Airborne antenna ground projection
A method and computer for determining a ground coverage footprint of a beam of an antenna mounted above the ground are disclosed. A method includes determining the far projection distance based at least in part on beam width and tilt angle, the far projection distance being a lesser of: a first distance from the antenna to the ground of a 3 dB far projection; two times a second distance from the antenna to the ground of a 3 dB near projection; and a third distance from the antenna to the ground of a projection of the maximum antenna gain multiplied by the square root of two. A ground footprint of the beam is determined based at least in part on the determined far projection distance. The method further includes causing the antenna to be pointed based at least in part on the determined ground footprint of the beam of the antenna.
1. A method for determining a far projection distance of a beam of an antenna on an airborne station, the antenna projecting the beam downward toward the ground at an angle of declination, the method comprising:
determining the far projection distance based at least in part on a width of the beam and the angle of declination, the far projection distance being a lesser of:
a first distance from the antenna to the ground of a 3dB far projection;
two times a second distance from the antenna to the ground of a 3dB near projection; and
a third distance from the antenna to the ground of a projection of the maximum antenna gain multiplied by the square root of two;
determining a ground footprint of the beam of the antenna based at least in part on the determined far projection distance; and
causing the antenna to be pointed based at least in part on the determined ground footprint of the beam of the antenna.
2. The method of claim 1 , wherein the far projection distance corresponds to a far projection angle that is based at least in part on the beam width and the angle of declination of the antenna.
3. The method of claim 1 , wherein the first distance is given by
Rf
=
A
sin
(
θ
-
Φ
)
;
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
4. The method of claim 3 , wherein an angle, α, of the far projection distance is based at least in part on at least one of the angle of declination, θ, and the angle ϕ.
5. The method of claim 4 wherein the angle α is selected from a lookup table based at least in part on at least the angle of declination, θ, and the beam width.
6. The method of claim 1 , wherein the second distance is given by
Rn
=
A
sin
(
θ
+
Φ
)
;
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
7. The method of claim 1 , wherein the third distance is given by
Rc
=
A
sin
(
θ
)
,
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
8. A computer for determining a far projection distance of a beam of an antenna on an airborne station, the antenna projecting the beam downward toward the ground at an angle of declination, the computer configured to:
determine the far projection distance, based at least in part on a width of the beam and the angle of declination, the far projection distance being a lesser of:
a first distance from the antenna to the ground of a 3 dB far projection;
two times a second distance from the antenna to the ground of a 3 dB near projection; and
a third distance from the antenna to the ground of a projection of the maximum antenna gain multiplied by the square root of two;
determine a ground footprint of the beam of the antenna based at least in part on the determined far projection distance; and
cause the antenna to be pointed based at least in part on the determined ground footprint of the beam of the antenna.
9. The computer of claim 8 , wherein the far projection distance corresponds to a far projection angle that is based at least in part on the beam width and the angle of declination of the antenna.
10. The computer of claim 8 , wherein the first distance is given by
Rf
=
A
sin
(
θ
-
Φ
)
;
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
11. The computer of claim 10 , wherein an angle, α, of the far projection distance is based at least in part on at least one of the angle of declination, θ, and the angle ϕ.
12. The computer of claim 11 wherein the angle a is selected from a lookup table based at least in part on at least the angle of declination, θ, and the beam width.
13. The computer of claim 8 , wherein the second distance is given by
Rn
=
A
sin
(
θ
+
Φ
)
;
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
14. The computer of claim 8 , wherein the third distance is given by
Rc
=
A
sin
(
θ
)
,
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
15. A method for determining a ground coverage footprint of a beam of an antenna mounted above the ground and projecting the beam downward toward the ground at an angle of declination, the method comprising:
receiving a beam width and the angle of declination of the antenna; and
determining a far projection distance based at least in part on the beam width and the angle of declination, the far projection distance defining the ground coverage footprint of the beam, the far projection distance being a lesser of:
a first distance to the ground from the antenna, the first distance corresponding to a −3 dB far projection;
twice a second distance to the ground from the antenna, the second distance corresponding to a −3 dB near projection; and
a third distance to the ground of a projection of a maximum antenna gain multiplied by the square root of two;
determining a ground footprint of the beam of the antenna based at least in part on the determined far projection distance; and
causing the antenna to be pointed based at least in part on the determined ground footprint of the beam of the antenna.
16. The method of claim 15 , wherein:
the first distance is given by
Rf
=
A
sin
(
θ
-
Φ
)
;
the second distance is given by
Rn
=
A
sin
(
θ
+
Φ
)
;
and
the third distance is given by
Rc
=
A
sin
(
θ
)
,
where A is a height of the antenna above the ground, θ is the angle of declination, and ϕ is an angle between the projection of the maximum antenna gain and the −3 dB near projection.
17. The method of claim 16 , wherein an angle, α, of the far projection distance is determined based at least in part on at least one of the angle of declination, θ, and the angle ϕ.
18. The method of claim 17 wherein the angle α is selected from a lookup table based at least in part on at least the angle of declination, θ, and the beam width.
19. The method of claim 18 , wherein the lookup table selection is further based at least in part on angle ϕ.
20. The method of claim 16 , wherein an angle α of the far projection distance is given by one of the following:
IF 0>=θ<= A TAN[(√2−cos Φ)/sin Φ)]
THEN α= A SIN[sin(θ+Φ)/2];
IF A TAN[(√/2−cos Φ)/sin Φ)]>θ<= A TAN[sin Φ/(1/√2−cos Φ)]
THEN α= A SIN[sin(θ)/√2]; and
IF A TAN[sin Φ/(1/√2−cos Φ)]>θ<=90
THEN α= A SIN[sin(θ−Φ)].