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.
–Subtense Bar –Distance H = cot( /2) m. Aiming Telescope
L L /2 /2 tan ( /2) = (L/2) / H H = (L/2) / tan( /2) If L = 2 m, then H = 1 / tan ( /2) = cot ( /2) H Example : what is the horizontal distance between A and B if the angle was 2 ?
Stadia Chapter (16) Principle of the 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 cos 2 (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
Distance Computation We only measure the phase angle shift (change), different signals of wave length: ,000 m are sent. Each fraction provides a digit(s). (Phase shift / 360)*wave length = non complete cycle length. Example: how a distance 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 Measurement EDM 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).
Concept of the fraction
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
u Distance = Velocity * Time = ((N * ) + ) / 2 Where is a fraction of wave length = ( /360) * N is the number of full cycles, ambiguity? Basic relationships Since is divided by 2, so is, we call /2 effective wave length
EDM Mounted on a theodolite
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
Aiming at a prism through the telescope of a total station in a zoo!
Reflectors (Prisms) Pole and bipod Prism and sighting target Fully rotating prism
A reflector might include a single prism or a group of prisms 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.
EDM Accuracy 3mm, and 3ppm is the most common. Estimated error in distance = E i 2 + e r 2 + e c 2 + ( ppm X D) 2 Where: E i and e r are the centering errors of the instrument and the reflector, e c 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 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.