Coordinate systems O.S. Grid Site Grid Norths Whole Circle Bearings Partials Polar Conversions...
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Transcript of Coordinate systems O.S. Grid Site Grid Norths Whole Circle Bearings Partials Polar Conversions...
Coordinate systemsCoordinate systemsO.S. GridO.S. Grid
Site GridSite Grid
NorthsNorths
Whole Circle BearingsWhole Circle Bearings
PartialsPartials
Polar ConversionsPolar Conversions
Radial Setting OutRadial Setting Out
Ordnance Survey GridOrdnance Survey Grid
• Greenwich origin for O.S. grid ( =0 Meridian) but causes –ve grid values, hence:
• Longtitude parallel to 2 West Meridian &• Origin Shifted west and south to allow only
positive grid values in UK• Ref. By two letters and six figures for 100m
accuracy (e.g. TH645589)• More accuracy not used with general OS maps• Eastings and Northings values for Surveying
involve 5 integers and 3 decimals these are then in metres. ( e.g. 64567.123mE, 58945.456mN)
Grid size and accuracyGrid size and accuracy
64772.123mE, 54752.765mN
60 6550
55
Km
640 650
540
550
100m grid
643, 542
to a 100m corner square
6455,5443 to nearest 10m
1km or 1000m grid
1000m = 1Km, 100m = 0.1km, 10m = 0.01km, 1m = 0.001km
OS Grid to Site Grid conversionsOS Grid to Site Grid conversions
Site grid point in terms of O.S. grid:
E = b + E1cos - N1sin
N = a +N1cos - E1sin
abOrigin New Grid
Origin Old Grid
Point on Old Grid
Easting
No
rth
ing
E 1 N1
Whole Circle Bearing (WCB)Whole Circle Bearing (WCB)• The angle to a line
measured from North in a clockwise direction.
• Partials (also known as latitudes and departures) are the East and north vector of the line AB
B
A
North
North Partial
East Partial
• East Partial = L x sin(WCB)
• North Partial = L x cos(WCB
WCB
• Not measured directly as North is difficult to find (Magnetic, True, Grid?) but by using two reference stations HENCE WCB will be to True or Grid North.
EA, NA
WCB
EB, NB
WCBAB = TAN-1(EB – EA / NB-NA)
Whole Circle Bearing (WCB) 2Whole Circle Bearing (WCB) 2
NORTH?NORTH?
• True or Geographic North – Top of globe, where lines of longtitude meet.
• Grid North – Lines parallel to 2 W meridian - in same direction over the drawn map area.
• Magnetic North – as indicated by magnetic compass needle. Not at true North and varies in position.
NORTH 2NORTH 2
True North
Gyro theodolite which utilises spin of earth for orientation will refer back to this
NORTH 3NORTH 3Grid North – as used on maps
Due to projection of spherical surface onto flat sheet
NORTH 4NORTH 4
MAGNETIC NORTH – Position varies seasonally and is away from the true north.
Due to molten iron core of earth.
Geologically evidence that it has flipped over several times.
No reason why it shouldn’t do so again.
Shift documented for navigation purposes.
Angle between Longitudes and Magnetic north depends also on latitude position
Cartesian to Polar ConversionCartesian to Polar Conversion
N
E
(E, N)
R
R,
The position of any point can be expressed by either cartesian coordinates or by using Polar coordinates.
Cartesian or Rectangular coordinates Polar
coordinates
WCB and POLAR coordsWCB and POLAR coords
R
R,WCB
NOTE:
E = R x cos()
N = R x sin()
NOTE:
Eastings = L x sin(WCB)
Northings = L x cos(WCB)
N
EEastings
Nor
thin
gs
L
Setting out using RADIALSSetting out using RADIALS
Observation Station
Reference Station
To set out from B using A as the reference station:
Find Deflection angle
and Setting out distance L
A
B
LPoint to be set out
Setting out using RADIALS -2Setting out using RADIALS -2
A
B
1. Sketch known points and stake out point correctly relative to each other. Do not try to scale coordinates
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN
Setting out using RADIALS -3Setting out using RADIALS -3
A
B
2. Add Coordinate values to axis.
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN
3060
3050
20005000 6450 6500
A
B
3. Identify Delection angle .
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN
5000 6450 6500
3060
3050
2000
Setting out using RADIALS -4Setting out using RADIALS -4
A
B
4. Identify components of Delection angle .
Reference Coordinates:
A: 5000mE, 2000mN
B: 6500mE,3050mN
Stake out Coordinate:
6450mE, 3060mN
5000 6450 6500
3060
3050
2000
α
β
Setting out using RADIALS -5Setting out using RADIALS -5
A
B
5000 6450 6500
3060
3050
2000
α
β
5. Identify relevant right angled triangles.
HINT: Start with Hypoteneuse to component deflection angles
Setting out using RADIALS -6Setting out using RADIALS -6
Setting out using RADIALS -7Setting out using RADIALS -7
A
B
5000 6450 6500
3060
3050
2000
α
β
6. Calculate Difference in Eastings and Northings for each triangle
Eref = EB –EA
Nref = NB - NA
EStakeout = EB –E
Estakeout = N –NB
1500
1050
1050
Setting out using RADIALS -8Setting out using RADIALS -8
A
B
5000 6450 6500
3060
3050
2000
α
β
7. Calculate components of deflection angles.
= tan-1 Nref /Eref
= tan-1 NStakeout /Estakeout
Hence = +
1500
1050
1050
8. Finally calculate the setting out length.
Note that all partials have already been computed
L = (NStakeout2 + Estakeout
2)
Best calculated using spreadsheet program.
Facility available on total Station for inputting reference stations and required stake out point – Setting out information calculated automatically ( but how do you check values?)
Consult user manual as each instrument is different
Setting out using RADIALS -9Setting out using RADIALS -9