This is intended as an aide mémoire of formulae, equations and
geometrical rules applied in Plane Surveying. Generally, these
formulae concern triangles, either Pythagorean Triangles (those
with a right angle) or general planar triangles in Euclidean space.
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(SOME OLD HAGS CANT ALWAYS HIDE THEIR OLD AGE) |
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Surveying and navigation uses the concept of a whole circle bearing, consisting of 360° subdivided into the sexagesimal system. The determination of position on a plane can be calculated through simple vector mathematics, breaking the vector into its two constituent components (displacement in X or East, displacement in Y or North)
The units of scientific measurement have been defined internationally,
and have been adopted almost universally crossing linguistic and
cultural boundaries. The SI units of measurement are the standards, and they are as follows:
Distance- The standard unit for distance measurement is the metre.
- The metre is defined as 1,650,763.73 times the wave-length of the Krypton-86 atom in transition between energy levels 2p10 and 5d5 in a vacuum.
- Repeatability of around 1 in 10
Time
- The standard unit of time is the second.
- The second is the time occupied by 9,192,631,770 cycles of radiation emitted by the Caesium-133 atom in transition between (F=4,MF=0) to (F=3, MF=0).
- Repeatability of around 1 in 10
Mass
- The standard unit of mass is the kilograms.
- It is defined by the standard kilogram kept by the Bureau International des Poids et Mesures at Sèvres in France.
Speed of Light
- In a vacuum, c = 299792.5 ±0.4ms
- Although time can be measured to 1 part in 10 this value is known to only around 1 in 10. This gives a limit to the precision of electromagnetic distance measurement
Angles
- The official unit is the Radian.
- '2 radians = One Circle'. It is however an impractical unit to use.
- The most common is the sexagesimal system that uses degrees and fractions of one sixtieth, where 360° equals a circle (359°59'60").
Temperature
- The SI unit is the Kelvin degree.
- The Celsius degree is also used and is 0°C = 273.15°K.
Force
- The unit of force is the Newton
- It is the force needed to give a mass of 1kg an acceleration of 1ms
- Standard gravity = 9.80665N
Pressure
- The unit of pressure is the Pascal.
- This is the pressure produced by the application of 1N over an area of 1m.
Other Systems of Measurement
There are other units in common usage, such as the Imperial system of feet and inches, with areas expressed in acres roods and perches. Other countries also have indigenous units of measurement, most of which now have metric equivalents. In Australia, early measurement was done with a unit known as a 'chain', being the length of a cricket pitch. Feet and inches were also used, so it is beneficial to know some of the standard conversions.
1 chain = 100 links = 4 rods = 20.1168m
1 foot = 12 inches = 0.3048m (exactly)
1 inch = 25.4mm
1 mile = 5280 feet = 80 chains
1 nautical mile = 6076.10 feet = 1 minute of arc at the equator
1 hectare = 10,000m = 2.471 acres
1 acre = 4 roods =160 perches = 10 square chains
Given these conversion factors it is possible to convert most other units into the SI system.
These notes are almost exclusively limited to mapping and position
fixing on a plane. Most people now agree that the earth is spherical, but for many
surveying applications it is acceptable to assume the earth is
a flat plane (over short distances). This radically simplifies
the mathematics associated with the survey computations, and is
a valid assumption given certain constraints on the size of the
area being surveyed.
Later years in the Geomatics Degree courses naturally deal with
a spheroidal reference surface, but a planar earth satisfies the
needs of many survey tasks, if not astronomers and sci-fi freaks.
But it must be emphasised this merely a computational aid, the
earth is really an oblate spheriod with a semi major axis of 6378160.000,
a semi minor axis of 6356774.719, and a flattening of 1/298.25!
 Go back to the Horizons page
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