Part I: Scale of a vertical photograph

Vertical photographs

8.1. Define the followings:

Photo scale; Point scale; Average scale; Nominal scale

8.2. How do you express scale?

8.3. What are the major factors that affect scale? Explain how you can reduce the effect of these factors on photo scale.

8.4. A vertical photograph was taken at 3000 m above a soccer filed that is 350 m above mean sea level. If the focal length of the camera used to take the photograph is 152.4 mm, what is the scale of a point on the photograph whose ground elevation is 500 m above mean sea level? Express the scale in representative fraction (RF) and unit equivalents (UE).

8.5. The average elevation of a vertical photograph is 300 m above mean sea level and its scale is 1 mm = 15 m. How high above mean sea level was the aircraft flying when taking the photograph with a 210-mm focal length camera?

8.6. The average ground elevation between two points is 280 m and the distance, measured on a vertical photograph, between these two points is 8.65 cm. The same 2 points were identified on a 1:24000 scale map and the distance was measured to be 2.73 cm. If the photograph was taken with a 152.4-mm focal length camera, find the scale of the photograph and the flying height above mean sea level at which the photograph was taken.

8.7. The distance between two points, measured on a vertical photograph, is 5.21 cm. The distance between these same two points, measured on a 1:50000 scale map, was found to be 1.43 cm. The average ground elevation between the two points is 300 m above mean sea level. Find the flying height at which the photograph was taken if the focal length used is 152.4 mm.

8.8. Vertical photographs was taken with a 152.4-mm focal length camera over an area whose elevation ranges between 280 m and 520 m. The smallest scale requested for the project is 1:10000. How high above mean sea level must the aircraft fly to meet this scale requirement and what will be the largest scale in the project?

8.9. A vertical photograph was taken at a flying height of 3500 m above datum. The distance between two points was measured to be 6.25 cm on the photograph and the corresponding distance on the ground is 1 kilometer. What was the focal length used to take the photograph?

8.10. On a 7.5-minute U.S.G.S topographic map, the distance between 2 points was measured to be 5.15 cm. On a photograph, taken with a 152.4-mm focal length camera, the distance between these same two points measures 8.65 cm. Find the flying height above datum at which the photograph was taken.

8.11. The distance between two points is 12.83 cm on a vertical photograph and 3.32 cm on a map, whose scale is 1:50000. What is the corresponding distance between these same two points on the ground and what is the scale of the photograph expressed in RF and UE?

8.12. Two points, A and B, are 450 m and 585 m above mean sea level, respectively. The average scale between these two points on a photograph taken with a 152.4-mm focal length camera is 1 mm = 12 m. What would be the scale of a point on the photograph whose elevation is 300 m above mean sea level?

8.13. A 152.4-mm focal length camera was used to take a vertical photograph. A 1.5 km road section was imaged as 4.78 cm on the photograph. What is the flying height above datum at which the photograph was taken?
 

8.14. The ground distance of a straight boundary of a corn field is 850 m. The field is nearly level and lies beside the principal point of the photo. The distance on the photo of this boundary is 5.15 cm.

a) What is the scale of the photograph?
b) Express this scale in unit equivalents in centimeter per kilometer and inch per mile.
c) If the focal length of the camera used to take the photograph is 305 mm, how high was the aircraft above the ground when taking the photograph?

8.15. A vertical aerial photograph was taken from 4500 m above MSL using a 305-mm focal length. What would be the variation in the photo scale if the ground elevation of the photograph varies between 270 m and 730 m? Find the average scale of the photograph and the scale of the top of a hill that is 580 m above MSL.

8.16. The image of a redwood log was identified on a photograph and measured to be 1.52 cm. The log was also measured on the ground and was found to be 182.5 m. How high was the aircraft above the log when taking the photograph if the focal length used is 152.4 mm?

8.17. A photograph was taken with a 152.4-mm focal length camera from 3800 m above MSL. Four points, a, b, c, and d were identified on the photograph and their ground elevations were found to be A = 460 m, B = 510 m, C = 395, and D = 615. Find the scale at each point and the average scale of the photograph. Conclude.

8.18. Two points A and B whose elevations are h_A = 335 m and h_B = 516 m above mean sea level are imaged at points a and b on a vertical photograph. The photocoordinates of a and b are x_a = -5.12 cm, y_a = -6.54 cm, x_b = -5.47 cm, and y_b = 2.73 cm. The photograph was taken with a 152.4-mm focal length camera and the ground distance between A and B is 2150 m. Find the flying height from which the photograph was taken.

