HORIZONTAL DISTANCE
MEASUREMENT I
Spatial and Horizontal Distances
Spatial Distance
- distance between any two
random points in 3D space
Spatial and Horizontal Distances
Horizontal Distance
- linear distance between two points on any surface
- if points are at different elevations, distance is the
horizontal length between plumb lines at the points
Factors to be Considered in Choosing
Methods of Determining Horizontal
Distances
1. Purpose of the Measurement
2. Required Accuracy
• Rough reconnaisance ( 1 part in 100 )
• First-order surveys (1 part in 1,000,000)
3. Cost
Methods and Instruments Used to
Determine Horizontal Distances
1.
2.
3.
4.
5.
6.
7.
8.
Pacing
Tacheometry
Graphical and Mathematical Methods
Mechanical Devices
Photogrammetry
Taping
EDM
Global Positioning Systems
Methods for Determining
Horizontal Distance
Pacing
Methods for Determining
Horizontal Distance
Pacing
Pace
– defined as the length of a step
in walking
– 2 paces is equivalent to a stride
or a double step
– Relative Precision: 1/200 to
1/100 seldom less than 1/300
Methods for Determining
Horizontal Distance
Pacing
How to Calibrate One’s Pace?
– walk at a uniform step along a line of known length on a level
ground and count the number of paces to cover the whole stretch
– compute the pace factor (in m/pace)
Factors Affecting Length of Pace:
• Speed of pacing
• Roughness of the ground
• Weight of clothing and shoes
• Fatigue on the part of the pacer
• Slope of the terrain
• Age and sex of the individual
Methods for Determining
Horizontal Distance
Mechanical Pace Counters
1. Pedometer
- a pager-size device worn on the belt
that simply records the number of steps
made based on the body’s movement (hips)
- old pedometers are hand
carried
- registers number of paces and
distances
Methods for Determining
Horizontal Distance
Mechanical Pace Counters
2. Passometer
- registers a pace by impact
each time a foot touches the
ground
- about the size of a watch
Methods for Determining
Horizontal Distance
Tacheometry
- an indirect method of measuring horizontal
distances
- it is based on the optical geometry of the
instruments used
- uses subtended intervals and angles
observed with a transit or a theodolite on a
graduated rod or scale
- relative accuracy is 1 part in 300 to 400
Methods for Determining
Horizontal Distance
Methods in Tacheometry
1. Stadia Method
2. Subtense Bar Method
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
Stadia Method
- uses a telescope with 2 horizontal cross hairs called stadia
hairs, and a graduated rod called stadia rod
Precision depends on the ff:

Refinement with which
instrument was manufactured

Skill of the observer

Length of measurement

Effects of refraction
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
Stadia Method
Formula:
D  Ks  C
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
Stadia Method Formula:
D  Ks  C
Where:
K = stadia interval factor
s = stadia interval
C = distance from the center of
instrument to principal focus
(instrument constant)
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
Stadia Method
Example:
A stadia rod held at a distant point B is sighted by
an instrument set up at A. The upper and lower stadia hair
readings were observed as 1.30m and 0.90m, respectively. If
the stadia interval factor is 100 and the instrument constant
is zero, determine the length of line AB.
ANS: 40.00 m
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
Subtense Bar Method
- a subtense bar is set up at a
distant station while a
theodolite at the end of the line
measures the horizontal angle
subtended by the distance
between the two targets
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
The formula for subtense bar
method is:
s
 
D  cot  
2 2
Where D = horizontal distance
s = length of the subtense bar
a = angle subtended by the
targets
Relative Precision:
1/3000 with sights of about 150m or less using a 1”
theodolite
Methods for Determining Horizontal
Distance:
Tacheometry
Methods in Tacheometry
Subtense Bar Method
Example:
Using a theodolite, a subtended angle of 0º22’20”
was read on a 2-m subtense bar. What is the
horizontal distance from the theodolite to the bar?
ANS: 307.86 m
Methods for Determining
Horizontal Distance
Graphical and Mathematical
Methods
- distances are determined geometrically
Example:
Compute the distances of lines AB, BC and CA using the
given coordinates of the three points
A
Eastings (X)
Northings (Y)
A
20,000.00
20,000.00
B
20,050.00
18,900.00
C
20,650.00
19,000.00
1192.69
C
1101.14
B
608.28
Methods for Determining
Horizontal Distance
Mechanical Devices
Odometer
- attached to a wheel for
purposes of roughly measuring
surface distances (speed)
Relative Precision:
1/200 on fairly level ground
Uses:
Route Location Surveys
Preliminary Surveys
Small-scale Mapping
Methods for Determining
Horizontal Distance
Mechanical Device
Measuring Wheel
- very similar to odometer except
that it is a more portable and selfcontained device
Use:
Determining distance along
irregular or curved lines and
boundaries
Methods for Determining
Horizontal Distance
Mechanical Device
Optical Rangefinder
- determines distances approximately by focusing
Methods for Determining
Horizontal Distance
Mechanical Device
Mileage Recorder
- attached to ordinary automobile speedometer
Methods for Determining
Horizontal Distance
Photogrammetry
Methods for Determining
Horizontal Distance
Photogrammetry
• Measuring of images on a photograph
• Uses scale to obtain ground distances
image distance
Scale = -----------------------------ground distance
Methods for Determining
Horizontal Distance
Example:
A line connecting two electric posts and defining a lot
boundary is 2.6cm long on a photo. Determine its
ground distance in meters if the photo scale used is
1:500
Solution:
TL (ground dist.)
= 500*0.026
= 13 m
Sources:
La Putt, J.P. (2007). Elementary Surveying. Philippines: National Book Store.
Davis, R.E., et. al (1981). Surveying: Theory and Practice. USA: McGraw-Hill,
Inc.
Subtense bar
http://www.answers.com/topic/surveying
About Hor. Dist. Measurement
ftp://ftp.fao.org/FI/CDrom/FAO_Training/FAO_Training/General/x6707e/
x6707e02.htm
Odometer
http://waspeeding.com/
Wheel
http://www.starsealfl.com/tools.htm