measurement on topographical maps

Distance measurements

Straight distance: Measure the straight distance between two points using a ruler and convert it to ground distance with a linear scale or representative fraction scale.

Curved/winding distance:

1. Dividers method: Used for short straight distances; measure the total length by transferring the units to paper and converting the map distance into actual ground distance.
2. String or thread method: A piece of string can be laid along the curved line, and the string is then measured using a ruler or scale to determine the ground distance.
3. Straight edge of paper method: A piece of paper with a straight edge is used to break down the curved distance into smaller straight segments. The total length is calculated by measuring each segment.

Area measurements

Regular shaped areas:

1. Regular shapes like rectangles, triangles, and circles can have their areas calculated using basic mathematical formulas after converting map dimensions into ground measurements.

Example: For a rectangle, Area = Length × Width.

Irregular shaped areas:

These shapes require more complex methods for calculation:

1. Grid method: The area is covered with complete and incomplete grid units (squares). The total area is calculated by counting the squares.
2. Strip method: The area is divided into strips, and each strip's area is calculated. The total area is the sum of the areas of all strips.
3. Geometrical figures method: The irregular shape is divided into geometric shapes (e.g., triangles, rectangles), and the areas of these shapes are added up to find the total area.

Map enlargement and reduction

Enlargement: When a small-scale map is redrawn with a larger scale, it appears larger. This technique is referred to as map enlargement.

Reduction: When a large-scale map is redrawn using a smaller scale, it appears smaller. This technique is referred to as map reduction.

Procedures for redrawing the map (enlargement/reduction)

• Study the map or the area of the map to be redrawn: Review the map and identify the area to be enlarged or reduced.

• Identify the map scale and convert it into a statement: This helps understand the scale's meaning, for example, "1:50,000" means 1 cm on the map equals 50,000 cm on the ground.

• Determine the changing factor (Scale Factor): The scale factor is calculated by dividing the new scale by the old scale.

  • Formula:

    $\text{Scale factor} = \frac{\text{New scale}}{\text{Old scale}}$

• Measure the length, width, and side of the grid square: This helps in scaling the map's features appropriately. If distances are already given, convert the map distance into ground distance.

• Use the scale factor to change the dimensions: Multiply the original map's dimensions (length, width) by the scale factor to get the new dimensions.

• Redraw the map: Using the new scale, redraw the map, and if the original map had grid references, include them in the new map.

• Show main features: Include essential features such as the title, key, scale, and any other relevant data for clarity.

Example

Suppose the original map has a scale of 1:50,000, and you need to redraw it using a scale of 1:100,000.

Step 1: Identify the old and new scales:

Old scale = 1:50,000 New scale = 1:100,000

Step 2: Calculate the scale factor:

$\text{Scale factor} = \frac{100,000}{50,000} = 2$

This means you need to multiply the original dimensions by 2 to obtain the new dimensions.

Step 3: Measure dimensions on the original map (e.g., length = 5 cm, width = 3 cm).

Step 4: Use the scale factor to adjust the map's size:

New length = 5 cm × 2 = 10 cm New width = 3 cm × 2 = 6 cm

Step 5: Redraw the map with the new dimensions using the scale of 1:100,000.

Determining locations and directions of places

Location:

• Absolute location: The precise identification of a place using a coordinate system like latitude and longitude.
• Relative location: Describes a place in relation to other places, considering physical and cultural characteristics.

Direction:

• Absolute direction: Based on cardinal points (North, South, East, West).
• Relative direction: Describes direction in terms like "far East" or "far West."

Distance:

• Absolute distance: The physical space between two points, typically measured in miles or kilometers.
• Relative distance: Describes distance in a way that's meaningful for spatial relationships.

Fixing or locating position on maps:

• Place names: Maps often identify places by their names, such as regions in Tanzania.
• Latitude and longitude: Geographical coordinates help in locating features on the Earth's surface.
• Grid reference system: Uses eastings (vertical lines) and northings (horizontal lines) for precise location identification on a map.
• Bearing and direction: Bearings are used to measure the angle between two points, often involving the use of a compass.

