Eventually, the locomotives became powerful to pull trains too heavy for normal draft teams. As early as 1839, a Gowan & Marx (4-4-0, 11 tons, 9 tons on drivers, driving wheels 42" diameter, cylinders 12 1/8" x 18," anthracite coal burner) hauled a train of 101 loaded four-wheeled cars, weighing a total of 423 tons, from Reading to Philadelphia at average speed of 9.82 mph. (Alexander PL10).
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Why not jump directly to diesel-electric (DE) propulsion? Modern locomotives use a diesel engine to power electric motors; the latter turn the wheels. DE locomotives are more fuel efficient, and less labor intensive to operate, than steam locomotives. They can exert high tractive forces at high speeds, and they can be wired so that one DE's crew can operate several at one time.
The problem is that we lack the infrastructure to support DE's. A diesel engine requires diesel fuel, and we don't have it yet. The oil fields of Germany are small, and we probably won't have a large, reliable supply of oil until we have control of the North Atlantic and can import it from the Middle East, Africa, or the Americas. In other words, we have to win the war first.
Then there is the electrical system. We will need insulated copper wire. The best insulation is rubber or plastic and, in 1632, neither rubbers nor plastics are commercially available. In OTL, the natural rubbers and plastics were obtained from non-European sources.
Finally, there is the issue of start-up costs; DE's are perhaps five times as expensive as a steam locomotive of equal horsepower. (NOCK/RE 203)
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Even if we recreate the steam locomotive technology, that doesn't mean that it will be suitable for all purposes. During World War One, Major Connor warned against use of steam locomotives to directly supply the front line, because a "steam locomotive would indicate too clearly its position by its smoke."
As one possible alternative, Connor provides data on Vulcan gasoline locomotives. Even the smallest can haul over 150 tons. It therefore is not so strange as it seemed at first blush that the USE is using "a modified pickup truck cab section" to draw Iona's train. Canon doesn't specify the modifications, but it probably has been equipped with locomotive-type wheels so it will run on the rails.
Gasoline locomotives were first developed for coal mines (WLW). If the Joanne mine locomotives (Elizabeth) passed through the Ring of Fire, they were presumably narrow gauge gasoline machines.
Fuel
Historically, fuel was the largest operating expense item for railroads, and the choice of fuel was based primarily on cost. The early American locomotives mostly consumed wood; it was not until 1870 that half the steamers in service were coal-burners (White 85). Fuel conversion was driven by both deforestation, and the opening of large new coal fields.
Early seventeenth-century Germany is experiencing a wood shortage because of the heavy use of wood as a fuel in home fireplaces and industrial furnaces, and as a raw material for carpentry.
On the other hand, because the Ring of Fire encompassed several up-time coal mines, and the up-time equipment for mining them, there is a readily exploitable coal supply in the Grantville area. There is also a lot of coal in Germany, notably west of Hannover, near Zwickau in Saxony, in Saarland, and in the famous Ruhr region.
So it is something of a no-brainer to prefer coal to wood. (What wood we have available for railroads is best employed in the wood-ties which support the rails.)
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The USE is rich in coal but impoverished in petroleum. Consequently, we cannot expect to have large supplies of either gasoline or diesel fuel within a reasonable time. Our gasoline locomotives are likely to be limited to rebuilds of up-time vehicles, and used only as a stopgap. And we aren't likely to consider building a diesel locomotive at all—at least, not until we are importing oil in large quantities.
Steam Locomotion
We have completed the first stage of the engineering process: conceptual design. The principal motive power for the new railroad is going to be a coal-burning steam locomotive.
Both the Encyclopedia Americana and the modern Encyclopedia Britannica provide a basic cutaway view of a steam locomotive. These diagrams show, and label, certain major components of the boiler system (the firebox and its grate, the water circulation, the steam dome, and the superheater tubes), the engine system (the steam chest, the valve, and the cylinder-and-piston), the transmission system (the crosshead, main rods, and connecting rods), the driving and leading wheels, the valve control system (the eccentric crank and rod), the exhaust system (exhaust pipes, smoke box and smokestack), and the control system (throttle valve, throttle lever, safety valve). Other parts are recognizable to a railroader (e.g., the ashpan), but are not labeled.
In a steam locomotive, fuel is burnt in the firebox, evaporating water in the boiler. The resulting high-pressure steam is directed by the valve slide in the steam chest to either the front end or the back end of a cylinder containing a piston. If the steam enters the back end, it drives the piston forward and, at the completion of this forward stroke, the steam is allowed to escape. Steam then is redirected to the front end, moving the piston backward. Then the front end is exhausted, and the piston is ready for the next cycle.
This to-and-fro movement of the pistons is converted by the rods and cranks into rotary motion, each piston turning the driving wheels one half turn on each stroke of the cycle. Another linkage, driven by the rotation of the axle, controls the position of the valve slide.
