108 TECHNICAL SURVEY 
NTER OF ANTENNA 
ALTITUDE IN FEET 
MODIFIED EARTH'S SURFACE 
O) 20. 40 60 80 
APPROX LOBE BY 
EQ NO. 62 (n=1) 
DEGREES 
100 120 140 160 180 200 
DISTANCE IN MILES 
Fieure 55. Lobe and null lines. (Example 13.)_ 
in Table 8. The values selected for d; should be 
small enough so that the denominator of equation 
(69) is positive. 
These two curves are plotted in Figure 55. For 
comparison is shown the first lobe as computed from 
equation (62), and it can be seen that this equation 
may lead to appreciable error in estimating low 
coverage. For most’*purposes it will suffice to calcu- 
late lobes higher than the first one or two by means 
of equation (62). 
The Calcutation of Lobes 
Three methods of computing lobe angles were 
given corresponding to low, medium, and high sites, 
in order to relate the labor of the computations to 
the complexity of the problem. A similar procedure 
will be followed in the calculation of the lobe shapes. 
The lobe diagram represents the locus of all points 
along a particular azimuth of a definite field intensity, 
usually the threshold of detection. If the site has 
horizontal symmetry throughout its sector of opera- 
tion one diagram will suffice. Usually several dia- 
grams are required, and it is common practice to 
prepare a diagram for the central azimuth of the — 
sector and for 10 degrees inside of each limit of scan. 
Low Site Lobes 
The electric field intensity at the target is the 
resultant of the direct and reflected waves which 
have the same amplitude and a phase angle which 
varies continually as the lobe angle y is increased. 
For a perfect reflector and horizontal polarization 
the phase lag is equal to +2 + (2m/d) X (nd/2) 
which adds up to na + 7. Odd integral values of 
n give lobe maxima, and intermediate values give 
other points on the lobes. 
The sum of the two vectors practically parallel 
and of equal magnitude, F,/d, is 
E= ae cos [om + 1) 5| ; (72) 
where £; is the electric intensity (microvolts per 
meter) in the equatorial plane 1 mile from the 
antenna in free space, that is, without a reflecting 
surface. H is the electric intensity at the point 
eonsideredl in microvolts per meter. d is the distance 
to the point, in miles. m is a number related to the 
angle of elevation. It is an odd integer for lobe 
maximums and dn even integer for nulls. For a 
given antenna and radar the electric intensity H 
will produce at the input of the receiver a voltage, 
V2 = "1 sin (90°n) , (73) 
where k, is a proportionality factor for the voltage 
applied to the receiver input. If V2 is set equal to 
the minimum operating voltage of the receiver 
equation (73) becomes 
d= Leal sin (90°n) . 
Vain 
The term k,F,/V,,, is usually obtained from test 
flights on the particular radar or on radars of the 
same type. The usual form is 
d = dmax sin (90°n) , (74) 
where d,z,x stands for ki#,/V,, and is a measure 
of the performance of the radar set. 
The lobes will be polar sinusoids and the minima 
will go to zero only when the amplitude of the direct 
and indirect waves are equal. These conditions will 
not obtain if the vertical directivity of the antenna 
affects the rays unequally, if the reflected wave 
suffers imperfect reflection or divergence, or the 
atmosphere or terrain has unequal effects on the — 
