buzz456 wrote:"A very general rule of thumb with steam locos is the (theoretical) max speed is roughly 1.2 times the driver diameter in inches so a loco with 50 inch drivers should max out at about 60 MPH. One with 80 inch drivers around 96 MPH. Obviously there are exceptions and other factors that apply. One important one is the amount of weight in reciprocating motion (side rods, connecting rods, cylinders, etc). The more drivers the more weight so a 4-4-2 isn't as hard on the track then a 4-8-4 at the same speed."
This is from a blog when I was poking around.
I'm not too sure about the last sentence. One of the advantages of more axles, apart from added traction, is that it distributes the weight over more spots on the rails. The disadvantage is that to get more axles along a given length of frame, the wheels have to be smaller, which means less speed (the wheel circumference is less so the wheels travel a shorter distance on each stroke.
I found another fantastic document, in PDF format, written by Llewellyn V. Ludy M.E., Professor of Experimental Engineering, Purdue University, American Society of Mechanical Engineers, called "A Practical Treatise on Locomotive Boiler and Engine Design, Construction, and Operation", for the American Technical Society, Chicago, in 1920 (the year the real Lima Consolidation was built). 177 pages full of extremely useful material.
One interesting bit is on page 128. It's a formula for the tractive effort.
T = (0.85 .p.d.d.L) / D
where
T = the tractive force in pounds
d = diameter of cylinders in inches (24" for the Consolidation)
L = stroke of the piston in inches (20" for the Consolidation)
D = diameter of the driving wheels in inches, including the tires (the Consolidations wheels are 40" in diameter, but then you have to add another 4" to allow for freshly applied 2" thickness tires)
p = boiler pressure in psi
It says that 0.85 relates to the mean effective pressure on the piston in psi.
There's a more complex formula for 2-cylinder compound locos (which have a low and a high pressure cylinder).
There's even a (very complex, but apparently very accurate) formula to calculate T, the number of tons including engine, which can be hauled over a grade, for a given starting velocity at the start of the grade and velocity at the top of the grade, taking into account the same parameters as before, as well as the tonnage of train, the grade and length of grade, etc. I'll have to calculate it for the Consolidation and then do some test runs to see if I can match it to T. Interestingly, it says that for empty cars, you have to add 40% to the friction with respect to loaded cars. i think might be because for the same tonnage, you'd need more empty cars than loaded cars, so the same tonnage of empty cars would indeed have greater friction (more wheels. more cars facing the direction of travel).
I put in the numbers for the Consolidation, and it comes out that if I begin a 1.8% grade at 20MPH, after 1 mile, hauling 885 tons of loaded cars, it should have slowed to 10MPH, assuming the locomotive is run as efficiently as possible. I'll set up a test to see.