# The Harmony Learning Community Blog

News, Updates, Program Recaps, and Homeschooling Information

### Calculating Our Position

September  19, 2013

Global Studies began last week with an introduction to the idea of Location. Where we are, where we are from, and where do we want to go? We looked at maps to answer the question of how we know where we are, and how we get where we want to go. During week two we expanded the question through a discussion of exploration. Does a map give you all the information you need to explore? How do people explore new places, and how did they do so before we had modern technologies? The resulting discussion was quite involved and I will relate as much of it as I can.

We started with a brief chat about the earth's orientation. I gave everyone an orange and had them draw the north and south poles and the equator. If you give a group a young people sharpies, paper plates and oranges and you will get back a variety of creatively decorated materials. That is one of the reason I love working with homeschoolers at Talking Stick. Even though I have an idea of what I want my orange to represent, the young people see the materials, ideas are sparked, and they are free to express themselves with their oranges.

While working on our oranges we continued to discuss the ways humans found to explore this earth. Last week we talked about how on land we can make maps and recognize landmarks. But what if we want to explore over oceans? Earliest sailors stayed in sight of land or waited until sunset or sunrise and see which way was east or west. They also used the stars. "But what about a compass?" With a magnetic compass you could follow a straight course. This was good for about a two week trip, but only in good weather. By using "dead reckoning" sailors could also estimate speed and distance to loosely estimate position.

We went out side to make compasses with water, needles and magnets.

Next we role-played how to calculate dead reckoning. The young people spread out over the lawn to form a ship. Particiants were chosen to be the captain, the log, and timekeepers. The captain tossed the log off the front off the ship, and the log quickly walked its length. Timekeepers marked the time it took for the log to pass from bow to stern.

We paced off the length of our ship at 54 feet, and "Bob the Log" speed walked the length in 7 seconds. We disembarked and retreated to the classroom for computation. After some trial and error we worked our way from feet per second to miles per hour, and determined that our log travelled at 3.9 miles/hour. Since that is how fast a human walks at a fast past, we decided we were "dead on with our dead reckoning."

As sailors, we now can figure out direction and speed, but what if we want to be more precise? "We can use GPS!" Yes! GPS tells us our latitude and longitude. But those concepts were invented long before GPS. Our latitude, or distance from the equator, is relatively easy to calculate. All we need to do is measure the angle of the sun above the southern or northern horizon at local noontime. This measurement can be taken accurately with a good sextant. We have set of navigation tables, which are the result of hundreds of years of solar and stellar observation. We look in our tables to see how high the sun should be at local noon for that date and our latitude is listed.

We practiced using homemade sextants to measure latitude at local noon. We were cutting into lunch time at noon, so we did a quick version of this activity. Unfortunately we have no horizon line in the woods, and were unable to get a close approximation, but we did get a good feel for the process.

What about Longitude? Where are we along that horizontal line? Early sailors used more "dead reckoning" to try and determine their position by heading, speed and time, but this was often extremely inaccurate. They had to stay on predetermined routes to avoid shipwreck. The young people felt this would not be convenient for war, secrecy (especially pirates) or in bad weather.

Longitude was a big problem that wasn't solved until 1773 with John Harrison's chronometer. (For more on his fascinating story I recommend the book Longitude by Dava Sobel.) The key to longitude was knowing the time. There are 24 hours in a day and 360 degrees in a circle, so the sun moves across the sky at a rate of 15 degrees per hour. Every hour that your local time is off from the time at your home port is 15 degrees of longitude. But in the days of sailing ships, that was a large problem! Clocks weren't precise and a tiny amount of time was a huge amount of distance. If your watch was off by 1 hour you could be over 1000 miles off course, because the earth spins at about 1038 miles per hour at the equator. You need a clock that stays accurate to the second with the time in your home port, and that is what Harrison invented. By comparing the clock's time with your local time you know how many degrees, seconds, and minutes you have travelled around the globe.

At some point it made sense for all sailors to use the same "home port" or zero longitude. Because of its contributions to the solution, Greenwich in Great Britain, which is home to the Royal Observatory, became the "home port". Zero longitude, the Prime Meridian, is firmly established in Greenwich, and is still the base line of Coordinated Universal Time (UTC), formerly known as Greenwich Mean Time.

We know Eastern Standard Time is UTC minus 5 hours. The young people calculated that Philadelphia must be 75 degrees longitude (15 degrees * 5) and they were correct!

We now know that with a sextant, an accurate watch and navigation tables, we can still find where we are on the ocean, even without GPS.