27 PHOTOGRAMMETRY
Asterisks
(*)
indicate problems that have partial answers given in Appendix G.
27.1 Describe the difference between vertical, low oblique, and high oblique aerial
photos.
27.2 Define the term interpretative photogrammetry.
From Section 27.1, Paragraph 1: “Interpretative photogrammetry involves
27.3 Define the term metric photogrammetry.
(a) From Section 27.1, Paragraph 4: “Metrical photogrammetry is accomplished
in different ways depending upon project requirements and the type of equipment
available. Simple analyses and computations can be made by making
27.4 Describe briefly an unmanned aerial system.
27.5 The distance between two points on a vertical photograph is ab and the
corresponding ground distance is AB. For the following data, compute the average
photographic scale along the line ab.
27.6 On a vertical photograph of flat terrain, section corners appear a distance d apart. If
the camera focal length is f compute flying height above average ground in feet
27.7 On a vertical photograph of flat terrain, the scaled distance between two points is
ab. Find the average photographic scale along ab if the measured length between
the same line is AB on a map plotted at a scale of Smap for the following data.
27.8 What are the average scales of vertical photographs for the following data, given
flying height above sea level, H, camera focal length, f, and average ground
elevation h?
27.9 The length of a football field from goal post to goal post scales 49.15 mm on a
vertical photograph. Find the approximate dimensions (in meters) of a large
rectangular building that also appears on this photo and whose sides measure 21.5
mm by 14.0 mm. (Hint: Football goal post are 120 yards apart.)
120 yds = 360 ft = 109.728 m.
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27.10* Compute the area in acres of a triangular parcel of land whose sides measure
48.78 mm, 84.05 mm, and 69.36 mm on a vertical photograph taken from 6050 ft
above average ground with a 152.4 mm focal length camera.
27.11 Calculate the flight height above average terrain that is required to obtain vertical
photographs at an average scale of S if the camera focal length is f for the
following data:
27.12 Determine the horizontal distance between two points A and B whose elevations
above datum are hA = 1410 ft. and hB = 990 ft and whose images a and b on a
vertical photograph have photo coordinates xa = 2.95 in., ya = 2.32 in., xb = −1.64
in., and yb = −2.66 in. The camera focal length was 152.4 mm and the flying
27.13* Similar to Problem 27.12, except that the camera focal length was 3-1/2 in., the
flying height above datum 4075 ft, and elevations hA and hb 983 ft and 1079 ft,
respectively. Photo coordinates of images a and b were xa = 108.81 mm, ya =
27.14 On the photograph of Problem 27.12, the image c of a third point C appears. Its
elevation hC = 1350 ft and its photo coordinates are xc = 3.20 in. and yc = −2.66 in.
Compute the horizontal angles in triangle ABC.
27.15 On the photograph of Problem 27.12, the image d of a third point D appears. Its
elevation is hD = 1170 ft and its photo coordinates are xd = 2.72 in. and yd = 3.09
in. Calculate the area, in acres, of triangle ABD.
27.16 Determine the height of a radio tower, which appears on a vertical photograph for
the following conditions of flying height above the tower base H, distance on the
photograph from principal point to tower base rd and distance from principal point
to tower top rt
27.17 On a vertical photograph, images a and b of ground points A and B have
photographic coordinates xa = 3.27 in., ya = 2.28 in., xb = −1.95 in. and yb = −2.50
in. The horizontal distance between A and B is 5350 ft, and the elevations of A and
B above datum are 652 ft and 785 ft, respectively. Using Equation (27.9), calculate
the flying height above datum for a camera having a focal length of 152.4 mm.
 
