Tuesday, December 18, 2012

Choosing a model car fleet -- numbers, Part 2

The previous post posed the problem of how to be quantitative about a realistic and prototypical fleet of model freight cars. It largely addressed the long-standing and knotty issue of what proportion of home-road cars would be in such a fleet. It may be helpful to read that post, so here is a link to it: http://modelingthesp.blogspot.com/2012/12/choosing-model-car-fleet-some-numbers.html .
     In the analysis of home-road cars, I had occasion to refer to the national fleet of freight cars in 1950, and also to the Southern Pacific fleet in 1950. The bar graphs showing those date were shown in the prior post, and are repeated here for covenience. The actual percentages associated with each bar are shown above them.

     I will begin with the foreign-car part of the box car component of my postulated 400-car model freight car fleet. The number of these foreign box cars was computed in the prior post to be 143 cars within that 400-car fleet. The graph above for the national fleet shows that box cars were in fact the largest group, and the third largest was gondolas, adding to 51% of all cars. Here we can get more specific, because I believe there is a good starting point for these cars: the Gilbert-Nelson theory of car distribution. I have introduced and commented on this idea in a couple of previous posts, starting with a general presentation in an early discussion about choosing a fleet: http://modelingthesp.blogspot.com/2010/12/choosing-model-car-fleet-2.html and then with further discussion about my own model car fleet at: http://modelingthesp.blogspot.com/2011/11/freight-fleet-rosters.html .
     The Gilbert-Nelson idea, in brief, is that free-running cars, that is, cars which were mechanically equivalent and could be substituted for each other, and were used for cargoes throughout the country, would be found anywhere in proportion to their share of the national car fleet. In other words, a road which owned 1% of the nation’s general-service box cars would have its box cars present as about 1% of the cars in trains or yards anywhere in the U.S. beyond the home road of those cars. The same should apply to many kinds of gondolas and, to a lesser extent, to flat cars. But non-free-running cars would not obey this theory.
     Another important condition stated by Gilbert and Nelson is that the theory should only apply in bridge-route or other long-distance traffic situations. Obviously, branch lines, short lines, and some geographically isolated routes might fail to obey the overall idea. And just to be completely clear, of course Gilbert-Nelson says nothing about home-road cars.
     So even if we fully accept Gilbert-Nelson principles, they only apply to certain conditions. On my own layout, the SP Coast Line is a reasonably representative traffic corridor, but the branch line I model might not be.
     How then should we proceed to identify the owners of the foreign cars in that 400-car fleet? Let’s look at them in two parts. First, for the box cars and gondolas, we can simply take the percentages of the national fleet occupied by the fleets of each major railroad, multiply that by the number of cars in the model fleet we are computing (such as 143 foreign box cars). This is pure Gilbert-Nelson. Where do we get those percentages by car type? At the end of most railroad entries in the Official Railway Equipment Register or ORER, the different car types are listed, and these totals can be divided by the number of national cars of that type, to form percentages of each type for that railroad.
     My graph above gives percentages of car types; the values shown can simply be multiplied by the size of the total national freight car fleet of all railroads plus all private owners. What was that value? In 1950 it was close to 2 million cars, nearly 600,000 of which were open-top hoppers and thus less widely interchanged. So exclusive of hopper cars, the remainder is 1.4 million cars. But to get the total number for any car type, we need to multiply 2 million times the percentages in the graph, because those are percentages of the total fleet. For box cars, it is 720,000 cars.
     The second part of the problem is foreign cars other than box cars and gondolas. Here I can make the guess that the foreign cars might be distributed like the graph above for the national car fleet. That national fleet, of course, cannot mimic any one railroad, because no one railroad had exactly the traffic mix of the nation as a whole; and nearly all tank cars, along with many reefers, were in private ownership and thus would not show up in any listing of railroad ownership. Among the lesser car types, I would not try to refine numbers for stock and flat cars, because they represent such a small part of the total. That mostly leaves private reefers and tank cars. Tank cars were 8% and private reefers about 7.7% of the national car fleet in 1950. Now let’s look at some examples.
     The largest American freight car fleet was that of the Pennsylvania Railroad, with about 112,000 cars exclusive of hoppers in 1950, or 8% of all non-hopper freight cars. Of these, box cars were 62,300, or 55% of the PRR non-hopper fleet. If we divide 62,300 by the total number of U.S. box cars, 720,000, we obtain 8.6%, so 12 of that 143 foreign-box-car group should be PRR box cars. As another example, the Missouri Pacific (including subsidiaries) rostered about 44,000 cars other than hoppers. Among that fleet, box cars were 15,000 cars, or about 2% of all box cars. That means that my 143 foreign box cars should include three Mopac box cars.
      The same approach should work for smaller roads; for example, among Southeastern roads, the Seaboard had about 23,500 cars (again, other than hoppers), with about 10,000 of them being XM box cars, which is 1.4% of the national box car fleet. In my 143-car sample, then, this would mean two SAL cars.
     One last example: Union Tank Car Company owned about 44,000 tank cars in 1950, out of about 150,000 total privately-owned tank cars, or about 30%. That means my 18-car group of tanks, likely being about 12 foreign cars and 6 SP tanks, should contain about 4 UTLX cars.
     I realize that this is far more numbers and far too many calculations for some folks (few of whom will have read this far!). And most of the numbers I’ve shown are rounded off, and in any case have been derived using simplified and weakly justified assumptions, so they are already more refined than I would want to defend anyway. But if you don’t mind numbers, they can give a broad scope to determining how many cars of specific ownerships, and what kinds of cars, one could prototypically expect to find in a modeled area such as my SP Coast Division layout. Whatever area or time period you model can be analyzed in a similar way.
Tony Thompson

No comments:

Post a Comment