d from a study of the 
cal aerial photographs 
em because of a distrust 
nt of tilt may so affect 
he tilt present in most 
cordingly, dip calcula- 
y vertical will not be 
raphy are expected to 
precise dip calculations 
described in sufficient 
raphs can calculate the 
grammetric experience. 
ons on vertical aerial 
or a bedding trace on 
a dip slope or bedding 
g trace) are terms used 
o be on the line of dip 
le of dip slopes is the 
and bedding plane are 
be covered with talus, 
"lying strata. Although 
s generally small if the 
eometry of the camera 
cry of the airplane and 
the scale of the photo- 
und, nor the absolute 
1e absolute elevation of 
nerally is not available. 
ch have been corrected 
the camera lens, and a 
) points on the ground; 
otograph. All measure- 
fied in millimeters for 
; of the University of 
ped. Grateful acknow- 
pleum Corporation for 
ng this paper, and for 
ent of the transparent 
> at the University of 
ginal manuscript. 
(513) 
II. Basic photogrammetric theory and considerations. 
A. Preliminary Considerations. 
In all calculations, photogrammetric definitions, and geometrical relation- 
ships in this paper, an absence of tilt is assumed as is the constant altitude 
of the airplane. Vertical aerial photographs flown by present-day standards 
are taken from nearly the same altitudes, and generally with but a small tilt. 
If precise photogrammetric dip calculations are required, the photograph may 
be rectified for tilt. With only three horizontal and vertical control points 
optimumly located on a stereo pair, tilt and the difference in altitude (which 
is directly related to scale) can be corrected by procedures of Anderson). 
However, to make approximately correct dip calculations, aerial photographs 
are considered truly vertical and taken from the same altitude. 
B. Geometrical Relationships. 
The fundamental equation upon which all calculations in this paper are 
based, is as follows: 
uius dp dh dH 
cod qu Em 
(Equation I) 
This equation is derived in part from similar triangles shown on figures 1 
and 2. On figure 1 from similar triangles (jkc: and kui:us), the following 
relationship is obtained: 
uj Ua ui us dp 
bh au bd 
  
Equation I is also derived in part from figure 2 from one set similar 
triangles (lens Cr, U1:) and (U5UsU1) which can be shown by construction to 
be similar to another set of similar triangles (lens ci ui) and (us us ui) as shown 
by the following relationships: 
ui us Us, Us dh dH 
au Egy Te phere 
C. Measurement of Difference in Height (dh). 
Both the difference in height between u and | (in the geometry of the 
photograph) and the adjusted horizontal distance between them are necessary 
to solve for the angle of dip trigonometrically. This distance (dh) is a theoreti- 
cal vertical distance which cannot be identified anywhere on the aerial photo- 
graphs. However, its relationship to the photo points and ground points 1s 
shown in equation I. 
1) Anderson, R. O., Applied photogrammetry, 4th ed., Ann Arbor, Edwards Brothers, 1946.