Lecture 2

Map Scale, directions

Scale

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 30^o West
--- North 45^o East
--- South 12^o West
--- South 87^o 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' = 1^o 60" = 1'
- 35^o 22' 40" + 5^o 15' 30" = 40^o 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 7^o 30' west of true north in 1985, decreasing at 12' annually".
- so in 1992, after seven years:
--- Magnetic North will be 7^o 30' west of true north, MINUS 7 times 12' = 84'
--- 84' = 1^o 24'
--- so in 1992 magnetic north is 6^o 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.