ANGLE-OF-ARRIVAL MEASUREMENTS 321 
NEW YORK GITY 
140 WEST ST 
TRANSMITTER 492' 
STATEN 
tSLAND 
BEER'S HILL 
RECEIVER 353° 
DEAL 
TRANSMITTER 210° 
400° TOWER TR -28 
BASE 128" ABOVE 
SEA LEVEL 
Fictre 5. Plan view of propagation paths. 
FREEHOLD 
between approximately 11 ft above the transmitter and 
225 ft below the receiver. 
The Angle of Arrival Deduced from 
Type Cases of Atmospheric Stratification 
When the path is confined to a layer between receiver 
and transmitter, there are two limiting paths, as illus- 
trated in Figure 6A: Path A leaving the transmitter 
at some angle 8 < 0 and arriving at the receiver with 
% = 0; Path B leaving the transmitter at an angie 
8 = 0 and arriving at the receiver with « > 0. By 
applying the equations deduced from theory and ex- 
pressed by data in Table 1, the necessary and sufficient 
Tass 1 
Deviation 
a at B at of a and B 
receiver transmitter from true 
Path (degrees) (degrees) bearing m 
A 0 — 0.125 + 0.111 0.64 
Intervening path + 0.0625 — 0.0625 + 0.17385 1.00 
B + 0.125 0 + 0.236 1.36 
modified refractive index distributions with height in 
the layer can be evaluated for the limiting paths A 
and B and for all intervening paths. Table 2 shows the 
value of the stratification parameter m required. We 
therefore conclude that, for a path confined to the 
layer between transmitter and receiver, the deviation 
from true bearing must be confined to the interval 
-|-0.111 to -++-0.236°, and the change in the modified 
refractive index between receiver and transmitter 
must be in range —2.4 to +2.4 M units. These 
limits hold for an approximately linear variation of 
index between receiver and transmitter. 
Radiation along paths of type C, which penetrates 
the layer below the receiver height (see Figure 6B), 
arrives at the receiver at an angle ~ < 0; therefore, M 
will of necessity increase by more than 2.4 units from 
receiver to transmitter. We consider three stratifica- 
tions producing paths of this category. 
1. The so-called “standard” atmosphere utilized 
for the purposes of representing “normal” propagation 
by rectilinear rays on an earth distorted to a radius 
4/3 that of the true earth. The increase of M is at a 
rate of 3.6 units per 100 ft. 
2. Adiabatic equilibrium for an unsaturated at- 
mospheric layer, representing the condition of a com- 
pletely stirred or mixed stratum of air. The increase 
of M is 4.0 units per 100 ft. 
3. Rectilinear propagation on a true earth. For this 
condition there is no variation of electromagnetic 
velocity with height, and M increases by 4.76 units 
per 100 ft, equal to the rate of curvature of the earth. 
The computed deviations of the angles % and B at 
the receiver and transmitter, respectively, are given in 
Table 2. It will be noted that the condition of recti- 
linear propagation on a true earth produces an angle 
HORIZONTAL PLANE a a che) 
¢ 
Cc 
XMTR 
RGVR 
EARTH 
SINGLE DIRECT PATH 
Figure 6. Types of vertical variation in ray paths. 
