Practical_Antenna_Handbook_0071639586

C h a p t e r 2 : r a d i o - W a v e P r o p a g a t i o n 33
index of refraction n measures the differential properties between adjacent zones in the
atmosphere.
The K factor, also called the effective earth’s radius factor, is determined by the relationship
of two hypothetical concentric spheres, both centered on the earth’s center. The
first sphere is an idealization of the earth’s surface, which has a nominal radius r o = 3440
nautical miles (nmi) or 6370 km. The second sphere is larger than the first by the curvature
of the signal ray path, and has a radius r. The value of K is then approximately
r
K =
r
O
(2.18)
A value of K = 1 indicates a straight path (Fig. 2.15); a value of K > 1 indicates a
positively curved path (refraction); and a value of K < 1 indicates a negatively curved
path (subrefraction). The actual value of K varies with local weather conditions, so one
can expect variation not only between locations but also seasonally. In the Arctic regions,
K varies approximately over the range 1.2 to 1.34. In the “lower 48” of the United
States, K varies from 1.25 to 1.9 during the summer months (especially in the south and
southeast), and from 1.25 to 1.45 in the winter months.
The index of refraction n can be defined in either of two ways, depending on the
situation. When a signal passes across boundaries between adjacent regions of distinctly
different properties (as occurs during temperature inversions, for instance), the
index of refraction is the ratio of the signal velocities in the two regions. In a homogeneous
region n can be expressed as the ratio of the free-space velocity c to the actual
velocity u in the atmosphere:
c
n = (2.19)
v
At the surface, near sea level, under standard temperature and pressure conditions,
the value of n is approximately 1.0003, and in homogeneous atmospheres it will decrease
by 4 × 10 –8 per mile of altitude. The units of n are a bit cumbersome in equations,
Figure 2.15 Refraction changes path length.