Puffing Away: Locomotive Smokebox Design
The waste steam leaving the cylinders passes through a constrictive blast pipe, and jets out. This creates a partial vacuum in the smoke box, which in turn elicits the draft which fans the flames in the firebox. The smoke box subsequently discharges the waste furnace air and steam through the smoke stack. EB11/R goes into an amazing amount of detail (see Figs. 18-20) as to the design of the smoke box, as well as that of its spark arrester (so the locomotive doesn't set the countryside on fire).
The basic problem with spark arrester design was that to be effective, it had to obstruct the smoke box, which in turn reduced the draft.
Speed
Just as the speed (in feet per second) at which you walk is the length of your stride (in feet) times the number of strides you take per second, the speed of a locomotive is the circumference of the wheel times the number of times the wheel turns each second-and it turns a half-turn on each piston stroke. For high speed, you need big wheels or fast-moving pistons.
The maximum speed is that at which the tractive effort exerted by the locomotive is only enough to overcome the movement resistance of the locomotive and its tender alone.
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In 1911 (EB11/R), the following train weights (long tons, ignoring locomotive) and speeds were considered typical:
Coal train (GB), 800-900 tons, 18-22 mph
Goods train (GB), 430 tons, 25-30 mph
Express goods train (GB), 300 tons, 35-40 mph
Mineral and grain trains (US), 2,000-4,000 tons, ~12 mph
Goods train (US), 600-1,800 tons, 15-30 mph (with 40-60 mph bursts)
Power
When the heat of burning coal converts water into steam, it's like putting money into a bank. The compressed steam stores energy, just like a bank stores money. When the engine uses that steam to move the pistons and, ultimately, the wheels, it's like withdrawing funds from your account. Some of the stored energy is used to do work, and the rest is lost.
Power is the rate at which energy is produced, converted, stored or used. If the engine is using "steam" energy faster than the boiler is producing it, then eventually it will use up whatever reserve the boiler had built up previously, and the locomotive will literally "run out of steam," and come to a stop. There is no overdrawing the energy account!
The maximum sustainable horsepower is the product of the combustion rate (the number of pounds of coal burned per hour), the energy value of the coal (BTUs per pound), the combined thermal efficiency of the boiler and engine (typically 0.06), and a conversion factor (0.00039)(EB11/R, 843, 847). The combustion rate is the product of the number of pounds of coal burned per hour per square foot of grate), and the square footage of the grate.
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Now power also equals force times speed. The power (in horsepower) corresponding to a particular tractive force at a particular speed is
Speed (mph) X tractive force (pounds) / 375
The tractive force when you start up the engine is determined by the formulae we looked at earlier. Initially, as you increase the speed, traction remains constant, so the power applied to the wheels increases.
Eventually, you reach the critical speed at which the rate at which the engine consumes energy equals the maximum rate at which the boiler can deliver energy to the cylinder. The latter determines the maximum sustainable power exercised by the engine at the rail.
Above the critical speed, the sustainable power is constant, so the sustainable tractive force must decline as the speed increases. (Krug)
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A parallel equation dictates the horsepower required to move the train against level, grade and curve resistance; we just set the tractive force equal to the total resistance. A further complication is that, as speed increases, so does resistance. So doubling the speed could double the required tractive force and thus quadruple the required horsepower (Clarke, 127).
The Steam Balance
Just as we can construct an energy balance for the locomotive, we can do the same for the steam which carries that energy. We multiply the combustion rate by the evaporation ratio (pounds of water evaporated by each pound of coal burnt), to get a water vapor production rate in pounds per hour. And we multiply the steam capacity of the cylinders by the piston stroke rate, and the density of the steam at cylinder pressure, to get the steam demand rate in the same units. For a given water vapor production rate, there will be an equilibrium speed at which steam demand equals steam production.
Assuming that the fuel and the grate are satisfactory, the ability of the boiler to properly supply the engine with steam can be judged by looking at the ratio of the "rated tractive force" (pounds) to the total heating area of the boiler (square feet). According to the Baldwin Locomotive Company, this ratio is 8-16 for the most common locomotive types, and is 10 for the "4-4-0." The lower the ratio, the easier it is for the locomotive to sustain that tractive force.
The ratio can be calculated for fourteen locomotives in EB11/R, and is 4.2-17.5.
Coaling Up
The nature of the coal available as fuel has an impact on the design of the firebox and, of course, on the overall performance of the boiler. (GW15, Sanderson, Robinson).
There are three basic types of coal. In order of increasing energy content, they are lignite ("brown coal," 9-17,000,000 BTU/ton), bituminous coal ("soft coal," 21-30,000,000 BTU/ton), and anthracite ("hard coal," 22-28,000,000 BTU/ton)(Wikipedia, "Coal").
All of the coal in Grantville is bituminous. U.S. railroads generally preferred low water, low ash, low sulphur content bituminous coal; it may be advantageous to test coals from different mines and seams to find the best "steaming coals."
