Slimgauge, you bring up an interesting topic, and despite my following explanation I'm sure that in our world of model trains, it isn't quite as critical as the prototype. But here goes since you baited me. 
To be able to calculate degree of curvature and then translate to radius (or actually vicve versa), you first have to decide what scale you are using. If we're talking Bachmann Big Haulers, aren't they about 1:22.5 scale? One degree of curvature in standard American gauge (4'-8.5") is achieved by using a radius of 5,729.65 feet. I have provided a reference URL for those interested in where that number came from. In 1:22.5 scale, the radius needed for 1 degree of curvature would be 5729.65 divided by 22.5 or 254.65 feet. More practically, if you are using 10 foot diameter curves (5 ft radius), in this scale you are representing 5 x 22.5 or 112.5 foot radius curves which equates to approximately 51 degrees of curvature (really really sharp curves).
That would mean that if you use 10 foot diameter curves on a grade, you would want to reduce the grade 51 x .04 or approviamtely 2% on the curved portions. So if you had a 3% grade, you would need to drop back to a 1% grade in the curved portion. Not always easy to do. By the same calculations, those engineers using 20 ft diameter track (Aristo's widest sectional track) are representing a 25 degree curve, so they would need to reduce grade by .04 x 25 or about 1.0 % in the curves.
You can see that this can easily become quite impractical in the space we have for our pikes so we compromise. In the end, we need to keep grades minimal in curved sections, but I don't think all this "compensated grade" calculation is required for 98% of our layouts. In the real world it's all done for proper engine loading and to try and minimize forces that would overcome dynamics and traction. But it's helpful to understand what would be ideal from an engineering perspective.
PLUS, the transition from one grade % to another % needs to be gradual. There is even more complex math to calculate the "vertical curve" required for the transition gradient, whether peaked (convex) or valleyed (concave). I would just make sure it's gradual enough to clear all cowcatchers, keep all engine wheels on the track, and not cause couplers to unhook. /DesktopModules/NTForums/themes/mls/emoticons/satisfied.gif I thkk most folks just try to maintain a steady gradient an not have an undulating track on any grade.
Reference: http://mysite.du.edu/~jcalvert/railway/degcurv.htm
AL
To be able to calculate degree of curvature and then translate to radius (or actually vicve versa), you first have to decide what scale you are using. If we're talking Bachmann Big Haulers, aren't they about 1:22.5 scale? One degree of curvature in standard American gauge (4'-8.5") is achieved by using a radius of 5,729.65 feet. I have provided a reference URL for those interested in where that number came from. In 1:22.5 scale, the radius needed for 1 degree of curvature would be 5729.65 divided by 22.5 or 254.65 feet. More practically, if you are using 10 foot diameter curves (5 ft radius), in this scale you are representing 5 x 22.5 or 112.5 foot radius curves which equates to approximately 51 degrees of curvature (really really sharp curves).
That would mean that if you use 10 foot diameter curves on a grade, you would want to reduce the grade 51 x .04 or approviamtely 2% on the curved portions. So if you had a 3% grade, you would need to drop back to a 1% grade in the curved portion. Not always easy to do. By the same calculations, those engineers using 20 ft diameter track (Aristo's widest sectional track) are representing a 25 degree curve, so they would need to reduce grade by .04 x 25 or about 1.0 % in the curves.
You can see that this can easily become quite impractical in the space we have for our pikes so we compromise. In the end, we need to keep grades minimal in curved sections, but I don't think all this "compensated grade" calculation is required for 98% of our layouts. In the real world it's all done for proper engine loading and to try and minimize forces that would overcome dynamics and traction. But it's helpful to understand what would be ideal from an engineering perspective.
PLUS, the transition from one grade % to another % needs to be gradual. There is even more complex math to calculate the "vertical curve" required for the transition gradient, whether peaked (convex) or valleyed (concave). I would just make sure it's gradual enough to clear all cowcatchers, keep all engine wheels on the track, and not cause couplers to unhook. /DesktopModules/NTForums/themes/mls/emoticons/satisfied.gif I thkk most folks just try to maintain a steady gradient an not have an undulating track on any grade.
Reference: http://mysite.du.edu/~jcalvert/railway/degcurv.htm
AL
