Turnout Frog Angle, Separation, and Clearance Point

ScopeThe frog number is a slope: a number 10 frog spreads one unit sideways for every ten units along, which puts the angle at 5.725 degrees, or 343.5 minutes, a shade under six degrees. Higher numbers are flatter, faster, and longer, and that length is the practical constraint, which is why yards use low numbers and main line crossovers use high ones. The number a track crew actually needs on the ground is the separation at a distance: how far past the frog do the two tracks stand apart by a given amount. That locates the CLEARANCE POINT, where a car may stand on the diverging track without fouling the main, and getting it wrong is how a car gets sideswiped. Taking 13 ft between track centres as the requirement, and counting from the frog point where the centerlines already stand one gauge (4 ft 8-1/2 in) apart, a number 10 turnout puts the clearance point about 83 ft beyond the frog; a number 20 puts it 166 ft out, twice as far, which is exactly why high-number turnouts consume so much real estate and why a yard track built with them runs out of room. The reverse check a crew makes with a tape: standing 150 ft beyond the frog on that number 10, the tracks are about 19.7 ft apart, well past the 13 ft requirement -- a car standing there is clear. Frog angle and approximate separation geometry. It does not lay out a turnout: lead, switch point length, closure curve radius, guard rail and frog dimensions, and tie spacing all come from the railroad's standard plan for the specific design, and no formula substitutes for that plan. The separation relation is a straight-line approximation that ignores the closure curve, adequate for locating a clearance point with a tape but not for design. It does not determine diverging speed, which the railroad and the turnout design set rather than frog number alone, and it does not address turnout geometry limits, switch point condition, guard rail check gauge, or frog wear, all of which are inspected under their own criteria. It does not handle turnouts in curved track, which have their own geometry entirely. The railroad's standard plans, the FRA Track Safety Standards at 49 CFR 213, and the track owner govern.

Formula or tablefrog angle F = 2 arctan(1 / (2 N)) (frog number N = 1/2 cot(F/2)), about 1 / N in radians; separation beyond the frog = track gauge (4 ft 8-1/2 in, the centerline offset at the theoretical point of frog) + distance / N; clearance point = (required separation - gauge) x N; track consumed from the point of switch = entered lead + clearance point.

Source and editionThe frog-number geometry relations, by name, with 49 CFR 213 and the railroad's standard plans named. Lead, switch point length, closure curve radius, and the other layout dimensions come from the standard plan for the specific turnout and are entered, not computed. The track owner governs.

Free accessTrigonometry on a frog number the user states; no railroad standard plan or turnout dimension table is reproduced.

What governsEstimate. AHJ and licensed professional govern.

API field namesfrog_number, distance_beyond_frog_ft, required_separation_ft, lead_ft, frog_angle_deg, frog_angle_min, separation_at_distance_ft, clearance_point_ft, total_from_switch_point_ft

• Frog number is a slope one unit sideways for every N units along; higher is flatter, faster, and much longerturnout geometry
• The clearance point is the field question where a car may stand on the diverging track without fouling the mainrailroad operating rules
• Lead comes from the standard plan switch point length, closure curve, and frog dimensions are design data, not a formularailroad standard plans