Can a Big Boy pull a 5 mile long train? (Some Sumpter content)

From Jeff Frost, Backyard Railroading group

Has anyone else heard the claim that a 4-8-8-4 could pull a train more than 5 miles long?

As far as I can tell, this is based off of theory. On a straight level grade, there is only 4 lbs/ton resistance so a Big Boy with 135,375 lbs of tractive effort, they could haul a 33,843 ton train on straight level track. Engine and tender weigh 625 tons leaving the trailing tonnage at 33,218 tons. That would be 738x 45 ton cars. If a 45 ton car is 38' long, the cars would be 28,050 feet long, which is 5.3 miles.

Now if the train heads up a very shallow 0.2% grade around a 2 degree curve, the total weight to be pulled on this track would be 16,590 tons, giving a trailing weight of 15965 tons. This would be 354x 45 ton cars at 38' long would be 2.55 miles long.

If the train were to head up a 1% grade with a 4 degree curve, the total weight that can be pulled is 4,977 tons which gives a trailing weight of 4,352 tons. That would be 96x 45 ton cars at 38' long would be 0.69 miles long.
thanks
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To figure out max tonnage it is tractive effort / resistance.
Resistance:
4 lbs/ton resistance for straight level track

plus 20 lbs/ton per % grade resistance

plus 0.8 lbs/ton per degree of curvature to figure out maximum tonnage.

To figure out how long the train is I used an estimate/average weight of a car being 45 tons and 38' long (they were 40-50 tons, 36-40' long in the days of steam).

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The rating on straight level track is just a statistical number and means nothing in real live. A straight 0.2% upgrade (2.4" rise over 100') cuts the train down to 50% of its tonnage on straight level track.

A straight 1% grade cuts a train down to 16.6% of the weight on straight level track.

A 1.2% grade on a 5 degree curve cuts the train down to 12.5% of what it can pull on straight level track.

A 2% grade on a 5 degree curve cuts the train down to 8.3% of what it can pull on straight level track.


The calculations for how much a steam locomotive can pull and the estimates for resistance apply to the live steam hobby too. By using the tractive effort of a steamer, 4 lbs/ton resistance for straight level track, 20 lbs/ton resistance per % grade and 0.8 lbs/ton resistance per degree of curvature, the calculated maximum train weight can be determined.

The degree of curvature is how many degrees the track turns across a 100' chord.

To figure out the degree of curvature, the formula is 2sin(50/radius). A 50' radius is a 180 degree curve. A radius smaller than 50' is not able to be computed as a degree of curvature.

So Russ adds:
A SVRy 2-6-6-2 has 42,100 pounds TE = 425- 25 ton 30' flat cars on the level= 2.4 mile long narrow gauge train!

On the 1.5% grade and 16 degree curves between Baker and Sumpter it could (theoretically) pull 34 cars but up the 4% grade and 16 degree curves to Larch it would be down to 17 cars.

Really something how grades and curves effect load...

Here is one working in Guatemala.


Russell Courtenay
Idaho, USA