Lesson 5

True North lesson

Lesson created by: Chris Copeland

Grade: Pre-Calculus

Length: Approximately 1 – 2 days

Goal: To understand the astrologically important aspects to consider when building a sundial. Students will learn about true north and how to find it using various methods.

Objectives: Students will be able to determine True North as well as understand the significance of position on the globe in relation to how the sundial is built.

TEKS:
111.35.c.3: The student uses functions and their properties to model and solve real-life problems. The student is expected to:
(A)  use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;
(D) solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas.

Engage: So when we finally have our sundial built, we’ll be completely done and able to instantly use it to accurately tell time, right? (No!) Let’s test something real quick. Let’s suppose that this student here was the gnomon and this flashlight were the sun. If I just face the sundial & gnomon any direction, then the sun could be casting a shadow onto 5pm when in fact it is actually 10am. So just having the sundial isn’t enough. Well, what else do I still have to do with it so that it correctly gives the time? The answer: we have to align it with true north.

Explore / Explain: There are several ways to go about finding true north. One common way is to take a compass and a map or chart of the area and find magnetic north using the compass, then add the magnetic variation listed on the map, and then align the 12pm mark with this. So then true north = magnetic north + variation.

But let’s say we don’t have a compass handy, what then? What else could we use something other than a compass to determine direction? (the sun, the north star)

If you’ve got a few hours, you can use the sun and the shadows it casts to determine true north. Place a vertical post in the ground and call it point P. At some time before noon mark the shade end on the ground. This is the point A. Using a cord, draw an arc centered at the post with the radius PA. Then patiently wait till in the afternoon time the shade length reaches the length of PA again and mark the point B on the arc where the shade touches the arc. The bisection of the angle APB gives the direction of the North.

Ok, we don’t have time to wait a few hours to find true north, so what then? Fortunately there is a method that uses the sun’s position to find true north without waiting several hours. In fact, it is a method that is very important for navigating. At any given moment, the sun’s azimuth, or angular distance from true north, can be predicted. So if we knew the azimuth of the sun (determined by casting a shadow), then we could make a correction in degrees from that shadow to find true north. The steps for doing this are:

· Place a vertical post in the ground.

· At some moment when the sky is clear mark the shade direction on level surface on the ground and note the time with accuracy to 1 second.

· Convert observation time to GMT.

· Using the Nautical Almanac and calculator find the azimuth of the Sun for the time of observation.

· Basing on the calculated azimuth and using good quality protractor find the direction of true North in your garden.

http://home.san.rr.com/slawek/Tata/astro/fnorth.html

Elaborate: So we know how to find true north, but why is it that sundials only tell time correctly when they’re aligned with true north? Take time in groups to discuss the significance of true north. Draw pictures, make diagrams, do anything necessary to come up with a reasonable answer.

(The reason is that the gnomon has to be parallel to the meridian, otherwise the angles the sun hits it at will cause the shadows to not cast correctly)

Evaluate: Have groups of students use either the compass and map method or the azimuth method to determine true north. When the class agrees that they’ve found true north, mark it and keep it marked, so that the sundials can be aligned with it.