Track represents the state of a vehicle by its current position, bearing and speed.

Course represents the cardinal direction in which the vehicle is to be steered.

Time to, and distance at, closest point of approach (CPA) as well as position of both tracks at CPA.

time to CPA.

distance at CPA.

position of track 1 at CPA.

position of track 2 at CPA.

Time, distance and position of intercept as well as speed and initial bearing of interceptor.

time to intercept.

distance at intercept.

position of intercept.

initial bearing of interceptor.

speed of interceptor.

course p b computes the course of a vehicle currently at position p and following bearing b.

positionAfter p b s d computes the position of a vehicle currently at position p following bearing b and travelling at speed s after duration d has elapsed assuming the vehicle maintains a constant altitude.

positionAfter p b s d is a shortcut for positionAfter' (course p b) s d.

Examples

>>> import Data.Geo.Jord.Kinematics
>>> import Data.Geo.Jord.Position
>>> 
>>> let p = s84Pos 53.321 (-1.729) (metres 15000)
>>> let b = decimalDegrees 96.0217
>>> let s = kilometresPerHour 124.8
>>> positionAfter p b s (hours 1)
53°11'19.368"N,0°8'2.457"E 15.0km (S84)
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trackPositionAfter t d computes the position of a track t after duration d has elapsed assuming the vehicle maintains a constant altitude.

trackPositionAfter (Track p b s) d is a equivalent to positionAfter' p (course p b) s d.

Examples

>>> import Data.Geo.Jord.Kinematics
>>> import Data.Geo.Jord.Position
>>> 
>>> let p = s84Pos 53.321 (-1.729) (metres 15000)
>>> let b = decimalDegrees 96.0217
>>> let s = kilometresPerHour 124.8
>>> trackPositionAfter (Track p b s) (hours 1)
53°11'19.368"N,0°8'2.457"E 15.0km (S84)

cpa t1 t2 computes the closest point of approach between tracks t1 and t2 disregarding their respective altitude. If a closest point of approach is found, height of cpaPosition1 - respectively cpaPosition2, will be the altitude of the first - respectively second, track.

Examples

>>> import Data.Geo.Jord.Kinematics
>>> import Data.Geo.Jord.Position
>>> 
>>> let p1 = s84Pos 20 (-60) zero
>>> let b1 = decimalDegrees 10
>>> let s1 = knots 15
>>> let p2 = s84Pos 34 (-50) zero
>>> let b2 = decimalDegrees 220
>>> let s2 = knots 300
>>> let t1 = Track p1 b1 s1
>>> let t2 = Track p2 b2 s2
>>> let c = cpa t1 t2
>>> fmap cpaTime c
Just 3H9M56.155S
>>> fmap cpaDistance c
Just 124.2317453km

intercept t p computes the minimum speed of interceptor at position p needed for an intercept with target track t to take place. Intercept time, position, distance and interceptor bearing are derived from this minimum speed. Returns Nothing if intercept cannot be achieved e.g.:

• interceptor and target are at the same position
• interceptor is "behind" the target

If found, interceptPosition is at the altitude of the track.

Examples

>>> import Data.Geo.Jord.Kinematics
>>> import Data.Geo.Jord.Position
>>> 
>>> let t = Track (s84Pos 34 (-50) zero) (decimalDegrees 220) (knots 600)
>>> let ip = s84Pos 20 (-60) zero
>>> let i = intercept t ip
>>> fmap (toKnots . interceptorSpeed) i
Just 52.633367756059
>>> fmap (toSeconds . interceptTime) i
Just 5993.831

interceptBySpeed t p s computes the time needed by interceptor at position p and travelling at speed s to intercept target track t. Returns Nothing if intercept cannot be achieved e.g.:

• interceptor and target are at the same position
• interceptor speed is below minimum speed returned by intercept

If found, interceptPosition is at the altitude of the track.

interceptByTime t p d computes the speed of interceptor at position p needed for an intercept with target track t to take place after duration d. Returns Nothing if given duration is <= 0 or interceptor and target are at the same position.

If found, interceptPosition is at the altitude of the track.

Note: contrary to intercept and interceptBySpeed this function handles cases where the interceptor has to catch up the target.

Examples

>>> import Data.Geo.Jord.Kinematics
>>> import Data.Geo.Jord.Position
>>> 
>>> let t = Track (s84Pos 34 (-50) zero) (decimalDegrees 220) (knots 600)
>>> let ip = s84Pos 20 (-60) zero
>>> let d = seconds 2700
>>> let i = interceptByTime t ip d
>>> fmap (toKnots . interceptorSpeed) i
Just 730.959238
>>> 
>>> fmap interceptorBearing i
Just 26°7'11.649"
>>> 
>>> fmap interceptPosition i
Just 28°8'12.047"N,55°27'21.411"W 0.0m (S84)
>>> 
>>> fmap interceptDistance i
Just 1015.3023506km
>>> 
>>> fmap (toSeconds . interceptTime) i
Just 2700