Railcar Curve Swing and Clearance Envelope

Its centre sits INSIDE the arc by the mid-ordinate of its truck-centre span, and its corners swing OUTSIDE it. Both matter and they matter in opposite directions: the middle of the car is the problem on the inside of a curve, near a platform or a signal, and the ends are the problem on the outside, near a structure or an adjacent track -- so a car that clears a platform may still catch a pole on the other side of the same curve. THE SWING GROWS WITH THE SQUARE OF LENGTH, which is the whole reason this is a routing question and not a car question. An eighty-nine foot car swings nearly six times as far as a forty-five foot one on the same curve, on identical track. That is why long cars, multi-level autoracks, and long flat loads carry routing restrictions that an ordinary boxcar does not, and why a dimensional load moves on an approved route rather than on any route -- the track is the same, the car is not. The job in the field is a fast go or no-go: given the car, the curve, and the measured distance to the obstruction, does it fit, and if not by how much. That last number is what decides whether the answer is a different route, a different car, or a shift of the load on the deck, and it is worth having before the car is loaded rather than after. The sharpest curve the load can negotiate at a stated clearance is the same relation worked backwards. A GEOMETRIC SCREEN ON ONE CURVE AND ONE OBSTRUCTION. It does not reproduce the AAR clearance plates, which define tangent-track envelopes by height as well as width and which the load has to fit inside before any of this applies. It does not account for superelevation, which leans a car toward the inside of a curve and moves the whole envelope; for lateral play in the trucks, worn centre plates, spring travel, or dynamic sway, all of which add to the static geometry; for the vertical envelope over crests and sags; or for the height of the obstruction against the height of the load, which is a separate check and often the governing one. Clearances measured from a nominal track centre do not account for track that has shifted. Dimensional and excess-dimension loads move under the carrier's clearance department and their approved route, and that approval is not this arithmetic. The AAR clearance plates and loading rules, the carrier's clearance department and route approval, and a field measurement govern.

R = 5,729.58 / degree of curve (arc definition); the car centre's mid-ordinate = truck centres squared / (8 R), swinging toward the INSIDE; the end overhang = (car length squared - truck centres squared) / (8 R), swinging toward the OUTSIDE; the effective half width adds the larger of the two to half the car width.

The chord-offset relations by name, using the same arc-definition constant as the degree-of-curve calculation. A geometric screen on one curve and one obstruction: it does not reproduce the AAR clearance plates, which define tangent-track envelopes by height as well as width, and it does not account for superelevation, truck lateral play, spring travel, dynamic sway, or the vertical envelope. The AAR clearance plates and loading rules, the carrier's clearance department and route approval, and a field measurement govern.

Two squares over a radius; no AAR clearance plate is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: truck_centres_ft, car_length_ft, car_width_in, degree_of_curve, clearance_to_obstruction_in, required_clearance_in, radius_ft, mid_ordinate_in, end_overhang_in, effective_half_width_in, remaining_clearance_in, sharpest_curve_deg

• A geometric screen on one curve no AAR plate, and the load must fit the tangent envelope firstthe AAR clearance plates
• No superelevation or truck play both move the envelope beyond the static geometrythe carrier's clearance department
• Width only, not height the vertical envelope is a separate and often governing checka field measurement and route approval