These standards are for track curvature and switch dimensions. Railroad curves are laid out by degree. For example when the surveyor wants to lay out a 1 deg curve he sets up his transit for the tangent (straight ahead) and then rotates it 1 deg. The chainman pulls the chain tight and moves until his staff is in the cross hairs of the surveyors’ transit. The surveyor then moves his transit to the new location. He sites back to the staff where he came from to establish the tangent to the curve at that point. After rotating the transit 180 deg he is now facing in the moving ahead direction and rotates 1 deg to establish the next point on the curve. The chainman marks the new location and the process continues until the curve is laid out. In surveying, the chain length is 100 ft. On a highway the 100 ft chain length is the cord of the arc, in other words the distance between surveyor and chainman’s staff. On railroads the 100 ft. is along the arc of the curve. This gives an accurate dimension for the feet of rail needed, important when ordering rail. Since the 100 ft. measure is along the arc the chainman must shorten the chain according to the deg of curvature being surveyed. To convert these dimensions to O Scale divide the radius of the curve by 48 since we model in 1/48th full size. Note that a 19 deg prototype curve is 303 ft. radius. Multiply 303 by 12 to get inches and divide by 48 and you will get 75.75 or 75-3/4 in. So your 19 deg O Scale curve would be 75-3/4 in. radius. For reference a USRA heavy Mikado has a minimum curvature of 19 deg that it will go around.
The turn out date will also be of help in modeling. When designing your layout look at the center to center distance of the tracks on crossovers and ladders. For example a 12 ft. center to center distance would be 12 ft times 12, to convert to inches, then divide by 48 and you get 3 in. for your model. If you use this for a cross over then the distance between the frogs will be 15ft on the prototype and 3-3/4in. on the model. The lead, or distance from the point of the frog to the point of the switch, would be 56 ft. 5 in. In O Scale this number would be 14-1/8 in. In modeling we tend towards larger distance between track because we are generally running on much tighter curves and therefore have greater overhangs when the equipment goes through the curve.