Geography 115A Lab #2: Photogrammetry, Height, and Scale Measurement Fall 2005, Instructor: Jeff Hemphill, TA: Nick Gazulis

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1 Geography 115A Lab #2: Photogrammetry, Height, and Scale Measurement Fall 2005, Instructor: Jeff Hemphill, TA: Nick Gazulis 1. Introduction For this lab you will be taking measurements from aerial photos and maps to derive real-world heights, distances, and scales (that s what photogrammetry is more or less). Please show all of your work and write down the formulas that you use to solve the problems. Also, when converting units, please show all work do not skip important steps and make sure to box your answers when you are done. Remember to label the answers with their corresponding letter/number and don t forget to put your name on the top. Make sure to answer ALL of the parts of each question. As always, working in groups is encouraged but you must do your own work. Refer to the reader and to the Jensen 2000 text for additional information as needed. 2. Measuring Heights of Displaced Objects The exaggerated displacement of tall objects near the edges of aerial photographs sometimes permits accurate measurement of object heights on single mono prints. This specialized technique of height evaluation is feasible provided that: A. The principal point can be accepted as the nadir position. (the center of the frame is the center point directly below the camera) B. The flight altitude above the base of the object can be precisely determined. C. Both the top and base of the object are clearly visible. D. The degree of image displacement is great enough to be accurately measured with available equipment, e.g. an engineer's scale or ruler. When all of these conditions can be met, object heights may be determined by this relationship: D is the length of the displaced object. R is the radial distance from the nadir to the top of the displaced feature. H is the altitude of the plane above the base of the object. * all units must match, i.e. every number in inches, centimeters or millimeters. Problems 1. Use color airphotos PW and PW (you may view these photos in stereo if you like). For this method only one photo is necessary. Assume that the flying height of the aircraft was 6,500 ft; estimate the height of Storke Tower using the displacement method. Give the height of Storke Tower in meters. While it is fine to use either photo for this question, if you had a choice, which of these photos are better suited for this method of height estimation? Why? 2. Assume that the flying height of the aircraft was 1,600 ft; estimate the height of a tall building which displays enough displacement that it can be accurately measured. Use one of the high resolution color airphotos of campus. (note: there are only a few prints available for this

2 question). Please report the height of the building you measure in feet and meters, and indicate whether you believe your measurement is reliable and why/why not. 3. (No photograph needed all the information is provided for you) On a photograph of California's "fog belt," the distance from the nadir to the top of a 500 foot redwood tree is measured as 2.00 inches. If the photograph was taken from a flying height of 2,500 feet, how much would you expect the image to be displaced on the photograph? (answer in centimeters, to two decimal places) 3. Parallax Two measures of parallax must be obtained in determining object heights on stereoscopic pairs. A. Absolute stereoscopic parallax (X parallax) is the sum of the distances of corresponding images from their respective nadirs to the neighboring image's conjugate principal point. It is always measured parallel to the flight line. B. Differential parallax is merely the difference in the absolute stereoscopic parallax at the top and base of the object being measured. It is measured parallel to the flight line. See Figure 1. The basic formula (i.e. for level ground) for determining object heights from parallax measurements is: where, A = the altitude of aircraft above ground datum P = absolute parallax at base of object being measured** dp = differential parallax ** For reasons of convenience and ease of measurement, the average photo base length of a stereo pair is commonly substituted as the absolute stereoscopic parallax (P) in the solution of the parallax formula.

3 Important: If object heights are to be determined in feet or meters, the height of the photographing aircraft (H) must also be in feet or meters. Once the photo scale is known, the flight altitude can be found by multiplying the RF denominator by camera focal length. Absolute stereoscopic parallax (P) and differential parallax (dp) must be expressed in the same units; ordinarily these units will be hundredths of millimeters or thousandths of inches.

4 Problem: 1. Determine the depth of Meteor Crater by measurement of differential parallax (answer in meters). Assume flight line is parallel to bottom edge of prints. (A = 14,800 feet; P = 2.75 inches) 4. Shadow Method of Height Determination If the height of any object on the photograph is known, and it is casting a measurable shadow in the photo, the "shadow method" can be used for height determination of all objects on the photo. Object heights can be determined by this relationship (see Figure 2): Height of object = shadow length * Tan a Where, "a" is the sun angle at that date and time and the shadow length is given in real world distance (not photo distance). This method assumes the following conditions are true: A. The object is vertical relative to the surface. B. Shadows are cast from the true tip of the object rather than the sides. C. Shadows fall on open level ground and are easily measured. The figure below illustrates various factors that affect the length of shadows cast by trees or similar objects.

5 Problems: 1. Determine the height of Storke Tower using the black and white photos of campus and IV (PW-SB1-68, PW-SB1-69, and PW-SB1-70) and the formula given above. Hint: You will need to determine the scale of the photograph and the tan(a) first. Assume another building in the same photographs is 69' tall and is casting a shadow of 100' (ground distance, of course). Fill in the known object height and the shadow length measurement in the shadow method algorithm shown at the top of the diagram below. Solve for "Tan a". Trigonometry, remember that the tangent of an angle (in degrees) is equal to the ratio of lengths of the opposite over adjacent sides. (soh-cah-toa). After tan a is calculated, determine the height of Storke Tower by measuring the shadow on the same black and white photos. Convert the photo distance to ground distance using the scale you calculated for this photo. Answer in feet and meters. 2. Which of the three height measurement methods (displacement, parallax or shadow) do you think most accurately measures height? Why do you think so? 5. Area Measurements 1. The following three questions involve calculating areas of Lake Cachuma using several different methods. Give your answers in square miles and square kilometers (remember since we are dealing with square units we can t just convert linearly). Feel free to work in groups but each person must turn in their own work. Since there is a lot of measuring to do, it is fine if you split up the different methods in your own group (i.e. one person does one method, another person does another method etc.). However, each person needs to turn in their steps for getting to a final area estimate. For example, if Joe, Alex, and I are working on this project, it is fine if Joe takes all the measurements from method 1, Alex takes all the measurements for method 2, and I take all the measurements for method 3. Then, once the measurements are taken, all three of us have to (in our own lab assignment) derive the realworld distances and show the steps involved. Remember to do a reality check to make sure

6 your estimate makes sense. Use the length on the map graphic below to find the scale of the traced outline that Lake Cachuma your TA gives you. Problems: A. Estimate the total area of lake Cachuma using the polygon method (i.e. draw polygons inside the lake and convert their photo areas to real world areas and come up with result). The outline of the lake has been traced, your TA will have a copy for you. The outline was traced from NHAP It is easiest to draw rectangles (area = base x height) of various sizes so that they fill the lake, draw triangles (1/2 base x height) in the areas where rectangles won't fit. Then compute and sum the area within the polygons. Don t go overboard with your polygons but provide enough to be accurate. B. Estimate the total area of lake Cachuma using the transparent dot grid at 64 dots per square inch. To figure out how much area each dot represents you need to measure one of the grid squares, compute its area and divide by four; remember you want the real world area so you will need to be certain to use the scale you calculate. C. Estimate the total area of lake Cachuma using the transect method (i.e. draw equally spaced through the lake, 1 cm intervals are ok, and make elongated rectangles that span the width of the lake outline, compute their photo areas and turn them into real workd areas). Then sum the results and derive a real-world area for the lake. D. Discuss these three measurement processes in terms of accuracy, which do you think is most accurate and why?