Methods for locating positions:

• Intersection method: Locates an unknown point by taking bearings from two known positions.
• Resection method: Used when you're at an unknown point and need to locate it using bearings from two or more known points.

Types of north:

• True north: The direction toward the North Pole.
• Magnetic north: The direction indicated by the magnetic needle of a compass.
• Grid north: The direction of north in maps using the Universal Transverse Mercator (UTM) grid system.

Magnetic variation: The angle between magnetic north and true north, which changes over time as magnetic north shifts.

Practical applications

• Calculation of bearings: Bearings can be forward or backward, and the difference between them is typically 180°.
• Trend and alignment: Used to describe the general direction or layout of elongated features like rivers, roads, or valleys.

The Grid Reference System is a critical tool in map reading, helping to pinpoint exact locations using a grid of horizontal (northings) and vertical (eastings) lines. Here's a breakdown of how it works:

Elements of the grid reference system

Grid lines:

• Eastings: Vertical lines, where values increase as you move eastward from the origin.
• Northings: Horizontal lines, where values increase as you move northward from the origin.

Zones: In regions like Africa, the grid system is often based on the Universal Transverse Mercator (UTM) projection. This divides the continent into specific zones, and each zone has its own set of coordinates.

Coordinate system:

• Each coordinate consists of a six-digit number, with the first three digits representing the eastings (horizontal) and the last three digits representing the northings (vertical).
• For example, a grid reference of 280610 means:
  • 280: The easting value, indicating 280 units east from the origin.
  • 610: The northing value, indicating 610 units north from the origin.

Usage

The grid reference helps precisely locate a feature or point on the map, making it easier for navigators, surveyors, and geographers to pinpoint exact locations, especially in large areas.

Bearing and direction are essential concepts in navigation and map interpretation, used to define the geographical position of a point relative to another. Here's a breakdown of the key ideas:

Compass and bearings

A compass is used to find direction and bearing. It contains a free-swinging magnetic needle that aligns with magnetic north. If you know the local variation between magnetic north and true north, you can adjust the direction for true north.

Compass directions are measured from north (0°) to 360° in a clockwise direction. The directions are represented in degrees, and specific bearings correspond to cardinal points (north, south, east, west), as well as intermediate points like northeast (NE), southeast (SE), etc.

Types of bearings

Forward bearing (FB):

• This is the angle measured from the observer's position to the object or point in the direction of sight.
• It is measured clockwise from the North direction (0° to 360°).
• Example: The forward bearing of point B from point A could be 060° (NE direction).

Back bearing (BB):

• This is the reverse of the forward bearing. It measures the angle from the object back to the observer's position along the line of sight.
• If the FB is greater than 180°, subtract 180° to get the BB. If the FB is less than 180°, add 180° to get the BB.
• Example: If FB = 060°, then BB = 060° + 180° = 240°.

Cardinal points and subdivisions

• Cardinal points: The basic directions are North (0°/360°), East (90°), South (180°), and West (270°).
• Eight cardinal points: These include intermediate directions like NE (45°), SE (135°), SW (225°), and NW (315°).
• Sixteen cardinal points: A more detailed system that includes directions like NNE, ENE, ESE, etc., with more precise bearings.

Calculation and measurement of bearings

Steps to measure bearings:

• Identify the two points you want to measure the bearing between (e.g., A and B).
• Draw a line connecting the two points.
• At one point (say point A), draw a line parallel to the North direction.
• Use a protractor to measure the angle from the north line to the line connecting points A and B. This gives you the forward bearing.

Forward and back bearing example:

• If the forward bearing of B from A is 060° (NE), the back bearing of A from B would be 240° (SW).
• The difference between forward and back bearings is ideally 180°.

Significance of back bearing

1. Back Bearing is used to verify the accuracy of the forward bearing.
2. If the difference between FB and BB is not 180°, it indicates an error in measurement.
3. Errors can occur during the surveying process, but they can be corrected using methods like the mean error method.