Photogrammetry involves, among other things, making accurate measurements from (usually) vertical air photos. In this exercise, we'll try out some of the more basic measuring techniques, including measuring heights and areas using very simple tools.We will also have demonstration of the parallax bar.
I. Computing Heights using Relief Displacement
How are relief displacement and position relative to the principal point used to estimate the height of an object on an air photo? (see Avery and Berlin, pp.74-77)
If you have a single large scale (e.g. 1:6,000) air photo on which are shown tall objects (e.g. smoke stacks, tall buildings, or very tall trees), you may be able to estimate their height using the displacement of the objects. However, the principal point and the nadir of the photo must be at the same point (that is, the air photo is perfectly vertical). You must also know the flight altitude above the base of the object. If you know the scale of the photo and the camera's focal length, you can calculate the flying height by multiplying the RF denominator (e.g. 6,000) by the camera's focal length: H = (Rfd)(f). You must be able to assume that the land surface is relatively flat, or be able to calculate the actual height of the camera above your object. Otherwise, if the elevation is variable, the scale of the object may be different from objects at the principal point. You must also be able to see clearly both the top and base of the object, and the degree of displacement (i.e. how much of the sides of the object you can see) must be great enough to be accurately measured with available tools (e.g. your engineer's ruler). The greatest displacement will be seen with tall objects that are farthest from the principal point. If you have all of this information, you can calculate the height of the object using the following equation:
h = (d/r)(H) where d = length of the displaced object from base to top
r = radial distance from the nadir to the top of the objectH = aircraft flying height above the base of the object
Question 1: Assume the following: You are looking at an air photo of the Shell Refinery at Richmond, and you see a number of oil storage tanks. The flying height is 900 m above the surface. you measure the displacement of the tallest tank at 9.5 mm on your photo, and the distance from the nadir (principal point) of the photo is measured at 122 mm. How tall is the oil storage tank? Show your work.
Question 2:
(a) Do you need one air photo or a stereo pair for this procedure?
(b) What information do you need to be able to do the calculations?
(c) Are the results precise or approximate?
II. Computing Heights using Stereoscopic Parallax.
What if you can't see the base of the object or its radial displacement is too small to measure? You can get a fairly accurate measurement of height by using stereoscopic parallax. (see Avery and Berlin, p. 78)
If you have a good, large scale air photo stereopair of the object, a stereoscope, a parallax-measuring device, and accurate measuring ruler, you can obtain a fairly accurate measure of the height of the object. Parallax is the apparent displacement of an object caused by a change in the point of observation. This is why you can see a single three-dimensional image by looking at two air photos that were taken of an object from slightly different angles.
When measuring the height of an object using stereoscopic parallax, you would do the following :
1. establish the principal points and conjugate principal points for each air photo.
2. draw a line between the principal point and the conjugate principal point for each air photo. Tape down the two air photos so that these lines are aligned along a single plane. This line represents the line of flight of the aircraft.
3. measure (in mm) the distance along the line between the principal point and the conjugate principal point for each air photo. This is the photo base length. Calculate the average of these two measurements. This is P in the parallax equation, in mm.
4. from the photo scale and focal length of the camera, calculate the flying height of the photo. This is H is the parallax equation, usually in meters or feet.
5. parallel to the flight line, measure the distance between the two tops of the object. Then in the same way, measure the distance between the two bases of the object
6. calculate the differential parallax by subtracting the top distance from the base. This is dP in the parallax equation, in mm..
The basic equation for determining the height (h) of an object from parallax measurements is:
h = (H)[(dP)/(P + dP)] where: H = flying height of the plane above the base of the object
P = stereoscopic parallax at the base of the objectdP = differential parallax
Since we don't have any appropriate stereopairs for this type of measurement, we'll fake it with a hypothetical stereopair of an isolated Coast Redwood snag.
Question 3. Calculate the height of the lonely Coast Redwood using equation 4-6 (page 78). Assume the flying height is 3,450 feet, the distance between the two tops (on the stereopair) is 1.49 inches, and the distance between the two bases is 1.94 inches. The photo base length is 3.3 inches. Please draw a diagram showing how the two photos would be set up, and where measurements on the air photos would be. Then show your calculations.
Under some circumstances, you can also compute heights using shadow length of an object. The object must be vertical, and its shadow must fall on open, level ground.
