the excitation system then gets control and starts limiting the current from the main. At this point, you'd start losing horsepower again as the excitation system is designed to protect the equipment from excessive current. A cool thing about Dash-2s, is that some of them were built with a different PF card, which has an additional "performance control" curve which allows the locomotive to load harder at those lower speeds, but now you're relying more on the engineer to keep the current to a safe level for the sake of the equipment. And those "performance control" curves don't affect the normal operation of the system above the full horsepower line. That's a lot of words and not a perfect explanation, but I wanted to take the opportunity to nerd out a bit lol.
When figuring the tractive effort of a steam locomotive, I’m thinking one should use inches when plugging in the diameters of the piston and drivers into the equation?
11:14 Let's also not forget rebuilds. You can rebuild a locomotive with larger or smaller drivers, bigger cylinders, and/or a higher-pressure boiler. It's probably a bit outside the scope of most people's thoughts on railroading, but it's definitely possible.
B&O converted 2-10-2 Sante Fe boilers to use on their 4-8-2 Mountains, as well as Mikado 4-8-2 boilers fitted to 4-6-2 Pacific frames. I am sure other roads recycled locomotive parts all the time.
That is my biggest frustration with that ToT video, he sort of concludes with "well the booster never worked in Britain really so it wasn't that great if an idea" while glossing over how many engines in the US still have them. 🤦♂️ToT is good overall, but there are a few moments like that where he either needs to look out at wider global history and expand his horizons, or admit his focus is primarily on British stuff and keep his focus there.
One of the other things that affected tractive effort especially on engines with long dry pipes was head losses in the dry pipe. Willamette actually used a factor of 0.75 for their saturation engines to account for losses as the steam ran from the throttle, out the smokebox, and then did a U-turn back to the cylinders on the side. To my knowledge they used the normal 0.85 factor on the superheated engines because the hotter and dryer steam didn’t experience as much loss
LOVE THE STARE AT THE PRR THE DECAPODS (( 2-10-0 )) A LOCOMOTIVE THAT WEIGHED 386,000 LBS 62 INCH DRIVERS 240 LBS BOILER PRESSURE YET KICKED OUT 105,000 LBS T.E. 13,000 MORE THAN U.P. CHALLENGERS
@@09JDCTrainMan depends on if your talking as built ,, Before superheated , with the extended pistons that went forward through the piston heads . Before the Worthington feed water heater and stokers were added .. YEH , THEM MONSTERS WHERE HAND FIRED WHEN BUILT ...... As built , boiler pressure was 190 lbs on the first ,, 205 lbs on the second ,,, I1 , I1s or the I1sa Then the larger tenders were added .......
TE is an awesome topic, i remember the Derail Valley video on the S282 multi wheel arrangements, from the 4-4-0, to the 0-12-0, my fave was the 2-10-0 (i think that was it, idk) but i remember the smaller wheels having more tractive effort, and if my feeble simple brain can simply put it, smaller wheel, shorter stroke, the shorter the piston has to stroke, the more (or less i think) effort it has to put in. love all the videos as always Hyce
I had a good friend who drove GG1s for the PRR and later Amtrak. He told me once that a steam engine can pull a train it can't start, and a diesel locomotive and start a train it can't pull, but the GG1 had no such limitation. What a shame they are no longer in service.
I finally understand how caprotti valve gear works. It essentially makes the cam lobe last longer in the corner and makes it shorter hooked up by using 2 lobes that rotate.
Excellent video. Definitly needs to be part of any steam locomotive class. It's interesting reading railroad engineering books about the wheel and rail dynamics. Steel is elastic, so the contact area between the wheels and rails changes depending on the steel types and weight. But generally speaking, more weight per axle means a larger contact area; conversely, less weight means a smaller contact area. It works out that a locomotive with one drive axle with X weight versus a locomotive with four drive axles with a total of X weight has nearly the same total contact area between the wheels and the rails. This is why the number of drivers isn't as important as one would think.
@@Hyce777@Hyce777 Yes, the hardness is important. The higher the hardness, the less elasticity in the steel, and the less traction can be developed. If the wheels/tires are too soft, they'll have good traction but wear faster, increasing repair downtime and raising maintenance costs. Also, the harder the wheels, the faster the rail will wear down. Thus, the railroad must balance how often it wants to replace rail vs. wheels. ASTM (A-504), AAR (M-107), and APTA (PR-M-S-012-99) each have standards for metallurgy and hardness of locomotive and car wheels depending on expected speeds and braking forces. In Grand Scale trains, car wheels are typically made of high-carbon steel and have hardened treads, while locomotives have medium-to low-carbon steel tires for increased traction.
@@CurtisFerrington : Also, to a first approximation, friction is proportional to the weight applied, and not proportional to the size of the contact patch. I suppose that there are second-order effects there, though, as well as effects on durability and rail wear, though?
That 3-chime at 0:29 is gorgeous (at least I think it's a 3-chime). Also, I didn't know that Reading 2102 had a booster. That's really cool. Maybe a video idea for the future is one covering boosters and the different type. I think that would be a cool idea. One question about boosters on the subject, as for RBM&N 2102, where does the exhaust steam for the booster come out? I've never seen any coming from the tender, and to me it would just seem impractical to pipe the booster's exhaust from the tender all the way to the smokebox. Anyway, love the video, and I had a few myths of my own busted. It was a ton of fun to watch!
They drop out right next to the booster itself. The big plume of steam from the rear in the videos of 2102 working hard pulling the coal hoppers is the easiest to see it.
Only tangentially related, but you NEED to come out to Pennsylvania and see 2102 in person. I got to ride behind her last fall and will be doing so again later this month. She put on a SPECTACULAR performance. That video of her charging out of Port Clinton? It's even more incredible in person.
It’s cool to hear the full explanation for why TE math works the way it does. I’ve heard you and others give some of the story before, so thanks for completing the lesson with this video!
8:24 I worked at a software company that did signalling and such. One day they passed around a news article with a photo of track that had been completely flattened by an engine. The entire height of the rail was gone and was converted to width. The cause? Every single automated brake was still engaged (software error). Wild stuff.
When the PRR tested the I1s using 50 percent cutoff, it measured more TE at speed (35 mph) than starting TE. When they changed the valve setting to 65 percent cutoff making them I1sa is when starting TE equaled at speed TE. It also lowered the FH on start up but at speed it was better than the modern 4 cylinder locomotives. Good job of explaining the math. Thank you.
Thank you for a great mini lecture on TE. Have always wondered about all of the mechanics and math behind TE. Appreciate the formulas for computing TE. It would be great to see one on calculating diesel electric TE.
A rule of thumb: large driver size increases (practical) speed, small driver size increases effective power. Hence why the D&RGW narrow gauge stuff is really slow but powerful, and why the Stirling Single was known for express running and not freight
Yup! When they were new to me, I had no idea how common they were, because (aside from the quite rare ones on tender trucks) they hide out of sight. But quite a lot of the larger locomotives have trailing-truck boosters.
Hey Hyce! A video idea for the future, you could show your honest opinions for the new Hydrogen Powered Locomotives! (It would make for a funny video!) And maybe talk more about some failed types of locomotives! Thanks for the amazing content! - Em Railfans
You have. To remember one thing, steam has no limit.You can generate steam until you blow the boiler up.But as far as power and forward motion or reverse motion steam has no believant
Owner of company I worked for believes the rails bend slightly under the wheels and "cup" them due to the wooden ties thus more traction than if using concrete ties.
I feel like this is something that would have been a segment on the kAN and Hyce Traincast a while back. I have my hopes it will return with Century of Steam :)
From a physics perspective, friction is a function of weight and the coefficient for the specific materials. Surface area of the contact is utterly irrelevant. So adding more wheels will only increase pulli g power IF the weight increases proportionally (ie its all about the weight the drivers exert on the rail, not the number of drivers)
11:16 There is one other thing! And that is called "piss off the FRA and put something heavy on top of the safety valve" More boiler pressure, more power!
