usands of 
ld like to 
otography 
sults seem 
mmetry is 
lum errors 
its length. 
mation for 
ra stations 
varying in 
hough the 
rotational 
f the strip, 
/s of error 
wever, the 
onal para- 
w the un- 
mation of 
o informa- 
e result is 
om 5 to 23 
! a point in 
lines show 
nt situated 
nt that the 
rdinates is 
le summa- 
ied from a 
reating the 
rmore, the 
that only 
ent. There- 
ANALYTICAL AERIAL TRIANGULATION, DISCUSSION 23 
fore, the information represents, statistically 
speaking, the optimum result obtainable by the 
process of strip triangulation. 
  
  
  
  
  
  
  
  
A A 
A A 
A A 
A A 
Fig. 4 
It is now possible to study the question about 
an optimum flying height for bridging a certain 
distance between given control. In other words, 
90 | 
st=star , 
6Q. 
  
  
  
S03 70 UTOR EUST 
No of photographs in the strip 
Fig. 5 
it is possible to determine the optimum number 
of photographs in a strip. Fig. 3 shows the 
corresponding results. For the assumed 66% 
overlap, a minimum for the mean errors of both 
the X- and Z-coordinates is reached already 
after 7 or 8 photographs, while the correspond- 
ing minimum value for the Y-coordinate occurs 
after about 12 photographs. 
From these results one must conclude, that 
extended photogrammetric multi-station trian- 
gulations will not give satisfactory results if only 
the principle of relative orientation is employed. 
The optimum strip or block is shown in Fig. 4, 
indicating that the optimum flying height must 
be chosen in such a way that two or respectively 
four adjacent but not overlapping photographs 
cover the area between the given control data. 
In order to assure the usefulness of aerial 
110 
mmis Ku M^ 1078 ÿ 
ys m) 4 
100 I yl l= Ky HM 10 iV 
m, [ml=K, uM 107$ NÉ 
H=Mean square error of unit weight ^ 
90) in microns 4 : 
Mz X (scalefactor) X 4 
80| 
70] 
60 
50] 
4Q| 
  
30] 
2.0] 
  
  
T T TT T T T T T T T 
9 1 13 15 17 19 23 
No. of photographs in the strip 
Fig. 6 
triangulation for more extended strips or blocks, 
it is obviously necessary to incorporate such 
auxiliary data which will influence favorably the 
aforementioned double summation of errors in 
the translatory components. 
Fig. 5 shows the influence of additional 
celestial data. Assuming auxiliary star photog- 
raphy (9 evenly distributed stars) at each station, 
the error propagation curves indexed “st” were 
obtained, and correspondingly, the curves in- 
dexed by "s" were computed, assuming auxiliary 
sun photography at each station. The result 
shows that additional astronomical information 
helps considerably in reducing the mean errors 
of the Y- and Z-coordinátes, but cannot do any 
good with respect to scale, (X-coordinate). This 
obviously is explained by the fact that the sun 
and stars are essentially in infinity. 
Fig. 6 shows the error propagation, assuming