Lab  #2 - Photogrammetry, Height & Area Measurement

I. 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:

Problems

1. Assume that the flying height of the aircraft was 6,500 ft; estimate the height of Storke Tower using the displacement method.  Use 8-1-86 color airphotos PW 24362-2 and PW 24362-3, view these photos in stereo using the folding mirror stereoscope. For this method only one photo is necessary. Give the height of Storke Tower in meters. Which of these photos is 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 11-14-00 high resolution color airphotos of campus.

The structure you choose to measure will depend of which set of photos you are given; make note of, a) the name of the building you are measuring, b) the frame number of the photo you using, and c) the height of the building in feet, and a comment about if you believe your measurement is reliable. Accurate measurement is important, carefully mark the principle point and use sufficient precision in your calculations.

3. On a photograph of California's "fog belt," the distance from the nadir to the top of a 340 foot redwood tree is measured as 4.00 inches.  If the photograph was taken from a flying height of 4,500 feet, how much would you expect the image to be displaced on the photograph? (answer in centimeters, to two decimal places)

4. The top of the Empire State Building, a 1250 ft. structure built in 1930-31, appears 2.25 inches from the nadir of a photograph and the displaced image is exactly 3/8 in long.  From what height above Manhattan was the photograph taken? (answer in feet and meters)

II.  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.

.

1. Determine the depth of Meteor Crater by measurement of differential parallax (answer in feet and meters).  Assume flight line is parallel to bottom edge of prints. (A = 14,800 feet;  P = 2.75 inches)

III. 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.

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.
Figure 3  illustrates various factors that affect the  length of shadows cast by trees or similar objects.

1. Determine the height of Storke Tower using the 12-7-72 black and white photos of campus and IV using the formula given above, you will need to determine the scale of the photograph first.  Assume another building in the same photographs is 69' tall and is casting a shadow of 100' (ground distance, of course).

A. 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 Fransisco Torres Dorms and 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.

B. Assume that sun angle, a, at the time the photo was taken was 33 degrees.  Calculate the height of Francisco Torres Dorms and Storke Tower, answer in feet and meters

2. Which of the three height measurement methods (displacement, parallax or shadow) do you think most accurately measures the height of Storke Tower?  Why?

IV.  Area Measurements

1. The following three questions involve calculating areas. DO NOT mark on the dot grids (please).
Give answers in square miles and square kilometers. Turn in the sheets on which you do your work, it can be messy but it has to show the work for the polygon method and transect methods. If you work together in groups of 2-4 put all of your names on the sheets and note who you worked with on your lab that you turn in.

A. Estimate the total area of lake Cachuma in the traced graphic provided by your TA, this outline came from NHAP-84 129-59.  You want to measure the area using the polygon method first. It is easiest to draw rectangles (area = base x height) of various sizes so that they fill the lake, draw triangles in the areas where rectangles won't fit.  Then compute and sum the area within the polygons.  Assume photo scale is 1:58,000.

B. Using the transparent dot grid at 64 dots per square inch, recalculate the aerial extent of Lake Cachuma using the outline of the NHAP-84 129-59 photo.

C. Using the transect method draw lines, equally spaced through the lake, 1 cm intervals are ok, and make elongated rectangles that span the width of the lake outline.

D. Discuss these three measurement processes in terms of accuracy.  Based on lecture there are several aspects to each method of manual area estimation you should mention for full credit.

V. Photo Coverage

 The following problem can be completed using information in Chapter 5 of Avery & Berlin (page 95-107 of the reader).  Please use the following information.  See Chapter 5, page 101 in Avery and Berlin for the proper formulas.  This exercise shall be completed prior to lecture material on mission planning.

 The unincorporated area of Goleta wants to have accurate maps made to  show Santa Barbara's county planners where the boundary's are for the cityhood initiative.  Pacific Western Aerial Surveys, a local company, was contracted to do the aerial photo acquisition.  Using the appropriate  formulas determine how many photos it would take to cover the Goleta Valley.  The basic information required is as follows:

Approx. area of coverage: L 30.6cm x W 22cm (on a 1:24,000 map)
Elevation of study area: 23m
Desired photo scale: 1:10,000
Film Format: 23 X 23cm
Focal length: 152mm
Overlap:  60 percent
Sidelap: 30 percent