Counting Knots and Cracking Booms: How We Learned to Measure Speed

Somewhere in the Atlantic in the 1620s, a ship's officer needed to know how fast his vessel was moving. He had no GPS, no speedometer, no instruments that could read velocity from the water itself. So a sailor grabbed a wooden panel, tossed it over the stern, and counted knots on a rope as they slipped through his fingers. That count was the ship's speed. The method was crude, clever, and accurate enough to cross oceans. It also gave us a unit of measurement that pilots and captains still use four hundred years later.

The Chip Log

The device was called a chip log, and its design was elegant in its simplicity. A flat wooden panel (the "chip"), roughly triangular and weighted on one edge so it would stand upright in the water, was tied to a long rope. Knots were tied along the rope at regular intervals, typically around 47 to 48 feet (roughly 14.4 to 14.6 meters). The other end of the rope wound around a reel held by the sailor.

Here is how it worked. A sailor threw the chip overboard. The panel hit the water and acted like a small sea anchor, staying more or less in place while the ship sailed away from it. As the rope unwound, the sailor counted how many knots passed through his hands during a 28-second sandglass. The number of knots equaled the ship's speed in nautical miles per hour.

The math behind the knot spacing is straightforward. A nautical mile (about 6,076 feet) divided by 3,600 seconds per hour, then multiplied by the 28-second timing interval, gives about 47 feet. Slight variations in knot spacing and glass timing were common across different ships, but the principle held. Each knot-to-knot interval represented one nautical mile per hour of speed. Count five knots in 28 seconds, and you were making five knots.

The chip log was in use from at least the late 16th century and remained a standard navigational tool well into the 19th century. Bowditch's American Practical Navigator, still published today by the National Geospatial-Intelligence Agency, documents the method in detail.

The Knot Today

The knot survived long after the chip log was retired. One knot equals one nautical mile per hour, which equals exactly 1.852 km/h. That "exactly" matters. In 1929, the International Hydrographic Conference in Monaco adopted 1,852 meters as the official length of a nautical mile.

The original concept was one minute of arc of latitude along a meridian. On a perfectly spherical Earth, that would be a single fixed distance. But Earth is not a sphere. It is an oblate spheroid, slightly flattened at the poles and bulging at the equator. One minute of latitude varies from about 1,842.9 meters at the equator to roughly 1,861.7 meters at the poles. The 1,852-meter standard was a compromise, splitting the difference.

The knot is not some archaic holdover that clings to life out of tradition. It is the standard speed unit in all modern aviation and maritime navigation, worldwide. Air traffic controllers, commercial pilots, naval officers, and merchant mariners all communicate speed in knots. Try converting knots to kilometers per hour or kilometers per hour to knots and you will see how often this comes up for anyone working near water or in the sky.

Speed vs. Velocity

Before going further, a distinction worth making: speed and velocity are not the same thing. Speed is a scalar, meaning it has magnitude only. Velocity is a vector, meaning it has both magnitude and direction.

A car driving 60 km/h around a circular track has constant speed but constantly changing velocity, because its direction changes at every moment. A satellite in orbit does the same thing on a grander scale. It moves at a constant speed (roughly 28,000 km/h in low Earth orbit), but its velocity is always changing because gravity continuously bends its path. That continuous change in velocity is what keeps the satellite in orbit rather than flying off in a straight line. Gravity provides the centripetal acceleration.

This is not pedantry. The distinction between speed and velocity is fundamental to mechanics and shows up constantly in engineering and physics.

Ernst Mach and the Speed of Sound

Ernst Mach (1838 to 1916) was an Austrian physicist and philosopher who studied shock waves and supersonic projectiles at a time when most people thought of sound as something that simply happened, not something that moved at a measurable and variable speed.

The Mach number is a ratio: the speed of an object divided by the local speed of sound. Mach 1 means the object is traveling at exactly the speed of sound. Mach 2 is twice the speed of sound.

The word "local" is critical. The speed of sound is not a constant. It varies with temperature, and temperature varies with altitude. At sea level on a standard day (15 degrees Celsius per the International Standard Atmosphere), sound travels at about 340 m/s, or roughly 1,225 km/h. At a typical cruise altitude of 11,000 meters, where the temperature drops to approximately negative 56.5 degrees Celsius, the speed of sound falls to about 295 m/s (1,062 km/h).

This means Mach 1 at cruise altitude is a significantly different ground speed than Mach 1 at sea level. An aircraft at Mach 0.85 and 35,000 feet is moving at about 903 km/h. The same Mach number at sea level would correspond to about 1,041 km/h. Pilots and engineers think in Mach numbers precisely because the aerodynamic effects of approaching the speed of sound depend on the ratio, not the absolute speed.

Breaking Through

On October 14, 1947, Chuck Yeager climbed into the Bell X-1 (a rocket-powered aircraft he had named "Glamorous Glennis") and was dropped from the belly of a B-29 bomber over Rogers Dry Lake, California, then climbed under rocket power to about 43,000 feet. He reached Mach 1.06, about 1,127 km/h, becoming the first person to fly faster than the speed of sound in level flight.

Fifty years and one day later, on October 15, 1997, Andy Green drove the ThrustSSC across the Black Rock Desert in Nevada at 1,227.985 km/h (763.035 mph, Mach 1.02). It was the first supersonic land speed record, certified by the FIA. Two jet engines from a Royal Air Force Phantom fighter powered the car.

For perspective on where human engineering has taken speed since then: NASA's Parker Solar Probe, launched in 2018, has exceeded 690,000 km/h (430,000 mph) on its close passes around the Sun, with each successive orbit pushing the record higher. At those speeds, the probe covers roughly 0.064% of the speed of light, making it the fastest object ever built by humans. Convert miles per hour to kilometers per hour and the numbers are staggering either way.

Speed Unit Reference Table

Common speed units and their equivalents, rounded for practical use:

For precise conversions between any speed units, try km/h to mph or knots to km/h.

From Rope Knots to Solar Probes

The sailor counting knots on a wet rope in the 1600s and the engineers tracking Parker Solar Probe's telemetry are doing the same thing: measuring how fast something moves through space over time. The tools have changed beyond recognition. The physics has not. Distance divided by time. That is all speed has ever been.

What has changed is the range. Humanity went from measuring single-digit knots on the open ocean to clocking an object at over 0.06% of the speed of light in about four centuries. The knot, born from rope and wood and a 28-second hourglass, is still in daily use. Some units earn their longevity.

Sources: Bowditch, "American Practical Navigator" (National Geospatial-Intelligence Agency); International Hydrographic Organization; NASA Glenn Research Center; International Standard Atmosphere (ISA); NASA History Division; FIA (Federation Internationale de l'Automobile); Smithsonian National Air and Space Museum