t = t'(cos a sin 8 -sin a cos 8 cos y) (50)- Find the true thickness, using Eq. 50
Thus, borehole through A: 8 = 49°; y = 180° - (58°30' + 61°22') = 60°08'; t' + 205 - 55
= 150 ft (45.7 m); t = 150(cos 52°13' sin 49° - sin 52°13' cos 49° cos 60°08') = 30.6 ft
(9.3 m). For the borehole through B: 8 = 73°; y = 61°22' - 44°50' = 16°32'; /' = 182 - 98
= 84 ft (25.6 m); t = 84(cos 52°13' sin 73° - sin 52°13' cos 73° cos 16°32') = 30.6 ft
(9.3 m). This agrees with the value previously computed.
Aerial PhotogrammetryFLYING HEIGHTREQUIRED TO YIELD
A GIVEN SCALE
At what altitude above sea level must an aircraft fly to obtain vertical photography having
an average scale of 1 cm = 120 m if the camera lens has a focal length of 152 mm and the
average elevation of the terrain to be surveyed is 290 m?
Calculation Procedure:
- Write the equation for the scale of a vertical photograph
In aerial photogrammetry, the term photograph generally refers to the positive photo-
graph, and the plane of this photograph is considered to lie on the object side of the lens.
A photograph is said to be vertical if the optical axis of the lens is in a vertical position at
the instant of exposure. Since the plane of the photograph is normal to the optical axis,
this plane is horizontal.
In Fig. 29a, point L is the front nodal point of the lens; a ray of light directed at this
point leaves the lens without undergoing a change in direction. The point o at which the
optical axis intersects the plane of the photograph is called the principal point. The dis-
tance from the ground to the camera may be considered infinite in relation to the dimen-
sions of the lens, and so the distance Lo is equal to the focal length of the lens. The air-
craft is assumed to be moving in a horizontal straight line, termed the line of flight, and
the elevation of L above the horizontal datum plane is called the flying height. The posi-
tion of L in space at the instant of exposure is called the exposure station. Where the area
to be surveyed is relatively small, the curvature of the earth may be disregarded.
Since the plane of the photograph is horizontal, Fig. 296 is a view normal to this plane
and so presents all distances in this plane in their true magnitude. In the photograph, the
origin of coordinates is placed at o. The jc axis is placed parallel to the line of flight, with
jc values increasing in the direction of flight, and the y axis is placed normal to the x axis.
In Fig. 29, A is a point on the ground, a is the image of A on the photograph, and O is
a point at the same elevation as A that lies on the prolongation of Lo. Thus, o is the image
of a
The scale of a photograph, expressed as a fraction, is the ratio of a distance in the