i'm curious about how lead/trailing wheels support the locomotive yet still have lateral motion?
greg - Philadelphia & Reading / Reading
gregc i'm curious about how lead/trailing wheels support the locomotive yet still have lateral motion?
On a steam loco, there is a complex suspension. Every wheel, including the drivers, is sprung and equalized. Equaling means groups of wheels are connected to each other from front to back with a system of rods and levers much like the anti sway bar connects the left and right wheels on an automobile.
The exact designs vary from era to era as designs advanced and as different approaches were tried.
I will explain one or two.
The "Delta" single axle trailing truck has a single pivot point at the front center of the truck, similar to its model equal, but it also has a large flat slide plate under the rear of the loco cab, attached to the frame of the loco. On the truck, at each rear corner, matching bearing plates simply slide from side to side in a bed of grease. The axle bearings slide up and down in slots and have coil springs above them and the bearing housings of the truck are linked to the driver equalizer links with rods and levers. So the truck frame moves side to side, but not up and down. Up and down motion of the axle is allowed within the frame on its axle bearing springs, but that movement increases or decreases pressure on the drivers through the equalizer system.
Most two and four wheel lead trucks worked in a similar fashion to the Delta trailer, as did most later 4 wheel trailers. Look at a picture of a NKP Berkshire, the frame mounted rear bearing plate sticks out each side slightly just above the rear of the trailing truck, this is usually represented some way on most models.
A similar but different trailer design was used by the PRR on most of their home designed/built locos like the K4 - while very similar to the Delta, it placed the slide plate in front of the axle, not behind it. If you look at most well detailed models of a K4 you can see the bearing plate on the frame simulated with its vertical support ribs.
Remember, that unlike our models, the curves real trains go around are much larger and require only small movements of these parts, typically only a few inches of travel in each direction even on the sharpest curves they could handle.
Sheldon
Think of automobile suspensions. They support the car but have lateral motion. Loco's are a bit more complicated but the same basic idea. Don't look at model train loco's as an example. The leading and trailing wheels are basically there for show and some guidance but don't support any weight.
Springfield PA
Hamltnblue Think of automobile suspensions. They support the car but have lateral motion.
Think of automobile suspensions. They support the car but have lateral motion.
Automobile designers go to great lengths to have minimal lateral motion. It can never be eliminated, but they try--under such constraints as cost and weight.
Ed
While Sheldon is essentially correct in his discussion of locomotive trucks, I must disagree that the Delta trailing truck was supported at the rear by two flat plates sliding laterally on grease. There was, between the rear of the truck and the frame member above it, a "rocker". I quote from my ever favorite book on steam locomotive technology, Alfred W. Bruce's "The Steam Locomotive in America":
"...the inverted-rocker device was introduced about 1914. The inverted rocker was a heart-shaped rocker resting on two rolling contacts at the bottom and supporting two inclined planes at the top--one on each side of its apex center point. Thus movement in either direction produces a rolling-contact support which permits ample lateral movement with nearly any desired resistance characteristic, a quality that has retained this device in use today [approx. 1952]."
See also reference to "inverted-rocker" in the below:
http://en.wikipedia.org/wiki/Trailing_wheel
The "resistance characteristic" (to lateral motion) was provided by the "inclined planes" noted above. If there was no incline, there was no lateral resistance.
Previous to the rocker system, I believe they used swing-links, which pretty much act like they sound.
Lead truck support is not mentioned in Bruce, but I would expect it to have been similar. The only thing that might make a difference is that a steam locomotive was a three-point suspension system: the equalized left side drivers and trailing wheels, the equalized right side drivers and trailing wheels, and, at least in the case of 4 wheel lead trucks, the lead truck. That might have caused design differences. Incidentally, for locomotives with no lead trucks, the first driving axle was used instead for the "third point". I'm not sure how the two wheel lead truck fit between these two.
As far as I am aware you should find that relatively little weight was put onto leading and trailing axles. To the best of my knowledge they were there to facilitate smooth operation of the loce - especially as higher speeds were used - and to accomodate the requirements of larger fireboxes and longer front ends.
The main weight of a loco was not just carried on the Drivers but the engineers wanted as much of it there as possible - the amount of weight on the drivers directly related to how much of the total power capacity of the loco could be put down on the track. To some extent weight distibuted to leader and/or trailing trucks meant a loss of capacity. As always there was a balance to be achieved. this is why you are likely to see more fast passnger types with leading and trailing trucks and more freight locos without them. Switchers, moving slowly most of their lives, rarely had trucks so that they could get all of their power down to shove cars around.
