Unlike the automotive internal combustion engine the steam locomotive existed in an age of history characterized in technology by the term Industrial Arts. This means that "science" as we would understand it today did not necessarily exist in the same terms. There were no computers to accomplish advanced mathamatical engineering calculations and no cad-cam electronic design facility that would allow three dimensional cyber engineering projections. Drafting Paper and pen were the advanced design tools.
Railroad steam locomotives as such were therefore designed by expertise on the part of the design engineers and their design was worked out over time and with experience in the "school of hard knocks." Yes, there were experts and "guru" talents like Paul Keifer of the New York Central who came up with uniquely workable engines, but on the whole, few paramaters existed that would define a particular set of standards that would produce a true "high performance" design.
Some railroad engines did, however, become famous for their unique ability to perform at speed and in acceleration with passenger work. Other engines owing to their overwhelming size and inherent power accomplished the same goal.
Possibly the Pennsylvania Railroad with its massive investment in "Duplex" engines with equally massive investment in diagnostic test facilities could lay claim to the title - the advent of a "Railroad Scientific Age."
Pennsy had the Altoona Test Plant with its stationary power test dyanometer and also the money and design department to develop the 6-4-4-6 the 4-4-4-4, the 6-8-6 turbine, the 4-6-4-4 and the 4-4-6-4.
Pennsy also did extensive work in the developing field of "poppet valve" design and utilization of "low cutoff" expansive steam usage, an area that really demanded future development. No records exist, however, as to whither the 4-4-4-4 duplex designs featuring "low cutoff" were engines of outstanding acceleration as well as top speed.
Even the locomotive manufacturers ALCO, BALDWIN and LIMA did not have test facilities like the Pennsylvania Railroad. Further none of the manufacturers ever did any performance testing of locomotive designs for themselves. All of this was left to operating railroads. Truely the railroad steam locomotive of the time existed in an age of Industrial Arts.
This brings us to the subject of "Practical Engineering" where rare occurances of recorded steam locomotive performance are documented. One of the few records I have ever seen on steam locomotive acceleration is included in Alvin Staufers book Thoroughbreds recounting the uniquely successful history of the New York Central J3 "Hudson" 4-6-4 passenger engine.
Here in Michigan, famed for automotive production, an engine crew took upon themselves to go about testing the performance of the NYC J3 "Hudson" in practical operation.
Here is their surviving report.
Raymond K. Smith fireman for NYC writing from Lansing, MI -
"I had the pleasure of firing one of these engines in a branch line passenger run in 1955 on trains 351 and 352."
"Our regular engine was J3 5429. It was a pure delight to fire this engine. While we had rather light trains, seven to eight coaches, there were places that we could test the true performance of the engine. One such place was Owosso, Mich. where southbound trains climbed a steady grade for about three miles out of town. We planned to test the time from stand still to sixty using standard stop watch."
"I allowed the water to just show in the glass and prepared a hand fire while doing station work."
"When we recieved the highball, the engineer, H. Brazee, started the watch and opened the throttle. The engine slipped once but otherwise worked at full power. In exactly 90 seconds the speed recorder crossed sixty, the track speed. It was interesting to note that on an L4 (NYC Mohawk 4-8-2 passenger engine) in good running condition with the same train required 2 minutes to obtain the same speed."
"Later, with steam-power retired, we tried this test with a single General Motors GP-7 (diesel electric) Passenger engine. Unfortunately we never completed the test as the engine never reached 60 mph until we passed the next town."
So many variables went into steam locomotive performance that unless you had an engine crew specifically capable of doing a test such as this - these performance paramaters of acceleration were seldom if ever tested.
Notice that the crew prepared a hand fire - also that the water level in the boiler was allowed to be "low in the water glass" - a particular trick that really let the engine perform, and pushed the boiler to its thermal limit - little tricks of the knowledgable engine crew.
Chesapeake and Ohio Railroad also did numerous engine tests using a full engineering staff with trains pulling a company dynometer car - testing for engine power, fuel consumption, loading etc. but not necessarily for acceleration. As did many other railroads also. No one I ever read was particularly concerned with steam locomotive acceleration in the modern engineering sense.
Hope this helps answer your question -