The Tide, Drawn as a Loop

A tidal current is not a number. It is an arrow — a speed and a heading — and it swings all day. Forget the clock; plot that arrow's tip on a compass and let it draw. The same moon pulls both these places. One draws a straight line. The other draws an ellipse, and never stops moving. Live from NOAA.

This is a hodograph — a plot not of where the water is but of how it moves. Each dot marks the current's velocity at one instant: distance from center is speed in knots, angle is the compass heading the water is flowing toward. Three days of six-minute readings, all laid on one rose. A current that simply ran back and forth would trace a line. A current that swung around the compass would trace a loop.

In the Cape Cod Canal the tide is a piston. Walls on both sides allow only one axis of motion, so the arrow shoots out to one tip, falls all the way back through zero — that pass through the center is real slack water, the moment twice a cycle when the canal genuinely stops — then shoots out the other way. Its ellipse is collapsed to a line: the minor axis is barely a twentieth of the major.

At the open mouth of Chesapeake Bay there are no walls, and something else takes over. As the current builds, the spinning Earth deflects it sideways — the Coriolis force — and it never gets the chance to reverse cleanly. Instead the arrow turns, sweeping a full ellipse once a tidal cycle, always clockwise, the sense Coriolis imposes everywhere in the Northern Hemisphere's open water. The loop is open and offset from the center, so the tidal current never falls to zero — there is no true slack water. It does not stop. It only changes which way it points. Same moon, same twelve-hour beat — but with the walls gone, a reversing tide becomes a rotating one.

How this was built. Three days of six-minute current readings from two NOAA real-time stations, fetched live in your browser from the public CO-OPS API (no key): Cape Cod Canal, West End (ca0101) and Cape Henry LB 2CH (cb0102), at the mouth of Chesapeake Bay — each reporting from its real-time depth bin. Each reading's speed and heading are turned into eastward and northward components and plotted on the rose. The mean tidal ellipse and the two figures of merit come from the covariance of those components: the eigenvectors give the ellipse's axes, the axis ratio (minor ÷ major) measures how line-like or round the flow is, and the sign of the swept area (∑ u·dv − v·du) gives the rotation sense — negative is clockwise. All of it is recomputed independently by the truth-check from the same readings. The clockwise rotation at the bay mouth is the textbook Coriolis sense for the Northern Hemisphere; near complex coastlines topography can locally override it. "No slack" refers to the deterministic tidal current — the ellipse's minor axis stays well off zero — not to every six-minute reading, since wind and eddies can momentarily slow either current near zero. What you see is whatever the live water is doing right now.