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Li = Intermediate Latitude l i = Intermediate Longitude
Hi = Initial True Heading D = Distance
H = Heading Angle Dt = Time between positions
GS = Groundspeed TC = True Course
Distance=60 * acos ((sin (Departure Latitude) * sin (Destination Latitude))+(cos (Departure Latitude) *
cos (Destination Latitude) * cos (Destination Longitude – Departure Longitude) ))
or Heading Angle = acos ((sin (Destination Latitude) – sin (Departure Latitude) * cos (Distance /60) ) /
(sin (Distance /60) * cos (Departure Latitude)))
Hi = H sin (l 2 – l 1 ) < 0
Hi = 360–H sin (l 2 – l 1 ) > 0
This formula computes the latitude of Li where l i intersects the great circle defined by (L1, l 1) and (L2,
l 2). This formula can be very useful when matching charts of different projections or scales.
or Intermediate Latitude = atan ( ( tan (Destination Latitude) * sin (Intermediate Longitude –
Departure Longitude) – tan (Departure Latitude) *
Sin (Intermediate Longitude – Destination Longitude)) /
Sin (Destination Longitude – Departure Longitude) )
A2.9. Computing Position By Dead Reckoning:
or DEST Latitude = (Elapsed Time * Ground Speed * cos (True Course) ) / 60 + Departure Latitude
396 AFPAM11-216 1 MARCH 2001
TC=90°, 270°
or DEST Longitude = Departure Longitude – ( (Elapsed Time * Ground Speed * sin (True Course) ) /
(60 * cos (Departure Latitude) ) )
Otherwise:
or DR Longitude = Departure Longitude – (180 / 3.14159) * (tan (True Course) *
Ln (tan (45 + 0.5 * Destination Latitude)) – Ln (tan (45 + 0.5 * Departure Latitude) )
NOTE: The flight path may not cross either pole.
For long distances, use formula below:
DR Latitude = 90.0 – acos (sin ( – Departure Latitude) * cos (Distance/60.0) +
cos ( – Departure Latitude) * sin (Distance /60.0) * cos (True Course))
DR Longitude = Departure Longitude +/– acos ( (cos (Distance /60.0 ) –sin ( – DR Latitude) *
sin ( – Departure Latitude)) / (cos ( – DR Latitude) * cos ( – Departure Latitude)))
NOTE: Distance can be replaced with (Ground Speed * Elapsed Time) where Elapsed Time is in hours
A2.10. Rhumb Line Planning:
Variables:
D t = Time between positions
C = Rhumb line True Course
D = Rhumb line Distance
p = Pi (»3.14159)
or True Course = atan( ( 3.14159 * (Departure Longitude – Destination Longitude) ) /
(180 * Ln (tan (45 + 0.5 * Destination Latitude))
– Ln (tan(45 + 0.5 * Departure Latitude) ) )
C = 0
or Distance = 60 * (Destination Longitude – Departure Longitude) * cos (Departure Latitude)
or Distance = 60 * (Destination Latitude – Departure Latitude) * cos (Rhumb line True Course)
AFPAM11-216 1 MARCH 2001 397
A2.11. Course Correction to Destination:
Variables:
M1 = Intended magnetic course M2 = Magnetic course flown to current position
D1 = Distance flown to current position D2 = Distance from start to destination
M3 = Magnetic course to fly from current
position to destination
DOC = Distance off course (+ left, – right)
D3 = Distance from start to checkpoint D4 = Distance from current position to destination
or Intended Magnetic Course = Current Magnetic Course +
atan (Distance Off Course/Leg Distance To Checkpoint)
Required Magnetic Course = Intended Magnetic Course + asin (Distance Off Course/Distance To Go)
or Distance To Checkpoint = sq rt (Distance Flown^2 – Distance Off Course^2)
or Distance To Go = sq rt ( (Total Distance – Distance Flown)^2 + Distance Off Course^2 )
A2.12. Point to Point:
Variables:
D1 = DME #1 D2 = DME #2
R1 = Radial #1 R2 = Radial #2
HA = Altitude MSL HT = Elevation of the TACAN
T = Time between positions A = Altitude above TACAN (in NM)
GS = Groundspeed MC = Magnetic Course
NOTE: These formulas are useful when flying from one radial and DME to another.
398 AFPAM11-216 1 MARCH 2001
or Ground Speed = sq rt ( FirstDME^2 + SecondDME^2 – 2 * ( ( (Aircraft Altitude MSL –
Target Altitude MSL) / 6076) ^2 ) – 2 * sq rt ( First DME^2 – ( ( (Aircraft Altitude MSL –
Target Altitude MSL) / 6076) ^2 ) ) * sq rt ( Second DME^2 – ( ( (Aircraft Altitude MSL –
Target Altitude MSL) / 6076) ^2 ) ) * cos ( First Radial – Second Radial) ) / Elapsed Time
NOTE: If you do not divide by Elapsed Time, the result is Distance instead of Ground Speed
or Magnetic Course Flown = Second Radial – asin ( ( First DME * sin (First Radial – Second Radial) ) /
(Ground Speed * Elapsed Time) )
NOTES:
1. This assumes that the magnetic variation of the TACAN is the same as the one affecting the aircraft
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