Distance Reductions

Objectives

After this lecture you will be able to:

Determine the spheroidal distance between two points on Earth’s surface from EDM measurements

Lecture Outline

Distances Normal Sections Curve of Alignment Distance Reduction

– Physical Corrections– Geometric Corrections

SP1 Conclusion

Geodetic Distances

Great Circle (sphere) Small Circle Two Plane Sections (also called

Normal Sections). Curve of Alignment Geodesic (spheroid)

Plane Sections (Normal Sections) Instrument set at B

Rotation axis is normal BN

Vertical plane containing A = ABN.

Instrument set at A Rotation axis is normal AM

Vertical plane containing B = BAM

Line A B Line B A

A B

M

N

Curve of Alignment Locus of all points where Bearing to A = bearing

to B + 180 is called Curve of Alignment. Marked on ground - A surveyor sets up between

A and B such that A and B are in same vertical plane

Horizontal angles are angles between curves of alignment– But can assume normal sections because start off same

Spheroidal triangles are figures formed by 3 curves of alignment joining the 3 points

Curve of Alignment

A B

Normal SectionB to A

Normal SectionA to B

Heights and Distances

HA

hA

NA

HB

NB

hB

Slope Distance (d2)

hM

Mean Terrain Height

Level Terrain Distance

Ellipsoidal Chord Distance (d3)

Ellipsoidal Distance (d4)

Geoidal (Sea Level) Distance (S’)

Geoid orSea Level

Ellipsoid

Terrain

A

B

(S”)

Measured Distance (d1)

Distance Reduction

Distance Reduction involves: Physical Corrections Geometric Corrections

Physical Corrections

1. Atmospheric correction• First velocity correction• Second velocity correction.

2. Zero correction (Prism constant).

3. Scale correction. 4. First arc-to-chord correction.

First Velocity Correction Covered in earlier courses Formula available - function of the

displayed distance, velocity of light and the refractive index.

Correction charts normally available– to set an environmental correction (in ppm)

or– to determine the first velocity correction to be

added manually

Some only require the input of atmospheric readings and the calculations

Second Velocity Correction

Zero Correction(Prism Constant)

Obtained from calibration results

Scale Correction

Obtained from calibration results

First Arc-to-Chord Correction(d1-d2)

km 30dfor mm 0.6 384R

d- Correction

MicrowavesFor

2

31

km 10dfor 0.02mm 1176R

d- Correction

LightFor

2

31

First Arc-to-Chord Correction(d1-d2)

Geometric Corrections

1. Slope correction 2. Correction for any eccentricity of

instruments 3. Sea Level correction (or AHD

correction) 4. Chord-to-arc correction (sometimes

called the second arc-to-chord) correction)

5. Sea Level to spheroid correction

Slope Correction

222 RL-d l

To calculate level terrain distance

Eccentrics

Try to avoid them! If they can’t be avoided - connect them

both vertically and horizontally Include redundant observations

AHD (Sea Level) Correction

m

"

R R Where

smRLR

lR

Chord-to-Arc Correction

d3 to d4 or S” to S’ if correct radius is used

Correction is

2

3

2

33

24

" or

24

R

S

R

dC ac

Ellipsoidal Chord Distance (d3)

Ellipsoidal Distance (d4)

Geoidal (Sea Level) Distance (S’)

(S”)

Sea Level to Spheroid Correction Where N is the average height

difference between spheroid and AHD s is required spheroidal length R is a non-critical value for earth’s

radius

NR

Rss

'

Ellipsoidal Chord Distance (d3)

Ellipsoidal Distance (d4 or s)

Geoidal (Sea Level) Distance (S’)

(S”)

NA NB

Example from Study Book

Follow example from study book for full numerical example

Geoscience Australia’s Formula

Combined and separate formula available

Spreadsheets– Will be used in Tutorials

Also in Study Book

SP1 Requirements In Study Book

Conclusion

You can now: Determine the spheroidal distance

between two points on Earth’s surface from EDM measurements

Self Study

Read relevant module in study materials

Review Questions