<s>
A	O
cosecant	B-Algorithm
squared	I-Algorithm
antenna	I-Algorithm
,	O
sometimes	O
known	O
as	O
a	O
constant	O
height	O
pattern	O
,	O
is	O
a	O
modified	O
form	O
of	O
parabolic	O
reflector	O
used	O
in	O
some	O
radar	B-Application
systems	I-Application
.	O
</s>
<s>
It	O
is	O
shaped	O
to	O
send	O
more	O
radio	O
energy	O
in	O
certain	O
directions	O
in	O
order	O
to	O
smooth	O
out	O
the	O
reception	O
pattern	O
of	O
objects	O
as	O
their	O
range	O
changes	O
in	O
relation	O
to	O
the	O
radar	B-Application
.	O
</s>
<s>
The	O
name	O
refers	O
to	O
the	O
fact	O
that	O
the	O
amount	O
of	O
energy	O
returned	O
from	O
a	O
target	O
drops	O
off	O
with	O
the	O
square	O
of	O
the	O
cosecant	O
of	O
the	O
angle	O
between	O
the	O
radar	B-Application
and	O
the	O
target	O
.	O
</s>
<s>
The	O
concept	O
originated	O
as	O
part	O
of	O
the	O
development	O
of	O
the	O
H2S	O
radar	B-Application
,	O
which	O
scanned	O
the	O
area	O
under	O
an	O
aircraft	O
to	O
provide	O
a	O
radar	B-Application
map	O
of	O
the	O
ground	O
below	O
.	O
</s>
<s>
The	O
terrain	O
at	O
further	O
distances	O
returns	O
much	O
less	O
signal	O
due	O
to	O
the	O
radar	B-Application
equation	O
.	O
</s>
<s>
The	O
slant	O
range	O
distance	O
between	O
the	O
radar	B-Application
and	O
the	O
terrain	O
is	O
the	O
cosecant	O
of	O
the	O
angle	O
between	O
the	O
fuselage	O
and	O
the	O
target	O
,	O
and	O
the	O
energy	O
falls	O
off	O
with	O
the	O
fourth	O
root	O
of	O
that	O
number	O
.	O
</s>
<s>
Without	O
correction	O
,	O
this	O
produced	O
a	O
display	O
where	O
the	O
ground	O
under	O
the	O
aircraft	O
was	O
very	O
bright	O
on	O
the	O
cathode	B-Device
ray	I-Device
tube	I-Device
display	I-Device
,	O
while	O
the	O
terrain	O
at	O
longer	O
distances	O
was	O
almost	O
invisible	O
.	O
</s>
<s>
To	O
counteract	O
this	O
,	O
the	O
scanning	O
antenna	O
was	O
re-aimed	O
so	O
that	O
it	O
was	O
pointed	O
almost	O
directly	O
forward	O
,	O
thereby	O
sending	O
most	O
of	O
the	O
radar	B-Application
energy	O
at	O
low	O
angles	O
relative	O
to	O
the	O
aircraft	O
,	O
thereby	O
increasing	O
the	O
energy	O
available	O
at	O
long	O
range	O
.	O
</s>
<s>
For	O
ground-based	O
radars	B-Application
,	O
the	O
same	O
modification	O
could	O
be	O
used	O
to	O
provide	O
scanning	O
at	O
high	O
angles	O
above	O
the	O
station	O
while	O
still	O
sending	O
most	O
of	O
the	O
energy	O
towards	O
low	O
angles	O
to	O
detect	O
aircraft	O
at	O
long	O
range	O
as	O
they	O
rose	O
above	O
the	O
radar	B-Algorithm
horizon	I-Algorithm
.	O
</s>
<s>
The	O
radar	B-Application
equation	O
states	O
that	O
the	O
signal	O
received	O
from	O
an	O
object	O
,	O
Pe	O
,	O
varies	O
inversely	O
with	O
the	O
4th	O
power	O
of	O
range	O
and	O
directly	O
as	O
the	O
square	O
of	O
the	O
antenna	O
gain	O
,	O
G	O
,	O
such	O
that	O
.	O
</s>
<s>
Since	O
the	O
constant	O
signal	O
is	O
desired	O
for	O
objects	O
at	O
a	O
constant	O
h	O
,	O
say	O
the	O
altitude	O
of	O
the	O
ground	O
scanning	O
aircraft	O
,	O
or	O
a	O
ground	O
radar	B-Application
watching	O
an	O
aircraft	O
at	O
constant	O
altitude	O
,	O
then	O
we	O
can	O
eliminate	O
h	O
as	O
well	O
,	O
leaving	O
,	O
the	O
cosecant	O
squared	O
relationship	O
.	O
</s>
