>
>Steam is a direct drive mechanism, the tractive force is coupled in a
>fixed manner and essentially without intervening linkages to the
>pressure in the cylinders. The relationship between the pressure in
>the cylinders and the tractive effort at the wheel is conditioned by
>the geometry of the link, varies roughly as the sine of the angle of
>rotation of the wheel (providing the connecting rod is "sufficiently
>long") and is the sum total of that contributed by the different
>cylinders (which, in a 2-cylinder engine are 90 degrees out of phase).
>Superimposed on this rhythmical variability is that introduced by the
>varying pressure within the cylinder. At slow speeds, the pressure in
>the cylinder is set primarily by the boiler pressure and how the
>"cut-off" is set. The pressure at the start of the stroke is high,
>near to boiler pressure, and remains at that level until cut-off.
>Thereafter it falls along an adiabatic/isentropic path according to a
>law essentially given by P*(V^x)= k, where x is about 1.33 and k is a
>constant. V is the volume, directly proportional to the excursion of
>the piston. At a certain point, the exhaust port is opened and the
>pressure falls quickly to a lower value, perhaps 1.2 atmospheres. It
>remains generally at this level while the steam is expelled during the
>return stroke, until the exhaust closes and the remaining steam is
>compressed along another adiabatic line (but with x=1.1 approx). The
>consequence is that the pressure follows a complex cycle and is
>mirrored on the other side of the piston, 180 degrees out of phase.
>The driving force is the difference between the two. This difference
>in pressure can be averaged over the entire cycle and is called the
>"mean effective pressure" (m.e.p.). mep rises as the cut-off rises,
>because the cylinder spends more of its time at the higher starting
>pressure and falls adiabatically a smaller amount during expansion.
>The relationship between cut-off (the "gear" of a steam loco) and
>pressure is a roughly hyperbolic one. At maximum cut-off, usually in
>the 70 to 80% range for locos with conventional valve gears, the mep
>in the cylinder will be 85% of the boiler pressure. The overall
>effect is that the force exerted on the rail follows a form that I
>would describe as roughly shaped by a bishop's mitre. The ratio of
>the peak of this curve to its average value is called the "coefficient
>of fluctuation", which is a measure of how "slippery" the locomotive
>will be. At any one point, the sum tractive effort of the coupled
>wheels will be the result of that contributed by each of the
>cylinders. This tends to raise the overall level and squash down the
>peakiness of the "bishops mitre"….. higher, less variable effort. At
>higher speeds, however, two things happen. First, the cut-off is
>shortened by the driver and secondly the admission pressure falls
>below that of the boiler. This is called throttling, it occurs
>because of "friction" in the (relatively) narrow pipes and valves, and
>is an isenthalpic process that essentially drops both the pressure and
>the ability of the steam to liberate energy for a given expansion. At
>very high speeds, say 400 rpm, the mep can be less than half the
>theoretical value because of this effect. From this, it will be
>realised that the tractive effort varies over a single wheel rotation
>and also falls off with speed. At high speeds, inertial forces in the
>system considerably distort the "mitre", although they do not alter
>the average level. Locomotives were rated by their tractive effort,
>which was the AVERAGE theoretical tractive effort over one wheel
>revolution for a given mep, usually 85% of boiler pressure. There is
>a standard formula for this, essentially TE= .85*d^2Pl/D, where
>d=cylinder diameter, P=mep, l = cylinder stroke and D = wheel
>diameter. This formula is relatively accurate in predicting mean
>tractive effort at low speed. If a further factor, the "diagram
>factor", varying with speed, is taken into account, this formula
>predicts the tractive effort at higher speeds too.
>
>Now, we can answer the question about speed tractive effort curves.
>Tractive effort is constant for a steam loco at low speeds, up to a
>certain speed, determined by the point at which the gear begins to be
>wound back or the effect of throttling begins to be become pronounced.
>This constant TE is, to some extent, also determined by whether it is
>high enough to slip the wheels despite the weight pressing down on
>them. Usually steel on steel has a coefficient of friction of about
>0.3, so the rule of thumb was to not design a loco where the rated
>tractive effort was more than 30% of the adhesive weight. As speed
>rises, the tractive effort falls away, first at a high rate, then at a
>slower rate, assymptoting toward zero. By the top rated speed of the
>locomotive, it could well be down to 15% of the rated value.
>
>Wheel slip, as mentioned, occurs when the peak tractive effort (the
>top of the "bishops mitre") exceeds the product: (coefficient of
>friction) * (adhesive weight). The adhesive weight depends upon the
>mass of the loco, how many wheels it presses down on and how much of
>the mass rests on the driving, versus the other wheels (a bit
>tautological, this is). The tractive effort, however, doesn't depend
>upon the number of wheels…. One could theoretically get the same
>tractive effort out of a 2-2-0 as a 4-14-4, provided you had machinery
>that wouldn't snap under the strain! But the adhesive weight
>determines whether this is possible without slipping. Two cylinder
>locos are for MOST of their wheel rotation, more prone to slip than 3
>or 4-cylinder engines (higher coefficient of fluctuation). Naturally,
>the chance of slipping is higher at low speeds where mep is higher and
>throttling is not prominent. The coefficient of friction of
>steel-on-steel also affects the propensity to slip. Damp, greasy
>rails might have a coefficient as low as 0.15; well-sanded, clean ones
>as high as 0.5.
>
>As for controlling a wheel slip when it occurs, the usual practice is
>to close the regulator, called a throttle in the U.S.. This throttles
>the pressure down (as in throttling, described above), and reduces the
>mep, so that the TE falls below the adhesion limit. The regulator is
>opened again when the slip is controlled. To my knowledge no-one ever
>developed an automatic system for this, it was always
>human-controlled.
>
>"High tech" steam locos are mostly oxymorons, at least as far as
>tractive effort goes. The high tech S.African loco probably refers to
>a loco with a modified "producer gas" combustion bed. The French,
>especially, high-teched their locos by reducing steam friction
>(throttling) and thereby increasing power and efficiency. The
>Argentinians were still doing this sort of thing in the late 1960's.
>For a couple of high tech locos, one a spoof, one probably not, see
>this newsgroup for April 1st and Railway Digest for November 1994.
>These proposals surface from time to time and were in fact the reason
>for my writing the book.
>
>
For once I am leaving Geoff's reply in!
If his proposed book is to be written like this, I for one would not
be buying it!
Pete.