Section ISurveying Measurements

Leveling, horizontal and slope distance, angles and directions

2. Horizontal and Slope Distances

Horizontal Distance Measurement

TapeOdometer

Subtense BarStadiaEDM

Readings: 6-1,6-4, 6-6, 6-7,6-8, 6-14, 6-17 to 6-24

Readings: 6-1,6-4, 6-6, 6-7,6-8, 6-14, 6-17 to 6-24

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

Other methods

• Odometer• Subtense Bar• Stadia

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.

Topcon EDM attached to a WILD theodolite

Topcon DM-S2 EDM attached to a WILD theodolite

Reflectors (Prisms)

Pole and bipodPrism and sighting target

Laser Distance measuring Devices

Distance Computation

• All measured is phase shift , 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.

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 device on (B).

Electronic Distance MeasurementEDM

•Knowing the 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).

Phase Angle φ

0°

90°

180°

270°

Assume that λ = 2 m If φ1 = 80°, it corresponds to a distance = (80/360) * λ = 0.44 mIf φ2 = 135°, it corresponds to a distance = (135/360) * λ = 0.75 mIf φ3 = 240°, it corresponds to a distance = (80/360) * λ = 1.33 m

Reflectors (Prisms)• Are made of high quality glass, excellent reflection

capability.• Accept rotation to right and left, and maybe up and

down, why?? And can be mounted on a tribrach or a pole, why??

• Reflect the energy at the same path it came through. The theory is that if a ray of light hits a mirror and is reflected to hit another mirror and exit the system, the angle between the first and last rays is double the angle between the mirrors. The angle between the mirrors is 90°, three of them resemble three mirrors installed on the walls at the corner of a room, That is why they are called “corner reflectors”

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

A

C

B

Prism Constant

Why to consider it?

Aiming at a prism through the telescope of a total station in azoo!

Reflectors (Prisms)

Pole and bipod

Prism and sighting target

Fully rotating prism

u A reflector might include a single prism or a group of prisms

u Reflectors can be a simple reflecting paper-sticker, they are called sheet-prisms, paper prism, or reflective sheeting. Very instrumental in construction sites and deformation monitoring of structures.

u The sighting target might be lower than the prism itself, why???

Remarks

• Accuracy: 3mm, and 3ppm is the most common

• Prismless EDM: up to 100 m, can reach hard places.