While anthracite burns smokelessly, it combusts slowly and requires a firebox several times larger than for a bituminous coal burner to achieve the same heat production rate.
Coke (25,000,000 BTU/ton) is bituminous coal which has been processed to eliminate the volatiles. It was used on British locomotives because it burns without smoke, but it was too expensive for acceptance by American railroads.
Locomotive Design: Putting It All Together
We have to analyze what we need the USE locomotive to do. What loads must it pull, over what speeds, and in spite of what grades? Freight locomotive designs tend to emphasize tractive force over speed; passenger engines must reverse these priorities. A general purpose locomotive—and that is what we probably want to build first—is a compromise.
We also must consider what limitations on locomotive weight and size are imposed by the quality of the track, the sharpness of the curves, the load capacity of any bridges it crosses, and the clearances of those bridges and other structures.
Of course, since we are starting from scratch, our locomotive design will affect the planning of the line. The first line is likely to be from Grantville to Magdeburg. This is not a mountain region, and the line can follow river valleys to minimize grades. So I think it reasonable to assume a maximum grade in the 1-3% range.
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My recommendation is that the USE first attempt to build a 4-4-0 rod locomotive. This "American" wheel arrangement was extremely successful as a general purpose engine. Even in 1884, 60% of the new engines were 4-4-0's, although that dropped to 14% in 1891 (White)
Alexander's Iron Horses has descriptions of a large number of 4-4-0's, starting with the 1837 Hercules (PL8), and ending with the 1893 locomotive used by the CB&Q (PL93). The first 4-4-0's obviously were able to cope with the light rails of the late 1830s.
My one reservation about using 4-4-0's is that our tractive force may be weight-limited if our rails are light. This could be a problem if the track is steeply graded. With forty pound steel rails (allowable wheel weight of 4-6 tons), the maximum weight on the drivers would be 16-24 tons, and maximum tractive force would be one-quarter that (4-6 tons). That in turn limits the maximum total train weight to 533-796 tons on level track or 107-161 tons on a 3% grade.
My suspicion is that the
USE will not have great difficulty in achieving "standard" wheel diameters and cylinder dimensions, but that boiler pressure will be more problematic. With sixty inch wheels, and 16X24 cylinders, the rated traction is 87 times the boiler pressure (p.s.i.) So, to achieve six tons of traction at the rail, we need 138 p.s.i.
If that isn't enough pulling power to satisfy USE engineers, we can instead design a 4-6-0 "Ten Wheeler" (Alexander PL30), which, with the same driving wheel load, could have 12,000-18,000 pounds traction, and could handle 800-1,200 tons level or 160-240 on the 3%. We might scale up to 20X30 cylinders, allowing us to make do with only 106 p.s.i. But the larger reciprocating masses will increase hammerblow on the rails, especially at high speed.
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After that we need to think about constructing more specialized locomotives. We will probably be more concerned about moving goods. Hence, the next locomotive might be a 2-8-0, which is the "Consolidation" type, first in 1875 to haul heavy freight. The first engine with this configuration in the Alexander book is the 1879 Uncle Dick (PL70), and the last one is the 1900 Number 1621 (PL96). An alternative is the 2-8-2 "Mikado," which replaced the "Consolidation" in the 1920s. If an "eight coupled" loco is too heavy for the relatively flimsy tracks we have in service, we could construct a "Decapod" 2-10-0 (the driving weight is spread over five axles instead of four) or a "Santa Fe" 2-10-2 (the trailing axle permits a larger firebox, hence more steaming capacity).
For passenger service, the 4-4-0 was eventually replaced by the more powerful 4-6-0. As a second generation general purpose engine, we might consider a "Northern" 4-8-4 (Sinclair, 681).
For switching purposes, the best choice may be the 0-6-0. An 0-4-0 could be used for light switching at an industrial site. For heavy switching, as in a hump yard, one might step up to a 0-8-0.
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One of the maddening things about locomotive design is how interrelated all the components are. It means that one which works fine in isolation may work poorly when it is in a locomotive which is actually running over track.
It may be tempting to take advantage of late twentieth-century knowledge and technology and design a "new" steam locomotive. However, if it fails, then you may not be sure whether it is because of the novel features, or because you overlooked something more basic. Hence, it may be prudent to first build a conventional nineteenth-century locomotive. In other words, duplicate, then innovate.
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The final engineering design step is the "detailed design." That is the blueprinting stage, and specifies, e.g., whether the boiler plates are lap welded or riveted.
After design, you build and test a prototype. If it works, you move on to the production phase. If it doesn't, you rethink the design.
Of course, our heroes are starting almost from scratch here. They not only have to do the system-level (locomotive) design, but also designs for virtually all of its components, even such seemingly simple ones as steam pressure gauges.
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I would strongly advise USE engineers to first build a reduced-scale steam locomotive, which would run on a scaled-down experimental track, first. That would allow them to discover some of the inevitable mistakes after only a limited investment in valuable materials. And lives.
