There were some tidbits which I couldn't fit into the main article ("Saddling the Iron Horse," Grantville Gazette 7), but I thought I should preserve for

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Locomotive Addendum


Iver P. Cooper

There were some tidbits which I couldn't fit into the main article ("Saddling the Iron Horse," Grantville Gazette 7), but I thought I should preserve for reference purposes.

I have grouped the information according to the headings in the Iron Horse article. Please note that this Addendum is going to seem very disjointed to anyone who has not read the main article recently.

1. Railroading in 1632 Canon

In Elizabeth, Ken Hobbs mentions that there was abandoned main line track in the middle of town, which was just paved over. This, he implied, could be salvaged--of course, at the cost of damaging asphalt roads in a world in which asphalt is relatively hard to come by.

More particulars on the Grantville-Halle line: "On a cold spring morning in 1634 a new train was loading up in Grantville to move north.... Another difference was the load on this train was made up of steel-wheeled railcars, not rubber tired vehicles. These trains were loaded on the standard gauge flatcars for transport to Halle, where they would be loaded on barges." (Elizabeth).

2. Grantville Railroading Knowledge

2.1. Several children's books, which may be in personal libraries in Grantville, are surprisingly informative.

Weitzman, Locomotive: Building an Eight-Wheeler (1999) is set in 1870 and describes the drafting stage, factory equipment (engine, drill press, lathe, planer, steam hammer, overhead crane), and various process steps (cutting, rolling, hole punching and riveting the sheets to make boilers; molding the bell, erecting the locomotive, and hand-finishing the parts so they fit together). The locomotive, a wood burner, is said to have taken eight weeks to construct, and to have 72 inch cast iron drivers, a boiler pressure of 12 p.s.i., and 3,000-pound cylinders.

Johnstone, Look Inside Cross-Sections: Trains (1995) depicts an American 4-4-0, using an exploded view, and notes that in 1870, 85% of U.S. locomotives had that wheel arrangement. The most interesting features depicted are the lead bogie truck (with one axle and wheel omitted), and the boiler flue tubes (I counted 109).

On the drawing of a 4-12-2, you can spot an equalizing lever over the drivers. Page 18 notes that "like most steam locomotives, the 4-12-2 was fitted with an arch made of fireproof bricks at the front of the firebox. It acted as a baffle to make the coals burn at maximum heat and cut down the quantity of smoke produced." Johnstone also notes that the front and rear driver had sideplay, enabling the 4-12-2 to negotiate a 16 degree curve.

The 4-12-2 is said to have three cylinders (27x32, 27x31), 67 inch drivers, a weight of 202 tons, a top working speed of 60 mph, and a wheelbase of 52'3".

There are also depictions of Pacifics (4-6-2) and a rack loco.


2.2. While there are no steam locomotives in Grantville, we can find other useful equipment. For example, the West Augusta Historical Society in Mannington, West Virginia apparently has a "captive caboose," designation "B&O C2283", which is a Class I-5d. That means that we have the opportunity to examine up-time couplers, brake, and wheels. The Society has other artifacts from the heyday of railroading in Mannington.

Others have no doubt been collected by rail fans.

Jeffrey S. Ward, Sr. explained on the Atlas forum that over the decades, B&O operators on the branch lines in the area "would have been glad for somebody to talk to, and would probably have been pretty loose with timetables, train orders, and other assorted railroad paraphernalia," and thus the local rail fans would have been able to pick up a fair amount of "railroadiana" in flea markets.

A search of attics and basements might also produced unexpected marvels; perhaps a former resident worked on the railroad, and left memorabilia behind.

Of the probable finds, the most useful would be rulebooks, textbooks, and tools.


2.3. By way of guidance as to what a Grantville railfan might have, Trynn Allen (on the Atlas forum) noted that his personal library comprised "about two dozen issues of Model Railroader, three books on engines, two books with lots of pictures of engines and rolling stock, and the models themselves."

2.4. One book I really hope the up-timers have in Grantville is Comstock's The Iron Horse (which I found at the Fairfax County Public Library). Its felicities include illustrations, with discussion, of the parts of a steam locomotive (front endplate), Jervis' three point suspension (39), locomotive stack designs (45), reversing mechanisms (46), the Bury firebox (54), Miller's traction increasing levers (62), Harrison's equalizing levers (66), Baldwin's flexible beam truck (74), sand domes (88-9), wagon-top boilers (102), an exploded view of The General (104-5), a double-ended locomotive (108), a swiveling engine unit (109), the Stephenson valve gear (110), the Walschaerts valve gear (111), the first Westinghouse air brake (125), pumps to increase draft (127), a firebox with a brick arch (129), Shay, Heisler and Climax geared locomotives (158-9), thermic siphons (194), water circulators (195), and an exploded view of a "Big Boy" (back endplate). There is a lot more here, too. For example, Comstock notes that the three-point suspension system made it possible for the seven ton John Bull to run on metal-surfaced wooden rails (38-9), and explains the problems encountered with water tube fireboxes (182).