22
2
f
yhHyhH
f
xhHxhH
Laabbaabb
2
0 1.39158 1978.12614 27,919,387.625897HH 
H = 5246 ft. = 5250 ft
27.18 Similar to Problem 27.17, except xa = −52.53 mm, ya = 69.67 mm, xb = 26.30 mm,
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27.19* An air base of 3205 ft exists for a pair of overlapping vertical photographs taken
at a flying height of 5500 ft above MSL with a camera having a focal length of
152.4 mm. Photo coordinates of points A and B on the left photograph are xa =
40.50 mm, ya = 42.80 mm, xb = 23.59 mm, and yb = −59.15 mm. The x photo
coordinates on the right photograph are xa = −60.68 mm and xb = −70.29 mm.
Using the parallax equations, calculate horizontal length AB.
 
mm. 18.10168.6050.40
1aaa xxp
 
mm. 88.9329.7059.23
1bbb xxp
ft. 89.128250.40
18.101
3205 a
a
Ax
p
B
X
ft. 35.80559.23
88.93
3205 b
b
Bx
p
B
X
ft. 74.135580.42
18.101
3205 a
a
Ay
p
B
Y
 
ft. 34.201915.59
88.93
3205 b
a
By
p
B
Y
DistanceAB =
 
ft. 70.340874.135534.201989.128235.805 22
27.20 Similar to Problem 27.19, except the air base is 6940 ft, the flying height above
mean sea level is 12,520 ft, the x and y photo coordinates on the left photo are xa
= 37.98 mm, ya = 50.45 mm, xb = 24.60 mm, and yb = −46.89 mm, and the x photo
coordinates on the right photo are xa = −52.17 mm and xb = −63.88 mm.
 
37.98 52.17 90.15 mm.
a a a
p x x
  
 
24.60 63.88 88.48 mm.
b b b
p x x
 
𝑋𝐴=𝐵
𝑝𝑎𝑥𝑎=6940
90.15 37.98 = 2923.81 ft
𝑌
𝐴=𝐵
𝑝𝑎𝑦𝑎=6940
90.15 50.45 =3883.78 ft
𝑋𝐵=𝐵
𝑝𝑏𝑥𝑏=6940
88.48 24.60 =1893.78 ft
𝑌
𝐵=𝐵
𝑝𝑏𝑦𝑏=6940
88.48 (−46.89)= −3609.72 ft
DistanceAB = √(2923.81 −1893.78)2+(3883.78 + 3609.72)2=𝟕𝟓𝟔𝟒 𝐟𝐭
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27.21* Calculate the elevations of points A and B in Problem 27.19.
 
ft. 54.672
18.101
4.1523205
5500
a
Ap
Bf
Hh
 
ft. 17.297
88.93
4.1523205
5500
b
Bp
Bf
Hh
27.22 Compute the elevations of points A and B in Problem 27.20.
ℎ𝐴= 𝐻 − 𝐵𝑓
27.23 List the four different categories of stereoscopic plotting instruments.
From Section 27.14:
27.24 Name the three stages in stereoplotter orientation, and briefly explain the
objectives of each.
From Section 27.14, Paragraphs 5 – 7: “A stereoplotter operator, preparing to
27.25 How can the operator’s left and right eyes restricted to the left and right images,
respectively?
27.26 What kind of images do softcopy stereoplotters require? Describe two different
27.27 Compare an orthophoto with a conventional line and symbol map.
From Section 27.15, Paragraph 4: “Orthophotos combine the advantages of both
27.28 Discuss the advantages of orthophotos as compared to maps.
aerial photos and line maps. Like photos, they show features by their actual images
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27.29* X = 8; H = 4000 ft; f = 152.40 mm
27.30 X = 10; H = 6000 ft; f = 6.000 in.
S = 6/6000 = 1 in./1000 ft.
27.31 and 27.32?
and 27.34?
27.35 Describe a system that employs GNSS and that can reduce or eliminate ground
control surveys in photogrammetry?
27.36 To what wavelengths of electromagnetic energy is the human eye sensitive? What
wavelengths produce the colors blue, green, and red?
27.37 Discuss the uses and advantages of satellite imagery.
27.38 Using photo coordinates for points 4 and GYM on image 5, determine the scale
27.39 Using photo coordinates for points 4 and GYM on image 5, determine the flying
27.40 Using photo coordinates for points 4 and GYM on image 5 and 6, determine the
ground coordinates of points WIL1A and WIL1B using Eq. (27.12) and Eq.
27.41 Using the exterior orientation option in WolfPack, determine the exterior
27.42 Using the exterior orientation option in WolfPack, determine the exterior
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