Blamed on the Arc: Sheet Flow Cannot Jump a Gutter, but Rivulets Can

When a gutter overflows in extreme rain, the explanation offered is often ballistic: the water came off the roof too fast and jumped the gutter. This paper computes the trajectory and finds the explanation wanting for ordinary sheet flow — and identifies what actually jumps. On a six-metre tiled slope at thirty degrees, uniform sheet flow leaves the eaves at 0.48 m/s even under 300 mm/h rain and throws only 0.085 m while falling to gutter level, well inside a standard gutter whose lip sits about 0.125 m out. The same discharge concentrated into rivulets occupying a tenth of the slope width — the normal condition between tile joints and below laps — leaves at 1.21 m/s and throws 0.181 m, clearing the lip; at a fifth of the width it throws 0.146 m. Overshoot is real but it is a concentration phenomenon, not a sheet phenomenon: the remedies are to break up rivulets and valleys before the eaves and to place the gutter for the concentrated case, not to blame the roof's speed in general. All results are simulated, not measured.