Copyright 1997, 2002.

All About GPS: Sherlock Holmes' Guide to the

Global Positioning System

Chapter 1, The Stage on Page: Holmes vs. GPS
The characters: Vickie, the hostage

A gang of kidnappers

Sherlock Holmes III, the super detective

Big Ben, the tower clock and a stereo radio receiver

The place: England

In the city of London there is a famous landmark, the Big Ben tower clock; see Figure 1-1. Let's assume that the clock rings every hour; it chimes 12 times at 12 o'clock, for example, and the interval between the chimes is four seconds.

Since the sound of the chimes can reach only a very limited distance, there is also a radio station in England that broadcasts the chimes at the exact same time that Big Ben is ringing them at 12 o'clock every day. This means that people all over England can hear the beautiful, cheerful sound of the chimes through their radio receivers.BigBen1.JPG (39589 bytes)

Fig 1-1 The world's most famous tower clock, popularly known as Big Ben. It was installed in 1859.

You need to know one more thing: sound travels at a speed of 1,000 feet (320 meters) per second in the air, while radio waves travel at the much faster speed of light: 186,000 miles (300,000 kilometers) per second. This is why you always see lightning before you hear its thunder. Radio waves and visible light both travel at the same speed. Since the speed of light is so much faster than the speed of sound, you can ignore the time it takes radio wave to travel when you are comparing it with the time it takes sound to travel the same distance.

Now, the story goes like this:

One night an armed gang kidnapped Vickie, a beautiful young lady from a very rich and famous family. After blindfolding her, they drove for a long time and finally arrived at a secret hiding place in an old building. Vickie could tell that the building was not new, for the wooden floor and stairs felt very old to her, and they made squeaking noises when she walked on them. As they forced her up the stairs, she counted 10 flights before they pushed her into a room. Behind her, she heard them shut the door and bolt the lock.

The criminals left Vickie blindfolded, and they turned on a radio in the room; obviously, they did not want her to find out what they looked like or even what their voices sounded like. The young hostage squeezed herself into a corner of the room and sat down, feeling frightened and in danger. The kidnappers were watching; all she could do was try to relax and listen to the radio. Eventually midnight must have come, for the radio ended the day's programming and began broadcasting Big Ben's chimes…1, 2, 3, 4, 5, 6….10, 11, 12, 13. Thirteen?! "Oh, no," Vickie thought. "I must be terribly frightened, because I obviously counted wrong. How could any bell toll 13 times, ever?" She tried very hard to calm herself. But she was very tired and hungry; how nice it would be to have some dinner and go to sleep in her bed! She believed that her family would pay whatever ransom the kidnappers demanded, and that she would soon be set free.

Her captors might have noticed that their hostage was on the verge of collapse, for they gave her a snack. After eating it, she fell asleep in her distress and her weariness.

She was awakened suddenly, not knowing how long she had slept. The kidnappers asked her to make a recording saying that she was well but frightened, and to plead with her family to pay the ransom. She did as they demanded, speaking into the microphone with a trembling voice: "Dad, Mom, this is Vickie. Somebody kidnapped me and they want a million pounds ransom. They've treated me okay so far. They're keeping me in a very old building, so old that the floor and stairs make terrible noises when I walk on them. I'm scared, Dad! They gave me something to eat, but they also threatened to kill me if you don't do exactly what they want or if you contact the police. They want the money in small notes, and they want it delivered where they ask.

"Last night I was so terrified and tired after climbing 10 floors that I heard the midnight bell on the radio strike 13 times. I'm so scared--please do what they want! I want to come home!"

The kidnappers checked the recording and found everything okay. They must have done a good job of scaring the poor girl half to death, because she clearly was so frightened that she couldn't count. Thirteen chimes! She must have thought that it was her death knell.

The tape recording was delivered to the anxious parents, together with instructions for delivering the ransom money. The shrewd kidnappers didn't make any telephone calls, so there was absolutely no way to trace their whereabouts by tracing a phone call.

Fig. 1-2 The hiding place must have been in a very old building at least 10 stories high, somewhere in England.

Here Comes Sherlock Holmes!

Sherlock Holmes III, grandson of the original detective of the same name, happened to be a good friend of Vickie's parents. So he was the one they turned to for help.

After considering the case briefly, the young Holmes suggested that the parents raise the money for the ransom, and do as the kidnappers asked. While they were doing that, he tried to detect clues in the recorded message. He assumed that the girl was indeed in an old building at least 10 stories high, as she said. But there are tens of thousands of such buildings in England, and there was no way that all of them could possibly be searched, even if all of the police in the entire country were mobilized.

After reviewing the recording one more time, however, Holmes knew exactly what to do.

When the ransom money was being delivered on the following night, as directed by the kidnappers, the gang members divided themselves into two groups. One of the groups went to collect the money, while the other stayed behind to guard the hostage. As the guards were watching, Holmes and his helpers broke into the very room where Vickie was held being, rescuing her and arresting her kidnappers in an instant.

Everybody was curious about Holmes’ seemingly superhuman powers of deduction: the grateful parents, the relieved hostage, the police, the press, the kidnappers themselves. How could he have known the exact location of the hideout? Holmes asked everyone who wanted to know, including the handcuffed kidnappers, to stay in the room where the hostage had been held until midnight. When the hour approached, he turned on a radio and tuned it to the station that broadcast Big Ben’s midnight bell. They counted the chimes, almost holding their breaths: 1, 2, 3, 4, 5, 6…10, 11, 12, 13! The all counted 13 chimes! How could that be? With bated breath, they all looked to Holmes for the answer.

Now, let’s take a break and think for a moment about what happened. Please stay tuned—this is not a commercial!

The principle on which GPS operates is truly fascinating, just like this little detective story. And it’s so simple that everybody can understand it. The most basic concept in GPS technology is the determination of the distance from a satellite to your receiver via synchronized ranging codes. What we are going to do is explain the principle of the GPS “tricks” by using Sherlock Holmes III’s investigation, and by illustrating the similarities and differences between the Holmes tale and the GPS story.

This is how Holmes did it:

“The hideout building is located 4,000 feet from Big Ben, near enough to hear its bell,” he explained. “On a circle with a radius of 4,000 feet drawn with Big Ben at its center, there are only three such old buildings at least 10 stories high that fit Vickie’s description. The police were able to check out each of these three buildings carefully, and it didn’t take them long to discover the one they were looking for.”

To be continued.......

Fig1_3.JPG (6258 bytes)

Fig. 1-3 Radius r = 4,000 feet, the distance from Big Ben to the hostage. Sound takes four seconds to travel that distance.

Fig1_4.JPG (27188 bytes)

Fig. 1-4 The period of delay—and this the distance—is determined by observing the pattern of chimes heard from both Big Ben (the source) and the radio receiver (the destination).

Fig1_56.JPG (22626 bytes)

Fig. 1-6. Determining the position by a system of 3 Big Bens

Fig1_7.JPG (9002 bytes)

Fig. 1-7 Different ways to differentiate one Big Ben from another:

    1. Different duration of ring
    2. Different interval between rings. The first two are by means of different code patterns, like GPS.
    3. Different pitch for each Big Ben (like GLONASS)

Fig1_89.JPG (23987 bytes)

Fig. 1-9 The time delay is determined by observing the pattern of ranging codes from both satellite (source) and receiver (destination). Compare with Fig. 1-4.

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Copyright 1997, 2002. All rights reserved.