2.5. While the main article only cites the 1911 Encyclopedia Britannica, and its modern counterpart, the enthusiastic efforts of encyclopedia salesmen pretty much guarantees that there are editions from the eighties, seventies, sixties, fifties and forties in homes in Grantville. They were probably purchased when the kids were in middle school or high school. The old encyclopedias may lie forgotten in an attic or basement, but they are there. I saw a 1955 set being given away at a library, and looked at the locomotive entry. While the article gave more space to diesel-electrics, it had a respectable amount of material on steam locomotives. This included some very detailed views of a Pacific 4-6-2 locomotive, with cab, firebox, boiler, drive wheel, cylinder and smokebox details. An encyclopedia from the forties or thirties, when steam was still dominant, would no doubt be even more helpful.

3. Motive Power

3.1. The smallest of the Vulcan gasoline locomotives listed by Connor weighs four tons, has a 25 horsepower engine, sixteen inch diameter drivers, and a rated drawbar pull of 1,600 pounds. Thus, if the train resistance per ton is ten pounds, then the locomotive can haul 156 tons of cargo, probably at about 5 mph. The largest locomotive in the table weighs fifteen tons, has a ninety horsepower engine, twenty-five inch drivers, and a rated drawbar pull of 6,000 pounds. So it can haul, under the same rail conditions, 585 tons of freight.


3.2. It is also possible to power a locomotive from a central station. The latter generates electricity and transmits it to the locomotive, which uses it to power electric motors which turn its wheels. While these electric locomotives are used in modern high speed transit systems, they require an extremely expensive infrastructure (the central station, electrified rails or overhead lines, etc.). Right now, we have to focus on what is feasible with the USE's present resources, which are stretched thin by the war. Steam locomotion seems the best approach.


3.3. In steam-electric locomotives, the steam engine drives an alternator or generator, which in turn powers an electric motor which drives the axles. The advantage is the elimination of the reciprocating rods; the disadvantage is the inefficiency of the energy conversion. There have also been a few steam-turbine locomotives.


3.4. Diesel-electric locomotives (in which the diesel engines power electric motors) have low operating costs, but high initial costs--perhaps five times that of a steam locomotive of equal horsepower. (NOCK/RE 203).


3.5. According to Douglas Jones (private communication), "Natural gas conversion may be used locally around Grantville. This is canon for the trolley system, but if I was using a pickup truck as an engine locally, I'd use a natural gas converted gasoline engine. These will need regular refills. Rubber and plastic hose is not safe for use with methane (it suffers from methane embrittlement and has a working life of only a few months at pressure), so they'll have real problems refilling high pressure portable methane tanks from fixed compressor stations. There will probably be corrugated stainless steel gas piping (the kind used to plumb natural gas into houses) that they can use, to a limited extent. The total supply of such pipe will probably be only a few tens of yards. Common air compressors will work just fine to compress the methane."

4. Fuel

4.1. Fuel Efficiency. One pound of good coal yields about 15,000 British Thermal Units (BTUs) heat energy, of which 50-80% is transferred to the water. When the steam is released from the steam dome into the cylinders, about 7-11% actually does work (i.e., moves the pistons), and the rest escapes. So the overall thermal efficiency is only about 6% (900 BTU per pound of coal). (EB11)

4.2. Exotic Fuels. In theory, it is also possible to burn natural gas, or crude biomass such as peat, rapeseed, hemp, corn, sawdust or sugarcane waste. However, these possibilities are best explored after we relearned how to build a more-or-less traditional locomotive.

4.3. In terms of heating capacity, the general rule is that 2,000 pounds of coal is equivalent to 5,250 pounds (1.75 cords) of wood.

4.4. The American Far West was coal-poor, so railroads in that area were eager to switch to oil burning after the big California oil strikes.

4.5. Another good reference on the subject of coal quality is Anonymous,"Australian Coal,"

5. Engineering Design 101

6. Steam Locomotion

7. Basic Train Resistance to Motion (Straight, Level Track)

7.1. EB11 formulae contemplate speeds of 37-77, or even 47-77, mph, which may be a trifle fast for the first few years of the USE rail system. USE engineers may therefore need to determine the appropriate formulae for their rail operations by putting a "dynamometer car" between engine and the train, and measuring the drawbar pull at different speeds.