8.19. A road section that is 1350 m long on the ground begins at point A, whose elevation is hA = 385 m, and ends at point B, whose elevation is hB= 575 m above mean sea level. These two points are imaged at points a and b on a vertical photo that was taken with a 152.4-mm focal length. The photocoordinates of points a and b are x_a = -19.85 mm, y_a = 73.36 mm, x_b = -27.37 mm, and y_b = -98.16 mm. What is the flying height the photograph was taken from?

8.20. On a 1:24,000 topographic map, the distance between two road intersections was measured to be 51.2 mm. The two road intersections were identified on a vertical aerial photograph and the distance between these two points was measured to be 122.3 mm. Find the scale of the photograph and the ground distance between the two road intersections.

8.21. A 152.4-mm focal length camera was used to take a vertical aerial photograph from 3260 m above MSL. What is the scale of the top of a hill that is 620 m above MSL?

8.22. In your aerial photography laboratory, find three photographs at different scales and compute the average scale of each photograph using the topographic maps (measure at least three distances on each photograph to accurately determine the average scale of these photos).

8.23. A soccer field that is 120 m long measures 15.3 mm on a vertical photograph. What is the scale of the photograph? How high above the ground was the aircraft flying when taking the photograph if a 152.4-mm focal length camera were used.

8.24. A rectangular corn field was measured on a vertical aerial photograph (photo 1) to be 5.26 cm long. This same field was identified on a 1:10,000 photograph (photo 2) on which the same length was measured to be 8.72 cm. Find the scale of photo 1.

8.25. Two road intersections were identified on a vertical aerial photograph (photo 1) and were measured to be 4.73 cm apart. The same distance was measured on a second photograph (photo 2) that was taken with a 210-mm focal length camera from 3280 m above the ground. Find the scale of photo 1 and the ground distance between the two road intersections.

8.26. Two points, a and b, are 6.35 cm apart on photo 1 and 8.32 cm on photo 2. Photo 2 was taken with a 152.4-mm focal length camera from 4260 m above MSL. If a is 820 m and b is 680 m above MSL, what is the average scale of photo 1? If photo 1 were taken with a 210- mm focal length, from what altitude above the ground was this photo taken?

8.27. A football filed was measured to be 0.3528 cm² on a vertical aerial photograph. The ground dimensions of the field are 50 m by 100 m. Find the scale of the photograph.

8.28. A ten-hectare cotton filed was delineated on a vertical aerial photograph and its photographic area was measured to be 3.24 cm2. Find the scale of the photograph and the altitude above the ground from which the photograph was taken if the a 152.4-mm focal length was used.
 

Tilted photographs

8.29. How does tilt affect the scale of a photograph?

8.30. What can you do to minimize the effect of tilt on aerial photograph?

8.31. A 3^o tilt aerial photo was taken from 3800 m above the ground using a 210-mm focal length. What is the scale of the photo at the principal point, at 8.32 cm from the principal point on the up side of the tilt, and at 6.85 cm from the principal point on the down side of the tilt?

8.32. Repeat problem 8.31 if the tilt of the photograph was 2^o45'.

8.33. A tilted aerial photo was taken from 3680 m above the ground using a 152.4-mm focal length. The scale of the photo was found to be 1:24890 at 10.43 cm from the principal point on the up side of the tilt and 1:23530 at 9.16 cm from the principal point on the down side of the tilt. By how much was the camera tilted from the vertical when taking the photo?

8.34. In problem 8.33, determine the scale at the same points (10.43 cm and 9.16 cm from the principal point) if the tilt were 1^o56'. Conclude.

8.35. Repeat problem 8.33 if the photograph were taken with a focal length of 210 mm instead of 152.4 mm. Conclude.

8.36. Repeat problem 8.33 if the photo were taken from 2800 m above the ground. Conclude.
 

Oblique photographs

8.37. A 152.4-mm focal length was used to take an oblique aerial photograph from 4260 m above the ground. Find the photo scale at the isoline (i.e., the line passing through the isocenter, which is a point halfway between the principal point and the nadir). How would the scales at the principal point and at the nadir compare to this scale (i.e., at the isocenter)?

8.38. An oblique photo was taken from 3500 m above the ground with a depression angle of a = 33^o and a focal length of 152.4 mm. Find the scale of the photo along the principal line (i.e., the line perpendicular to the principal meridian and passing through the principal point).

8.39. The scale, at the principal line, of an oblique aerial photograph is 1:15,000. If the photograph were taken with a 210-mm focal length camera inclined 66^o30' from the vertical, how high above the ground was the aircraft flying when taking the photograph?

