Voyagers outlines one old method for estimating the distance Voyagers outlines one old method for estimating the distance traveled on the open sea. This technique, called dead reckoning, involves dropping a wooden plank, called a billet, overboard. Tied at its end is a long knotted rope that trails behind the board (Figure 16). As the rope reels out, a sailor counts each knot that slips between his fingers.

All the while, another sailor keeps track of time either with a sandclock or by singing out a short verse. (We still do this today when we say, one one-thousand ... two, one thousand, and so forth to count time). The ship's speed is gauged by the number of knots counted out. To this day, a ship's speed is still given in knots.

Each day, the ship's captain enters this speed into a log, or diary. To estimate the distance a ship has sailed, one simply multiplies this average speed by the travel time:

**Distance = speed x time**

### Activity:

Try some dead reckoning while you're in a bus or car. Instead of counting the knots that are equally spaced on a rope, count telephone poles. According to GTE, telephone poles are spaced 100 feet apart. While you travel between the planetarium and your campus, have one student count telephone poles (the starting pole is zero). Another student times the count for 1 minute. This gives you your speed in poles (as opposed to knots), where 1 pole equals 100 feet per minute.

This speed in poles is nearly equal to your speed in miles per hour. In order to convert from poles to miles per hour, use the following formula:

**SPEED (miles per hour) = 1.14 x SPEED (poles)**

Have the students compare their speeds with the vehicle's speedometer. Students should provide reasons (sources of error) why the two values may be off. Estimate the distance between your campus and the planetarium.

### Further Reading:

Mariam Schlein,I Sailed with Columbus, 1992.