Prismatic Compass

The prismatic compass is a fundamental instrument used in surveying for measuring horizontal and vertical angles. It is particularly useful for traversing, which is the process of establishing a network of control points. The key feature of the prismatic compass is its ability to read bearings directly, making it efficient for field work.

Components of a Prismatic Compass

A prismatic compass consists of several essential parts, each serving a specific function:

• Graduated Circle (Ring): This is a circular ring marked with degrees from 0° to 360°. In a prismatic compass, the graduations are typically inverted because the prism reads them upside down. The 0° mark is usually at the south end, and the readings increase clockwise towards the east (90°), north (180°), and west (270°).
• Magnetic Needle: A magnetized needle that pivots freely on a sharp pin at the center of the graduated circle. The needle always aligns itself with the Earth's magnetic meridian, with its north pole pointing towards magnetic north.
• Pivot: A fine, hardened steel pin on which the magnetic needle rests and rotates.
• Prism: A triangular prism mounted on the casing. Its primary function is to magnify the graduations on the ring and allow the surveyor to read the bearing simultaneously while sighting the object. It also reflects the image of the graduated circle into the observer's eye.
• Sight Vane: Two vanes are provided for sighting the object:
  • Fore Sight Vane: A taller vane with a narrow slit, used for sighting distant objects.
  • Back Sight Vane: A shorter vane with a wide slit and a horsehair or fine wire, used for aligning the compass in the opposite direction.
• Index Arm: An arm attached to the casing that moves with the prism assembly. The line of sight is aligned with an object using the vanes, and the prism is then moved until the bearing of the object is read against the north pole of the magnetic needle.
• Box: A protective case for the compass, often made of brass or aluminum.
• Reflector: A small mirror or reflector that can be raised to reflect sunlight onto the graduated circle, making the readings visible in dim light.
• Damping Mechanism: Some modern prismatic compasses have a damping mechanism to reduce the oscillation of the needle, making readings quicker and more stable.

Working Principle of a Prismatic Compass

The working of a prismatic compass is based on the principle of magnetic north. When the compass is held level, the magnetic needle aligns itself with the Earth's magnetic field. The surveyor sights an object using the vanes. As they look through the prism, they see the reflected image of the graduated circle and the north pole of the magnetic needle. The prism is adjusted until the line of sight from the vane to the object is aligned with the north pole of the needle. The bearing of the line of sight is then read directly from the graduated circle through the prism.

Types of Bearings

Bearings are the angles measured from a reference meridian (usually magnetic north) to a line. Prismatic compasses are typically used to measure bearings in the whole circle bearing (WCB) system.

• Whole Circle Bearing (WCB): In this system, bearings are measured clockwise from the magnetic north meridian (0°) to the line, ranging from 0° to 360°. This is the system commonly read by a prismatic compass. For example, a line pointing East would have a bearing of 90°, South 180°, West 270°, and North 0° or 360°.
• Reduced Bearing (RB) or Quadrant Bearing (QB): In this system, bearings are measured from the nearer end of the north or south meridian towards the east or west. It is expressed as a quadrant (e.g., N 45° E, S 30° W).

Conversion between WCB and RB

Understanding the conversion between WCB and RB is crucial for calculations in surveying.

• WCB to RB:
  • If WCB is between 0° and 90°, RB is N (WCB)° E.
  • If WCB is between 90° and 180°, RB is S (180° - WCB)° E.
  • If WCB is between 180° and 270°, RB is S (WCB - 180°)° W.
  • If WCB is between 270° and 360°, RB is N (360° - WCB)° W.
• RB to WCB:
  • N θ° E corresponds to WCB = θ°
  • S θ° E corresponds to WCB = 180° - θ°
  • S θ° W corresponds to WCB = 180° + θ°
  • N θ° W corresponds to WCB = 360° - θ°

Traversing with a Prismatic Compass

Traversing is a fundamental surveying technique used to determine the relative positions of points by a series of connected lines. Compass traversing uses a compass to measure the bearings of the traverse lines and a chain or tape to measure their lengths.

Steps for Compass Traversing:

1. Station Marking: Mark the starting point (station) of the traverse.
2. Setting up the Compass: Place the compass over the station, ensuring it is perfectly level. The magnetic needle should swing freely.
3. Sighting the Next Station: Sight the next station (or a visible point ahead) using the fore sight vane.
4. Reading the Bearing: While keeping the object in sight, adjust the prism to read the bearing of the line from the graduated circle. This is the fore bearing (FB).
5. Sighting the Previous Station: Turn the compass around and sight the previous station using the back sight vane.
6. Reading the Back Bearing: Read the bearing of the line from the previous station. This is the back bearing (BB).
7. Checking for Local Attraction: In ideal conditions, the back bearing should be exactly 180° different from the fore bearing (i.e., BB = FB ± 180°). If the difference is not 180°, it indicates the presence of local attraction.
8. Recording Data: Record the fore bearing, back bearing, and the length of the line in a field book.
9. Moving to the Next Station: Move the compass to the next station and repeat the process until the traverse is completed.
10. Closing the Traverse: The traverse should ideally close on the starting point or a known point. If it doesn't, adjustments are made to correct for errors.