That was something done in the early days of rail travel, and every one who wasn't killed outright by the ensuing boiler explosion quickly called it a bad idea.
8:27 The bigger wrench idea only applies when you're exerting force from the end toward the center. Take a board and put a weight toward the middle and lift from one end, keeping the other end on the ground. Pretty easy, right? Now swap the weight to the end and lift near the middle while still keeping the other end on the ground. Much harder because you'll need 4x the force as lifting from the end. (For my example, I imagined a 10 ft board and 100 lbs weight. 100 lbs at 5 ft is 500 ft-lbs, to make 500 ft-lbs force at 10 ft only needs 50 lbs force. 100 lbs at 10 ft is 1000 ft-lbs, to generate that at 5 ft distance takes 200 lbs force, or 4x as much. Really, you'd need more force either way to actually lift the weight, but that's beside the point.)
The maximum allowed axle load of course depends on the lines where the locomotive will operate. Each line having a limitation there (in continental Europe there are classes A, B, C, D from light to heavy with subclasses about weight per meter for bridges). Back in the steam age for a long time the military required all Austrian locomotives to be used universally in times of war. That and the limited length of turntables put pretty severe restrictions on the growth of locomotives and lead to ingenious constructions. For example the first locomotive with five coupled wheelsets, kkStB class 180 (built from 1901) designed by Karl Gölsdorf with just 13.5 t axle load. Distributing the load over five wheelsets allowed it to have sufficient tractive force anyway (though I can't find the kN in my sources). Even today some locomotives aren't permitted on certain lines for which they are too heavy.
No mention of how geared locomotives factor into tractive effort? For shame, Hyce! Jokes aside, this was very informative either way. As for the myth about sand, I think it's better to describe it as "assistive" instead of "additive". It's not adding any additional tractive effort, it's assisting the locomotive in making better use of it where it is necessary. Also the myth about "more wheels = more good" is more complicated, as duplex and articulated (ie the 3000 class Challenger or the 4000 class Big Boy) locomotives using more than one set of drivers are where this myth is more truth than fiction. It's a case of "This is true, but only under very specific circumstances".
If I may ask how did railroads calculate how much tonnage they could haul? Obviously TE plays into the equation as you said but I figure fairly early on the railroads made a system beyond "Keep throwing cars on until the train can't move at all or without breaking something.".
In the old steam vs diesel power video you mentioned that a diesels power is measured really low like 11mph. However you've also talked about how steam loco's as the reverser is more centered (for less end-of-stroke shock at higher speeds or something?) then the steam isn't delivered for as long of the stroke, so steam locos should also have a decreasing torque output as RPM increases right? It would be really cool to see a dynograph of bigboy vs AC6000 from 0mph>60mph. Even though the pistons valve is close to the steamchest it still has the steam expanding but it'll decrease in pressure way faster right?
Would be very interested to see the TE formula expanded into a mathematical model that could describe/predict how a locomotive and train will behave at different speeds. It should be possible to derive the optimum throttle and reverser settings if the model is detailed enough.
There are several ways to account for it at speed, from pg. 23 of Principles of Locomotive Operation and Control: T.F.=[(0.85P*s*d^2)/D]* speed factor. P= pressure in inches, D= diameter of drivers in inches, d= diameter of piston in inches, and s= stroke in inches. The speed factor is basically has to be derived to show the locomotives tractive effort changes at speed, and the book isn't super clear there on how to derive it. But pg. 24 shows a Baldwin table that calculated out various common tractive effort curves as speed changes.
@jacoblyman9441 I wonder how much of that is theoretical and how much of it is empirical. Wouldn't surprise me if the theory is actually very complicated but if you stick your locomotive on a test rig you can take readings.
(I know this is a lot of text, but it's a pretty abstract idea so I wanted to explain it throughly) The 0.85 coefficient isn't calculated from the area of a circle and/or area under a sine curve. Literally every singe possible variable affects the tractive effort of a locomotive, so you would need to know the entire universe to get the correct tractive effort. The formula just includes the major elements that affect the TE. If the result should increase when the value increases (like boiler pressure or piston diameter), you multiply it, if the result should decrease (like wheel diameter), you divide by it. of course you don't multiply it directly, you do it with a coefficient that is determined by the effect it has on the TE, but you don't need to know it, that's why it's beautiful. When you multiply all the elements and coefficients together, you can simplify the coefficients into one. Now you wouldn't know what this number is because you don't know the numbers it came from. The way you find it is by getting one locomotive, getting the variables you have in the formula, and putting them in, then you get a number. After that you actually measure the TE of the locomotive in real life, by whatever method and you get it's TE. After that you have to find "what number multiplied by my result will give the same number I measured in real life?". And that's it. Assuming you have all possible variables in the formula, it will be perfectly precise for _any_ locomotive. Of course the formula we use doesn't have all possible variables, so we need more real measurments to get a more precise aproximation. What is even better is that you can put any measuring system in the formula, calculate the new coefficient from the real number and the one your formula has, and then it just works. thanks for reading my book :-)
Well said my friend, thanks for the cheers! Yeah, it's impossible to classify *everything* that influences it, and lord knows many manufacturers altered their coefficient based on things they learned experimentally.
I was taught many years ago, in a very simple way, the larger a steam locomotive's wheel diameter, the faster it can go, but its harder to start a train from stop. The smaller the wheel diameter the slower your top speed, but starting a train from stop is easier. I know all the other things mentioned play a part as well.
That's pretty much it. Like he said about the bigger wrench, but backward. With a wrench, you're applying the force to the center from the end. That's why you get an increase in torque (100 lbs force at 1 ft from center is 100 ft-lbs torque, 100 lbs force at 2 ft from center is 200 ft-lbs torque). But when driving from the center, distance decreases your torque output (100 ft-lbs torque from the center at 1 ft distance exerts 100 lbs force, 100 ft-lbs torque at 2 ft distance exerts 50 lbs force).
Surprised to know that myth #2 exists. Since every description/ explanation i have come across, only mentioned that sand is used to increase the friction between wheel and rail.
I think that one may just be a case of misunderstanding that "tractive effort" is the force the engine could exert assuming no slipping, and possibly also misunderstanding that engines are normally designed so that they won't generally be able to slip on dry clean rail.
@@BrooksMoses Oh. Seems like "tractive effort/ input" being confused with "tractive output". And the ratio of the 2 dependent the coefficient of friction.
Hey Hyce! I know its off topic. But I simply can't think of where else to reach out with my question. Way back when you did stuff for railroad online. You did a livestream where you showcased this awsome tunnel technique that one of the guys had done. If my memory serves me right, it worked by somehow intersecting terrain with a object. And where it intersects, it made the terrain invisible and non colliding. But what was that technique called? I can't for the life of me figure it out by just googling. I hope you can answer my question! Thanks for all your videos!
It has occurred to me on a second watch that your explanation of '0.85 as cutoff' was much nearer to the (I'm going to say) mark in your first video than the one advanced in your second video above - because cutoff does play a significant part in the mean effective pressure exerted on the piston face through one stroke. What you've done above in "Myth 1: 0.85 Cutoff" with the inclusion of some fraction of Pi and some average of the power waves takes the explanation further away from how the equation works, thus perpetuating a myth rather than busting it. It's a shame because a correct understanding of the equation is really interesting - and much more straightforward than that pdf the model engineering bloke did. Oh well, I still enjoy your other videos.
Where I live in Illinois, they mined sand for the railroads from very specific quarries. C&NW got (and UP gets) a lot of their sand from Troy Grove (as I understand it). They wanted a flatter sand grain for the railroads. Round sand was more inclined to roll off the rail before the wheel got to the sand. The flat sand laid on the rail better. All sands are not the same. River sand tends to be more round. As sand in the river moves, it crashes into other grains of sand rounding off the edges, making marbles of sand.
