Question

1. The image of a point whose elevation is 1,475 ft above datum appears 53.87 mm from the principal point of a vertical photograph taken from a flying height of 6,000 ft above datum. What would this distance from the principal point be if the point were at datum?

2. Images a, b, and of ground points A, B, and C appear on a vertical photograph taken from a flying height of 8,350 ft above datum. A 6-in-focal length camera was used. Points A. B. and C have elevations of 1.725 ft, 1.640 ft, and 095 ft above datum, respectively. Measured photocoordinates of the images are xa= -371 in, ya= 1.864 in, xb=062 in. yb = 3.183 in, xc=3.704 in, and yc=-3.138 in. Calculate the lengths of the lines AB, BC, and AC and the area within the triangle ABC.

3. The images of the top and bottom of a utility pole are 5.11 in and 4.93 in, respectively, from the principal point of a vertical photograph. What is the height of the pole if flying height above the base of the pole is 2,850 ft?

4. An area has an average terrain elevation of 1,200 ft above datum. The highest points in the area are 1,850 ft above datum. If the camera focal plane opening is 9 in square, what flying height above datum is required to limit relief displacement with respect to average terrain elevation to 0.20 in? If the camera focal length is 8in, what is the resulting average scale of the photography?

5. The datum scale of a vertical photograph taken from 3,000 ft above datum is 1:6,000. The diameter of a cylindrical oil storage tank measures 6.87 mm at the base and 7.01 mm at the top. What is the height of the tank if its base lies at 590 ft above datum?

6. Assuming that the smallest discernable and measurable relief displacement that is possible on a vertical photo taken from 3,000 ft above ground is 0.5 mm, would it be possible to determine the height of a telephone utility box imaged in the comer of a 9-in-square photo which stands 4 ft high above the ground?

7. If the answer to Prob.6 is yes, what is the maximum flying height at which it would be possible to discern the relief displacement of the utility box? If the answer is no, at what flying height would the relief displacement of the box be discernable?

PLEASE SOLVE ALL

Answer 1

1. Flying height H = 6000 ft

h = 1475 ft

r = 53.87 mm

Relief Displacement (Distance from principal point if the point were at datum) = rh/H = 53.87 * 1475 / 6000 = 13.24 mm

2. H = 8350 ft

f = 6 in

hA = 1.725 ft, hB = 1.640 ft, hC = 0.95 ft

xa = -3.71 in, ya= 1.864 in, xb = 0.62 in. yb = 3.183 in, xc = 3.704 in, and yc = -3.138 in

Ground coordinates are calculated as below:

XA = xa * (H-hA) / f = -3.71 * (8350 - 1.725) / 6 = -5162.016 ft

XB = xb * (H-hB) / f = 0.62 * (8350 -1.640) / 6 = 862.663 ft

XC = xc * (H-hC) / f = 3.704 * (8350 - 0.95) /6 = 5154.146 ft

YA = ya * (H-hA) / f = 1.864 * (8350 - 1.725) / 6 = 2593.531 ft

YB = yb * (H-hB) / f = 3.183 * (8350 -1.640) / 6 = 4428.805 ft

YC = yc * (H-hC) / f = -3.138 * (8350 - 0.95) /6 = -4366.553 ft

AB = sqrt [ ( XA - XB )2 + ( YA - YB )2 ] = 6298.015 ft

BC = sqrt [ ( XB - XC )2 + ( YB - YC )2 ] = 9786.478 ft

AC = sqrt [ ( XA - XC )2 + ( YA - YC )2 ] = 12444.516 ft

Area of triangle = sqrt (s*(s-AB)*(s-BC)*(s-AC)) where s = (AB+BC+AC)/2

s = 14264.5045

Area of triangle ABC = 30432630.34 ft

(Doubt regarding the values of elevation of A,B,C)

3. Flying height above base of pole H = 2850 ft

Distance of top of image r = 5.11 in

Distance of bottom of image = 4.93 in

Length of image d = 0.18 in

d = rh/H

Height of the pole h = dH/r = 0.18 * 2850 / 5.11 = 100.391 ft

4. Avg terrain elevation = 1200 ft

Highest points in the area = 1850 ft

Camera focal plane opening = 0.9 in2

Relief displacement dh= 0.20 in

dh = rh/H

H= rh/dh = 0.9*1850/0.2 = 8325 ft

S=f/(H-h) = 8in/(8325ft - 1200ft) = 8/(7125*12) = 1:10687.5

5. Datum scale = 1:6000

Flying height = 3000ft

Base elevation = 520 ft

Height of tank = d(H-h)/r = (7.01-6.87)(3000-520)/(7.01) = 49.529 ft