§  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:
   [MATH:  :MATH]

   The slant distance, D , is given by:
   [MATH:  :MATH]

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

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

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

   Where:

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

   Where:

   a Tis the geographic latitude of the transmitting terminal (degrees)

   a Ris the geographic latitude of the receiving terminal (degrees)

   b Tis the geographic longitude of the transmitting terminal (degrees)

   b Ris the geographic longitude of the receiving terminal (degrees)

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

   b Mis the geographic longitude of the midpoint of the great-circle path
   (degrees) and is given by:
   [MATH:  :MATH]
   [MATH:  :MATH]

   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 | F[M]| < 40

   Δ = 0.2 | F[M]| − 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:
   [MATH:  :MATH]

   Where:

   d=distance in kilometers

   n=1 for 50% field strength values

   n=2 or 3 for 10% field strength values

   and where

   K[1]=0.00752

   K[2]=0.00938

   K[3]=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]

Subpart B—FM Broadcast Stations