8.40. A 152.4-mm focal length camera, inclined 31^o40' from the true horizon, was used to take an oblique photograph from 4260 m above the ground. Two points were identified on the photograph and their distances from the true horizon were measured to be 12.73 cm and 19.37 cm. Find the average scale between these two points.

8.41. The average scale between two points that are 21.16 cm and 13.93 cm from the true horizon on an oblique photograph is 1:14560. If the photograph were taken with a 210-mm focal length camera inclined 57^o25' from the vertical, how high above the ground was the aircraft flying when taking the photograph?

8.42. In problem 8.41, if the two points were 19.75 cm and 12.14 cm from the true horizon, the scale of the photograph were 1:13600, the focal length were 152.4 mm, and the height of the aircraft above the ground were 1560 m above the ground, by how much was the camera inclined from the vertical when taking the photograph?
 

Part II: Area measurements

8.43. What affects the accuracy of area measurements? Explain.

8.44. How does slope affect area measurements on aerial photographs?

8.45. What are the different techniques for determining area on aerial photographs? Briefly explain the principle of each technique and state its advantages and disadvantages.

8.46. A 5 sided polygon was delineated on a 1:15840 vertical photograph. Taking the photo center as the coordinate origin, the photo coordinates of the polygon vertices are: x₁ = 23.8 mm, y₁ = 42.6 mm, x₂ = 32.4 mm, y₂ = 61.2 mm, x₃ = 63.7 mm, y₃ = 53.6 mm, x₄ = 63.2 mm, y₄ = 29.8 mm, x₅ = 32.1 mm, and y₅ = 18.1 mm. Find the area of the polygon using the coordinate method.

8.47. A forester desires to estimate the total area of forested land on a U.S. Geological Survey 7.5- minute map covering 18292 hectares. The forested areas were delineated on the map and 40 equally spaced transect lines were drawn horizontally (i.e., east-west) on the map, which is 32.5 cm wide. The total length of all the transects passing through the forested areas was measured to be 730 cm. Find the total area of the forested land on the 7.5-minute map.

8.48. Find a set of three photographs in your laboratory and, using the appropriate procedure you have learned through your photo-interpretation class, determine the effective area on the central photo of your set. Next, using the photo-interpretation techniques, interpret and delineate the different classes inside the effective area. Finally, determine the area of each class category using the transect, the dot grid, and the planimeter methods. Use tables 8.1 and 8.2 as models for your calculation. Compare the three techniques

8.49. Lay down a dot grid transparency on top of a section of a U.S.G.S 7.5-minute map and determine the area, in hectares, of the section.

8.50. In Problem 8.49, if the area of the section were 259 hectares, how accurate was your area determination of the section in problem 8.49? Use table 8.2 to correct for the discrepancies.

8.51. A 10-dot-per cm² dot grid is overlaid on top of a polygon, which is delineated on a 1:15840 photograph. If 127 dots are counted within the polygon, what is its area in hectares?

8.52. Assume the total area of the rectangle bellow is 460 hectares. Use a dot grid to determine the area of polygons A, B, C, D, and E by the total known area technique.

8.53. Repeat problem 8.52 using the transect technique.

8.54. In problem 8.52, assume the total area of the rectangle is unknown, but the average scale of the map is 1:20,000. Use a 10-dot-per-cm² dot grid to determine the area of the five polygons.

8.55. It is desired to determine the number of hectares of wetlands in a project area containing 1000 23 cm by 23 cm vertical aerial photographs at 1:15800. The effective area of each photograph was determined and cut out to make a mosaic of the project area. Each effective area was found to represent 30 percent of the total area of the 23 cm by 23 cm photograph. The wetlands were delineated and were found to represent 23% of the entire area covered by the mosaic formed by the effective areas. If one photograph weighs 16 grams, find the total area of the wetland areas.

8.56. One section of a U.S.G.S. 7.5-minute map was identified on a 1:15,000 photograph. Three fifth of the section was interpreted to be forest land. Find the area of this forest land if the 23 cm by 23 cm photograph weighs 16 grams.

8.57. Starting one half cm from the edge of the rectangle bellow, properly draw 10 equally spaced transect lines and determine the area of polygons A, B, and C if the scale of the map is 1:12,000.

8.58. Repeat problem 8.57 using a dot grid. Compare the results.

8.59. Assuming the scale of the diagram in problem 8.57 is 1:14500. Use a known scale dot grid and the corresponding calculation formulae to determine the area of the three polygons.