7j43k While Sheldon is essentially correct in his discussion of locomotive trucks, I must disagree that the Delta trailing truck was supported at the rear by two flat plates sliding laterally on grease. There was, between the rear of the truck and the frame member above it, a "rocker". I quote from my ever favorite book on steam locomotive technology, Alfred W. Bruce's "The Steam Locomotive in America": "...the inverted-rocker device was introduced about 1914. The inverted rocker was a heart-shaped rocker resting on two rolling contacts at the bottom and supporting two inclined planes at the top--one on each side of its apex center point. Thus movement in either direction produces a rolling-contact support which permits ample lateral movement with nearly any desired resistance characteristic, a quality that has retained this device in use today [approx. 1952]." See also reference to "inverted-rocker" in the below: http://en.wikipedia.org/wiki/Trailing_wheel The "resistance characteristic" (to lateral motion) was provided by the "inclined planes" noted above. If there was no incline, there was no lateral resistance. Previous to the rocker system, I believe they used swing-links, which pretty much act like they sound. Lead truck support is not mentioned in Bruce, but I would expect it to have been similar. The only thing that might make a difference is that a steam locomotive was a three-point suspension system: the equalized left side drivers and trailing wheels, the equalized right side drivers and trailing wheels, and, at least in the case of 4 wheel lead trucks, the lead truck. That might have caused design differences. Incidentally, for locomotives with no lead trucks, the first driving axle was used instead for the "third point". I'm not sure how the two wheel lead truck fit between these two. Ed
Ed, You are correct and I am aware or the that part of the design, I left out those details for simplicity of an already complex mechanical system.
In fact, all lead and trailing wheel systems incorporate various forms of laterial motion resistance that help steer and stablize the the loco entering and exiting curves - but for the purpose of explaining how thE weight is carried transfered - it is esentially two plates in direct contact.
Dave-the-Train As far as I am aware you should find that relatively little weight was put onto leading and trailing axles. To the best of my knowledge they were there to facilitate smooth operation of the loce - especially as higher speeds were used - and to accomodate the requirements of larger fireboxes and longer front ends. The main weight of a loco was not just carried on the Drivers but the engineers wanted as much of it there as possible - the amount of weight on the drivers directly related to how much of the total power capacity of the loco could be put down on the track. To some extent weight distibuted to leader and/or trailing trucks meant a loss of capacity. As always there was a balance to be achieved. this is why you are likely to see more fast passnger types with leading and trailing trucks and more freight locos without them. Switchers, moving slowly most of their lives, rarely had trucks so that they could get all of their power down to shove cars around.
Dave, this is not true, many steam locos had lead and trailer axle loadings equal to anywhere from 60% to 100% of whatever the driver axle loading was.
A NKP Berkshire has 254,000 lbs on the drivers - 63,500 on each. The locos total weight is 421,000 lbs, leaving 167,000 to be carried by the lead axle and two trailing axles - about 55,666 lbs each.
I don't think that it is completely "not true". I'm not an engineer but I have read an awful lot of stuff from engineering journals and similar from steam days - and in this case more from the USA than the UK - because they provided more of this kind of information.
I am not saying that some weight was not wanted on the leading and trailing trucks but that the majority of weight was wanted on the Drivers. As far as I can see it is exactly the same as wanting to get the power down with any vehicle.
I think that one possibly confusing factor is that as boilers and fireboxes got larger the need for trucks increased. This meant that an increasing % of the weight had to be distributed out to leading and/or trailing trucks. They simply couldn't focus the weight over the Drivers. They needed a certain amount of weight on the non-driven wheels to keep them firmly on the track and, in the case of a single axle leading truck, to keep it doing its job of leading the front end of the loco into curves at higher speeds. But. apart from keeping the truck on the rails what purpose would putting weight onto trucks serve? Every pound not on the drivers is weight that has to be carried/ moved that isn't doing anything. Yes, it has to be there in the form of the boiler/firebox/frame etc but the job of the whole thing is to get power down onto the track. Leading and trailing wheels don't do that... but they do and are necessary to carry the total weight of the loco.
As to the specific example... I don't recall the terminology and certainly not the type. (You had a few more wheel arrangements than we had and didn't always use the same nomenclture). I'm guessing that the NKP Berkshire was a fast passenger loco.
If I am correct the engineer's targets would have included proportionately more boiler capacity for sustained high speed runs against the need to get a lot of traction down on the track to get and keep heavy freight drags moving.
As I understand it this is why there were such enormous differences between fast passenger locos and heavy freights in steam days while there can be almost no external differences except styling and whether a loco is streamlined or not with both diesel and electric traction.
I hope that someone can clarify this.
Another factor that comes to mind is rail and bridge loading. I know that some locos had their weight distributed to accomodate lighter rail. weak bridges or both. this can be why relatively small and short narrow gauge locos were built with the complication and greater costs (first cost and maintenance) of articulation.
Dave,
The loco I referenced is a Nickel Plate Road, Berkshire type, 2-8-4. These were fast freight locos and considered by many to be one of the best of modern North American Super Power steam.
A photo or two:
http://www.rr-fallenflags.org/nkp/nkp-s765dgd.jpg
http://www.rr-fallenflags.org/nkp/nkp-s726.jpg
http://www.bachmanntrains.com/home-usa/products.php?act=viewProd&productId=1952
A review of loco driver weights and total weights of most 20th Century North American locos will provide similar results to those I posted.
A lot of this data is a available at www.steamlocomotive.com
It is a combination of all the factors you mentioned, and balance is the key. Enough weight on the drivers to maximize tractive effort, enough on the lead and trailing trucks for good "steering" and high speed stability. And a light enough axle load overall so as to not damge track while carrying the largest, most efficient boiler possible.
Actually, the loco I used as an example, could have been built with single axle trailing trucks for some railroads who had very heavy track. And you are correct, they would have had even more TE, at the expense of needing heavier rail and wearing track faster.
In my modeling I actually model such a loco for my freelanced ATLANTIC CENTRAL.
If we had to pick and "average" weight on lead and trailing axles compared to weight on drivers, it would likely be at least 2/3rds of the driver axle load in most cases.
Here are a few more examples:
Pennsylvania RR, K4 Pacific, 4-6-2, designed 1930 http://www.steamlocomotive.com/pacific/?page=prr
loco weight - 304,500 lb
on three drive axles - 199,500 lb / 3 = 66,500 lb
on three idle axles - 105,000 ib / 3 = 35,000 lb
C&O H8, 2-6-6-6, designed 1941 http://www.steamlocomotive.com/allegheny/
loco weight - 771,300 lb
on six drive axles - 508,000 lb / 6 = 84,666 lb
on four idle axles - 263,300 ib / 4 = 65,825 lb
USRA 2-8-2 Heavy, designed 1917/18 http://www.steamlocomotive.com/mikado/?page=usra
loco weight - 325,000 lb
on on four drive axles - 240,400 lb / 4 = 60,000 lb
on two idle axles - 85,000 lb / 2 = 42,500 lb
Detroit, Toledo & Ironton 800 class 2-8-2, designed 1940 http://www.steamlocomotive.com/mikado/?page=dti
loco weight - 369,500 lb
on on four drive axles - 248,500 lb / 4 = 62,125 lb
on two idle axles - 121,000 lb / 2 = 60,500 lb
It is said that on this loco, the lead truck carried about 50,000 lb and the trailer 71,000 lb, making the trailer actually carrying 115% of the drive axle loading.
I have previously done a moderate amount of study into this question, mainly for my own understanding and to make my freelanced locos all plausable.
And a few examples of smaller, earlier locos:
C&NW G3 Atlantic, 4-4-2, designed 1900 http://www.steamlocomotive.com/atlantic/?page=cnw
loco weight - 159,500
on two drive axles - 92,500 lb / 2 = 42,250 lb
on three idle axles - 67,000 ib / 3 = 22,333 lb
IC class 57 Ten Wheeler, 4-6-0, designed 1904 http://www.steamlocomotive.com/ten-wheeler/?page=ic
loco weight - 140,000 lb
on three drive axles - 111,500 lb / 3 = 37,166 lb
on two idle axles - 28,500 lb / 2 = 14,250 lb
Yes, at the turn of the century the amount of weight on lead wheels (few locos had trailing wheels yet) was less, but as you can see from the examples, not far into the 20th century this changed quickly.
As fro the difference between freight and passenger designs, the easiest way to understand that is to compare the USRA light 2-8-2 ( freight loco) to the USRA light 4-6-2 ( passenger loco).
