Miscellaneous information.

Joy valve gear is best suited to valves above cylinders.

Compounding showed little benefit in loco's and ideally needs about 600 - 700 psi for maximum economy. Exceptions were the Chapelon-designed loco's (France) which were extremely efficient (partly due to compounding).

Slide valves consume most power, then piston valves, and poppet valves least. Poppet valves only consume about 2% of the power available.

Simple blast pipe in British loco is generally satisfactory up to about 2,000 HP.
Usual blast pipe pressure is about 5 psi.

Multiple blast pipes / double chimneys enable more draft and higher powers within the same height.

Superheating can reduce water / coal consumption by about 25%. Maximum benefit is obtained at around 100 ^o superheat, and higher superheat is of little benefit in the average engine/ boiler, although some locomotives used up to 175 degrees of superheat.

On full-size loco, typical ratio of superheater to grate = 10 to 15 (x grate area).

Coal usage of 2 ½ lb. per sq. ft of grate per minute = practical maximum.
(But consider the fireman if, as usual, he has no mechanical assistance. With a grate of 30 sq. ft. ,an average size for a British  express loco, he is shovelling over 2 tons of coal per hour into the firebox.)

By 1946 a loco would haul 1 ton on one cup-full of water + 2 ozs coal.

Haulage on railway track = 5 x distance of road haulage for same fuel.

Weight of rail in lbs. per yd / 5 = max axle load in tons. (often exceeded).

Although a GWR locomotive (a Castle class 4-6-0, in 1924) attained an efficiency of 2.83 lbs. of coal per drawbar horsepower, the lowest figure regularly achieved was about 3 lbs. / dbhp.

A frequently-quoted figure is that an engine can generate one horsepower per 2.5 square feet of heating surface.  (But see next sentence.)

Although the size of the firebox and tubes is often used to gauge power (as above), the limiting factor may often be the water space around them, but this information is not usually apparent without a study of drawings etc..

A limit to the weight of locomotives is imposed by the civil engineering department according to the track and underlying structure. This is usually 20 tons per axle (later increased to 22 tons), which gives, for example, a maximum weight of a loco of 100 tons for a 4-6-0. (UK figures.)

This limit may be increased for a four cylinder loco as the lower "hammer blow* " reduced the stress on the track and bridges.
( * Hammer blow is caused by the rotation of the balance weights etc, which causes the wheel to rise and fall during its rotation. At the extreme, the wheel may lift completely off the track.)

There are many formulas for calculating the resistance of
trains. As the train may consist of a wide variety of rolling stock , with different characteristics, and the operating
conditions vary, it is impossible to find a "perfect" formula.
The resistance will vary with the number as size of wheels, and type of bearings on the vehicles; the gradient & track curves.
The frontal area will have an increasing effect as speed
increases, as does the airflow along the sides and
underneath although streamlining is of little benefit below 60 mph.
Wind speed and direction can increase train resistance
considerably, with side winds (which can press the wheel flanges onto the rail) having more effect than headwinds.

Given all the above, plus the wide variety of vehicles and loading gauges, it is hardly surprising that no formula is
satisfactory in every situation.

The following will give a guide.
R = 4 + 0.025V + 0.00166 V²

Where
R = resistance in lbs. per ton train-weight,
V = speed in mph.

OR.

R = 1.5 + ( 106 + 2V ) + 0.001 V²
( W + 1 )
R = resistance in lbs. per to train-weight,
W= weight of vehicles
V = speed (mph)

Tractive Effort. TE = C P d2 S
D
where:
C= efficiency (85% of boiler pressure)
P= pressure
d= piston diameter
S= stroke
D= wheel diameter
(all dimensions in inches)

The Tractive Force that can be developed by a
locomotive is:

T = 374S / V

Where:
S = heating surface in square feet
T = tractive force in lbs.
V = speed in m.p.h.

The force exerted at the edge of the driving wheel of a locomotive expressed in pounds. = D² x S x P,
where D is cylinder diameter (inches), S is piston stroke (inches) and P is 85% of boiler pressure (psi).

Locomotive weight.
A rough guide to the maximum weight of locomotive for a given rail weight, is to take the weight of the rail in lbs. per yard,
divide it by five, and that gives the maximum weight per axle in tons.
(This assumes a well constructed and maintained track bed.)

A steam locomotive develops its maximum force at zero-low speed, thus aiding starting.
This then  diminishes with  increasing speed, whilst the power output increases up to the speed for which the engine is designed.
The usual limiting factor is the ability of the boiler to generate sufficient steam or (more commonly) the fireman's ability to shovel on enough coal.

The weight on the driving wheels of a locomotive should be at least 4 times the rated tractive effort if it is to give the maximum possible tractive force.