Jones1945
Yes, the PRR S2 had 68" drivers, even smaller than N&W J's driver by one inch ...
Two inches. Very important inches for a number of classes of power...
but still capable to pull a 17-car train over a distance of 30 miles (level track) at a speed of 110 mph, so a properly-balanced 72" driver on M1a/b variant should have been adequate for express passenger train.
The problem is that these are not comparable.
The S2 is manifestly not a reciprocating locomotive. There is a certain amount of 'statutory imbalance' in the quartered connecting rods, but they can be balanced rotating, so the only real augment-inducing couple that 'matters' is the difference laterally between where the center of mass of the counterweight in each driver is a bit 'inside' the center of mass of the net rod mass for that driver. So there is a bit of induced hammer-blow, but it is rather obviously a tiny fraction of adhesive weight up to substantial rotational speed; far more speed,likely, than the corresponding much higher (fixed by the reduction-gear train ratio) speed where windage, exhaust clearance and other losses begin to seriously beset the steam turbine doing the rotational drive.
The situation with the 72" M1b driver is quite different; it has all the augment forces described in Johnson's book. For example you have the reciprocating mass of the mains to deal with, plus the rotating component of the mains carried proportionally far outboard, so the balancing is more complex; there is also the small vector component of the piston thrust in the vertical plane (which is the thing Voyce Glaze left the 80lb of reciprocating balance in the main driver to deal with) -- for 'maximum speed potential' you calculate this for open throttle at about 40% cutoff, which would correspond to peak achievable balancing speed.
We assume well-adjusted Franklin wedges with appropriate spring pressure, so there is no slack in the longitudinal 'fit' of the axleboxes/lateral-motion devices in the pedestals. We further assume a good spring pressure on the Franklin radial buffer between engine and tender ... which raises the spectre of surge at high piston thrust or resonant conditions. This is what the Langer balancer is designed to counteract, and geometrically it ought to do so very well; this leaves nosing and hunting to be compensated as Voyce Glaze intended, with stiffer lateral and better lateral damping, including better lateral-motion control of the lead driver pair in curves.
But not only PRR's S1: MILW, CNW's, and ATSF's 3460 Class Hudson also had 84" drivers, I wonder why Alco, Baldwin, and RRs had blind faith on driver larger than 80" for their express passenger steam engine?
It was not blind faith, it was conventional wisdom. That it was erroneous wisdom, and relatively quickly overcome by events, does not detract from its validity as a topic for discussion.
As far back as the Monster of 1836, the idea was that a good honkin' tall driver diameter would translate into high speed. In fact the spokes on Monster's drivers were paneled in to avoid strewing levitated ballast at lethal velocities ... something I do think would have been observed. You have Cramptons. You have geared-drive engines of various kinds that spin drivers faster 'by other means'. You have all the 'singles' that constitute the early age of 'duplexing' with single axles in an age when side-rod clearances and bearing technology meant 'coupled wheels would be slower'.
And yet, even then it was clearly recognized that high speed came from boiler steam-generation capacity, not from high drivers. Each inch over about 78" results in a severe toll in 'default' tractive effort, with the 86" on NYC 999 clearly putting the engine over the line into skittish-racehorse performance. And the presence of side rods capable of sharing Super-Power levels of piston thrust pretty well meant relegation to slow speeds, or the use of three-cylinder drive to keep the thrusts down and augment better distributed... and so we come to Eksergian, in 1928, carefully analyzing the different components of balance.
Now, in the early Thirties it was 'common knowledge' that the only true high-speed power was going to be at most six-coupled. In the absence of a careful analysis of balance the 'solution' for 100mph had to be 84" drivers (ideally with the main in line on the lead driver pair, and four-coupled to keep mass and bending stress in the rodwork bearable) and ... in some cases ... it was a reasonable prescription.