Both locos used the exact same boiler.
The 2-8-2 had four sets of 63" drivers, cyl 26" x 30" stroke, produced 54,724 lb of tractive effort with 221,500 lb on the drivers and had a top speed of about 50 mph. More power/less speed
The 4-6-2 had three sets of 73" drivers, cyl 25" x 28" stroke, produced 40,753 lb of tractive effort with 162,000 lb on the drivers and had a top speed around 75 mph. More speed/less power
Same boiler HP, approximately the same loco total weight - simply traded speed for power by changing driver size, quantity and cylinder bore and stroke.
The long stroke and small drivers of the 2-8-2 provides power, but lmited speed.
The shorter stroke and large drivers of the 4-6-2 provides much higher loco speed, while keeping piston speeds similar (and thereby steam consumption), at the expense of starting torque and tractive effort.
In the last days of steam, super power designs found the perfect balance of speed and power for both freight and passenger - the SP GS4, N&W J, N&W Class A, UP FEF,UP Big Boy & Challenger, C&O J-3, just to name a few.
You have done a good example of axle loading and how the weight is distributed across the locomotive. There were also some examples that Baldwin had the patent for in shifting some of the weight from the tender to the loco for heavy traction needs. These were mainly applied to switcher and light road units. I read about this in an old locomotive cyclopedia.
As for comparing a locomotive suspension system to a cars is way off. It would be a lot closer to a semi trailers 4 spring equalized suspension. Not the modern air ride type. The sprung and equalized suspension tied the two axles together between the axles with a rocking type equalizer that when the front axle would ride up the rear axle would also ride down and take some weight from the front axle and transfer it to the rear. This would give a smoother ride than a non equalized system. This PDF of a Reyco trailer suspension shows the rocking equalizer between the springs.
http://www.reycogranning.com/Support/elibrary/PDF%27s/Products/Brochures/86_88%20Tearsheet.pdf
Pete
I pray every day I break even, Cause I can really use the money!
I started with nothing and still have most of it left!
locoi1sa Sheldon You have done a good example of axle loading and how the weight is distributed across the locomotive. There were also some examples that Baldwin had the patent for in shifting some of the weight from the tender to the loco for heavy traction needs. These were mainly applied to switcher and light road units. I read about this in an old locomotive cyclopedia. As for comparing a locomotive suspension system to a cars is way off. It would be a lot closer to a semi trailers 4 spring equalized suspension. Not the modern air ride type. The sprung and equalized suspension tied the two axles together between the axles with a rocking type equalizer that when the front axle would ride up the rear axle would also ride down and take some weight from the front axle and transfer it to the rear. This would give a smoother ride than a non equalized system. This PDF of a Reyco trailer suspension shows the rocking equalizer between the springs. http://www.reycogranning.com/Support/elibrary/PDF%27s/Products/Brochures/86_88%20Tearsheet.pdf Pete
Pete, Thank you. I agree cars and trains are nothing alike. The OP obviously is starting from scratch so I thought the sway bar might be something he already understood, and it does work from left to right like and equalized suspension. The truck example is great, just like a steam loco. I grew up around trucks, my father ran a truck shop and was a terminal manager for Carolina for many years.
But I figured most people don't really know a lot about trucks either.
All of this info just begins to scatch the surface of this suspension thing - I tried to keep the explaination of the OP's question as simple as possible, we see how that worked out.
Hello Sheldon,
You've made many good points in this discussion, but in stating that the USRA light Pacific and light Mikado had the same boiler you are perpetuating an error that has caught a few model manufacturers as well. The first ring of the light Pacific boiler was 76 inches in diameter, and the largest ring had a diameter of 86 inches. The light Mikado boiler was 78 inches in diameter at the first ring, and its largest ring was 90 inches in diameter. That makes the light Mike's boiler bigger than the light Pacific's.
This difference also shows up in the numbers of boiler flues and tubes. The Pacific had 36 5-1/4-inch flues and 188 2-1/4-inch tubes. The Mikado had 40 5-1/2-inch flues and 216 2-1/4-inch tubes. Tube length was the same for both, 19 feet.
Where the two engines were the same was the firebox, 115 x 85 inches for both, with a grate area of 66.7 square feet. Both engines had combustion chambers, the Pacific's 23-1/2 inches in length and the Mike's just 1/2 inch longer.
