weston1879 Wrote:
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> How many loaded cars could a locomotive the size
> of 346 handle on a 4% grade by itself?How far
> could it go on a full tender of coal?Of water?How
> fast could it go upgrade? downgrade(safely without
> a runaway) while hauling this size of train?
Your question is missing a few important details. First, what kind of 4% grade? There's a large difference between a grade on straight track, and an uncompensated grade with sharp curves. Second, how heavy are the cars? 346, if I'm not mistaken, started life as a D&RG class 70 in 1881. In that era narrow gauge boxcars often weighed about 15 tons loaded; by the 1940's era common on model railroads narrow-gauge car weights were often more than twice that.
Using 19th century methods of calculation, you can figure the following. Figure 20 pounds of resistance per percent of grade. Figure half a pound to a pound of resistance per degree of curve (.7 is commonly used). Figure 8 to 10 pounds per ton rolling resistance at 6-8 miles an hour, decreasing as equipment weight increases. Using this you can come up with a rough estimate of what a given locomotive could pull in ordinary conditions simply by adding up the weight of the locomotive, tender, and consist and dividing the combined train resistance into the locomotive pulling power. This will result in slightly conservative figures--by design, as this is how roads of the day figured it and they didn't want stranded trains.
Figure a typical freight locomotive will make something like 95% of its rated tractive force at 6-8 MPH. I do not suggest this method for the Baldwin N.G. consolidations because most such designs were limited more by adhesion than cylinder force (hence also the type's general reputation for slipperiness).
Another method used, probably a little more conservative, was to multiply the locomotive's adhesive weight by .225 (9/40) and use that as it's available pulling power on grades. This is the method most often used by Baldwin for calculating pulling capability in its period advertisements. Since D&RG 346 was built as D&RG class 70--baldwin class 10-26E--it would have had something around 60,000 pounds on its drivers in original condition. That would have increased over time with rebuilds and additional components being added.
All the above should be sufficient for you to work out, very roughly, what you wanted to know about pulling capability. Actual pulling capacity depends so heavily on the specifics of a railroad (even things like track condition and the weather) that more than a ballpark figure cannot be estimated.
Operating range is based on the size of the tender and work required from the locomotive. A hard-working locomotive will consume much more fuel and water per unit of time than an easy-working machine. Therefore it is totally impossible to figure range without knowing the work desired and route particulars. As a general rule a locomotive will run out of water long before it runs out of fuel, assuming a full load of both, simply because water tanks tended to be much more abundant than fuel stops.
You can figure an approximate value for coal and water use per hour (endurance, as opposed to range) based on firebox and boiler dimensions, but that was not requested and therefore I'll omit it because this is already a very long post.
As other posters have explained, speed uphill will often be limited by the capability of the locomotive (figure 6-8 MPH for a locomotive straining at its maximum capacity). Downhill speeds will be limited by track and safety conditions. On long downgrades where time must be taken to stop and let the brakes cool, it wasn't uncommon for running downgrade to take longer than running upgrade.
Why 6-8 MPH uphill? Simple. As speed increases, available tractive power will decrease, as does factor of adhesion. Hence you want to go slower to pull harder. Why not slower than 6-8 MPH then? Below about 5 MPH or so, the rolling resistance of journal bearings massively increases due to such speed being inadequate RPM for hydrodynamic lubrication to work properly. Starting resistance of such bearings was often 25 pounds per ton or more (30+ in winter if frozen), so if a hardworking locomotive slowed to less than about 5 MPH or so, odds are the whole train would stall and potentially be unable to restart itself again (certainly not without bunching up the slack first).
Long story short: There is no quick and easy answer to the questions posted.
As an added piece of trivia, I believe that the class 125 (K-27) 2-8-2's were designed specifically to be able to do the work of two class 60 2-8-0's (C-16).
Edited 1 time(s). Last edit at 11/19/2012 02:29AM by James.