7.2. Physicists teach that rolling friction is inversely proportional to wheel diameter [cite]. However, in practice, wheel diameter doesn't have much effect on train resistance. I believe that this is because rolling friction is only one of many factors contributing to train resistance.

7.3. Initially, to get a train moving, you need about twenty pounds of force for every ton of load. Fortunately, because of coupling slack, the locomotive only needs to start one car at a time.

Starting resistance is to overcome friction with the wheel bearings, and is higher (25-30) for journal bearings than for roller bearings (5-15)(AREMA). Once the train is actually moving, the "basic resistance" is much lower.

7.4. The train "punches a hole" in the air, so the locomotive encounters much more air resistance than do the cars it is hauling.

8. Extra Train Resistance (Grades and Curves)

8.1. The locomotive must be given sufficient tractive force to haul the expected load over the "ruling grade" of the track. The first "mountain railway" in Germany (Windbergbahn, 1856) had a gradient of 2% (steep by modern standards), but even higher gradients were occasionally tolerated on main lines in early nineteenth century America (e.g., 5% at Kingwood Tunnel on the original B&O).

8.2. The sharper the curve, the greater the problems presented. (Armstrong, 26). Sharpness can be expressed as 1) the angle through which the track turns in 100 feet, say, one degree, or as the radius of the circle corresponding to the curve (for a one degree curve, it is 5,729 feet). The Windbergbahn had a twenty degree (286 feet radius) curve.

When a train goes around a curve, centrifugal force causes its wheel flanges to grind against the rail. This creates curve resistance.

It also cause the train to tip outward. Depending on the exact design of the track, a train on a curve might have to slow down to avoid derailing. The speed on a fifteen degree curve might be half that on a five degree one, and one-quarter that on a mild one degree veer.

As it comes out of the turn, the train must accelerate to regain its former speed.

8.3. You need extra tractive force (above and beyond that needed to overcome the base train resistance) whenever you want to accelerate; as Newton said, Force equals mass times acceleration. According to EB11, the acceleration resistance equals the weight of the train, multiplied by the ratio of the desired acceleration to gravitational acceleration.

9. Rated Tractive Force

9.1. To achieve the maximum traction, the engine would need to have appropriately sized cylinders, piston rods and wheels, and the boiler needs to generate sufficient pressure in the cylinders.

9.2. The mean effective pressure in the cylinder is a function of the actual boiler pressure, and the "cutoff"; steam is admitted only for part of the stroke; and then is just allowed to expand against the piston. A long cutoff is used when you want to start the train, or pull an especially heavy load. A short cutoff is more economical. For starting the train, the cutoff is typically such that the mean effective pressure is about 85% of the boiler pressure.

9.3. Even when you have a full head of steam, there is no point in admitting steam into the cylinder for the entire stroke. That is because the steam does work only when the crank is not parallel to the main rod. (Maximum work is done when the crank is at right angles to the main rod.) For the remainder of the stroke, the steam expands and the cylinder pressure drops accordingly. So the cylinder pressure, averaged over the entire stroke, is less than the actual boiler pressure. See

9.4. Even with a long cutoff, the boiler pressure drops below the nominal value if you increase the piston speed, and the boiler can't keep pace with the demand for steam. Hence, it is customary for the cutoff to be reduced when speed is increased, so that the steam demand is sustainable. Reducing the cutoff naturally also reduces the mean effective pressure.

9.5. The standard value 0.85 is apparently a compromise value representing the effect of steaming capacity on mean effective pressure. One online source quotes a classic text (Hay's Railroad Engineering, 1953) as giving the following dependence of mean effective pressure on locomotive speed:

Speed (mph) Proportion of Rated Tractive Effort Available

10 .997

20 .90

30 .705

40 .535


Note that 0.85 corresponds to a speed in the 20-30 mph range.

9.6. Other sources express mean effective pressure as a function of piston speed. Connor (88) says that the mean effective pressure is 42.5% of boiler pressure at a piston speed of 750 feet/minute, 30% at 1,075, and 22% at 1,500.