I wasnt ready for math, I failed this class. Boosters! God, Id love an in depth view on boosters. Maybe theres not enough there for a full video but honestly I have no idea.
How well does that formula scale down for live steam model trains? I'm not sure if there's live steam models below HO scale... I'm guessing most average-or-higher quality models will produce so much TE that any reasonable amount of rolling stock (which is relatively lighter than prototypical from its construction material) can't even come close to putting up resistance to match it.
Sorry Hyce. K = 0.85 has been significantly misstated in your video. It's simply a number based on numerous indicator card tests. K as 0.85 was adopted by the American Association of Master Mechanics in about 1900 or so. It is simply the mean effective pressure through the entire stroke and is relevant from start-up to about 10 mph. The 10 mph is actually stroke speed rather than road speed - but is good to about 10 mph. Equally sorry, the wheel diameter explanation is also misstated. It's nothing to do with leavers. It's that power is delivered at four piston strokes combined for one revolution but enjoyed at the rail through one circumference. You need to have consulted Ralph Johnson (1944) or François Marie Guyonneau de Pambour (1836), or any Locomotive engineering book written between the two - rather than that incorrect model engineering pdf. Johnson explains the application at the end of steam, and de Pambour wrote the equation. Ultimately, it's in the category of things that don't particularly matter anymore - but even so, it's a shame your reach was used to inadvertently misstate things.
The one thing that still bothers me is that 0,85 in the tractive effort equation for non-American locomotives. While American locomotives are built with a coefficient about 0,85. Non-American locomotives have very different values. I saw them ranging from 0,274 for Soviet locomotive class IS 2-8-4 to 0,638 Class A4 Mallard 4-6-2. Most others (at least those I've checked) are between these two values. Why?
I'm not an engineer like Hyce, but if I can give my own opinion. I believe it has to do with the job and the type of engine it is. American built are needed for moving heavy freight (for the most part) compared to British which was needed for light to medium freight and passengers.
@@Johndoe-jd well it wouldn't be of much use if you don't know the actual tractive effort. you know the actual number and then you run the locomotive how you consider depending on the load. but because different regions use different measuring systems you must have different coefficients, which all multiply into a single one. after that you can count the different pros and cons of locomotive which change the coefficient
Mallard was a 3-cylinder locomotive, so a different formula is used to account for the different valve timing and 6 impulses per rotation vs 4 impulses of a 2 cylinder. I do not know what formula was used for the Russian locomotives.
When figuring the tractive effort of a steam locomotive, I’m thinking one should use inches when plugging in the diameters of the piston and drivers into the equation?
Yes. The thing that helps to make sense of the equation is that cylinder bore rather than cylinder radius is used to calculate the surface area of the piston because the equation requires four power impulses - and using pi x bore squared produces four times the area of pi x radius squared. The reason why you don't see pi in the equation is that it's deleted as a common factor along with pi x driver diameter in the driver circumference part of the equation.
Hyce, you mentioned that torque comes from the length of piston stroke. I wonder if that should not be calculated from the length of the crank arm related to the driver diameter. There are basic calculations of leverage ratios in that combination. Yes, the longer crank arm would result in a longer piston stroke. But cylinder pressure (NOT boiler pressure) is a factor. The more pressure on the piston the more effort goes to turn the crank arm - And you have friction losses along the way piston rings, stuffing box, cross head slides and main axle bearings. The minor contributors would be all the bearings and bushings for the connecting points of the moving parts. Unlike liquids, steam is a gas, subject to heat loss and condensation as it travels through the exposed pipes going from the smoke box, through the valves, into the cylinder. What is your though on this?
Also Torque is an result of Piston stroke and Bore, because all the pressure needs a Point to lay on for the time of expansion. And the fact where on the wheel the crank pin is located, far out or very centered.
The formula for tractive force divides by driver diameter, so the ratio of piston stroke to driver diameter is contained in the formula. The *0.85 figure for "Mean Effective Pressure" was not universally used by every locomotive maker in every country, but it became standard over time. It is an approximation which lumps several things together, and Hyce mentioned three big ones. Frictional losses and back pressure in the cylinders were not mentioned, but they affect real life tractive force too. And in non-superheated steamers condensation losses in the cylinders would have a much larger effect. For the most part these issues grow in importance as speed increases and have only a small effect at low speed. If a boiler can produce enough steam to keep pressure up the condensation losses could be mostly negated. It just takes more steam to replace the volume loss from condensation. That uses more water and fuel. The advantage of superheating came from a combination of expanding the steam further and reducing the condensation losses.
Note that the piston stroke is equal to twice the length of the crank arm, so it's effectively the same thing. And the "related to the driver diameter" then is why the driver diameter is on the bottom of the equation.
First, simply use the equation twice and add them together - but multiply the second equation by 0.5. Second, Pi is struck from the equation as a common factor in cylinder face area and driver circumference.
I was wondering, why U.S. steam engines for freight services have higher tractive effort than engines elsewhere. Even the largest German steam engine, the Class 45, had a tractive effort of 420 kN or 94400 pounds-force, compared with 600 kN or 135000 pounds-force for the Big Boy.
The rated tractive effort equation ignores machine friction. The use of K = 0.85 makes no allowance for machine friction. Some jurisdictions use K as low as 0.60, and if you see this it is an indicator that that particular road wanted to make an allowance for machine friction.
Some of that, I think, has to do with rail loading and clearances. A 135000-pound-force engine has to have about 540000 pounds of weight on the drivers to avoid slipping, and my impression is that European railroads aren't designed for that. They also have tighter clearances, and fitting a boiler large enough and long enough to produce that much steam into those clearances is difficult if not impossible. (As an example of the latter -- if you look at the design of the NYC 4-8-4s, you can see that they were pretty much at the limit of what they could fit through some of their tunnels. And I'm pretty sure the NYC clearances were still bigger than German ones, even though they were small by U.S. standards.)
Feel like i need to put on my black framed glasses after that math :P . " I became an engineer So i don't have to do math " .. does this sound familiar Hyce ?? Thanks for passing on your knowledge and busting these myths ,hope to meet you in person someday .... T W M
It would depend on the number of power impulses per revolution of the driving wheels - which depends on the gear ratio - which varies from locomotive class to locomotive class. So it would be a much more convoluted equation.
@@theimaginationstation1899I would assume (Bad word I know) that since Lima built every shay that they most likely had the same gear ratio on every locomotive, The difference being I think the number of pistons and trucks that were on each locomotive that really changes the way a Shay's tractive effort works realistically aside from gearing itself.
@@jeremeymcdude Fair point. The TE equation is very blunt. Number of power impulses is what counts - hence the equation for 2 cylinder locomotives allows for four power impulses. Lima publish the tractive effort in their catalogues, so I guess the TE equation could be reverse engineered.
@@theimaginationstation1899 So i went back to a video to just check and it looks as though depending on class you have 2 or 3 cylinders all on the right that all they do is drive a drive shaft that then powers the truck wheels via gears on the shaft and trucks. it seems that it could be relatively simple for someone who ACTUALLY knows math unlike myself to figure out something that works.
That should be fairly simple. Just do the same calculation but multiply it by whatever the gear ratio is between the cranks and the wheels. So if the cranks turn 3 times per wheel rotation then you have 3x as much TE.
What about an engine that has a super heater for the steam that adds around 100 degrees F to the steam. Wouldn’t this increase the pressure coming from the boiler. Should this be factored into the equation instead of the boiler pressure. According to one steam pressure vs temp F chart the extra 100 degrees would add 1.1 lbs for each 2 degrees F rise in temp. So that would make 200 lbs become 255 lbs under standard conditions.
