Additional Math Pages & Resources

Monday, June 25, 2012

Knot So Fast: Calculating Nautical Miles

On June 26, 1946 the U.S. Army, Air Force, and Navy adopted the "knot" and "nautical mile" as standard aeronautical units for speed and distance. This unit of measurement is used by all nations for air and sea travel. A nautical mile is about 6.080 ft. (1,853 m), and a knot is the equivalent of one nautical mile per hour.

This table shows conversions between knots and other common measurements used for velocity:
convertintomultiply by

The nautical knot finds its origin in a method sailors once used to measure their speed at sea (invented circa 1500-1600)It is believed the concept originated in the Netherlands. Back in the days of sailing vessels, captains needed a way to measure the speed of their ships through the water. The Dutch had devised a method of tossing a piece of wood into the water and measuring how quickly it drifted away from the ship, called "heaving the log."

A more accurate method, based on this technique, was the chip log. Sailors would tie knots in a long line at regular intervals (about 50 feet apart), then cast out one end (weighted down by a piece of wood) behind their vessel. They would count number of knots let out in a given period of time (measured, usually, by a small sandglass that measured half a minute) to calculate the distance (and consequently, the speed) at which the boat was moving. This was a major advance that made dead-reckoning much more accurate. From this crude speedometer, the sailor could determine the speed the vessel was moving. Read more at

This system remained in use for many centuries. Some simple arithmetic confirms that this system actually does approximate a nautical mile per hour, the definition of a knot:

Interestingly, the chip log has long since been replaced by equipment that is more advanced, but we still refer to miles per hour on the water as knots. Read more at

USS Constitution (“Old Ironsides”) Boston, MA
U.S. Navy photo by Journalist Seaman Joe Burgess.
USS Constitution (“Old Ironsides”), the oldest commissioned warship afloat, can travel at 13+ knots (approx. 14.95 miles per hour, 24 km. per hour).  Here she is pictured making her annual 4th of July “turnaround cruise” in Boston Harbor where a 21-gun salute was rendered off Castle Island’s Fort Independence in South Boston. In 2002, the Secretary of the Navy, The Honorable Gordon England witnessed a swearing-in ceremony aboard the ship, where more than two-dozen immigrants were sworn in as naturalized citizens. 

In Excel Math, we help students learn to calculate distance and speed. Here's one of the 6th Grade Excel Math Create A Problem exercises to help students solve word problems and calculate distance and speed using a map drawn to scale. Click here for a PDF copy you can use with your class. (The answers are included below.)
Excel Math problem

(June 21, 2012) Artist rendering of the Virginia-class submarine
USS Colorado (SSN 788).
(U.S. Navy photo illustration by Stan Bailey/Released)
Secretary of the Navy Ray Mabus will host a ship naming ceremony in honor of USS Colorado, today at 2 p.m. MST at the Colorado State Capitol Building in Denver, Colorado.

Colorado, a Virginia-class submarine designated SSN 788, is the fourth ship to bear the name and the third to be named for the state. The second ship was a battleship that participated in the Tarawa invasion and suffered two kamikaze hits while supporting the landings at Leyte Gulf in November 1944.

This next-generation attack submarine will have enhanced stealth, sophisticated surveillance capabilities, and special warfare enhancements. Here's a photo of an artist rendering of the USS Colorado.

The future USS Colorado will have the capability to attack targets ashore with highly accurate Tomahawk cruise missiles and conduct covert long-term surveillance of land area, littoral waters or other sea-based forces. Other missions include anti-submarine and anti-ship warfare; mine delivery and minefield mapping. It is also designed for special forces delivery and support.

SSN 788 will be built at Electric Boat in Groton, Conn and will be 7,800 tons and 377 feet in length, and will operate at more than 25 knots submerged. It is designed with a nuclear reactor plant that will not require refueling during the planned life of the ship. Read more at

Here are the answers to the Grade 6 Create A Problem exercise shown above:

Since Excel Math uses a unique spiraling strategy, you will need to teach multiple lessons sequentially within each grade level in order to get the concepts into your students' long-term memory. A student's learning of new concepts takes place during Excel Math Lesson Plans and Activities. The concepts are refreshed through Guided Practice, Homework, Create A Problem and TestsLearn more about how Excel Math gives students a strong foundation in elementary math at