9.7. A table in the Baldwin Locomotive Company catalogue assumes that the longest cutoff is such that the mean effective pressure is no higher than 85% of the boiler pressure. I have studied the various trend lines to deduce the underlying formula relating the mean effective pressure to the locomotive speed and a measure of steaming capacity (the ratio of rated tractive force in pounds to heating area in square feet). Above a speed equal to 120/ratio (e.g., 12 mph for the typical American, ratio 10, the MEP as a percentage of nominal boiler pressure is

0.85 * 15,000 /(speed mph * ratio)

So, if speed 30 mph, and ratio is 10


For lower speeds, the mean effective pressure, as a percentage of boiler pressure, is

0.85-(.000354*ratio*speed) * 100

So at 10 mph, with ratio 10, the MEP is about 81.5% of the boiler pressure.

The same catalog also says that the rate of supply of steam is only just adequate for the desired engine power when there is one horsepower for each 2.5 square feet of heating area.

10. Maximum (Adhesion-Limited) Tractive Force

10.1. If the rolling friction is so small (a few pounds per ton of load), why is the coefficient of adhesion so high (400-500 pounds per ton of locomotive)? In essence, we are looking at the difference between rolling friction, and sliding friction. The coefficient of adhesion is actually measuring the tendency of the locomotive to slip, and that is related to sliding friction rather than rolling friction. With many surfaces, it requires much less force to roll than to slide.

For steel on steel, the coefficient of rolling friction is [insert], while that of sliding friction is [insert] (static, i.e., from rest) or [insert] (dynamic, i.e., if you are already moving).

Iver, Check

11. Weight and Size

11.1. Clarke (121) simply says that ordinarily no more than 12,000 to 16,000 pounds should be placed on a wheel.

11.2. The more driving wheels a locomotive has, the greater the length of its wheelbase. The maximum rigid wheelbase which can negotiate a curve is proportional to the square root of the radius of the curve. (Profillidis, 237)

11.3. The practical limit for non-articulated locos running on normal track is probably twelve coupled driving wheels, and even those were rare. The only fourteen-coupled locomotive ever built was the Soviet AA20. According to Doug Self, "It was clear (though never publicly admitted) that the AA20 was a complete disaster. It spread the track, wrecked every set of points it passed over, and derailed almost every time it moved. Steaming was poor and the locomotive too powerful for existing couplers and too long for the turntables. After 1935, it was stored for 25 years at the Shcherbinka test facility and finally scrapped in 1960."

11.3. On the issue of loading gauge, Douglas Jones commented, "The few existing rail cars within the Ring of Fire (has anyone got an inventory of these -- a flatcar here or a boxcar there) may force the issue by being built in conformance to the North American loading gauge. Other equipment will be built to match."

11.4. With respect to mismatch between car width and track gauge, Douglas Jones has told me, "2 foot gauge railroads in Maine used equipment that was 6 feet wide. The WW&F railroad has drawings of some of their cars on their web site."

12. Making Steam: Locomotive Boiler Design

12.1. The best illustration I have seen of the brick arch and deflector plate is on page 21 of Tufnell, The New Illustrated Encyclopedia of Railways (2000). It also has a coherent description of three-point suspension on page 20 (see also 73).

Unfortunately, that is too late to have been passed down through the RoF.


12.2. EB11 doesn't have any teachings as to a preferred tube length, but you could probably estimate it by comparing boiler length to wheelbase for selected locomotives in the Alexander book. More educated guesswork is needed to arrive at the number of tubes, and their diameters.

12.3. Kinney (see refs) has a nice study of the internals of a 1880s-1920s locomotive boiler.

13. Putting Steam To Work: Locomotive Engine Design

13.1. The maximum piston acceleration (feet/sec^2) is ((W^2 * S)/2189) * (1 + (1/(2*N)), where W is drive wheel speed (rpm), S is piston stroke length (inches), and N is the ratio of the main rod length to the stroke length.

14. Cranking the Wheels: Locomotive Transmission Design

14.1. Adding additional weight to the counterbalance, beyond that needed to balance the rotating masses, is called overbalance. The overbalance transforms the horizontal imbalance created by the reciprocating parts into a vertical imbalance. The latter causes hammer blow on the rails. Ludy 100 says that the hammer blow is proportional to the overbalance mass, and to the square of its rotational velocity about the center of the wheel.

More detailed analyses are available online. According to Rai University, Theory of Machines II, Lessons 16-19, if R is the mass of the reciprocating parts (piston, crosshead, etc.), then the force needed to accelerate them in accordance with a simple crank and connecting rod arrangement is R times

W^2*r*(cos theta + (cos (2*theta)/n),

where W is the angular speed (radians per second) of the crank, r is the length of the crank, n is the ratio of the length of the connecting rod to the length of the crank, and theta is the crank angle (radians). The first part is called the primary force and the second is the secondary force.