Superheat doesn't add pressure, only temperature. It's one of the oddities of water - when it's contained, under pressure, as water and steam, yes the temperature and pressure are linked - i.e. temp goes up pressure goes up, but when you start talking superheat you can't have liquid water, which means that the pressure can stay the same while the temp increases. It's a separate thermodynamic table for superheated steam.
The Tractive effort equation was first published, in English, in 1836 - so it significantly pre-date superheaters. The only change to the equation was circa 1900 when 'K' was added to reflect mean effective pressure throughout the entirety of one stroke. 'K' = 0.85 is the assumed standard for mean effective pressure from starting to eight to ten miles per hour (it's actually piston speed rather than road speed, hence 8-10 mph). As piston speed increases K drops away. Where superheated steam affects the tractive effort result is not in any increase in boiler pressure, but that the more fluid steam may well have a higher mean effective pressure through one stroke. From time to time locomotives are touted as producing more than their rated tractive effort, but what that means is that the mean effective pressure through one stroke is higher - say 0.90, and that produces a higher tractive effort result. The 225 pounds you suggest would not be achievable because the safety valves would lift at 200 pounds. In any event, by the time superheaters became standard designers were looking for locomotives that could perform at higher road speeds, and the consideration shifted to producing horsepower at that desired road speed.
I believe the coefficient in the tractive effort isn't something calculated from other prrcise things like area of a circle or of a sine wave, but instead something to make the numbers work. this is because the ratio of the radius of the drivers and the diatance from the crank shaft pivot to the center of the driver isn't considered, even though it is really important, because it doesn't change _much_ across locomotives. So because all values rise linearly (other than the piston diameter but who cares) a simple cefficient can be used so that the funcion mathches real behaviour.
The ratio between crank diameter and wheel radius IS in the equation, it's just disguised. The piston stroke (last term on the top of the division) is just another way of saying crank diameter. And of course wheel diameter is on the bottom of the division.
It's difficult to break it down easily, because the preceeding 10.46 is error-riddled. But at higher speeds less steam is admitted to the cylinders, so the mean effective pressure through one stroke is less, thus the tractive effort is less.
@@theimaginationstation1899 Thanks. That makes sense. When he was talking about it being bad for the locomotives I thought he was talking about diesel.
One thing that's seldom mentioned when considering the T.E. equation is that you get the maximum tractive effort when the cylinders are bored out almost to the condemning limit (3/4-inch oversize for a PM Berkshire) and the driver tires are likewise almost at the tread worn too thin limit (4 inches under nominal for that same PM Berkshire). This can add a surprising amount to T.E., but also makes the engine more slippery.
Very true! Good point. That would've been a fun thing to include directly in the video.
This reminds me of the C&O Alleghenies. It's said that it exerted up to 119,500 lbf of tractive effort with worn 65.5" drivers.
So a worn out engine basically will pull hardest if I am understanding you correctly?
@@Hybris51129 The trouble with a worn-out engine is that K = 0.85 is probably lower on account of the mean effective pressure in the cylinders through one stroke being lower on account of deferred maintainance.
Every railroader knows that turning on the bell and “generator” gives a 10% boost in tractive effort when climbing the switchbacks to the iron mine.
don't forget pushing a snow plow in front of you gives a 10% boost in top speed.
I almost made a joke about that in the video but figured it'd be more of a hornets nest kick than a joke for some... Lol!
Ah yes, the bell, activated by “hand valve”
They would get another 10% if they painted them red
The same way a fire engine is actually powered by its air horns. LOL
An ES&DT logo on the tender can give a +15% to top speed but a -20% to stability, (-35% if an aroma of "Kenosha" is detected).
Lol
One of the sounds I shall never forget is a drawbar breaking. Another is a trio of 10,000 amp fuses blowing from a bolted dead short. One was a huge very loud ka-blam, and the other was little plinking sounds. Both were really expensive.
Layman´s terms:
1) Tractive effort: the maximum weight of your car that your engine can power without choking and dying
2) Adhesion: are you able to use that power without spinning the wheels?
3) Drivers´ size: final gear -> big = more revolutions, needs more torque
4) Piston stroke, surface, pressure: torque
Lesson:
1) If you want to tow a cargo ship, your super ultra tuned, high tractive effort semi truck may not be enough if it has only one powered axle (and low weight), as it would overcome the adhesion limit of its tires and produce only wheelspin.
2) Converting your cheap little grocery-getter car into all wheel drive won´t increase its tractive effort. In fact it may decrease it a little bit (due to increased inner friction). But it may help on a slippery surface.
3) Higher gear (bigger wheels) is only good if you have enough tractive effort and adhesion, and just want to go faster.
Thanks. This clears up a lot of my questions. Less confusion for me!
Meanwhile Jeremy Clarkson towed a ferry 100m with a grocery getter.
@@kornaros96 Ferry is surely nothing like a cargo ship. Anyway, if the car has enough torque and adhesion to overcome the resistance of the water, then why not?
I instantly recalled the Drivers video you did some months back on the 4th myth, and recalled you saying "Generally, medium to large wheels were used for passenger service, and smaller to medium were generally used for freight service, but this isn't always the case." Nice to see a bit more train mythbusting
Since you mentioned diesel, I thought I'd do my own nerding out, lol.
In diesel locomotives, (I'll only mention those with DC traction because I'm not remotely qualified to talk about the minutia of AC traction) your tractive effort is related to your traction motor amperage. (I think you actually mentioned the approximation EMD uses in your other video. The equation that uses horsepower, a constant, and divides that by the speed) As such, you get the most tractive effort with the motors at (or near) stall. The nerdy part and nuance comes into play when you consider low speeds and how the excitation system works.
Starting simple, diesels have a spec called "minimum speed for full horsepower" (which depends on the gear ratio selected by the railroad) Above that speed, the approximation of tractive effort based off horsepower works pretty well, but below that speed the actual tractive effort will be less than the equation says.
This is where the complexity (and my nerding out) begins. So as the motors slow down, they draw more and more current, which means we get more torque out of the motors. But, it also means that the motors and main have to pass more current, which causes things to heat up. As such, the excitation system is designed to limit the current from the main to help avoid overheating issues. Above the "minimum speed for full horsepower," the load regulator and excitation system will work to keep the engine running at full horsepower (or a constant horsepower based on what throttle notch you're in). However, below that line the excitation system is designed to "override" (sort of) the load regulator to (try to) keep the current in the main at a relatively safe level. The excitation system does a similar thing at high speeds, except it's limiting voltage instead of amperage. So, (ignoring transition) if you were to watch the load regulator on a locomotive in 8th notch at a high speed as it pulled up a hill to a stall, you see the load regulator start out at "full field" because the excitation system is limiting the voltage from the main and the engine isn't producing full horsepower. Then, as things started to slow down, the excitation system would allow for more horsepower and eventually the engine would reach full horsepower, at which point the load regulator would start to back off a bit to keep the engine at full horsepower. As you continued to slow down, eventually the load regulator would start to move back to "full field" position as the excitation system starts limiting current from the main. Once you reach the "minimum speed for full horsepower" the load regulator would hit "full field" and then the excitation system then gets control and starts limiting the current from the main. At this point, you'd start losing horsepower again as the excitation system is designed to protect the equipment from excessive current.
A cool thing about Dash-2s, is that some of them were built with a different PF card, which has an additional "performance control" curve which allows the locomotive to load harder at those lower speeds, but now you're relying more on the engineer to keep the current to a safe level for the sake of the equipment. And those "performance control" curves don't affect the normal operation of the system above the full horsepower line.
That's a lot of words and not a perfect explanation, but I wanted to take the opportunity to nerd out a bit lol.
When figuring the tractive effort of a steam locomotive, I’m thinking one should use inches when plugging in the diameters of the piston and drivers into the equation?
