Knots and the Nautical Mile

Why do we use knots? I know that was probably imported from the naval arena, but why do they use it?
- question from Alan
How fast is a knot?
- question from name withheld
The dictionary defines a knot as a unit of speed equal to one nautical mile per hour, where a nautical mile is 6,076.12 ft (1,852 m) in length. The following table provides conversions between knots and other common measurements used for velocity:

convert into multiply by
knots ft/s 1.688
knots mph 1.151
knots m/s 0.5146
knots km/h 1.853

It is believed the term originated in the Netherlands sometime in the 1500s. Back in the days of sailing vessels, captains needed a way to measure the speed of their ships through the water. One of the methods the Dutch had devised was the practice of tossing a piece of wood into the water and measuring how quickly it drifted away from the ship, a concept called "Heaving the Log."

Chip Log ship speed measurement system

A more accurate method based on the same idea was the "Chip Log" technique. The chip log system, depicted above, consisted of a wooden weight tied to a reel of rope with knots tied in it at equal intervals. When the wooden weight was tossed overboard, the rope would be pulled out along with it. The faster the ship was traveling through the water, the more rope would be unwound from the reel. Sailors would simply count the number of knots that were pulled off the reel in a given amount of time, as determined by an hourglass, and that would determine the speed of the ship in "knots."

This system remained in use for many centuries. Most applications of the technique employed ropes with knots spaced out every 50 feet and a sand glass that measured half a minute. Some simple arithmetic confirms that such a system does indeed approximate a nautical mile per hour, the definition of a knot, as shown below.

So if a ship were to toss a chip log into the water and ten knots were pulled off the reel in 30 seconds, the ship would be traveling at a speed of 10 knots. Even as late as 1917, the US Navy still employed a chip log technique on some of its ships. The official US Navy sand glass measured 28 seconds and the knots on the rope were spaced exactly 48 feet apart, equal to eight fathoms. According to Navy research, the system allowed a ship's speed with respect to the water to be measured to within 1.5%. Of course, that error estimate assumes the wood panel remains in the position where it was dropped and the rope does not stretch, both of which are probably not the case. In addition, the water itself is not perfectly still with respect to land, so the velocities of the currents will add to or subtract from the actual speed of the vessel.

Having described the origins of the knot and how it equates to other common units for measuring speed, the next question you might be wondering is where does the nautical mile come from? That discussion leads us to the origins of the mile itself. The term mile has been around since the time of the Roman Empire, but it has acquired many different meanings over the centuries. The Roman army created the unit of a mille passus, or 1,000 double paces, later referred to simply as a milion. Since two paces was equal to 5 feet, the Roman mile was 5,000 Roman feet in length. The unit of a foot also comes down to us from Roman times, but the Roman foot was only 11.65 inches in length when compared to the modern dimension. A Roman mile is therefore the equivalent of 4,850 feet, 1,615 yards, or 1,479 meters in modern dimensions.

The mile most of us are familiar with goes by the more official name of land mile or international mile. By an international agreement made in 1959, it is defined to be precisely 5,280 international feet, 1,609.344 meters, eight furlongs, or 1,760 international yards in length. The US also makes use of a "survey mile" or "statute mile" that is equal to 5,280 survey feet and is longer than the international mile by only a quarter of an inch. The US statute mile was enacted by Congress before the international mile had been established and has been retained by the U.S. Coast and Geodetic Survey. The term "statute mile" comes from the fact that its length is specified by law. The term originated in England when the definition of the modern mile was decreed by Queen Elizabeth I, who redefined the mile from 5,000 feet to its present length of 5,280 feet.

Other nations have also defined their own lengths of the "mile" over the years, some varying wildly from the international mile. These definitions are compared below.

Mile Length
[yards]
Notes
Norway 12,182
Brunswick 11,816
Sweden 11,660
Hungary 9,139
Switzerland 8,548
Austria 8,297
Prussia 8,238
Denmark &
Germany
8,115 was also called the "geographical mile"
in Norway and Sweden
but used only at sea
Poland 8,100
Geographical 2,029
Nautical 2,025 international nautical mile,
air mile
Italy 2,025
UK & US 1,760 international mile,
land mile,
statute mile
Metric 1,641 "mile" in the Metric system
Roman Empire 1,615 original mile
Spain 1,552
Netherlands 1,094

The majority of the values listed in the above table refer to land miles of one variety or another, but the system of "knots" used at sea equated to a different mile in its own right--the nautical mile. To understand the nautical mile, we need to explain a related unit called the geographical mile. A geographical mile is probably the most scientifically derived mile. It is a unit of length determined by one minute of arc along the Earth's equator, which is approximately 1,855 meters or 6087.15 international feet in length.

To better understand the concept, imagine slicing the Earth in half along its equator. Now divide the perimeter, or circumference, of this circle into 360° segments. Then divide each degree into 60 equal segments called arc minutes. The length of one of these arc segments, 1/60th of a degree of the Earth's equatorial circumference, is a geographical mile.

The nautical mile is almost exactly the same concept, except that it is equal to one minute of arc along a great circle of the Earth. A great circle is a circle on the surface of a sphere that has the same diameter as the sphere. What does that mean? The Earth itself is an imperfect sphere since it is slightly flattened at the poles. If you were to measure its diameter at the equator and its diameter at the poles, you'd find that the equatorial distance is greater by about 142,181 feet. Because of this difference, a geographical mile along the equatorial circumference would be 6087 ft long but the same mile along the polar circumference would be only 6066 ft in length. The great circle of Earth instead assumes that the Earth is actually a perfect sphere, and the differences between the equatorial and polar circumferences are averaged out.

When the definition of the nautical mile was specified by international agreement, its value was based on this idealized Earth so that it is the average of one minute of arc in both the equatorial and polar planes. The nautical mile is therefore slightly shorter than the geographical mile and is defined precisely as 1,852 meters or 6,076.115 international feet.

Both ship navigation and aerial navigation share many of the same principles. Since the nautical mile and the knot are some of the fundamental cornerstones of navigation at sea, it is natural that they transferred to aviation as well. Aircraft velocity gauges are almost universally calibrated in knots, and flight routes are typically denoted by distances in nautical miles. Some sources also refer to the air mile, which is the same unit as a nautical mile, but much less commonly used.
- answer by Jeff Scott, 31 August 2003

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