For example, you might be able to measure the height of a scoreboard whose shadow falls on a playing field. You also need some way to get a handle on the scale of the shadow. So you either need to be able to measure the shadow on an object of known height in the photo, and then calculate the proportion of the known object and its shadow to the unknown object and its shadow. Or, if you have no object of known height in the photo, you need to know the actual length of the shadow (the scale of the photo at that elevation), plus the elevation or angle of the sun at the time the photo was taken. For this you could use a solar ephemeris (astronomical tables) plus the month, day, and hour the photo was taken. Oh, well ...
III. Parallax Bar
Mike has set up a lab using the parallax bar, attached to a pocket stereoscope, to calculate the height of a San Francisco hill using sea level as the base elevation. Read the description of the parallax bar in your text, page 80, and then ask Mike to explain the use of the equipment to you. Then, please show your calculations as you estimate the elevation of the hill using the parallax bar and the following (now familiar) equation:
h = (H)[(dP)/(P + dP)] where: H = flying height of the plane above the base of the object
P = stereoscopic parallax at the base of the objectdP = differential parallax
Question 4. Height of S.F. Hill above mean sea level:
IV. Area Measurements
In this lab, you will try your hand at two types of planimeters: a standard manual polar planimeter, and a digital polar planimeter. We will make a dot planimeter (p. 82, Avery and Berlin) when we do a lab on land use and land cover mapping.
One of the problems to keep in mind when making area measurements is the change in scale with variations in topography. Where the topography is flat or gently rolling, the scale is reasonably uniform, considering the variation with distance from the principal point. But where the relief is more variable, with steep slopes and few level areas, the scale can vary considerably from place to place on a photo. When the scale changes, the area measurements will be inaccurate unless you can constantly change your planimeter to adapt to the variations. This is impractical.
IV. A. Manual planimeter
The air photos used for this part of the lab are blow-ups of the area around SSU. Both planimeters are set up to measure the area around the campus.
1. First you must find the scale of the air photo. For this photo, you can use the distance between Snyder and Petaluma Hill Road, which is approximately one mile on the ground. Calculate the RF by measuring the distance on the air photo and calculating the ratio between the distance on the ground and this measure (in the same units). (see pages 73-74, Avery and Berlin)
2. Zero the vernier scale on the planimeter. Place the tracer lens of the planimeter on a beginning point, for example, the southwest corner of campus, on East Cotati Ave. (Pick a precise point that is easy to identify so that you don't miss it when you come around). Run the tracer lens around the perimeter of the SSU campus, clockwise, beginning at East Cotati on the west edge of campus, going north past the dorms, then east along Copeland Creek, following the creek bed, then following the tree line south along the east side, then south along East Cotati, back to the south west corner.
3. Make a note of the reading on the planimeter. (Ask for help with this.) Then zero the planimeter again, and go around the perimeter again and take a second reading. Average these two readings. This should be the area, in square inches.
4. Go around twice more, and calculate the area again. Average your four measurements.
5. Use your calculated scale to convert the square inches on the air photo to square feet on the ground. You can calculate acreage, if you like. One acre equals 43,680 square feet, or 4840 square yards.
Scale of Air Photo:
Area of Sonoma State Campus:
IV. B. The Digital Planimeter
The digital planimeter ordinarily would have a manual telling you which settings to use for which scale, but since there is no manual for this planimeter, we will have to figure out what a particular setting represents on this air photo.
1. Once again, find the scale of the air photo. The scale of this photo is different from the first.
2. Then, on a blank sheet of paper (the back of this page will do), draw a perfect square with each side representing 2090 feet. This box represents 100 acres. (An acre equals 4840 square yards, 69.57 yds on a side.)
3. With Mike's instructions, go around the perimeter of your 100 acre square several times (at least three), beginning and ending in precisely the same place each time. Make a note of the measurement on the digital display each time, then average the three. This number represents 100 acres.
4. Then trace the perimeter of the SSU campus, as you did above. Note the read-out on the digital display. Go around the perimeter at least twice, then average your readings. Use your averaged results relative to the read-out for 100 acres to calculate the acreage of the SSU campus. Hopefully, it will be similar to the area found with the manual planimeter.
Scale of Air Photo:
Area of SSU Campus: