(EB11/R) Forney says that the most coal which can be burnt is about two hundred pounds per square foot of grate per hour, and then only at most six pounds of water would be evaporated by each pound of coal fired.

The size of the grate determines how much coal can be burning at one time. So a big grate seems like a good thing. However, there are problems of increasing its size. First of all, it means increasing the overall size of the locomotive. Secondly, once the grate exceeds a certain size, it becomes too difficult for a single "fireman" to keep it "fired" properly. (This was a problem with hand-fired "Pacific" locomotives, NOCK/RE 175.) You either need to provide two fire doors, for two firemen, or engineer a "mechanical stoker."

The firebox is positioned within the boiler so that there are water s.p.a.ces to the sides and in back of the firebox, to maximize the direct firebox-to-boiler surface area (Alexander PL79). There is also water above the top of the firebox, the "crown sheet," and indeed the most common cause of a boiler explosion is that the crown sheet loses this protective blanket, and melts.

Heat transfer takes place not only at those walls of the firebox which are in contact with the water reservoir, but also at the walls of the tubes. So having lots of small diameter tubes is good-unless you are the fellow who has to make sure that those tubes are tight.

The longer the tubes, the greater the heat transfer area, but the weaker the combustion-promotingdraft in the firebox. Having lots of tubes increases the heating area, but weakens the tube plate of the firebox.

EB11/R discloses both the grate area and the total heating surface for 36 locomotive designs.

Disregarding the Stephenson Rocket, the total heating surface ranged from ~1,400 to ~6,100 square feet, and the grate areas from 20 to 100 square feet. The average ratio was 71:1.

The steam pa.s.ses up into the steam dome, from which it is released to the cylinders by the throttle valve. Some locos had two steam domes, or other provisions for storing more steam.

The boiler pressure is a function of the rate at which steam is produced (evaporation rate), the rate at which steam is used, and the size of the steam reserve. Taking advantage of a large steam reserve to briefly make faster-than-normal speed or pull an extra-heavy load is called "mortgaging the boiler."

If you are producing a lot of steam quickly, the boiler pressure will increase. The pressure which the boiler can tolerate is dependent on the thickness of the walls, as well as the nature of its construction.

Thicker walls can hold higher pressure steam, but the boiler will weigh more.

Alexander provides only limited boiler pressure data. An 1860 engine had 130 p.s.i. (PL47); locomotives built as late as 1882 had 125 p.s.i. pressure (PL76-7); three later locos were 180-190 (PL80, 85, 96). The highest pressure in the EB11/R table was 235.

Bear in mind that since the cab is behind the boiler, a large boiler limits the crew's view of what is in front of them.

Putting Steam To Work: Locomotive Engine Design Usually, the locomotive will have a pair of pistons, which operate one-quarter of a cycle out of phase, so when one is in "neutral" the other is ready to receive steam.

The cylinders can be mounted outside or inside the main frame. In general, during the nineteenth century, the British preferred to use inside cylinders, and the Americans, outside ones (Nock/RE 164).

There are some locomotives which have a second pair of cylinders, in which case it is very common to have one pair on the inside and the other on the outside. However, both pairs can be on the outside.

(EB11/R).

There was experimentation with other positions in the early days, but the cylinders of late nineteenth-century locomotives were mounted horizontally, and at axle level.

Looking at the locomotive data in EB11/R, and ignoring both the primitive "Rocket," and engines with more than one pair of cylinders, we can see that the cylinders are 18 3/8-23 inches wide, and the piston stroke is 26-30 inches long. For the American locomotives in the Alexander book, if we ignore the pre-1840 models, cylinder diameter is 12-22 inches, and piston stroke 15-30 inches (save for one "13/54" locomotive).

For both the British and American locomotives, the stroke length was, on average, 50% greater than the cylinder diameter.

Cranking the Wheels: Locomotive Transmission Design In the standard "rod" locomotive, the pistons are connected to cranks on the driving wheels, so two power strokes by the piston, make one turn of the crank, resulting in one revolution of the wheel.

The driving wheels of a high speed locomotive may turn at a rate of more than five revolutions persecond. During each half-revolution, each piston accelerates to full speed (say, 35 feet per second) and then decelerates to a full stop. The necessary force on it is the ma.s.s times the acceleration. The piston weighs, say, 500 pounds (Forney), and the maximum acceleration is proportional to the stroke length and the square of the wheel speed (EB11/SE 837). The piston transmits that force to the piston rods, cranks, and other elements. They all must be able to withstand the resulting stresses, and, unless they are balanced, they cause unpleasant, perhaps dangerous, vibrations in the locomotive structure.

The engine and running gear include both rotating and reciprocating ma.s.ses (some parts do both).

The perturbations caused by the rotating ma.s.ses (e.g., crank pin) can be completely balanced by a wheel-mounted counterbalance.

However, the reciprocating ma.s.ses (e.g., piston head, piston rod, crosshead, main rod, coupling rods) would still cause the locomotive to yaw right and left. This horizontal disturbance can be reduced by "overbalancing" the wheels, but at the price of causing a vertical imbalance (pitching up and down).

This alternately hammers the rails, and lifts the locomotive.

Usually, the compromise is to balance all of the rotating ma.s.s and 25-50% of the reciprocating ma.s.s, so that there is both horizontal and vertical imbalance.

The vertical imbalance increases with the square of the wheel speed (Addendum). The rails have to be able to withstand this dynamic load, not just the static weight on the wheels. And, of course, when the disturbance is upward, the locomotive must be heavy enough, and the balanced reciprocating ma.s.s light enough, so that the locomotive remains on the track.

Usually, with an outside cylinder, the piston rod fits into a crosshead, and the main rod connects the crosshead to the main crank pin, near the rim of one driving wheel. One driving axle is cranked directly, and the other driving axles are turned by the action of connecting rods, which run from one crank pin to another.

With an inside cylinder, the main rod will act on a cranked axle, rather than a crank pin. One advantage of an inside cylinder was that it could be mounted close to the center line, reducing the disturbances caused by the piston action. Another advantage is that the cylinder is warmed by the smokebox, and insulated by the frame. However, Ellis (51) warns the up-timers that "persistent breakage of crank axles" bedeviled inside cylinder designs. Crank axles were also expensive, large, heavy, and difficult to inspect and repair (White 208-9; EB11/SE 841).

The axle rotation also regulates the slide valve on the cylinders. EB11/R mentions five different mechanisms for this purpose, but for a description, you must turn to EB11/SE. The mechanisms are the Stephenson (Figs. 29, 32), Goochs (Fig. 30) and Allan (Fig. 31) type link motions, and the Joy (Fig. 36) and Waelschaert radial gears. EB11/SE also depicts the Hackworths (Fig. 33) and Marshalls (Fig. 34) valve gears. One 1887 valve control mechanism is depicted in Alexander (PL79); I believe this is a "link motion."

In the modern Waelschaert gear, the movement of (1) the crosshead, together with that of an "eccentric crank" connected to (2) the main crank pin, serves to move forward and back the valve rod (which directly controls which valve is open). However, the valve rod leads the piston rod.

Rolling Forward: Locomotive Wheel Design In the EB11/R table, the driving wheel diameter ranged from 54 to 85 inches. Among Alexander's American locomotives, the range was 30 to 96 inches. In general, the bigger the wheel, the higher the intended operating speed of the locomotive. With typical locomotive designs, and adequate track, maximum speeds (mph) were usually 75-150% of the wheel diameter (inches).

