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e-CFR data is current as of September 24, 2020

Title 47Chapter ISubchapter CPart 73Subpart A → §73.190


Title 47: Telecommunication
PART 73—RADIO BROADCAST SERVICES
Subpart A—AM Broadcast Stations


§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, Fc(50), for a characteristic field strength of 100 mV/m at 1 km is given by:

eCFR graphic ec01mr91.068.gif

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The slant distance, D, is given by:

eCFR graphic ec13no91.020.gif

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

ΦM = arcsin[sin aM sin 78.5° + cos aM cos 78.5° cos(69 + bM)]degrees                        (Eq. 3)

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

eCFR graphic ec13no91.021.gif

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Where:

d° = arccos[sin aT sin aR + cos aT cos aR cos(bRbT)]degrees                              (Eq.5)

Where:

aT is the geographic latitude of the transmitting terminal (degrees)

aR is the geographic latitude of the receiving terminal (degrees)

bT is the geographic longitude of the transmitting terminal (degrees)

bR is the geographic longitude of the receiving terminal (degrees)

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

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

eCFR graphic ec01mr91.069.gif

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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., bR >bT), 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, Fc(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:

eCFR graphic ec01mr91.071.gif

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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

Note: Computations using these formulas should not be carried beyond 0.1 degree.

(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.

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[28 FR 13574, Dec. 14, 1963, as amended at 30 FR 12720, Oct. 6, 1965; 33 FR 15420, Oct. 17, 1968; 48 FR 42959, Sept. 20, 1983; 49 FR 43963, Nov. 1, 1984; 50 FR 18844, May 2, 1985; 51 FR 4753, Feb. 7, 1986; 52 FR 36879, Oct. 1, 1987; 56 FR 64869, Dec. 12, 1991]

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