47 CFR 73.190 : Telecommunication (§ 0.1 To Parts 401-499) — (Parts 70-72 To § 79.110) — Federal Communications Commission (Continued) (Parts 70-72 To § 79.110) — Broadcast Radio Services (Parts 70-72 To § 79.110) — Radio Broadcast Services (§ 73.1 To § 73.8000) — Am Broadcast Stations (§ 73.1 To § 73.190) — Engineering charts and related formulas.

(a) This section consists of the following Figures: 2, r3, 5, 6a, 7, 8, 9, 10, 11, 12, and 13. Additionally, formulas that are directly related to graphs are included.

(b) Formula 1 is used for calculation of 50% skywave field strength values.

Formula 1. Skywave field strength, 50% of the time (at SS + 6):

The skywave field strength, F c(50), for a characteristic field strength of 100 mV/m at 1 km is given by:

The slant distance, D, is given by:

The geomagnetic latitude of the midpoint of the path, ΦM, is given by:

ΦM = arcsin[sin a M sin 78.5° + cos a M cos 78.5° cos(69 + b M)]degrees (Eq. 3)

The short great-circle path distance, d, is given by:

• Where:

d° = arccos[sin a T sin a R + cos a T cos a R cos(b R − b T)]degrees (Eq.5)

• Where:

a T is the geographic latitude of the transmitting terminal (degrees)

a R is the geographic latitude of the receiving terminal (degrees)

b T is the geographic longitude of the transmitting terminal (degrees)

b R is the geographic longitude of the receiving terminal (degrees)

a M is the geographic latitude of the midpoint of the great-circle path (degrees) and is given by:

b M is the geographic longitude of the midpoint of the great-circle path (degrees) and is given by:

Note (1): If |FM| is greater than 60 degrees, equation (1) is evaluated for | FM| = 60 degrees.

Note (2): North and east are considered positive; south and west negative.

Note (3): In equation (7), k = −1 for west to east paths (i.e., b R >b T), otherwise k = 1.

(c) Formula 2 is used for calculation of 10% skywave field strength values.

Formula 2. Skywave field strength, 10% of the time (at SS + 6):

The skywave field strength, F c(10), is given by:

Fc(10) = Fc(50) + Δ dB(µV/m)

• Where:

Δ = 6 when | FM| <40

Δ = 0.2 | FM| − 2 when 40 ≤| FM| ≤60

Δ = 10 when | FM| >60

(d) Figure 6a depicts angles of departure versus transmission range. These angles may also be computed using the following formulas:

• Where:

d = distance in kilometers

n = 1 for 50% field strength values

n = 2 or 3 for 10% field strength values

and where

K1 = 0.00752

K2 = 0.00938

K3 = 0.00565

(e) In the event of disagreement between computed values using the formulas shown above and values obtained directly from the figures, the computed values will control.