Lecture 2Map Scale, directionsScalePrecise 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 groundExample:- 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 examplesexample: 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 mScale (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 = 1:70,921DirectionsThree 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 East3. 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 degreesBe able to convert between bearings and azimuths!Adding AnglesUseful in surveying and navigating.- Remember: 60' = 1o 60" = 1'- 35o 22' 40" + 5o 15' 30" = 40o 38' 10"Definition of northThree 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 north3. 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.