Forest Mensuration14 January 2004
Determining Direction
1. Units of angular measure
a. Sexagesimal System
- the circle is divided into 360 equal parts (°)
- each ° = 60’ (minutes)
- each ‘ = 60 ‘’ (seconds)
- used exclusively in North America
b. Centesimal System
- the circle is divided into 400 equal parts known as grads (g)
- each g = 100 c (centesimal minutes)
- each c = 100 cc (centesimal seconds)
- used widely in Europe
c. “Military” system
- unit is a “mil” = 1/6400 of the circumference of a circle
- the circle is divided into 6400 mil
- there are no sub-units
- 1/6400 is very nearly the same as 1 unit in 1000 units
d. Radians
- the angle of a circle with the length of the arc equal to length of the radius
- angle equals approximately 57.30°
- known as the “natural” unit
Determining Direction (cont’d)
2. Bearings and Azimuths
- for our purposes (i.e. direction rather than angle measurement), it is convenient to relate angles to a reference line known as a “meridian”
- our concern is with three types of meridians
a. true – a line passing from true N to true S
b. magnetic – the line indicated by a magnetized compass needle (i.e. magnetic N)
c. grid – a line parallel to the Y-axis (i.e. on a map or on the blackboard)
i. Bearing – the acute angle (<90°) formed by a line and the reference meridian
- includes both the reference meridian (either N or S) and the offset direction (either East or West)
ii. Azimuth – the angle, measured clockwise, formed by a line and the reference meridian (usually N)
Note: to switch back and forth between bearings and azimuths, draw a picture.
3. Magnetic and True angles
- why are they different?
- need to be able to switch back and forth
- examples:
- how to do it? See Field Manual (pg. 3.9)
- Agonic line (defn:)
- Isogonic lines (defn:)
- how to determine if the declination is East or West?
The earth as a dipole magnet.
Daily Movement of the North Magnetic Pole
It is important to realize that the position of the North Magnetic Pole given for a particular year is an average position. The Magnetic Pole wanders daily around this average position and, on days when the magnetic field is disturbed, may be displaced by 80 km or more. Although the North Magnetic Pole's motion on any given day is irregular, the average path forms a well-defined oval. The diagram shows the average path on disturbed days.
What is a Magnetic Pole?
The North Magnetic Pole is the point on the Earth's surface where the magnetic field is directed vertically downward. Based on this simple definition the North Magnetic Pole also has the following properties.
- Inclination is 90° .
- Horizontal intensity is 0 nT.
- Magnetic meridians, lines tracing the path one would take by following a compass needle, converge on the Magnetic Pole.
- Lines of equal magnetic declination also converge on the Pole; therefore declination is undefined at the Pole.
As an aid to understanding the definition and properties of the Magnetic Pole it is useful to look at the magnetic field produced by a simple bar magnet. The magnetic field around a simple bar magnet can be visualized in terms of "lines of force", or "magnetic field lines"; these are commonly illustrated by iron filings sprinkled on a sheet of paper held over the magnet. Field lines start near one end of the magnet and enter near the other end, forming an arc in between. By convention, the end at which the magnetic field is directed outward is termed the "north" pole of the magnet; the end at which the magnetic field is directed inward is termed the "south" pole of the magnet. The magnetic field of a bar magnet is called a "dipole" field, so named because it has two poles.
To a first approximation the Earth's magnetic field is a dipole field. You can visualize it being produced by an imaginary bar magnet placed at the Earth's centre. Consequently the definition of poles, established for a bar magnet, has been applied to the magnetic field of the Earth. However, the shape of the Earth's magnetic field is much more complex than that of a simple dipole, and as a result the observed positions of the magnetic poles are displaced a considerable distance from the end-points of the imaginary bar magnet. The complexity of the magnetic field has another important consequence: a compass does not point directly at the North Magnetic Pole. If you set out following your compass needle you will eventually reach the Pole, but not by the most direct route.
The magnetic field is directed downward in the northern hemisphere and upward in the southern hemisphere. This implies that the magnetic pole in the Canadian Arctic is really a "south pole". However, by long custom and because of its geographical location it is called the North Magnetic Pole.
Early Concept of the North magnetic Pole
(