@@billmorris2613 Yes. The working pressure of the boiler is in psi, so multiplying by square inches (diameter squared) will give you force.
@@CDROM-lq9iz Thanks.
To quote Adam Savage: “I REJECT YOUR REALITY AND SUBSTITUTE MY OWN!”
and Jamie: "QUACK DAMN YOU!"
Hyce as Jamie: Hyce want big Kenosha (in games)
Which is a perfectly valid thing to do. Time is fake and space is a bad idea.
11:14 Let's also not forget rebuilds. You can rebuild a locomotive with larger or smaller drivers, bigger cylinders, and/or a higher-pressure boiler. It's probably a bit outside the scope of most people's thoughts on railroading, but it's definitely possible.
Yes, 2102 actually started life as a 2-8-0 and then got rebuilt to a 4-8-4.
@@awildjared1396 I didn't know that, I'll need to look into it, it sounds interesting. Thanks.
EBT 16 got a higher pressure boiler in its last rebuild, so I assume it's tractive effort changed as well.
@@jacoblyman9441 I would have to agree with you.
B&O converted 2-10-2 Sante Fe boilers to use on their 4-8-2 Mountains, as well as Mikado 4-8-2 boilers fitted to 4-6-2 Pacific frames. I am sure other roads recycled locomotive parts all the time.
11:34 Ah, the booster engines I learned from ToT; I'm glad they're still in preservation.
That is my biggest frustration with that ToT video, he sort of concludes with "well the booster never worked in Britain really so it wasn't that great if an idea" while glossing over how many engines in the US still have them. 🤦♂️ToT is good overall, but there are a few moments like that where he either needs to look out at wider global history and expand his horizons, or admit his focus is primarily on British stuff and keep his focus there.
One of the other things that affected tractive effort especially on engines with long dry pipes was head losses in the dry pipe. Willamette actually used a factor of 0.75 for their saturation engines to account for losses as the steam ran from the throttle, out the smokebox, and then did a U-turn back to the cylinders on the side. To my knowledge they used the normal 0.85 factor on the superheated engines because the hotter and dryer steam didn’t experience as much loss
Great video, Hyce! Thank you for the tractive effort explanation and mythbusting!
Cheers my friend!
LOVE THE STARE AT THE PRR
THE DECAPODS (( 2-10-0 ))
A LOCOMOTIVE THAT WEIGHED 386,000 LBS
62 INCH DRIVERS
240 LBS BOILER PRESSURE
YET KICKED OUT 105,000 LBS T.E.
13,000 MORE THAN
U.P. CHALLENGERS
250 psi boiler pressure
@@09JDCTrainMan depends on if your talking as built ,,
Before superheated , with the extended pistons that went forward through the piston heads . Before the Worthington feed water heater and stokers were added ..
YEH , THEM MONSTERS WHERE HAND FIRED WHEN BUILT ......
As built , boiler pressure was 190 lbs on the first ,,
205 lbs on the second ,,,
I1 , I1s or the I1sa
Then the larger tenders were added .......
TE is an awesome topic, i remember the Derail Valley video on the S282 multi wheel arrangements, from the 4-4-0, to the 0-12-0, my fave was the 2-10-0 (i think that was it, idk) but i remember the smaller wheels having more tractive effort, and if my feeble simple brain can simply put it, smaller wheel, shorter stroke, the shorter the piston has to stroke, the more (or less i think) effort it has to put in.
love all the videos as always Hyce
Most interesting & educational.
Been into steam and early diesel for over 55 years.
Thoroughly enjoy your channel.
All the best from Scotland. 🏴
I had a good friend who drove GG1s for the PRR and later Amtrak. He told me once that a steam engine can pull a train it can't start, and a diesel locomotive and start a train it can't pull, but the GG1 had no such limitation. What a shame they are no longer in service.
I finally understand how caprotti valve gear works. It essentially makes the cam lobe last longer in the corner and makes it shorter hooked up by using 2 lobes that rotate.
That sounds about right. You've been doing your research!
@@Hyce777 Franklin valve gear is turbo cursed
Excellent video. Definitly needs to be part of any steam locomotive class.
It's interesting reading railroad engineering books about the wheel and rail dynamics. Steel is elastic, so the contact area between the wheels and rails changes depending on the steel types and weight. But generally speaking, more weight per axle means a larger contact area; conversely, less weight means a smaller contact area. It works out that a locomotive with one drive axle with X weight versus a locomotive with four drive axles with a total of X weight has nearly the same total contact area between the wheels and the rails. This is why the number of drivers isn't as important as one would think.
That's interesting! I'd imagine tire hardness plays a lot into that as well. Makes sense.
@@Hyce777@Hyce777 Yes, the hardness is important. The higher the hardness, the less elasticity in the steel, and the less traction can be developed. If the wheels/tires are too soft, they'll have good traction but wear faster, increasing repair downtime and raising maintenance costs.
Also, the harder the wheels, the faster the rail will wear down. Thus, the railroad must balance how often it wants to replace rail vs. wheels.
ASTM (A-504), AAR (M-107), and APTA (PR-M-S-012-99) each have standards for metallurgy and hardness of locomotive and car wheels depending on expected speeds and braking forces.
In Grand Scale trains, car wheels are typically made of high-carbon steel and have hardened treads, while locomotives have medium-to low-carbon steel tires for increased traction.
@@CurtisFerrington : Also, to a first approximation, friction is proportional to the weight applied, and not proportional to the size of the contact patch. I suppose that there are second-order effects there, though, as well as effects on durability and rail wear, though?
That 3-chime at 0:29 is gorgeous (at least I think it's a 3-chime).
Also, I didn't know that Reading 2102 had a booster. That's really cool. Maybe a video idea for the future is one covering boosters and the different type. I think that would be a cool idea.
One question about boosters on the subject, as for RBM&N 2102, where does the exhaust steam for the booster come out? I've never seen any coming from the tender, and to me it would just seem impractical to pipe the booster's exhaust from the tender all the way to the smokebox.
Anyway, love the video, and I had a few myths of my own busted. It was a ton of fun to watch!
They drop out right next to the booster itself. The big plume of steam from the rear in the videos of 2102 working hard pulling the coal hoppers is the easiest to see it.
Also that's the DT&I 5 chime. One of my favorite whistles.
Only tangentially related, but you NEED to come out to Pennsylvania and see 2102 in person. I got to ride behind her last fall and will be doing so again later this month. She put on a SPECTACULAR performance. That video of her charging out of Port Clinton? It's even more incredible in person.
I've thought about doing that this fall when I have a week off.
Booster engine is a neat idea!
Loved the D&RGW clips early in the video 🎶
It’s cool to hear the full explanation for why TE math works the way it does. I’ve heard you and others give some of the story before, so thanks for completing the lesson with this video!
8:24 I worked at a software company that did signalling and such. One day they passed around a news article with a photo of track that had been completely flattened by an engine. The entire height of the rail was gone and was converted to width.
The cause? Every single automated brake was still engaged (software error). Wild stuff.
Beating the ROW to pieces? (Glaring at 1920s D&RGW engine purchases)
Yes I knew it, what an awesome video Hyce 🔥🔥🔥💪🏻 it was so *** amazing. I loved the (mythbusters)theme in it 🤟🏻
When the PRR tested the I1s using 50 percent cutoff, it measured more TE at speed (35 mph) than starting TE. When they changed the valve setting to 65 percent cutoff making them I1sa is when starting TE equaled at speed TE. It also lowered the FH on start up but at speed it was better than the modern 4 cylinder locomotives.
Good job of explaining the math. Thank you.
I'm so happy there are still nerds like you in this world who explain nerd stuff that no one else cares to explain. 🙏
I love these kinds of videos, the math, logic, and principles behind the mechanics are the most interesting part of steam technology to me.
Thank you for a great mini lecture on TE. Have always wondered about all of the mechanics and math behind TE. Appreciate the formulas for computing TE.