Thanks to Newton's Third Law, the force accelerating the reciprocating parts elicits an equal but opposing force (the inertia force) on the rest of the locomotive.

The inertia force varies with the crank angle, and if unbalanced, this creates "horizontal" shaking (i.e., along the line of reciprocation). That shaking, please note, is proportional to the square of the wheel speed. An unbalanced horizontal inertial force creates a variation in tractive force, and swaying.

If the horizontal force is balanced by a weight mounted on the wheel, the balancing weight itself creates an unbalanced vertical inertial force, the latter creates hammering on the rails, alternating with lifting of the wheel off the rail. (This is euphemistically called "dynamic augment".)

The variation in tractive force and the swaying are proportional to 1) the unbalanced portion of the reciprocating weight, 2) the crank radius (which is half the stroke length), and 3) the square of the crank (wheel) speed.

Likewise, the alternating hammer blow down on the rails, and the lift up from the rails, are proportional to 1) the overbalance weight, 2) the radius at which the counterbalance is placed, and 3) the square of the wheel speed.

Thus, the locomotive cannot be allowed to travel with a wheel speed higher than the square root of: the weight on the wheel, divided by the product of the horizontally balanced reciprocating weight and the counterbalance radius.

The crescent-shaped counterbalance is placed on the wheel as far as possible from the center of the axle (Ludy, 100), so the counterbalance radius is nearly equal to the wheel radius.


It can be proven that the "resultant" (vector combination) of the horizontal and vertical unbalanced forces is smallest when the half the reciprocating mass is balanced by the wheel-mounted counterbalance. However, when the track is light, one may deliberately balance less than half, or in special cases, none at all. (Self, Balanced Locomotives)

14.2. The need for counterbalance, and thus the amount of hammering, is reduced if the locomotive has a second pair of pistons, so that, on each side of the locomotive, one piston is moving forward while the other is moving back. The engine parts can then be made lighter, too, since four cylinders share the work of driving the wheels. (Self; Sinclair 491-3, 692; Alexander PL75). Several four-piston locomotives were introduced, but the approach never won widespread acceptance, because of the additional mechanical complexity.

15. Rolling Forward: Locomotive Wheel Design

15.1. Reducing the wheel size increases the forces acting on the connecting rods, making them more liable to failure (Forney).

16. Locomotive Wheel Arrangements

16.1. Tufnell says (190) that over 24,000 4-4-0s were built in the US. Late model 4-4-0 PaRR Class L 1890: 18,5 x 26 cylinders, 90 inch drivers, 200 p.s.i. boiler, 1900 ft2 heating area, 32 ft2 grate, 134,505 lb weight, tractive force 18,900 lb, indicated horsepower of 660 at 70 mph. (191)

17. Puffing Away: Locomotive Smokebox Design

17.1. One pound of coal requires about twenty pounds of air to burn properly (EB11).

18. Speed

18.1. Speed, as noted in the main text, is a function of both drive wheel diameter and piston speed. Specifically, speed (mph) is .01785 times drive wheel diameter (inches), times average piston speed (feet/minute), divided by stroke length (inches). The drive wheel speed (rpm) is six times the piston speed, divided by the stroke length.

Note that the greater the stroke length, the faster the piston must move in order to achieve the desired rpm or locomotive speed.

18.2. In the early 1900s, Baldwin Locomotives recommended a maximum piston speed of 1,600 feet/minute, and an "economical" one of about 1,100.

18.3. Maximum Speed. A model railroading site says,

"A steam locomotive's top speed capability in mph is normally around the same as the diameter of the driving wheels in inches.... In fact any driving wheel rotating at 336 rpm will be running at a speed equal to the diameter in inches. This is called the "diameter-speed."

At 336 rpm, the piston speed (feet/min) is 56 times the stroke length (inches). So a twenty inch stroke would imply a piston speed of 1,120 feet/minute.

A more complex rule of thumb is

latter 19C, use 0.75 X driver diameter

~1900, use 1.0 X driver diameter

1910, use 1.25 X driver diameter

end of steam, use 1.6 X driver diameter


What is going on here is that changes in materials technology made possible higher driver RPMs.

The designers of a 21C steam loco (5AT) use 1.5 times driver diameter as the estimate for the maximum speed. [5AT]

19. Power

19.1. For a given engine design, there is a piston speed for which the power is a maximum (EB11).

19.2. Armstrong (43) says that "a 3,000-hp locomotive can move more than 5,000 tons at 30 mph on level track."
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