Handbook of Civil Engineering Calculations

2. Solve this equation for the flying height
   Take sea level as datum. From the foregoing equation, with the meter as the unit of
   length, H= h +/S = 290 + 0.1527(1/12,000) = 290 + 0.152(12,000) = 2114 m. This is the
   required elevation of L above sea level.

DETERMINING GROUND DISTANCE

BY VERTICAL PHOTOGRAPH

Two points A and B are located on the ground at elevations of 250 and 190 m, respective-
ly, above sea level. The images of A and B on a vertical aerial photograph are a and 6, re-
spectively. After correction for film shrinkage and lens distortion, the coordinates of a
and b in the photograph are xa - -73.91 mm, ya = +44.78 mm, xb = +84.30 mm, andyb =
-21.65 mm, where the subscript identifies the point. The focal length is 209.6 mm, and
the flying height is 2540 m above sea level. Determine the distance between A and B as
measured along the ground.

Calculation Procedure:

1. Determine the relationship between coordinates
   in the photograph and those in the datum plane
   Refer to Fig. 29, and let X and 7 denote coordinate axes that are vertically below the x and
   y axes, respectively, and in the datum plane. Omitting the subscript, we have x/X=y/Y=
   oalOA = S =fl(H- h), giving X = x(H- /*)//and Y = y(H- h)/f.


2. Compute the coordinates of A and B in the datum plane
   For A, H-h = 2540 - 250 = 2290 m. Substituting gives XA = (-0.07391)(2290)/0.2096 =
   -807.5 m and YA = (+0.04478)(2290)/0.2096 = + 489.2 m. For £,//-/* = 2540 - 190 =
   2350 m. Then XB = (+0.08430)(2350)/0.2096 = +945.2 m, and YB = (-0.02165)
   (2350)70.2096 =-242.7m.


3. Compute the required distance
   Let &X = XA — XB, A7 = YA — YB, and AB = distance between A and B as measured along
   the ground. Disregarding the difference in elevation of the two points, we have (AB)^2 =
   (kX)
   2

• (AT)
  2
  . Then AZ=-1752.7 m, A7= 731.9 m, and(AB)
  2
  = (1752.7)
  2


• (731.9)
  2
  , or
  AB= 1899m.

DETERMINING THE HEIGHT OF A

STRUCTURE BY VERTICAL PHOTOGRAPH

In Fig. 30, points A and B are located at the top and bottom, respectively, and on the verti-

cal centerline of a tower. These points have images a and b, respectively, on a vertical aer-

ial photograph having a scale of 1:10,800 with reference to the ground, which is approxi-

mately level. In the photograph, oa = 76.61 mm and ob = 71.68 mm. The focal length is

210.1 mm. Find the height of the tower.