I apologize in advance for veering off the subject of preservation and into the realm of the hypothetical, but I need information from someone better grounded in engineering & physics than I.

The hypothetical question is this: A locomotive's factor of adhesion is defined as the percentage of its weight that the friction existing between wheel and rail will convert into tractive effort. Therefore, all other things being equal, would a six-drivered locomotive have superior adhesion and pulling power to an eight-drivered locomotive?

It seems to me that if weight, operating pressure, driver size etc. are equal between two engines, the one with six drivers would have better adhesion due to more pressure (weight) at the wheel/rail interface. On the other hand, some would argue that an eight-coupled engine, with less weight on each wheel but multiplied by more wheels would have the advantage.

So...was the historical progression of more drivers on locomotives (e.g. 4-4-0 to
2-6-0 to 2-8-0) an attempt to gain adhesion, or merely a function of building larger locomotives and a need to spread the weight out more to avoid damage to the track structure?

Thanx in advance for any & all answres.
J

In theory the horizontal force resulting from friction is dependent on the vertical force down (mass) and the coefficent of friction. It is completely independent of the number of wheels. To increase the locomotive's pulling force, if it is not limited by the available horsepower, the locomotives weight is increased. When increasing the weight on the drivers, bearing capacity and material limitations must be considered.

As locomotive weights were increased, the number of driving axles was increased. As bearing and material issues were resolved, the weight of the locomotive could go up without increasing the number of driving axles.

All of these same issues carried over into the diesel era. Slip control on modern locomotives now optomizes the available friction way beyond anything seen in the steam era.

first, I think competition was the driver for bigger better engines.

From what I recall, adhesion is about a 1 to 4 factor, or closer might be about 1 to 3.89 weight to tractive effort, 4000 pounds of weight could make 1000 pounds of tractive effort.

Adding a wheel probably creates another point of connective adhesion but does not change the weight, and you know lighter weight on a wheel, the slipperier it gets.

Designing a locomotive for a railroad comes down to its needs and where it could run, for comparison the N&W Y6b vs the Class A 2-6-6-4, the Y6 made for the heavy duty drag up the Blue Ridge mountain, all possible weight on the drivers, small drivers slow speed. The Class A is equally as large even slightly longer than the Y6, larger drivers but slightly less tractive effort than the Y6, built for level track running higher speed. (but not afraid to be out tugging on the heavy grades)
Consider the Allegheny 2-6-6-6, fewer wheels, but yet, equally or more Tractive effort than the Y6.

Now look at the 4 truck shay, or a 2-10-0, built a little more for lighter rail and economy of operation and restrictive weight areas. Then you have the 4-4-4-4, slippery dude, but for high speed passenger.
You tune to the needs, but the adhesion factor seems to stay about the same, so there may be a mathematical formula to figure out weight vs metal/metal adhesion, I can't think of a more slippery medium than 2 metals trying to stay in one place, especially at a pinpoint spot. All that weight on one wheel you would think it would even crush the steel. Consider a model railroad train having traction tires to gain adhesion, my BLI 2-8-2 with traction tires drags the 35 cars around on my layout the same as my BLI Y6b no traction tires, lighter engine, better adhesion!

So I tend to think if you made a Y6b as a 2-6-6-2 you would still have the same tractive effort, but you might be killing the ties.

overNout

One of the things that I have always admired is how engineers were able to figure all of this stuff out with a pencil, paper, and slide rule. In addition to the tractive effort part they were ale to figure out how to balance these machines well enough that they could travel at speeds above the century mark and not fly apart.

working with 765 and its devices, everything is designed down to clockwork precision. Think of all the watchmakers from yesteryear.