Still, the larger boiler diameter allowed the Mike's firebox to have a greater heating surface, 253 square feet as opposed to 242 for the Pacific. The Mike is also ahead in evaporative heating surface, 3,777 square feet to 3,341, because of the difference in the numbers of flues and tubes.
So any comparison of the USRA light 2-8-2 and light 4-6-2 should consider the Mikado's larger boiler and its advantage in heating surfaces.
So long,
Andy
Andy Sperandeo MODEL RAILROADER Magazine
Andy,
Somewhere in the deep of my memory I do recall those differences, and "very similar" would have been a better discriptor. Thank you for reminding me of that.
That fact that they are so similar still makes it a great example of speed vs power in steam design.
You know the old saying, "A picture is worth a thousand words" - so I thought I would find some pictures of lead trucks to give the OP a good idea about how they do what they do. However, I soon found out that pictures of steam locomotive pilot truck suspensions are hard to find... I think there are more pictures of the Loch Ness Monster than pilot trucks!
Anyway, a pilot truck has to rotate and move laterally to guide the locomotive around the curve. The lateral motion also needs to be self centering in order to properly guide the locomotive. It is interesting to note that in steam locomotive development, the four wheel lead truck was really the first in general use. Even the famous John Bull - having been modified with the addition of a two wheel lead truck - had the lead truck tied to the front "driver" axles, and the connecting rods removed from the axles so the 0-4-0 was really turned into a 4-2-0. Norris and Baldwin were known for their 4-2-0 locomotives, with the 4 wheel pilot truck using just a simple pivot. It wasn't until the advent of the 4-4-0 that a lateral motion device was needed, and even then some early 4-4-0's used just a simple pivot instead of the swing links or heart shaped rockers. So, we start with 0-4-0 for maximum traction, go to 4-2-0's for tracking ability, which then expanded to 4-4-0 and 4-6-0's for greater tractive effort while maintaining the tracking ability afforded by a 4 wheel lead truck and three point suspension. It wasn't until the Bissell 2 wheel lead truck was invented in 1857 or '58 that 2-6-0 and 2-8-0 freight locomotives became practical... again, a step to putting more weight on the drive wheels for tractive effort. However, it was generally felt that the four wheel lead truck was more stable at speed, hence the use of four wheel lead trucks on most of the later high speed passenger, freight and dual purpose steamers (4-6-4, 4-8-4, etc.)
First, this is the pilot truck for Northern Pacific #1364:
You can see the frame that holds the axles and springs in place. At the top center, there is a round area where the kingpin goes to allow the truck to rotate. That is part of a carrier that is supported by rockers, which allow the truck to move sideways in relation to the kingpin.
Next up is a Gresley two wheel lead truck:
Again, you can see a round plate on top that supports the locomotive's frame. The top hinges for the swing links can be seen on either side of it. The long tongue to the right of the locomotive actually goes back and attaches to the loco frame with a pivot. When the truck rotates, it rotates around the pivot at the end of the tongue (out of the picture to the right), while the round plate on top supports the locomotive frame, the rest of the truck moving laterally by means of the swing links. This is an adaptation of the original Bissell design.
Last and most certainly least, this is a four wheel pilot truck I built for a live steam 4-4-0:
It is a little crude, but the basic elements are there. The locomotive frame bolts to the rectangular plate at the top center of the truck. That plate is attached to the kingpin, which rides in a tapered roller bearing to allow the truck to swivel. The housing for the bearing is then supported by four swing links as seen in the picture. Those links go to a sub-frame for the truck, which is then supported by the springs to the main frame of the truck. Note that when the kingpin is centered on the truck, it is at its lowest position. As it moves to either side, it will actually rise so it transfers more weight to the pilot truck. This is what guides the locomotive around the curves. Again, this is somewhat different from a prototype 4-4-0 pilot truck, but just mainly due to the fact that I used coil springs instead of leaf springs, which made it necessary to change the frame. More sophisticated four wheel lead trucks used the heart shaped rockers, which gave a more positive centering mechanism and an accelerated rate of weight transfer to help guide the engine around the curves.
Whew! I'll let somebody else find pictures of trailing truck suspensions! Anyway, I hope that helps explain what the lead trucks do...