Big wheels also have the advantage of a larger wearing surface (proportional to diameter). So the abrasion by the rail is spread more broadly.However, if you increase the wheel size, you need to increase the size of the connecting rods, the cylinders, the frames, and so forth. Which means, given size and weight constraints, that much less room and weight allowance for the boiler. (Forney) * * *

The wheel is not a single piece construction. Rather, there is a wheel proper, over which is mounted a metal "tire." This is the "wearing surface" of the wheel, the part that is gradually worn away by the action of the rails.

The tire also includes a f.l.a.n.g.e, a thin, flat, short metal projection. A f.l.a.n.g.ed wheel looks a little bit like a stovepipe hat; the crown is the wheel, and the brim is the f.l.a.n.g.e.

In nineteenth-century America, the tires were made of wrought iron, case-hardened cast iron, or, once the price came down, steel. Steel tires were preferred because they lasted at least five times as long. (White, 175-83).

There are a number of little expedients used to make it easier for the driving wheels to hold onto curved track. One is to put non-driving pilot (leading) wheels in front of them.

Secondly, one or more of the axles may be allowed "sideplay," that is, the ability to shift left or right.

The Bavarian Ep 3/6 had an inch or so of sideplay in several of its axles. Side play was even more marked in Baldwin's 1842 flexible-beam engine (Alexander PL14).

Thirdly, the wheels can be tapered. Wheels are slightly conical (standard "taper" is 1 in 20), with the narrowest diameter on the outside. As the train moves onto a curve, the wheels shift outward, so the outer wheel's diameter at the point of contact increases, and that of the inner wheel decreases. That corrects for the curve.

Finally, one or more pairs of driving wheels can be "blind" (f.l.a.n.g.eless)(Alexander PL20, 83, 84).

Locomotive Wheel Arrangements Locomotive wheels are mounted on axles; the transmission system turns the axles, which in turn rotate the wheels.

Some of the axles are driven, directly or indirectly, by the engine. Others turn pa.s.sively as a result of the action of the car on the wheel. If your car has front wheel drive, then the front axle is a driven axle, and the rear one isn't.

Locomotives are described according to a standard wheel configuration nomenclature which, usually, but not always, uses three numbers, like so: X-Y-Z. The X value is the number of leading wheels. These wheels are not driven by the engine, but help to give stability to the ride. They are mounted on what is called a "truck" or "bogie," which can turn if the wheels encounter a curved track. X might be 4 for a pa.s.senger locomotive, 2 for a freight locomotive, and 0 for a switching yard locomotive. The American-style four wheeled leading bogie is mentioned in EB11/R.

The Y value is the number of driving wheels. Usually, the main rods directly drive one axle, to which the other driving axles are coupled. The driving wheels transmit the power of the engine to the rail and, by adhering to the rail (if there were no friction, the wheels would just spin in place), create the reactive force which impels the locomotive forward. A freight locomotive will usually have more driving wheels than a pa.s.senger locomotive of equal horsepower.

The Z value is the number of trailing wheels. Like the leading wheels, these are unpowered.

However, by providing additional support, they permit a locomotive to enjoy a long, wide firebox. It can produce steam at a greater rate, and thus supply more power to the cylinders. Like the leading wheels, the trailing ones are mounted on a rotating truck.

If a train has both a leading and a trailing truck, that means that it can back easily into a curve. Thiscan come in handy on a branch line serving a mining area.

Occasionally, a locomotive has a wheel configuration necessitating more than three numbers. This implies that there is more than one set of coupled driving wheels For example, instead of a 4-8-4, you could have a 4-8-8-4, in which one pair of cylinders drives four driving axles, and a second pair drives the other four.

Puffing Away: Locomotive Smokebox Design The waste steam leaving the cylinders pa.s.ses 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 circ.u.mference 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.

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 squarefoot of grate), and the square footage of the grate.

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) * * *

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.

a.s.suming 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. c.o.ke (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 a.n.a.lyze 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; pa.s.senger 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 a.s.sume a maximum grade in the 1-3% range.

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 ma.s.ses will increase hammerblow on the rails, especially at high speed.

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 d.i.c.k (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).