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Questions and Answers
What is the equivalent of one radian in degrees?
What is a forward bearing?
How do you obtain the back bearing from the forward bearing?
What is the rule for determining back azimuth when the forward azimuth is greater than 180 degrees?
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Which of the following correctly describes azimuth?
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What type of angle is formed by the directions to two objects in a horizontal plane?
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Which meridian is defined as being parallel with the magnetic force of the Earth?
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In the context of angular measurement, how is a degree defined?
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What is the complementary angle to the vertical angle called?
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What term describes the angles between adjacent lines in a closed polygon?
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How is the principal direction of angles to the right measured?
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Which type of angle is measured between a line and the prolongation of the preceding line?
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What is the primary purpose of an assumed meridian?
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What range does a bearing cover?
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When converting from bearing to azimuth, which formula applies when the bearing is in the southern hemisphere?
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Which type of compass is known for its versatility and is often used in various surveying applications?
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Which of the following statements about azimuths is correct?
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In the relationship between bearings and azimuths, which equation correctly describes their equivalence?
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What is a key characteristic of a lensatic compass?
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What does a plain pocket compass lack compared to a surveyor's compass?
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Which compass is often referred to as a liquid compass?
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Study Notes
Angles
- Defined as the difference in direction between two convergent lines.
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Types of Angles:
- Horizontal Angle: Formed by object directions in a horizontal plane.
- Vertical Angle: Formed by two intersecting lines in a vertical plane; one line is horizontal.
- Zenith Angle: Complementary to the vertical angle; formed in a vertical plane directed toward the zenith.
Direction
- Defined by the horizontal angle with a fixed reference line known as the meridian.
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Types of Meridian:
- True Meridian: Geographic lines through the north and south poles, fixed and not parallel.
- Magnetic Meridian: Parallel to Earth's magnetic force, varying with time and location.
- Grid Meridian: Parallel to the central meridian of a rectangular coordinate system, coinciding with the true meridian for plane surveys.
- Assumed Meridian: Arbitrary line chosen for reference convenience.
Horizontal Angles
- Interior Angles: Angles between adjacent lines in a closed polygon.
- Deflection Angles: Angle between a line and the prolongation of the preceding line; can be clockwise or counterclockwise.
- Angles to the Right: Measured clockwise from the preceding to the succeeding line; also known as azimuths.
Units of Angular Measurement
- Degree: 360 parts in a circle; subdivided into 60 minutes, each minute further into 60 seconds.
- Grad: Circle divided into 400 parts (grads); subdivided into 100 centesimal minutes and seconds.
- Mil: Circle divided into 6400 parts; used in military applications, 1600 mils equal to 90°.
- Radian: Angle subtended at the circle's center by an arc equal to the radius; 1 radian ≈ 57.2958°, 1° = π/180 rad.
Bearing
- The acute horizontal angle between the reference meridian and the line.
- Notation: Letters N or S precede the angle, E or W follows it.
Forward and Back Bearings
- Forward Bearing: Observed in the direction of survey progress.
- Back Bearing: Observed in the opposite direction; obtained by changing N/S and E/W.
Azimuth
- The horizontal angle measured clockwise from the meridian to the line.
- Back azimuth determination rules:
- If forward azimuth > 180°, subtract 180°.
- If forward azimuth < 180°, add 180°.
Relationships Between Bearings and Azimuths
- For bearings north (N):
- B = 360° - A
- A = 360° - B
- For bearings west and east (W, E):
- B = A - 180°
- A = 180° + B
- B = 180° - A
- A = 180° - B
- For bearings south (S):
- Similar relationships as other bearings can be derived.
Compass
- Hand-held instrument for determining horizontal direction relative to the magnetic meridian.
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Types of Compasses:
- Brunton Compass: Versatile, with clinometer; mountable.
- Lensatic Compass: For military use, features a luminous magnetic needle; shows mils and degrees.
- Surveyor's Compass: Popular in plane surveying and geological exploration; mountable.
- Plain Pocket Compass: Handy version of the surveyor's compass without sight vanes.
- Prismatic Compass: Liquid-filled to reduce friction; common in sailing navigation.
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Description
Test your understanding of angles and directional concepts such as horizontal and vertical angles, as well as different types of meridians. This quiz will challenge your knowledge with definitions and applications related to angular measurements. Perfect for students learning navigation and surveying.