It would be great to see one on calculating diesel electric TE.
A rule of thumb: large driver size increases (practical) speed, small driver size increases effective power. Hence why the D&RGW narrow gauge stuff is really slow but powerful, and why the Stirling Single was known for express running and not freight
There's also cases of tractive effort being decreased on locomotives, like the P2 2-8-2 being turned into the A2/2 4-6-2.
Very informative video answered a lot of questions I had about it
Steam locomotive "boosters?" That's new to me and here I thought I knew everything.
Yup! When they were new to me, I had no idea how common they were, because (aside from the quite rare ones on tender trucks) they hide out of sight. But quite a lot of the larger locomotives have trailing-truck boosters.
Hey Hyce! A video idea for the future, you could show your honest opinions for the new Hydrogen Powered Locomotives! (It would make for a funny video!) And maybe talk more about some failed types of locomotives! Thanks for the amazing content! - Em Railfans
That sounds like a fun idea!
and here i thought that tractive effort already includes the FoE. well you learn something new every day
You have.
To remember one thing, steam has no limit.You can generate steam until you blow the boiler up.But as far as power and forward motion or reverse motion steam has no believant
I come back from a long gameing break and hear “weight”
Me: pauses vid
“Ok, mark. I am waiting.”
It be fun to relate real-world railroading to model scale in HO to see if real-world models react the same or similar.
Owner of company I worked for believes the rails bend slightly under the wheels and "cup" them due to the wooden ties thus more traction than if using concrete ties.
Thanks for that, Hyce, very informative.
Great video, never understood TE before, but very well explained, thank you.
I feel like this is something that would have been a segment on the kAN and Hyce Traincast a while back. I have my hopes it will return with Century of Steam :)
More stories from Interbay that involve Mr Smiley please and thank you :D
Great explanation Mr. Hyce!
For a future video could you talk about the bottom dump gons and how they work?
From a physics perspective, friction is a function of weight and the coefficient for the specific materials. Surface area of the contact is utterly irrelevant. So adding more wheels will only increase pulli g power IF the weight increases proportionally (ie its all about the weight the drivers exert on the rail, not the number of drivers)
The term "tractive effort" is decieving. It makes it sound like traction is involved when it is not involved at all.
It is poorly worded, I agree.
11:16
There is one other thing! And that is called "piss off the FRA and put something heavy on top of the safety valve"
More boiler pressure, more power!
Lol, well, that's against the rules. Also I'm pretty sure setting something *on* the safety would cause it to pop. You'd need to gag it.
That was something done in the early days of rail travel, and every one who wasn't killed outright by the ensuing boiler explosion quickly called it a bad idea.
8:27 The bigger wrench idea only applies when you're exerting force from the end toward the center. Take a board and put a weight toward the middle and lift from one end, keeping the other end on the ground. Pretty easy, right? Now swap the weight to the end and lift near the middle while still keeping the other end on the ground. Much harder because you'll need 4x the force as lifting from the end.
(For my example, I imagined a 10 ft board and 100 lbs weight. 100 lbs at 5 ft is 500 ft-lbs, to make 500 ft-lbs force at 10 ft only needs 50 lbs force. 100 lbs at 10 ft is 1000 ft-lbs, to generate that at 5 ft distance takes 200 lbs force, or 4x as much. Really, you'd need more force either way to actually lift the weight, but that's beside the point.)
The maximum allowed axle load of course depends on the lines where the locomotive will operate. Each line having a limitation there (in continental Europe there are classes A, B, C, D from light to heavy with subclasses about weight per meter for bridges).
Back in the steam age for a long time the military required all Austrian locomotives to be used universally in times of war. That and the limited length of turntables put pretty severe restrictions on the growth of locomotives and lead to ingenious constructions. For example the first locomotive with five coupled wheelsets, kkStB class 180 (built from 1901) designed by Karl Gölsdorf with just 13.5 t axle load. Distributing the load over five wheelsets allowed it to have sufficient tractive force anyway (though I can't find the kN in my sources).
Even today some locomotives aren't permitted on certain lines for which they are too heavy.
I definitely would like to see a version of this for the diesels.
MOM HYCE UPLOADED A NEW VIDEO!!!
No mention of how geared locomotives factor into tractive effort? For shame, Hyce!
Jokes aside, this was very informative either way. As for the myth about sand, I think it's better to describe it as "assistive" instead of "additive". It's not adding any additional tractive effort, it's assisting the locomotive in making better use of it where it is necessary.
Also the myth about "more wheels = more good" is more complicated, as duplex and articulated (ie the 3000 class Challenger or the 4000 class Big Boy) locomotives using more than one set of drivers are where this myth is more truth than fiction. It's a case of "This is true, but only under very specific circumstances".
Fair!
Now do the tractive effort calcs for the kitson-still Steamdiesel engine. :P yes, steamdiesel.
Hyce I got to see Midland at the EBT yesterday for a 4.5 hour trip. He said you might go there in mid September.
That's the plan! Yeah. Glad you got to meet him. He's delightful.
Thanks for giving us a fantastic list of things to say in chat to make you blow your safety Mark!
I imagine figuring out a shay would be near impossible
Nope. Three cylinder equation and then you multiply by the gear ratio.
If I may ask how did railroads calculate how much tonnage they could haul? Obviously TE plays into the equation as you said but I figure fairly early on the railroads made a system beyond "Keep throwing cars on until the train can't move at all or without breaking something.".
In the old steam vs diesel power video you mentioned that a diesels power is measured really low like 11mph.
However you've also talked about how steam loco's as the reverser is more centered (for less end-of-stroke shock at higher speeds or something?) then the steam isn't delivered for as long of the stroke, so steam locos should also have a decreasing torque output as RPM increases right?
It would be really cool to see a dynograph of bigboy vs AC6000 from 0mph>60mph.
Even though the pistons valve is close to the steamchest it still has the steam expanding but it'll decrease in pressure way faster right?
How oil burning steam engines work
Would be very interested to see the TE formula expanded into a mathematical model that could describe/predict how a locomotive and train will behave at different speeds. It should be possible to derive the optimum throttle and reverser settings if the model is detailed enough.
There are several ways to account for it at speed, from pg. 23 of Principles of Locomotive Operation and Control: T.F.=[(0.85P*s*d^2)/D]* speed factor. P= pressure in inches, D= diameter of drivers in inches, d= diameter of piston in inches, and s= stroke in inches. The speed factor is basically has to be derived to show the locomotives tractive effort changes at speed, and the book isn't super clear there on how to derive it. But pg. 24 shows a Baldwin table that calculated out various common tractive effort curves as speed changes.
@jacoblyman9441 I wonder how much of that is theoretical and how much of it is empirical. Wouldn't surprise me if the theory is actually very complicated but if you stick your locomotive on a test rig you can take readings.
@jacoblyman9441 it's not the change of road speed, it's a change in piston speed.
(I know this is a lot of text, but it's a pretty abstract idea so I wanted to explain it throughly)
The 0.85 coefficient isn't calculated from the area of a circle and/or area under a sine curve.
Literally every singe possible variable affects the tractive effort of a locomotive, so you would need to know the entire universe to get the correct tractive effort. The formula just includes the major elements that affect the TE. If the result should increase when the value increases (like boiler pressure or piston diameter), you multiply it, if the result should decrease (like wheel diameter), you divide by it. of course you don't multiply it directly, you do it with a coefficient that is determined by the effect it has on the TE, but you don't need to know it, that's why it's beautiful. When you multiply all the elements and coefficients together, you can simplify the coefficients into one. Now you wouldn't know what this number is because you don't know the numbers it came from. The way you find it is by getting one locomotive, getting the variables you have in the formula, and putting them in, then you get a number. After that you actually measure the TE of the locomotive in real life, by whatever method and you get it's TE. After that you have to find "what number multiplied by my result will give the same number I measured in real life?". And that's it. Assuming you have all possible variables in the formula, it will be perfectly precise for _any_ locomotive. Of course the formula we use doesn't have all possible variables, so we need more real measurments to get a more precise aproximation.
