Answer:

Precise geometric relationship between a map and the region it portrays.

- One of the most important characteristics of a modern map.

- Most maps are greatly reduced in size compared to their subjects, so scale is a small fraction.

Definition: Ratio of the size of the map to its subject:

Scale = distance on a map / distance on the ground

Example:

- Two points on the ground are 1000 m apart.

- Represented on the map by points only 1 cm apart

- Calculate scale as follows:

- 1 cm represents 1000 m

- 1000 m = 100,000 cm

- so 1 cm represents 100,000 cm

- so scale = 1 cm / 100,000 cm = 1/100,000

- Scale is a fraction, expressed in 3 ways:

- Representative Fraction (RF), e.g. 1:100,000

- Verbal Scale 'One cm represents one km'

- Graphic Scale - a line labelled with the distance it represents.

Graphic scale remains accurate if a map is enlarged or reduced. Verbal and RF scales do not.

On a graphic scale, the intervals must be convenient round numbers.

Scale examples

example: ground distance = 5 km, map distance = 2 cm.

- STEP 1: - 2 cm represents 5 km - (write in full)

- STEP 2: - 1 cm represents 2.5 km - (divide so left side = 1)

- STEP 3: - 1 cm represents 250,000 cm - (convert to same units)

- STEP 4: - scale is 1 : 250,000 - (express as a representative fraction)

example: distance on map = 3.5 cm, map scale = 1:15,000

- what is the real distance?

- STEP 1: - 1 cm represents 15,000 cm - (express scale in words, same units as your measurement)

- STEP 2: - 3.5 cm represents (3.5 x 15,000) cm = 52500 cm - (multiply both sides by map distance)

- STEP 3: - 3.5 cm represents 525 m - (convert to more convenient units)

answer: 525 m

Scale (2)

Large and small scales:

- Scale is a fraction.

- 1/2 is larger than 1/4.

- 1/5000 is larger than 1/100,000.

- 1:5000 is a larger scale than 1:100,000.

- 'Large scale' depends on context but usually refers to scales larger than about 1:50,000.

(NOTE - this has nothing to do with an expression like 'a large-scale construction project')

ENLARGING or reducing:

- Scale is map distance / ground distance.

- If the map is made larger (on photocopier etc.) the map distance increases, so scale changes.

- Larger map = larger scale, smaller map = smaller scale.

- Multiply the map distance by the percentage change and recalculate scale.

example: Map distance = 1 cm, Ground distance = 1 km.

- Scale = 1:100,000

- Enlarge by 141% on photocopier.

- Map distance = 1.41 cm Ground distance = 1 km

- Scale = 1.41/100,000 = 1:70,921

Directions

Three main ways to express a direction.

1. Points of the compass

- Acceptable for ROUGH directions, not for exact work.

- Directions usually lie between points of the compass, however often you subdivide.

2. Bearing (numerical version of # 1)

- STEP 1: Look due north if the point you are interested in is at all north of you. Look due south if it is south of you.

- STEP 2: Turn towards east or west until you face the point.

- STEP 3: Measure the angle of that turn.

- STEP 4: Express the bearing using all three pieces of information from steps 1, 2 and 3:

--- North 30o West

--- North 45o East

--- South 12o West

--- South 87o East

3. Azimuth

- STEP 1: Look due North.

- STEP 2: Turn clockwise until you face the point you are interested in.

- Step 3: Measure the angle of the turn. This angle is the NORTH AZIMUTH, usually just called azimuth:

--- 330 degrees

--- 45 degrees

--- 192 degrees

--- 93 degrees

Be able to convert between bearings and azimuths!

Adding Angles

Useful in surveying and navigating.

- Remember: 60' = 1o 60" = 1'

- 35o 22' 40" + 5o 15' 30" = 40o 38' 10"

Definition of north

Three common approaches:

1. True North (from the latitude - longitude grid).

- Points exactly at the north geographic POLE (axis of rotation).

2. Magnetic North (the direction a compass NEEDLE points).

- Points along magnetic field lines, roughly towards the north magnetic pole (in NWT).

- Differs from True North in most places because magnetic and geographic poles are not the same.

- Changes over time as the magnetic pole drifts.

- Position of magnetic north must be recalculated if map is more than a few years old.

- Rate of change printed on edge of map.

example:

- "Magnetic North was 7o 30' west of true north in 1985, decreasing at 12' annually".

- so in 1992, after seven years:

--- Magnetic North will be 7o 30' west of true north, MINUS 7 times 12' = 84'

--- 84' = 1o 24'

--- so in 1992 magnetic north is 6o 6' west of true north

3. Grid North (refers to UTM grid).

- same as True North at the centre of each six degree UTM zone.

- Changes to each side because the square grid does not FOLLOW the convergence of meridians towards the pole.

- Most topographic maps show the three Norths in a margin.

- Some maps show only one North. If it is not TRUE North, it MUST be identified....

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