www.TeachEngineering.org: Free Curriculum for K-12

Major improvements to navigation initially involved creative mathematical thinking and engineering. Before computers existed, engineering was the prime tool to make navigation easier. The sextant, a device used to determine latitude and longitude, used angled mirrors, graduated scales, and sturdy materials to make astronomical measurements much more accurate than previous methods. The sextant is a convenient, reliable, and accurate tool still used today. Even the sextant can use the assistance of computers when they are available.

Currently, we take computers and calculators for granted. We use them to help us with our homework, play games and even talk to friends. It was only 25 years ago that buying a calculator cost over $500, and desktop computers, like the ones in your classroom, school lab, or home, did not even exist.

Before computers, the math needed to perform accurate navigation had to be done either by hand or by looking up information in tables, a very tedious task and prone to errors. Today, luckily, we have computers and calculators to help us with math. Computers are very fast at figuring out calculations and repeating tasks, but we still need to understand how the math works so that we can efficiently use the computer. Electrical engineers and computer scientists write the programs that help us in our daily use of computers. Although computers help you complete difficult tasks easier, you still need know how things work so that you can tell the computer what to do and verify that your results make sense.

There are two basic concepts to any collection of measurements, accuracy and precision. Accuracy is how close the measured data is to the actual value. For example, if you know that you have a mass standard that is 50.00 grams, and you measure it to be 49.98 grams, then your measurement is very accurate. On the other hand, if you measure it to be 43.24 grams, your measurement is not very accurate.

Precision is how close your measurements are relative to each other, not the actual value. For example, let say you measured that same mass standard and came up with the values:

43.24, 43.30, 43.20, 43.25, 43.32

You could say that your measurement was very precise because all the values are very close to each other. On the other hand, if your measurements were:

50.03, 43.40, 53.01, 47.54, 30.23

Your measurements would not be very precise because they are all far apart relative to each other.

A dartboard is a common example of showing the difference between accuracy and precision (please see Figure 1). Assume that someone throws four darts at a dartboard. If they are far apart and unevenly spaced, they have neither precision nor accuracy (#1). The closer the darts are to the center, the better accuracy they have. The closer the grouping of darts is to one another, the better precision they have (#2). If the darts are evenly spread around the center, the dart thrower has low precision but high accuracy — they are not close to each other but all of the darts are equally far from the center (#3). And finally, if all of the darts are closely grouped in the center of the dartboard, the thrower has both high accuracy and precision (#4) because the darts are either on or very close to the target.

Four circles, representing dartboards, illustrate precision and accuracy using darts. Circle #1: four yellow dots are scattered around the dartboard, indicating neither accuracy nor precision. Circle #2: four yellow dots are placed very close togther, yet distant from the target, indicating precision, but not accuracy. Circle #3: four yellow dots are evenly placed around the target, indicating accuracy, but not precision. Finally, circle #4: four yellow dots are inside the target, indicating precision and accuracy.

Figure 1. Precision and accuracy.
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Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

In the 1880s, it was estimated that the next American census in 1890 would need to tally data from more than 62 million Americans. This was not only expensive, but the existing system of tallying marks in small squares on rolls of paper and then adding the marks by hand was extremely time consuming. Workers realized that continuing to take the census with this method would be impossible and that, somehow, the system would have to be automated.

An American inventor, Herman Hollerith, developed the solution to this problem. Cards punched by a tram conductor's ticket punch were fed into a mechanism that could read the presence of holes in each card by using spring-mounted nails that passed through the holes to make electrical connections. The electrical connection would then move a clock-like counter that accumulated the results.

In addition to solving the census problem, Hollerith's machines were useful for a wide variety of statistical applications. Subsequently, these same techniques were significant in the development of the computer. In February 1924, Hollerith's company changed its name and continued to grow; in fact that compnay is still around today. It is very unlikely you have not heard of it: International Business Machines. Does it ring a bell? Perhaps you know it by its initials: IBM.

A picture of a sextant, a device used to determine latitude and longitude.

Figure 2. A sextant, a device used to determine latitude and longitud
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The earliest explorers did not have computers or satellites to help them know their exact location. The most accurate tool developed was the sextant. Although sextants are still used today, even they have benefited from the development of computers.

The sextant is a complex device, but luckily it is very easy to use. Basically, a sextant measures the angle between two objects, with at least one of those objects being celestial. (Remember, never look directly at the sun, as permanent damage can occur to the eye! Shields and filters on sextants protect against eye injuries.) The user looks through the sextant's eyepiece directly at the first object (usually the horizon). There is actually a mirror in the line of sight, but because it is only partially silver, the user can see beyond it (to the horizon). The other mirror is connected to a movable arm and directs light from the second object (usually the sun or moon) and reflects it into the half-silvered mirror. The movable arm is adjusted until you can see both the first object (the horizon) and the second object (the sun or moon), overlaid on top of each other. Finally, you read the measurement of the angle, which is located on the movable arm.

The most common use of a sextant is measuring the angle between the horizon and the sun. By knowing this angle and your local time, your latitude can be determined. If you also know the Greenwich Mean Time (GMT), your longitude can also be determined.