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below the celestial horizon.
Astronomical Twilight—That period which ends in the evening and begins in the morning when
the sun reaches 18° below the horizon.
Civil Twilight—That period which ends in the evening and begins in the morning when the sun
reaches 6° below the horizon.
Nautical Twilight—That period which ends in the evening and begins in the morning when the sun
reaches 12° below the horizon.
Variable Range Marker (VRM)—An electronic marker, variable in range, displayed on a CRT for
purposes of accurate ranging.
Variation (var)—The angle difference at a given point between true north and magnetic north,
expressed as the number of degrees which magnetic north is displaced east or west from true north. The
angle to be added to true directions to obtain magnetic directions.
Wind—Moving air, especially a mass of air having a common direction or motion. The term is
generally limited to air moving horizontally or nearly so; vertical streams of air are usually called
currents.
Wind Direction and Velocity—The horizontal direction and speed of air motion. Windspeed is
generally expressed in nautical miles or statue miles per hour.
Zenith—The point on the celestial sphere directly above the observer's position.
Zenith Distance (ZD)—Angular distance on the celestial sphere measured along the great circle from
the zenith to the celestial object. Zenith distance is 90° minus celestial altitude.
ZN (Pressure Pattern Displacement)—In pressure pattern flying, the displacement in nautical miles, at
right angles to the effective airpath, due to the crosswind component of the geostrophic wind.
390 AFPAM11-216 1 MARCH 2001
Attachment 2
MATHEMATICAL FORMULAS
A2.1. Computers. Technological advances have made programmable handheld computers readily
available at a reasonable cost. A variety of computers are acceptable for use in flight. Using the formulas
in this chapter, the navigator increases calculating power for both preflight and in-flight situations. In
addition to ease of operation, both speed and accuracy will improve significantly over manual and MB–
4 computations. Also, the new handheld computers have capabilities never before available without
expensive avionics. Use the following formulas as an aid in both preflight and in-flight computations.
NOTES:
1. All formulas are valid when trigonometric functions compute in degrees (not radians).
2. Unless otherwise indicated, velocities are in knots, temperatures are in degrees Celsius, and directions
and angles are in degrees.
3. North, West, and Left are represented by positive values while South, East, and Right are represented
by negative values.
4. "Sq rt" denotes the Square Root function; "sin," "cos," "tan," "asin," "acos," "atan" are the standard
trigonometric functions; and the "^" symbol represents the "power of" function.
A2.2. Flight Planning:
Variables:
TC = True Course TH = True Heading
TAS = True Airspeed GS = Groundspeed
W = Wind Direction V = Wind Velocity
DCA = Drift Correction Angle VAR = Variation
TW = Tailwind Component CW = Crosswind Component
or Drift Angle = asin ((Wind Speed / True Air Speed) * sin (Wind Direction – True Course))
or Ground Speed = sin (Wind Direction + 360 – True Course – Drift Angle) * True Air Speed /
sin (True Course – Wind Direction – 180 )
or Ground Speed = True Air Speed * cos (Drift Angle) – Wind Speed * cos (Wind Direction – True
Course)
GS = TAS cos (TH – TC) – V cos (W – TC)
or Ground Speed = True Air Speed * cos (True Heading – True Course) – Wind Speed *
cos (Wind Direction – True Course)
AFPAM11-216 1 MARCH 2001 391
TW = V cos (W – TH)
or Tailwind Component = Wind Speed * cos (Wind Direction – True Heading)
CW = V sin (W – TH)
or Crosswind Component = Wind Speed * sin (Wind Direction – True Heading)
A2.3. In-flight Wind Determination:
Variables:
TC = True Course GS = Groundspeed
TAS = True Airspeed TH = True Heading
D = Drift Angle DCA = Drift Correction Angle = –D
or Wind Speed = sq rt (Ground Speed^2 + True Air Speed^2 – 2 * Ground Speed * True Air Speed *
cos (Drift Correction Angle) )
TAS > GS
or Wind Direction = True Course + asin (True Air Speed * sin (Drift) / Wind Speed )
TAS < GS
or Wind Direction = True Course – asin (True Air Speed * sin (Drift) / Wind Speed ) + 180
A2.4. Pressure Pattern:
Variables:
K = Constant ML = Mid Latitude between DRs
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