I have been thinking of adding a branch line to my layout , but it would need a good sized grade to make it work so I wanted to test my most power steam locomotive on my layout and figure it could pull 25% on a 2% grade on same radius curve as rest of layout. So 8-10 cars max. Is this a correct formula for a 2% grade? As the video shows 44 is a bit much for this engine. All cars are 40 foot , but loaded gondolas are heavy.

Is the a formula for grade and pulling ability? My sidings only allow about a 12-15 cars anyway so a 7-9 car train is fine.

I found a "dynamometer car" to measure the tractive effort of a model locomotive: I bought that at an estate sale. It's a 250g/9oz scale glued to a flat car. The left end has a conventionally mounted coupler, while the coupler on the right is attached to the movable slider. I couple it to the engine and hold the other end with my fingers and turn up the throttle until the engine slips. I can also measure the rolling resistance of a train with it, placing it between the loco and the train. I was able to calculate that each car has about 2.5 grams or 1/10-1/12 oz of flat rolling resistance on average. Divide the pulling force of the engine by the flat rolling resistance of one car and that tells you how long a train you can pull on level track. For going up-grade, add the weight of the train multiplied by the sine of the angle of your slope (2% = 1.146 degrees) to the flat rolling resistance. The sine of 1.146 degrees is about 0.02. If your train is NMRA weighted and it's 10 cars of 40 feet in length, you'll have about 1000 grams of train weight. 1000 grams x 0.02 = 20 grams of extra coupler force. Add that to the 2.5 grams/car x 10 or 25 grams, you'll have 45 grams of drag on your rear coupler. My experience shows that most heavy locos I have can lift a ten car train up a 2% slope. But I wouldn't give that job to a 44-tonner... Now you know what other kinds of fun I have

It will have to be determined experimentally. Each locomotive has a different pulling power, and wheelset friction will vary based on brand and model quality. You may be able to do some basic free body diagrams and solve for equilibrium forces, but I think there are too many variables for a universal equation.

I did something similar using my "dynamometer car" and an Excel spreadsheet. I did the pulling test and noted each value. I did an average trend curve to see how adhesion works. It's around 20%. I noted that most locos have pulling power in the range of 100-120 grams. There are some exceptional pullers, like a Proto E8, which can pull 170 grams (it weighs over 700 g!). Then there's the Bachmann 44 tonner that barely can pull 30 grams. Basically, it comes to weight on drivers, just like the real ones. Another surprise was my BLI USRA 2-8-2 which has an engine weight of 328 grams and it can pull 135 grams - that's over 40%. Sometimes there are outliers off the average curve. Which comes to another consideration: gearing. Just like the real ones. I used the same spreadsheet file, on another tab, to keep track of car weights and how much I need to add (in pennies, nice 2 gram weights). It's a lot of fun. That's the best part of it.

Does the BLI model have traction tires? That could affect pulling power? Based on your data, pulling power is proportional to weight, which makes sense. The force of friction is related to the normal force and the coefficient of friction. If the BLI model has rubber tires, then the coefficient would be higher.

I just took a look (after a few years of having it... ), and yes, there are traction tires on the rearmost drive axle wheels. The other three axles are bare metal. One mystery solved. Thanks for the pointer. Edit: here's a screenshot of the graph I plotted for the data I gathered: X axis is weight of engine, Y is tractive effort. All in grams.