Horizontal Distance
Measurement
Tape
Odometer
Subtense Bar
Stadia
EDM
Distance Measurement
Devices and accuracy:
•
Older technologies “ quick look”
•
•
•
•
•
•
Pacing : 1:50
Optical rangefinders: 1: 50
Odometers: 1:200
Tacheometry / stadia 1: 500
Subtense bar 1: 3000
Tapes: 1: 10,000
• Modern Technology:
- Electronic Distance Measuring (EDM) devices: 2 +2 ppm
Tape Measurement
Accuracy and speed considerations for
civil engineers.
• Sources of Errors:
•
• Incorrect length of the tape
• Temperature difference
• Sag
• Poor alignment
• Tape not horizontal
• Improper Plumbing
Odometer and Subtense Bar
•
•
The idea of an
odometer.
Subtense bar: a 2 m
rod.
•
Distance H=
cot(/2) m.
Aiming Telescope
–Subtense Bar
–Distance H = cot(/2) m.
L
H
L /2
tan ( /2) = (L/2) / H
/2
H = (L/2) / tan( /2)
If L = 2 m, then
H = 1 / tan (/2) = cot (/2)
Example:

what is the
horizontal distance
between A and B if
the angle  was
2?
• Chapter (16)
• Principle of the Stadia:
Stadia
• Horizontal Distance = 100 rod intercept for a
horizontal line of sight and a vertical rod
• Symbols:
• (I) rod intercept, or stadia interval
• (i) spacing between stadia hair
• (f/i) = k = 100: stadia interval factor
• C = (c + f) approximately 0, Stadia constant
D = KI + C = 100 I, for horizontal sight
H = 100 I cos2(α)
V = 100 I sin(α) cos(α)
Electronic Distance Measurement
•
Early types:
Transmit light, measure up to 25 miles
• Transmit microwaves, measure up to 50
miles
• Classification of EDM:
• Electro-optical: laser or infra red reflected
from passive prism or surfaces, the US has
installed a prism on the moon.
• Microwave: two positive units, GPS
replaced them for most engineering
applications such as hydrographic surveys
•
Electromagnetic Spectrum
Distance Computation
•
•
•
We only measure the phase angle shift
(change) , different signals of wave length: 10
100 1000 10,000 m are sent. Each fraction
provides a digit(s).
(Phase shift / 360)*wave length = non complete
cycle length.
Example: how a distance 3485.123 is measured.
Electronic Distance Measurement
EDM
The Idea:
To measure the distance between two points (A)
and (B) the EDM on point (A) sends
electromagnetic waves. The waves received at
(B) are reflected back or resent to (A) by a
•Knowing
device onthe
(B).speed of electromagnetic waves in
the air, the EDM computes the distance by
measuring the time difference or the shift of the
wave phase angle (will be explained in details
later).
Concept of the fraction
90
0
180
270
Phase Angle 
Assume that  = 2 m
If 1 = 80, it corresponds to a distance = (80/360) *  = 0.44 m
If 2 = 135, it corresponds to a distance = (135/360) *  = 0.75 m
If 3 = 240, it corresponds to a distance = (80/360) *  = 1.33 m
Basic relationships
u
Distance = Velocity * Time = ((N *) + ) / 2
Where  is a fraction of wave length =
(/360) *
N is the number of full cycles, ambiguity?
Since  is divided by 2, so is , we call /2 “effective
wave length”
Wave Modulation
EDM Mounted on a
theodolite
A
C
The angle between the rays A and C is
double the angle between the two mirrors =
2 *90 = 180
Notice that the objects will look upside
down, notice the box at the tail of the arrow
Aiming at a prism through the telescope of a total station in a
zoo!
Reflectors (Prisms)
Fully rotating
prism
Prism and sighting
target
Pole and bipod
•
•
A reflector might include a single
prism or a group of prisms
Reflectors can be a simple reflecting
paper-sticker, they are called sheetprisms, paper prism, or reflective
sheeting. Very instrumental in
construction sites and deformation
monitoring of structures.
EDM Accuracy
3mm, and 3ppm is the most common.
• Estimated error in distance =
Ei2 + er2 + ec2 + (ppm X D)2
• Where: Ei and er are the centering errors of the
instrument and the reflector, ec is the constant
error of the EDM, and PPM is the scalar error of
the EDM
Example 6-5 page 156: if the estimates errors of
centering the instrument and target were ± 3mm
and ± 5mm respectively, the EDM had a
specified error of ± (2mm +2ppm) what is the
estimated error in measuring 827.329 m?
Answer: ± 6.4 mm
•
•Prism
constant
consideration.
•Total
station Vs EDM.
•Data
collectors.
•Prismless
EDM: up to
100 m, can reach hard
places, figure 6-14.
Handheld laser measuring devices