What is even better is that you can put any measuring system in the formula, calculate the new coefficient from the real number and the one your formula has, and then it just works.
thanks for reading my book :-)
Well said my friend, thanks for the cheers! Yeah, it's impossible to classify *everything* that influences it, and lord knows many manufacturers altered their coefficient based on things they learned experimentally.
Love your videos man!
very interesting..i thought TE was the most it could pull in 'tonnage' or similar, the pull power. But apparently it's more like HP/Torque combo.
It's not. The video is incorrect.
I was taught many years ago, in a very simple way, the larger a steam locomotive's wheel diameter, the faster it can go, but its harder to start a train from stop. The smaller the wheel diameter the slower your top speed, but starting a train from stop is easier. I know all the other things mentioned play a part as well.
That's pretty much it. Like he said about the bigger wrench, but backward. With a wrench, you're applying the force to the center from the end. That's why you get an increase in torque (100 lbs force at 1 ft from center is 100 ft-lbs torque, 100 lbs force at 2 ft from center is 200 ft-lbs torque). But when driving from the center, distance decreases your torque output (100 ft-lbs torque from the center at 1 ft distance exerts 100 lbs force, 100 ft-lbs torque at 2 ft distance exerts 50 lbs force).
and enter the indirect dive locomotive, or to really complicate things, Turbomotive.
Surprised to know that myth #2 exists. Since every description/ explanation i have come across, only mentioned that sand is used to increase the friction between wheel and rail.
I think that one may just be a case of misunderstanding that "tractive effort" is the force the engine could exert assuming no slipping, and possibly also misunderstanding that engines are normally designed so that they won't generally be able to slip on dry clean rail.
@@BrooksMoses Oh. Seems like "tractive effort/ input" being confused with "tractive output".
And the ratio of the 2 dependent the coefficient of friction.
Hey Hyce! I know its off topic. But I simply can't think of where else to reach out with my question. Way back when you did stuff for railroad online. You did a livestream where you showcased this awsome tunnel technique that one of the guys had done. If my memory serves me right, it worked by somehow intersecting terrain with a object. And where it intersects, it made the terrain invisible and non colliding. But what was that technique called? I can't for the life of me figure it out by just googling. I hope you can answer my question! Thanks for all your videos!
You should do a video with every model you have. Lego oscale hoscale ect
It has occurred to me on a second watch that your explanation of '0.85 as cutoff' was much nearer to the (I'm going to say) mark in your first video than the one advanced in your second video above - because cutoff does play a significant part in the mean effective pressure exerted on the piston face through one stroke. What you've done above in "Myth 1: 0.85 Cutoff" with the inclusion of some fraction of Pi and some average of the power waves takes the explanation further away from how the equation works, thus perpetuating a myth rather than busting it.
It's a shame because a correct understanding of the equation is really interesting - and much more straightforward than that pdf the model engineering bloke did.
Oh well, I still enjoy your other videos.
What kind of sand do you use? Would a 200grit garnet be more efficent per pound than an 80grit riversand?
Where I live in Illinois, they mined sand for the railroads from very specific quarries. C&NW got (and UP gets) a lot of their sand from Troy Grove (as I understand it). They wanted a flatter sand grain for the railroads. Round sand was more inclined to roll off the rail before the wheel got to the sand. The flat sand laid on the rail better. All sands are not the same. River sand tends to be more round. As sand in the river moves, it crashes into other grains of sand rounding off the edges, making marbles of sand.
@@larrylawson5172 Thank you for this wealth of information kind stranger. I love the internet.
I wasnt ready for math, I failed this class.
Boosters! God, Id love an in depth view on boosters. Maybe theres not enough there for a full video but honestly I have no idea.
There probably would be if I could see one and show it off in person.
@@Hyce777 Contact the Reading & Northern.
How well does that formula scale down for live steam model trains? I'm not sure if there's live steam models below HO scale...
I'm guessing most average-or-higher quality models will produce so much TE that any reasonable amount of rolling stock (which is relatively lighter than prototypical from its construction material) can't even come close to putting up resistance to match it.
Sorry Hyce. K = 0.85 has been significantly misstated in your video.
It's simply a number based on numerous indicator card tests. K as 0.85 was adopted by the American Association of Master Mechanics in about 1900 or so. It is simply the mean effective pressure through the entire stroke and is relevant from start-up to about 10 mph. The 10 mph is actually stroke speed rather than road speed - but is good to about 10 mph.
Equally sorry, the wheel diameter explanation is also misstated. It's nothing to do with leavers. It's that power is delivered at four piston strokes combined for one revolution but enjoyed at the rail through one circumference.
You need to have consulted Ralph Johnson (1944) or François Marie Guyonneau de Pambour (1836), or any Locomotive engineering book written between the two - rather than that incorrect model engineering pdf. Johnson explains the application at the end of steam, and de Pambour wrote the equation.
Ultimately, it's in the category of things that don't particularly matter anymore - but even so, it's a shame your reach was used to inadvertently misstate things.
yes plz talk about diesel tractice effort
What effects does elevation have on steam locomotives in terms of starting and running them and maintaining efficiency?
So what you're saying is anything above an FoA of 4.0 is heavier than necessary? (Stares at Big Boy with its FoA of 4.03)
Basically, 4.03 isn't a big deal because it's not an exact ratio, but something more like 4.5 or 5 would be getting excessive
@@Hyce777 I think there was a loco (I think a 4-6-0 that got rebuilt into a 4-6-0ST) that had an FoA of 6
thumbnail felt very Train of Thought, I thought it was his a first heh
Please do talk about diesel tractive effort!
How does the PRR tracive effect equation differ?
I know once you get the train up to speed momentum helps
The one thing that still bothers me is that 0,85 in the tractive effort equation for non-American locomotives. While American locomotives are built with a coefficient about 0,85. Non-American locomotives have very different values. I saw them ranging from 0,274 for Soviet locomotive class IS 2-8-4 to 0,638 Class A4 Mallard 4-6-2. Most others (at least those I've checked) are between these two values. Why?
measuring systems
that's pretty much it
I'm not an engineer like Hyce, but if I can give my own opinion. I believe it has to do with the job and the type of engine it is. American built are needed for moving heavy freight (for the most part) compared to British which was needed for light to medium freight and passengers.
@@Johndoe-jd well it wouldn't be of much use if you don't know the actual tractive effort. you know the actual number and then you run the locomotive how you consider depending on the load.
but because different regions use different measuring systems you must have different coefficients, which all multiply into a single one. after that you can count the different pros and cons of locomotive which change the coefficient
@@torfley i did say it was own opinion. I work MoW for a short line not an engineer.
Mallard was a 3-cylinder locomotive, so a different formula is used to account for the different valve timing and 6 impulses per rotation vs 4 impulses of a 2 cylinder. I do not know what formula was used for the Russian locomotives.
Very informative
Very good video. Well done.
When figuring the tractive effort of a steam locomotive, I’m thinking one should use inches when plugging in the diameters of the piston and drivers into the equation?
Yes. The thing that helps to make sense of the equation is that cylinder bore rather than cylinder radius is used to calculate the surface area of the piston because the equation requires four power impulses - and using pi x bore squared produces four times the area of pi x radius squared. The reason why you don't see pi in the equation is that it's deleted as a common factor along with pi x driver diameter in the driver circumference part of the equation.
