At this point in our navigation education, we're able to find our latitude and longitude using the position of the sun, and we know how to deal with magnetic declination when setting a course. But we have one more step before we've passed our sailor's exam and can navigate a ship without power: we need to be able to determine how fast our ship is moving without any electronic equipment.

Sailors use nautical miles to measure distance. These are different than land-based miles or kilometers. One nautical mile is equal to one minute, or 1/60 of a degree of latitude. It is equal to about 6076 feet, 1.15 miles, or 1.85 kilometers. And because of this, sailors don't measure speed in miles per hour or kilometers per hour: they measure speed in nautical miles per hour, or knots. One knot is defined to be one nautical mile per hours. But why do we call it a knot?

Back in the 16th century, sailors didn't have electronic tools to measure things like speed or distance. They had to use low-tech tools for these sorts of tasks. And to measure a ship's speed, sailors used a tool called a chip log or a common log. This has nothing to do with logarithms: it actually goes back to the days when sailors used actual logs from trees. While designs eventually got more advanced, they originally tied a log to the end of a long rope, which had knots tied into it at regular intervals. They would toss the log into the sea, use an hourglass to keep time, and calculate how many knots in the rope had gone overboard in a set amount of time. They would then use this to figure out the distance the ship had traveled, and using the distance and time, they could calculate the ship's speed.

One way to do this would be to use a piece of rope that was several nautical miles long, to put one knot every nautical mile, and to let the rope out for one hour. If, for example, there were seven knots in the rope that was let out over the course of the hour, then the ship's speed was about 7 knots. However, this is impractical for two reasons. First, we wouldn't want to have to deal with several nautical miles of rope. It would be inconceivably heavy! And second, it would take a whole hour to let out the rope and figure out the ship's speed. That would take way too long! So we need a way to scale this down.

Suppose that we wanted to let out the rope just for a minute. Well, that's 1/60 of an hour. This means that the distance between the knots needs to be 1/60 of a nautical mile, which is approximately 101 feet. If we want to be able to measure speeds of up to 20 knots, then we need 101*20 = 2020 feet of rope in total.

This is still less than ideal. First, that's still a lot of rope. And second, if we have to let the rope go out for one minute, then reel back in 2020 feet of rope, that still takes quite a bit of time. So it would make sense to go for less rope and a shorter amount of time. In the sample problems below, you can determine how to create a smaller-scale chip log.

Sample Problems

1. Suppose you wanted to let out the rope just for thirty seconds. How many feet apart would each knot need to be? How many feet of rope would you need to be able to measure speeds of up to 20 knots? Round your answers to the nearest tenth of a foot.

2. Suppose you wanted to let out the rope just for twenty seconds. How many feet apart would each knot need to be? How many feet of rope would you need to be able to measure speeds of up to 20 knots? Round your answers to the nearest tenth of a foot.

3. Suppose you wanted to let out the rope just for ten seconds. How many feet apart would each knot need to be? How many feet of rope would you need to be able to measure speeds of up to 20 knots? Round your answers to the nearest tenth of a foot.