Bearings

As discussed earlier, bearings are the angles measured from a meridian. In compass traversing, we deal with fore bearings and back bearings.

• Fore Bearing (FB): The bearing of a line measured in the direction of progress of the survey.
• Back Bearing (BB): The bearing of a line measured in the direction opposite to the progress of the survey.

The relationship between FB and BB is fundamental:

• If FB < 180°, then BB = FB + 180°.
• If FB > 180°, then BB = FB - 180°.
• If FB = 180°, then BB = 0° (or 360°).

Local Attraction

Local attraction refers to any magnetic disturbance in the vicinity of the compass that causes the magnetic needle to deviate from the true magnetic meridian. This deviation leads to incorrect bearing readings.

Causes of Local Attraction:

Various factors can cause local attraction:

• Presence of iron or steel objects (e.g., buildings, bridges, vehicles, railway lines, steel towers).
• Underground iron ore deposits.
• Electrical currents or magnetic fields.
• Carrying metallic objects like keys, knives, or even mobile phones near the compass.

Detection of Local Attraction:

Local attraction can be detected by comparing the fore bearing (FB) and back bearing (BB) of a line. If BB = FB ± 180°, the readings are generally assumed to be free from local attraction at both stations. If the difference is not 180°, then local attraction exists at one or both stations.

Methods to Correct for Local Attraction:

Several methods are used to identify and correct for local attraction:

1. Using a Line whose Bearings are Free from Attraction: If there is a line in the traverse whose FB and BB differ by exactly 180°, it is considered free from local attraction. The bearings of all other lines can then be corrected relative to this unaffected line.
2. Using a Station Free from Attraction: If a station is identified as being free from local attraction (e.g., by checking several lines passing through it), its bearings can be used as a reference to correct other affected lines.
3. Observing Bearings of Intermediate Points: Sometimes, by taking bearings to intermediate points or objects not affected by local attraction, one can deduce the correct magnetic meridian.
4. Assuming Attraction at One Station: If a line AB has inconsistent FB and BB, and we suspect attraction at station A but not B, we can assume the BB of AB (read at B) is correct. Then, we can calculate the correct FB of AB by adding 180° to the correct BB. Similarly, we can correct the bearings of all lines originating from A. The same logic applies if we suspect attraction at B but not A.
5. Assuming Attraction at Both Stations: If attraction is suspected at both ends of a line, and there are multiple lines in the traverse, a systematic approach is needed. For a traverse with stations A, B, C, D, etc., if line AB shows attraction at both ends, and BC also shows attraction at both ends, we can:
   1. Assume the FB of AB is correct and correct all subsequent bearings originating from A.
   2. Assume the BB of BC is correct (which is the FB of CB) and correct all bearings originating from C.
   3. Compare the corrected bearing of BC (read from A's reference) with the corrected bearing of CB (read from C's reference). The difference will help determine the actual magnitude of attraction at B.
   A common method involves calculating the true bearings of all lines by assuming the attraction at one station is zero and then calculating the attraction at other stations. The average of the calculated attraction at the two ends of a line is often used for correction.

Plane Table Surveying

Plane table surveying is a graphical method of surveying in which field observations and plotting are done simultaneously. It is particularly suitable for small-scale mapping and surveys where high precision is not critical. The main instrument used is the plane table itself.

Components of a Plane Table:

• Drawing Board: A flat wooden board, usually about 35 cm x 30 cm, on which the drawing sheet is clamped.
• Tripod: A three-legged stand to support the plane table and keep it steady.
• Alidade: An instrument used for sighting objects and drawing lines on the drawing sheet. There are two main types:
  • Plain Alidade: Consists of a metal ruler with sighting vanes at each end.
  • Telescopic Alidade: A plain alidade with a small telescope mounted on it. This allows for sighting distant objects and also for measuring vertical angles, making it useful for topographical surveys.
• Trough Compass: A straightedge with a magnetic needle pivoted at its center. It is placed along the edge of the drawing board to orient the plane table with respect to magnetic north.
• Plumb Bob: Used to center the plane table exactly over a ground station.

Principles of Plane Table Surveying:

The fundamental principle of plane table surveying is to draw the map in the field by drawing rays from the instrument station to the various objects, with the directions of the rays being the same as the directions of the objects from the station. This is achieved by orienting the drawing board so that it is parallel to the corresponding lines on the ground.