The process may sound simple, but it is important not to underestimate the difficulties of building a practical steam locomotive. There are no steam locomotives in Grantville. That means that the design for the USE's first steam locomotive must be based on inspection of books and videos.
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The next engineering design step is called "preliminary design" or "embodiment design." That is when engineers decide things like the size and weight of the locomotive, the fire grate size, the desired boiler pressure, the diameter of the cylinders, the piston stroke length, the number of wheels, the wheel diameter and so forth. These in turn determine how much the locomotive can pull, how fast.
To make those decisions, we have to determine the tractive force (pull) necessary to overcome the expected train resistance to motion.
Basic Train Resistance to Motion (Straight, Level Track)
The "basic" resistance on straight, level track is the result of rolling friction between wheel and rail, friction among all the mechanical parts driving the wheel (cylinder and piston, bearings and axle, etc.), air resistance, and other factors.
The starting resistance is about 20 pounds per ton of load, but the engineer can bunch up the cars and then take advantage of slack, starting the train one car at a time.
Resistance drops once the train is moving slowly. It then climbs again as train speed increases.
EB11 provides some formidable equations, of dubious relevance, for calculating resistance. I instead quote two simple historical formulae which are likely to be known to model railroaders. The resistance, measured in pounds of force per ton of load, equals
(1) 2 + (speed (mph) / 4)(the "Engineering News" formula; Ludy, 131), or
(2) 3 + (speed (mph) / 6)(the Baldwin Locomotive Company formula; Connor, 89).
Equations (1) and (2) are useful at the speeds the USE will be operating. However, for high speed modern trains, air resistance becomes important, and this introduces a factor which is proportional to the square of the speed.
Extra Train Resistance (Grades and Curves)
In nineteenth-century America, poorly capitalized pioneer railroads economized on track building by taking the path of least resistance: going up and down, or around, hills. As a result, American locomotives had to be engineered to cope with steep grades and sharp curves. This could be true in the USE, too.
Total train resistance is the sum of the basic resistance mentioned above, and extra resistance attributable to grades and curves.
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Grade (Slope). If it is going uphill, the
locomotive has to overcome gravitational force as well as rolling friction. This grade resistance is roughly 20 pounds per ton of load, for every 1% of slope. (Armstrong, 20)
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Curves force the train to reduce speed (so it doesn't derail), and also result in an effective increase in resistance. A curve with a turning radius of 5,729 feet (called a one degree curve) increases resistance by 0.8 pounds per ton of load. Halve the radius, and you double the resistance.
Rated Tractive Force
EB11/R explains how to calculate the average tractive force (in pounds) exerted at the rail by the driving wheels of a two-cylinder steam locomotive engine: it is the product of the mean effective pressure (p.s.i.) of steam in the acting cylinder, the square of the piston diameter (inches), and the length (inches) of the piston stroke, divided by the diameter of the wheel. (See also Ludy, 131). The mean effective pressure at start-up is usually assumed to be 85% of the boiler pressure.
In this article, when I refer to "cylinder diameter," what I really mean is the size of the bore, which is, roughly, the piston diameter. Also, I may express the cylinder bore diameter and piston stroke length in shorthand form as, e.g., "16X24" (16 inch bore, 24 inch stroke).
The drawbar pull—which determines the load that the locomotive can haul—is its tractive force at the rail, less the resistance imparted by the locomotive itself.
The steam locomotive develops the rated tractive force made possible by its boiler and engine only if it can adhere to the track.
Maximum (Adhesion-Limited) Tractive Force
The effective tractive force applied to the wheel rims cannot exceed the "adhesion," which is the product of the weight which the locomotive places on its driving wheels, and the "coefficient of adhesion." This coefficient (Armstrong and others use 0.25; EB11/R, 0.2.) expresses how well the wheels resist sliding on the rails; higher is better. The engine can apply more force to the wheels, but they will just slip, not turn.
Consider the rail-riding pickup truck on the Grantville-Halle line. We are probably talking about a 200-300 horsepower engine, and a vehicle weight of around 5,000 pounds. At 10 mph, that engine could develop a pull of 9,000 pounds—if only the wheels didn't slip. But its maximum tractive force, thanks to the adhesion limit, is just 1,250 pounds. That means that it is way over-muscled, relative to its adhesion. Of course, "its muscles are designed for rubber tires on pavement, which have a much higher coefficient of friction." (Douglas Jones comment)
Designing for Adequate Traction
The desired tractive force can be calculated if we know how much tonnage the locomotive must move, over what grades and curves.
We then first ensure that the weight on the drivers is sufficient to generate adhesion at least equal to that desired tractive force. We distribute this weight across a sufficient number of axles so that the rail can handle the load.
