Calculate for a set of beam elevations elev the altitudinal normalized distribution of radiated energy by those beams.

```
beam_profile(
height,
distance,
elev,
antenna = 0,
beam_angle = 1,
k = 4/3,
lat = 35,
re = 6378,
rp = 6357
)
```

- height
numeric. Height in meter.

- distance
numeric. Distance from the radar as measured along sea level (down range) in m.

- elev
numeric vector. Beam elevation(s) in degrees.

- antenna
numeric. Height of the center of the radar antenna in meters

- beam_angle
numeric. Beam opening angle in degrees, typically the angle between the half-power (-3 dB) points of the main lobe

- k
Standard refraction coefficient.

- lat
Geodetic latitude of the radar in degrees.

- re
Earth equatorial radius in km.

- rp
Earth polar radius in km.

numeric vector. Normalized radiated energy at each of the specified heights.

Beam profile is calculated using beam_height and beam_width. Returns a beam profile as a function of height relative to ground level.

Returns the normalized altitudinal pattern of radiated energy as a function of altitude at a given distance from the radar, assuming the beams are emitted at antenna level.

```
# plot the beam profile, for a 0.5 degree elevation beam at 50 km distance from the radar:
plot(beam_profile(height = 0:4000, 50000, 0.5), 0:4000,
xlab = "normalized radiated energy",
ylab = "height [m]", main = "beam elevation: 0.5 deg, distance=50km"
)
# plot the beam profile, for a 2 degree elevation beam at 50 km distance from the radar:
plot(beam_profile(height = 0:4000, 50000, 2), 0:4000,
xlab = "normalized radiated energy",
ylab = "height [m]", main = "beam elevation: 2 deg, distance=50km"
)
# plot the combined beam profile for a 0.5 and 2.0 degree elevation beam
# at 50 km distance from the radar:
plot(beam_profile(height = 0:4000, 50000, c(0.5, 2)), 0:4000,
xlab = "normalized radiated energy",
ylab = "height [m]", main = "beam elevations: 0.5,2 deg, distance=50km"
)
```