One of the great catastrophes of steam design happens right at the cusp of this: the ACL R-1s as initially balanced. Wrong understanding, wrong formula ... revealed "I told you so" wisdom producing amazing levels of track wrecking from a locomotive that should have been one of the best. While the conventional practice puts together the C&NW E-4, which couldn't even get its test train over 100mph, or the ATSF 3460 class, which fell off the porch between 102 and 106mph or so as its inadequate valves and passages ran out of ... well, steam. And the ominous lack of true high-speed test data for the Milwaukee F-7s, suspiciously similar to E-4s in many significant dimensions, which would run all day at 100mph but ... perhaps ... not that much higher.
ATSF now turns to rebuilding the sow's-ear 3751 class to larger drivers, better valves and passages, suspension and bypass valves ... and lo! winds up with a high-horsepower locomotive that is just as fast, in fact faster, than the 84"-drivered short-stroke conventional-wisdom speedster. They take a leaf from this to build 2-10-4s with relatively high drivers (the 'sweet spot' for freight or most dual-service being somewhere in the 74" to 76" range) with a longer rigid wheelbase than a PRR Q2 duplex ... and we get into the world in which the C&NW works over its H-class 4-8-4s not once, but twice, probably winding up with an engine the effective equal in speed of the E-4 but dramatically more useful in just about every context where the track could handle the additional weight and forces of a locomotive that size.
What happens at the end of the Thirties is that across a wide range of designs, it becomes clear that large-firebox eight-coupled power is capable of going just as fast as a given railroad will permit. In the case of the PRR, that meant that an 80"-drivered duplex would not only reach the speeds expected of the heavy improvements in the Sam Rea Line and other 'new main line' improvements, but the highest speeds safe to reach with reciprocating power of any practical driver diameter. The only reason to go to 84" drivers would be to preserve the (driver-center structurally limited) 26" short stroke on a T1 'follow-on' (likely not a derivative of the E8 Atlantic design, but something like an improved S1 with all four sets of rods common and very little if any formal overbalance) and by then it was increasingly recognized that 26" was ridiculously short for what modern balancing could give you...
By the time of the 'late' AMC Berks, the NYC L-4 (and prospective later power) and the PRR re-tiring of some of the J1as, we see the interesting formula of drivers somewhere in the low 70s 'new', comparatively long stroke (suicidally long by even late-Thirties standards; sometimes 34") but smaller bore to lower reciprocating mass and peak piston thrust, and lightweight rods ... with or without roller bearings and dramatic thin section/deep web. (Note carefully the main-bearing design on the UP 800 rods, which accomplished many of the real-world ends of rod rollers without either the first cost or the careful twitchiness necessary in maintenance.)
It is difficult to imagine 'cost-effective' M&E on PRR, even with some form of palletization or containerization that would work with such trains, involving even peak speed above 90mph; on the other hand, the ability to accelerate quickly after checks and over difficult profiles without corresponding expense of fuel and water is nearly as quickly and easily recognized as it was in the France of the artificial socialist speed limit. Which leaves two things: the future of nonreciprocating steam power, which is succinctly the story of the S2 and V1 with proper drive technology, and the use of high-horsepower locomotives with limited water rate. On the latter would founder all the advanced design of the Forties: the contest was still there, barely, in 1946, but even by the time Kiefer's report was issued the game was visibly over. For steam to 'look good' you needed the appropriate traffic -- long distances, very high speed, guaranteed profit margins, very quick turnaround, well-organized maintenance from guys in asbestos suits willing to use them. Remove almost any of those factors -- and in the late Forties all of them were disappearing at an accelerating rate -- and the opportunity costs of dieselization look as compelling as history bore out.
Which is where a sensible-dimensioned locomotive capable of extraordinary performance beats the tar out of a high-wheeled prima donna. Even a Niagara could be operated fast, strong, or almost inconceivably cheaply depending only on the service expected of it. A Kiefer-corrected C1a would still have had some of the limiting faults of obligate high-speed design, most particularly the 26" preserved stroke (which was almost certainly a necessary part of the design in giving true run-through on 64T) and ... knowing what we know about Dieseliners ... would likely have suffered the fate of the poppet-valve Niagara and the PRR T1 as a first-line express locomotive. On the other hand, any driver greater than 69" that would fit under an A-2a shell would have been interesting in a great many ways...
... were even a couple more years given to modern Eastern steam.