7 Odometer and Subtense Bar The idea of an odometer.Subtense bar: a 2 m rod.Distance H= cot(/2) m.33
8 Aiming TelescopeSubtense BarDistance H = cot(/2) m.
9 what is the horizontal distance between A and B if the angle was 2? tan ( /2) = (L/2) / HH = (L/2) / tan( /2)If L = 2 m, thenH = 1 / tan (/2) = cot (/2)/2Example:what is the horizontal distance between A and B if the angle was 2?
10 Stadia Chapter (16) Principle of the Stadia: Horizontal Distance = 100 rod intercept for a horizontal line of sight and a vertical rodSymbols:(I) rod intercept, or stadia interval(i) spacing between stadia hair(f/i) = k = 100: stadia interval factorC = (c + f) approximately 0, Stadia constant44
13 Electronic Distance Measurement Early types:Transmit light, measure up to 25 milesTransmit microwaves, measure up to 50 milesClassification 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 surveys55
15 Distance Computation Example: how a distance 3485.123 is measured. 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.66
16 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 device on (B).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).
20 Phase Angle Assume that = 2 m 901800270Phase Angle Assume that = 2 mIf 1 = 80, it corresponds to a distance = (80/360) * = 0.44 mIf 2 = 135, it corresponds to a distance = (135/360) * = 0.75 mIf 3 = 240, it corresponds to a distance = (80/360) * = 1.33 m
21 Basic relationships 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”
26 ABCThe angle between the rays A and C is double the angle between the two mirrors = 2 *90 = 180Notice that the objects will look upside down, notice the box at the tail of the arrow
27 Aiming at a prism through the telescope of a total station in a zoo!
28 Reflectors (Prisms) Prism and sighting target Pole and bipod Fully rotating prismPrism and sighting targetPole and bipod
29 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.
31 EDM Accuracy 3mm, and 3ppm is the most common. Estimated error in distance =Ei2 + er2 + ec2 + (ppm X D)2Where: 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 EDMExample 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 mm77
32 Prism constant consideration. Total station Vs EDM.Data collectors.Prismless EDM: up to 100 m, can reach hard places, figure 6-14.