Hyce, you mentioned that torque comes from the length of piston stroke. I wonder if that should not be calculated from the length of the crank arm related to the driver diameter. There are basic calculations of leverage ratios in that combination. Yes, the longer crank arm would result in a longer piston stroke. But cylinder pressure (NOT boiler pressure) is a factor. The more pressure on the piston the more effort goes to turn the crank arm - And you have friction losses along the way piston rings, stuffing box, cross head slides and main axle bearings. The minor contributors would be all the bearings and bushings for the connecting points of the moving parts. Unlike liquids, steam is a gas, subject to heat loss and condensation as it travels through the exposed pipes going from the smoke box, through the valves, into the cylinder. What is your though on this?
Also Torque is an result of Piston stroke and Bore,
because all the pressure needs a Point to lay on for the time of expansion.
And the fact where on the wheel the crank pin is located, far out or very centered.
The formula for tractive force divides by driver diameter, so the ratio of piston stroke to driver diameter is contained in the formula.
The *0.85 figure for "Mean Effective Pressure" was not universally used by every locomotive maker in every country, but it became standard over time. It is an approximation which lumps several things together, and Hyce mentioned three big ones. Frictional losses and back pressure in the cylinders were not mentioned, but they affect real life tractive force too. And in non-superheated steamers condensation losses in the cylinders would have a much larger effect. For the most part these issues grow in importance as speed increases and have only a small effect at low speed.
If a boiler can produce enough steam to keep pressure up the condensation losses could be mostly negated. It just takes more steam to replace the volume loss from condensation. That uses more water and fuel. The advantage of superheating came from a combination of expanding the steam further and reducing the condensation losses.
Note that the piston stroke is equal to twice the length of the crank arm, so it's effectively the same thing. And the "related to the driver diameter" then is why the driver diameter is on the bottom of the equation.
What about the triple cylinder locomotives that run in Europe, like the Tornado and the Mallard? And what about non round pistons?
First, simply use the equation twice and add them together - but multiply the second equation by 0.5. Second, Pi is struck from the equation as a common factor in cylinder face area and driver circumference.
I was wondering, why U.S. steam engines for freight services have higher tractive effort than engines elsewhere. Even the largest German steam engine, the Class 45, had a tractive effort of 420 kN or 94400 pounds-force, compared with 600 kN or 135000 pounds-force for the Big Boy.
The rated tractive effort equation ignores machine friction. The use of K = 0.85 makes no allowance for machine friction. Some jurisdictions use K as low as 0.60, and if you see this it is an indicator that that particular road wanted to make an allowance for machine friction.
Some of that, I think, has to do with rail loading and clearances. A 135000-pound-force engine has to have about 540000 pounds of weight on the drivers to avoid slipping, and my impression is that European railroads aren't designed for that. They also have tighter clearances, and fitting a boiler large enough and long enough to produce that much steam into those clearances is difficult if not impossible.
(As an example of the latter -- if you look at the design of the NYC 4-8-4s, you can see that they were pretty much at the limit of what they could fit through some of their tunnels. And I'm pretty sure the NYC clearances were still bigger than German ones, even though they were small by U.S. standards.)
Feel like i need to put on my black framed glasses after that math :P .
" I became an engineer So i don't have to do math " .. does this sound familiar Hyce ??
Thanks for passing on your knowledge and busting these myths ,hope to meet you in person someday .... T W M
Lol, this was at least somewhat simple math!
What's the Tractive Effort equasion for geared Locomotives like a Shay? I assume theres something that works for those as well.
It would depend on the number of power impulses per revolution of the driving wheels - which depends on the gear ratio - which varies from locomotive class to locomotive class. So it would be a much more convoluted equation.
@@theimaginationstation1899I would assume (Bad word I know) that since Lima built every shay that they most likely had the same gear ratio on every locomotive, The difference being I think the number of pistons and trucks that were on each locomotive that really changes the way a Shay's tractive effort works realistically aside from gearing itself.
@@jeremeymcdude Fair point. The TE equation is very blunt. Number of power impulses is what counts - hence the equation for 2 cylinder locomotives allows for four power impulses.
Lima publish the tractive effort in their catalogues, so I guess the TE equation could be reverse engineered.
@@theimaginationstation1899 So i went back to a video to just check and it looks as though depending on class you have 2 or 3 cylinders all on the right that all they do is drive a drive shaft that then powers the truck wheels via gears on the shaft and trucks. it seems that it could be relatively simple for someone who ACTUALLY knows math unlike myself to figure out something that works.
Please cover diesel tractive effort
Anyone know the name of the tune playing at 5:26?
What about geared steam locomotives tractive effort calculations?
That should be fairly simple. Just do the same calculation but multiply it by whatever the gear ratio is between the cranks and the wheels. So if the cranks turn 3 times per wheel rotation then you have 3x as much TE.
That was great.
How do you calculate the tractive effort of a cog railroad engine?
You don't have wheel slippage.
Same, what you have is unlimited adhesion.
Mark the myth buster
What about an engine that has a super heater for the steam that adds around 100 degrees F to the steam. Wouldn’t this increase the pressure coming from the boiler. Should this be factored into the equation instead of the boiler pressure. According to one steam pressure vs temp F chart the extra 100 degrees would add 1.1 lbs for each 2 degrees F rise in temp. So that would make 200 lbs become 255 lbs under standard conditions.
Superheat doesn't add pressure, only temperature. It's one of the oddities of water - when it's contained, under pressure, as water and steam, yes the temperature and pressure are linked - i.e. temp goes up pressure goes up, but when you start talking superheat you can't have liquid water, which means that the pressure can stay the same while the temp increases. It's a separate thermodynamic table for superheated steam.
The Tractive effort equation was first published, in English, in 1836 - so it significantly pre-date superheaters. The only change to the equation was circa 1900 when 'K' was added to reflect mean effective pressure throughout the entirety of one stroke. 'K' = 0.85 is the assumed standard for mean effective pressure from starting to eight to ten miles per hour (it's actually piston speed rather than road speed, hence 8-10 mph). As piston speed increases K drops away.
Where superheated steam affects the tractive effort result is not in any increase in boiler pressure, but that the more fluid steam may well have a higher mean effective pressure through one stroke.
From time to time locomotives are touted as producing more than their rated tractive effort, but what that means is that the mean effective pressure through one stroke is higher - say 0.90, and that produces a higher tractive effort result.
The 225 pounds you suggest would not be achievable because the safety valves would lift at 200 pounds.
In any event, by the time superheaters became standard designers were looking for locomotives that could perform at higher road speeds, and the consideration shifted to producing horsepower at that desired road speed.
I believe the coefficient in the tractive effort isn't something calculated from other prrcise things like area of a circle or of a sine wave, but instead something to make the numbers work. this is because the ratio of the radius of the drivers and the diatance from the crank shaft pivot to the center of the driver isn't considered, even though it is really important, because it doesn't change _much_ across locomotives. So because all values rise linearly (other than the piston diameter but who cares) a simple cefficient can be used so that the funcion mathches real behaviour.
The ratio between crank diameter and wheel radius IS in the equation, it's just disguised. The piston stroke (last term on the top of the division) is just another way of saying crank diameter. And of course wheel diameter is on the bottom of the division.
@@John73John i did figire that out a few minutes after I wrote that, too lazy to edit
@@torfley Yeah we've all been there mate.
It's not. See Johnson (1944) and De Pambour (1836).
@@theimaginationstation1899 I don't know what that is, can you explain a bit more on what those are and how I can get to them?
Personally I'd really like little feet that grab and pull the track
10:46: I don't understand this part. Can anyone break it down a little? Thanks.
It's difficult to break it down easily, because the preceeding 10.46 is error-riddled. But at higher speeds less steam is admitted to the cylinders, so the mean effective pressure through one stroke is less, thus the tractive effort is less.
@@theimaginationstation1899 Thanks. That makes sense. When he was talking about it being bad for the locomotives I thought he was talking about diesel.
seems "tractive effort" is a bit of a misnomer since it doesnt include adhesion