Curvature and Gradability Ratings

Surely, locomotive manufacturers (and to perhaps a lesser extent, manufacturers of railcars) use some sort of formula (or formulae) to determine maximum curvature (minimum radius) and rate of change in grade.

While I'd like the formula (or formulae) to determine all that (especially if such takes into account the severity of conditions created by a combination of grade-change and curvature), just the ability to work backwards through design parameters to determine the curvature limits of prototypical equipment would be *really* helpful.

So, does anyone have anything helpful?

I can convert radius to degrees of curvature, and vice-versa.

Thanks!

Locomotive manufacturers do determine the minimum curvature that their products can negotiate. However there are multiple parameters for each locomotive model. This is because the minimum permissable curvature depends not only on the configuration of the locomotive, but also on the configuration of what, if anything, is coupled to the locomotive. For example, a single SD70MAC-T1 is capable of negotiating a 213-foot radius curve; but a consist of two of those units will require a curve with a radius of at least 255 feet. I'm unaware of the specific process by which the minimum-curvature parameters are calculated.

I expect that the closest that manufacturers come to determining what might be called maximum-gradient parameters for their locomotives is to make a determination of their tractive-effort ratings. Railroads use these ratings, as well as the results of their own operational experience, to determine the amount of tonnage that a given locomotive model can be expected to move over a given route. And, although the tonnage ratings are primarily dependant on gradient, curvature is also a factor since it, like gradient, produces resistance to a passing train that the locomotives must overcome in order to move the train. In other words, the question most typically asked is not what maximum gradient a given locomotive will climb but, rather, what amount of tonnage a given locomotive will move over a given route, which happens to be characterized by a certain combination of gradients and curvatures.

Another thing to consider is what speed will the train run for its given tonnage. For each increase in gradient of one percent you double the amount of horsepower to maintain the same speed.

Other considerations would be journal friction, flanges, track condition, and air and wind may cause additional train resistance.

"Compensated curve," referance calculas text book for formula. In laymans terms a compensated curve is one which has a constantly decreasing gradiant the more lengthy the curve so as to produce a constant load to the motive power. Read a civil engineering text.

SSW9389 wrote:For each increase in gradient of one percent you double the amount of horsepower to maintain the same speed.

Quintuple, more like.

I don’t think curve ratings are a special formula. They are simply a case of translating the radius and truck center distance into the angle the truck needs to be rotated from the chassis. Then check the drawing details to see if the truck parts will still clear all the frame parts, will the corners stay inside the clearance gauge and will the traction motor, blower air and brake connections stretch far enough. While these shouldn’t be hard to make flexible, there isn’t much need to put extra range in them either, I think you’ll finds bits getting bent or broken very quickly if you exceed the ratings. Also the overhang of the chassis at the corners and at the inner middle of the frame needs to be checked for clearance.

A similar calculation would be run for the overhang and angle of the coupler on a curve, designing it with a lot of swing in the draft gear pocket results in excessive sideways slack when you are on the road. An easier curve is needed to get the coupler to engage and latch with a car.

Vertical curves as grades start could also be calculated and but are probably covered by having allowed enough flexibility for rough track.

I recollect watching a passenger train detoured through some waterfront switching tracks. The limit was that end hand rails on the cars bent each other up and the side pressure on the flanges caused the wheels to bind up and slide. So the limits are not from broad formulas but rather a number of little details for which you would need a full set of locomotive drawings. I suspect the makers have collected some experience about how much margin they need in their figures for flexing of the springs and other variables too so that the ratings they publish are reliable.

Bill