Methods of Plane Table Surveying:

There are three main methods used in plane table surveying:

1. Radiation: This method is used when all the points to be plotted are visible from a single station.
   1. Set up the plane table over a station (e.g., A).
   2. Orient the drawing board using a trough compass or by back-sighting.
   3. Place the alidade along the line of sight to an object (e.g., point P).
   4. Draw a ray from A on the drawing sheet along the line of sight.
   5. Measure the distance AP on the ground using a chain or tape.
   6. Plot the point P on the ray at the map scale (e.g., if the scale is 1:1000 and AP = 100m, then plot P at 100mm from A on the ray).
   7. Repeat for all visible points (B, C, D...).
   This method is simple and quick but requires measurement of distances from the station to each point.
2. Progression (or Traversing): This method is used when the area to be surveyed is extensive and cannot be commanded from a single station. It involves setting up the plane table at successive stations along a traverse.
   1. Set up the plane table at the first station (A).
   2. Draw a ray towards the next station (B) and measure the distance AB on the ground. Plot B on the ray at the map scale.
   3. Draw rays from A to other visible points (P, Q, R...) and plot them using measured distances.
   4. Move the plane table to station B.
   5. Orient the plane table at B by placing the alidade along the line BA on the drawing sheet and rotating the board until the object B is sighted through the alidade. The board is now oriented.
   6. Draw rays from B to other visible points (C, P, S...) and plot them using measured distances.
   7. Repeat the process for subsequent stations (C, D...) until the entire area is covered.
   This method is similar to compass traversing but the plotting is done simultaneously.
3. Intersection: This method is used when the distances to the points cannot be measured conveniently (e.g., on inaccessible points like a church spire or a point in a river). It relies on the principle of intersecting rays from two or more stations.
   1. Set up the plane table at the first station (A).
   2. Draw rays towards all visible points (P, Q, R...).
   3. Move the plane table to a second station (B), ensuring that A and B are visible from each other.
   4. Orient the plane table at B by placing the alidade along the line BA on the drawing sheet and sighting A.
   5. From B, draw rays towards all visible points (P, Q, R...).
   6. The points P, Q, R... on the map are found by the intersection of the corresponding rays drawn from A and B. For example, the point P is located at the intersection of the ray AP (from A) and ray BP (from B).
   7. If a third station (C) is used, it provides a check on the plotted positions.
   This method requires careful orientation and accurate drawing of rays.
4. Re-sectioning: This is a crucial technique in plane table surveying, especially for the Progression and Intersection methods. It involves determining the position of the plane table on the drawing sheet when it is set up over a new ground station, without measuring distances from known points. There are three common methods for re-sectioning:
   1. By Intersection: Set up the plane table over the new station (say, B). Ensure that two known points on the plan (A and C) are visible from B. Place the alidade on the line BA on the plan and sight A. Rotate the board until A is sighted. Then, place the alidade on the line BC on the plan and sight C. Rotate the board until C is sighted. The intersection of the rays from A and C will give the correct position of B on the plan. This method requires at least two known points.
   2. By Radiation: This is a simpler method used when the plane table is moved to a new station (B) and at least one known point (A) is visible. Set up the plane table at B. Place the alidade on the ray from A to B on the plan. Sight A and orient the board. Then, measure the distance AB on the ground and plot B on the ray AB at the map scale. This method is essentially a part of the progression method.
   3. By Three-Point Problem: This is the most important method and is used when the position of the plane table on the plan is unknown, but three known points (A, B, C) on the ground are visible from the new station (P). The plane table is set up at P. The alidade is placed on the ray PA, PB, or PC on the plan. The direction of the sighted point is drawn. This is repeated for rays from the other two known points. Ideally, the three rays should intersect at a single point (P). In practice, they form a small triangle (called the "triangle of error"). The true position of P is then estimated within this triangle. Several graphical methods exist to solve the three-point problem, such as the Bessel's graphical method or the Leickert's method.

Advantages of Plane Table Surveying:

• It is a graphical method, so the map is prepared in the field simultaneously with the observations.
• It is simple to operate, and extensive fieldwork is not required compared to other methods.
• It is well-suited for small-scale mapping and topographical surveys.
• The plotting is done directly to scale, which helps in visualizing the terrain and making decisions in the field.
• Errors due to incorrect orientation are easily detected during the plotting process.

Disadvantages of Plane Table Surveying:

• It is not suitable for very precise work.
• The drawing board is exposed to weather conditions (rain, dust), which can damage the map.
• It is difficult to work in foggy or rainy weather, or in dense forests where visibility is limited.
• The accuracy depends heavily on the accuracy of orientation and the measurement of distances.