What I have in mind for initial prototyping is what model railroaders would call a "garden railroad" with "small-scale live steam." This is most commonly operated on #1 gauge (45 mm) track. These have working boilers and engines. However, they burn either alcohol or butane, not coal. (Miller) It is possible that one of the model railroaders in Grantville already has one of these setups.
The garden railroad will be helpful not only for testing the engine design, but also for showing down-time smiths (and investors!) what we are working toward.
The next step up might be a "ride-aboard," coal-burning locomotive. This still need not be a full-size machine; think amusement park ride. If it is built to two foot gauge, it can use the TacRail track.
Finally, we build the real thing. Expect surprises.
Geared Locomotives
On "rod" locomotives, there is a limit to how much wheel size can be reduced. The stroke length is equal to twice the crank radius, and the latter is necessarily smaller than the diameter of the driving wheel. That implies that at some point, driving wheels cannot be made any smaller without reducing the stroke length, which would defeat the purpose of increasing the tractive force.
The solution to this conundrum is a geared locomotive, which uses the piston to drive a geartrain. If the piston applies a torque to a small gear, whose teeth engage a larger one, then the larger gear experiences a higher torque, but turns more slowly. (This is what is literally meant by "gearing down.") You get even more tractive force, at the expense of speed. A geared locomotive with forty inch diameter wheels, and a 2:1 gear down, will have the tractive force of an equivalent rod locomotive with twenty inch wheels.
But wait. What about the adhesion limit on tractive force? A rod locomotive applies a strongly pulsating torque, and it is its maximum torque which determines the adhesion limit. A geared locomotive applies an almost constant torque, and thus it has a higher effective coefficient of adhesion. Since geared locomotives are intended to operate at low speeds, they are designed so that all of their wheels are drivers, thus maximizing the adhesion.
Because gears replace most of the rods, there is less mass flying about. This reduces the hammer on the rails, and hence geared locomotives can be used on lighter track. It is safe to assume that the up-timers know something about geared locomotives. Grid character "Monty" Szymanski, Sr. overhauled locomotives of the Cass Valley Scenic Raiload, which operates geared "Shays." There are also photos of Shays in two books in the public library (Ellis, 109; Rails West, 12). The documented sources don't explain the differences between the Shay and the other common geared locomotives (Climax, Heisler, etc.)
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Some knowledgeable members of Baen's Bar have strongly urged that the first USE steam locomotive should be geared.
I disagree. It is important to remember that in OTL, geared locomotives occupied an important but small niche (perhaps 3,000 were built). Geared locomotives were developed in the late 1800s to meet the needs of the logging industry for a high traction engine that could ride on temporary tracks (sometimes mere logs) which were curvy, steep and rough. What about the mining industry? Geared locomotives were used if the branch serving the mine had a steep enough grade. However, mining companies typically planned for longer-term operations than loggers. They expected to work the mine for years, and therefore were usually willing to go to some trouble to reduce the grade of the track. In contrast, nineteenth-century loggers expected to "saw and scoot," so they tolerated a steep route.
Now, I just don't see there being a great deal of logging activity in early seventeenth Germany. And, to service mines, I expect that USE railroad entrepreneurs are going to cut-and-fill as needed to provide a reasonably graded roadbed for permanent track, just as was done in OTL. According to a Mannington Public Library book, in Minnesota, the Shays were used on logging railroads, but iron ore was transported on 4-4-0's. (Rails West, 12, 14).
So geared locomotives service a niche which probably won't exist. But it is possible that they will be used on a rough-and-ready narrow gauge rail connection into the Thueringerwald hill country, which is a source of both ore and timber.
Geared locomotives are not well suited to hauling passenger and perishable goods trains. They had a top speed of 10-15 mph, which is inferior to even an 1830 0-4-0 rod locomotive (Alexander PL42; 21 mph).
But will the down-timers care? After all, they are accustomed to the pace of draft horses, mules and oxen.
In OTL, without knowing that they were even possible, investors, shippers and passengers clamored almost from the beginning for higher speed trains. In 1831, the B&O held a contest whose entries were required to draw 15 tons at 15 mph over level track—already in excess of what horses could do.
Moreover, in t
his timeline, people will know what they are missing. They can read in the library that an 1893 4-4-0 supposedly set a speed record of 112.5 mph (Alexander PL85). (Its true speed was probably 82 mph, but steam locomotives can exceed 120 mph.) Down-timers can see high speed movement on the occasions when a modern automobile barreling down the asphalt roads of Grantville.
So, thanks to popular demand, the main lines, at least, will be dominated by fast-moving rod locomotives.
Second Generation Locomotive Concepts
Compound Expansion. The steam can be expanded in two or more stages. Typically, compound locomotives have two pairs of cylinders, a high pressure pair and a low pressure one. The exhaust steam from the former is directed into the latter, and each pair of cylinders drives one set of driving axles.