TE == ee — — ————————=
From Fig. 12 we see that for all points outside the effective atmosphere, vef:
the refraction as encountered by an observer on the ground and in the air for P Witt
a specific ray add up to astronomical refraction.
This fact is illustrated in Fig. 11 where, as example, for an elevation
and depression angle of 30°, the sums of the ordinates of the solid and dotted
lines have been plotted for altitudes outside of the effective atmosphere, The
resulting line, designated "astronomical refraction for 50°", agrees with the
corresponding value of 99" in Table No. l fore = 30° and H =.
For precision triangulation of points within the atmosphere, especially if
large distances between observer and target are encountered as in guided missile
applications, the numerical integration by formula (94) based on an index of
refraction profile will be unavoidable. For many cases, however, especially in
aerial photogrammetry, an expression for the refraction can be used which avoids
the cumbersome numerical integration.
Assuming a constant atmospheric temperature gradient, refraction ex-
pressions were derived in[ 9] for both an observer on the ground and in the air,
However, these formulas are restricted to a situation where one of the end
points of the light curve is situated at the height of the ellipsoid of refer-
ence. Moreover, the expressions obtained in[ 9] are unnecessarily complicated
for numerical evaluation. In the following a derivation is given which, follow-
ing the general approach of [9] , overcomes the above mentioned restriction and
results in expressions more suited for numerical evaluation. .
From the well known pressure altitude relationship it follows that for a
linear ‘decrease of temperature with altitude,
X. A) "+ 3
3 7) where a ap and T Ta + 1H (101)
o o
R is the gas constant for air, T absolute temperature
and L = = the temperature gradient,
Similarly well-known is the density - altitude - pressure relationship.
T a-l
£ = REoa- Gp (102)
Po Po Oo
FH
64,