Next, we must size the engine and boiler so that the rated tractive force is sufficient and sustainable. A logical starting point would be to use the design parameters of an old timeline (OTL) locomotive. EB11/R provides some useful comparative data for thirty-six different locomotives: wheel configuration, the position (inside or outside), diameter, and stroke length of the cylinders; the diameter of the driving wheels, the weights of the engine and its tender; the weight carried by the driving wheels; the grate area and total heating surface of the firebox. In fourteen cases, it also states the boiler pressure.
While EB11/R has something of a British bias, Alexander provides significant design parameters for over fifty American locos.
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It should be evident from the discussion of rated tractive force that this can be increased (up to the "adhesion limit") by
1) increasing the mean effective pressure (usually by increasing the boiler pressure),
2) increasing the cylinder diameter or the piston stroke length, or
3) decreasing the driving wheel diameter
Decreasing the drive wheel diameter is the only way of increasing long-term tractive effort which does not require that the boiler and firebox be enlarged to pay for it. However, it, too, has a price: reduced speed.
Large wheels are reserved for express passenger service, while small wheels are used on freight locomotives to maximize tractive effort. But the wheel diameter cannot be made too small, because it must remain larger than the piston stroke length.
For a freight locomotive, 42 inch driving wheels are typical. On a general purpose locomotive, a typical wheel diameter might be 54 inches. A little more speed, a little less tractive force. For a dedicated passenger locomotive, wheel diameter is likely to be in the 60-90 inch range, resulting in a more pronounced tradeoff of hauling ability for speed.
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If you want to increase the boiler pressure, you will have to evaporate water at a faster rate. This will require various firebox and firetube modifications. And to contain that pressure, you will have to use thicker boiler and firebox walls, which will make the locomotive heavier.
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If you increase the cylinder diameter or piston stroke length, you increase the engine's steam requirements. If the boiler is mismatched to the engine, then the boiler pressure will drop, the engine will gulp for steam, and the tractive force will decline. So changes in the engine ultimately affect boiler and firebox design.
Increasing the cylinder diameter or the boiler pressure also increases the force on the piston so the piston rod must be made larger and heavier to withstand the stresses imposed by piston motion. Which in turn affects the size of the main rod, the coupling rods, the axles, and even the frames.
Making the reciprocating parts (e.g., piston) more massive will increase shaking, which will mean more wear and tear on the engine, the running gear, the wheels and even the rail.
Increasing the stroke length necessarily increases the length of the piston rod, and hence its diameter must be increased so it doesn't buckle when compressed. The rest of the running gear then needs to be scaled up, too. With the same consequences as before.
Any mechanical engineer (there are at least ten in the Grid) will have studied, and will have textbooks describing, the basic mechanics of columns and beams, crank-and-rod mechanisms, etc. and hence will appreciate the mechanical limitations on piston rod length and cylinder diameter. It is no doubt because of the forces at work that cylinder diameters and piston strokes on locomotives rarely exceed 30 inches, even though a more massive design would increase tractive force.
Weight and Size
Because of the role of adhesion weight, lightening a locomotive is not necessarily advantageous. Indeed, in 1835 Baldwin built the first locomotive (The Black Hawk) in which the tender was integrated into the locomotive body, so that part of its weight would contribute to the traction. (Alexander, 50).
A locomotive is likely to be designed so that the weight it places on its drivers is at least four times the desired tractive force. Of course, its boilers and engines should then be sized accordingly.
However, the basic rolling resistance of a locomotive is still proportional to its total weight. There is substantial additional resistance, again proportional to total weight, when the locomotive steams up a slope, or accelerates.
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We also need to consider wheel weight. The greater the weight, the greater the wear on the rail, and the risk of rail failure.
The quality of the track is the principal limit on wheel load. EB11/R (847) says that a weight of 37,000 pounds "could be easily carried on one axle," and that implies 19,500 on each wheel. The heaviest rail mentioned by EB11/R is 100 pounds per yard, so a conservative rule of thumb would be to allow a wheel load of 195 pounds per pound of rail weight.
A contemporary Baldwin Locomotive Company catalogue states that if steel rails are properly supported by cross-ties, they can support a maximum wheel weight of 225 to 300 pounds for each pound per yard of rail. Thus, if a rail is dimensioned so that its weight is forty pounds per yard, no more than 12,000 p
ounds weight should be placed on a single wheel.
For a given weight on the drivers, wheel load can be reduced by increasing the number of driving wheels. In OTL, there was an increase in the number of coupled driving wheels.
One 1893 locomotive (Alexander PL87) had 84,000 pounds on four driver wheels, and thus the individual wheel load was 21,000 pounds (suitable for 70 pound or heavier rail). In contrast, another (plate 90) had 172,000 pounds on the drivers, but it was spread over ten wheels, and thus it could actually run on lighter track.
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The wheelbase is the distance from the first driven axle to the last one. If the normal axle spacing and wheel diameter are maintained, increasing the number of driving axles lengthens the wheelbase, which makes it more difficult for the locomotive to handle a curve. (Clarke, 122). Or turn around in a turntable or wye.