- James
Sheldon chose poorly when he compared an equalized suspension to a sway bar on a car. Sway bars do not (and should not) support the weight of a car as do the suspension springs. Sway bars help limit the roll of the car body on its suspension during cornering. Sway bars have no effect in a straight line or over bumps. If they do, they were installed incorrectly. Examples of equalized suspensions can sometimes be seen on tandem axle car trailers using rigid axles and leaf springs. The leading and trailing spring mounts are fixed on the trailer chassis while the center spring mounts attach to either end of a common rocker arm that pivots on it's center. The idea is that when one wheel must lift to go over a bump, the rocker arm transfers, or equalizes, weight to the other wheel(s).
Also, Ed rightly corrected Hamiltnblue in that auto suspensions ideally should not have any lateral travel. However, the real reason that lateral travel occurs in auto suspensions is due to the rubber or other resilient material bushings and attachment points in a suspension used to make sure the suspension is quiet. It blew me away the few times I had to be towed back to the pits in my race car how much noise a suspension makes with all the rubber pieces replaced with solid bushings and ball joints. I just couldn't hear all that racket with the engine running!
Hornblower
hornblower Sheldon chose poorly when he compared an equalized suspension to a sway bar on a car. Sway bars do not (and should not) support the weight of a car as do the suspension springs. Sway bars help limit the roll of the car body on its suspension during cornering. Sway bars have no effect in a straight line or over bumps. If they do, they were installed incorrectly. Examples of equalized suspensions can sometimes be seen on tandem axle car trailers using rigid axles and leaf springs.
Sheldon chose poorly when he compared an equalized suspension to a sway bar on a car. Sway bars do not (and should not) support the weight of a car as do the suspension springs. Sway bars help limit the roll of the car body on its suspension during cornering. Sway bars have no effect in a straight line or over bumps. If they do, they were installed incorrectly. Examples of equalized suspensions can sometimes be seen on tandem axle car trailers using rigid axles and leaf springs.
This was previously commented on and answered - I did not mean to imply that an automotive anti sway bar supported the weight of the car, but rather that it transfers loads in a similar fashion as an equalized suspension. In my earlier post with Pete I aknowledged that the sawy bar was not the best example, but I figured if the OP did not have this knowledge of trains, he might not have a background in truck or trailer suspensions either. BUT, a much broader base of people have some basic understanding of an anti sway bar, which do more than just minimize body roll in cornering. They do load, or transfer force, to the other side of the suspension on straight line bumps that effect only one wheel.
The earlier post is copied below:
locoi1sa: Sheldon You have done a good example of axle loading and how the weight is distributed across the locomotive. There were also some examples that Baldwin had the patent for in shifting some of the weight from the tender to the loco for heavy traction needs. These were mainly applied to switcher and light road units. I read about this in an old locomotive cyclopedia. As for comparing a locomotive suspension system to a cars is way off. It would be a lot closer to a semi trailers 4 spring equalized suspension. Not the modern air ride type. The sprung and equalized suspension tied the two axles together between the axles with a rocking type equalizer that when the front axle would ride up the rear axle would also ride down and take some weight from the front axle and transfer it to the rear. This would give a smoother ride than a non equalized system. This PDF of a Reyco trailer suspension shows the rocking equalizer between the springs. http://www.reycogranning.com/Support/elibrary/PDF%27s/Products/Brochures/86_88%20Tearsheet.pdf Pete
As already noted in the thread, the weight of the locomotive is transferred to the springs and equalizers at three points. Two points are the rear corners of the frame, the third point is between the cylinders. The theory is that a tripod can accommodate an uneven surface, while a chair with four legs would rock.
The suspension is divided into two sections. As an example, on a 2-8-4 the lead truck is equalized with the first two driving axles. The weight rested on the equalizer between the lead truck and the first driving axle. The two rear driving axles are equalized with the trailing truck. There is no connection between the two sections.
The swing links on the Gresley lead truck pictured above are similar to U.S. practice. The truck differs from U.S. practice in that the British did not use equalizers.
Examples of spring rigging and provisions for lateral movement of leading and trailing trucks can be found in the "Model Railroader Cyclopedia- Vol. 1 Steam Locomotives" and the "Locomotive Cyclopedia 1941", both published by Kalmbach.
The drawing for the Union Pacific 4-12-2 in the "Model Railroader Cyclopedia" may not be correct. The blueprints and photographs in the book "The Union Pacific Type" by Kratville and Bush show the lead truck equalized with the first two driving axles.
Eugene Crowner