Track represents the state of a vehicle by its current horizontal 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.

horizontal position of ownship CPA.

horizontal position of intruder at CPA.

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

time to intercept.

distance travelled to intercept.

horizontal 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 horizontal position of a vehicle currently at position p following bearing b and travelling at speed s after duration d has elapsed. For example:

>>> let p = Geodetic.s84Pos 53.321 (-1.729)
>>> let b = Angle.decimalDegrees 96.0217
>>> let s = Speed.kilometresPerHour 124.8
>>> Kinematics.positionAfter p b s (Duration.hours 1)
53°11'19.367"N,0°8'2.456"E (S84)

This is equivalent to:

Kinematics.positionAfter' p (Kinematics.course p b) s d

positionAfter' p c s d computes the horizontal position of a vehicle currently at position p on course c and travelling at speed s after duration d has elapsed. Note: course must have been calculated from position p.

trackPositionAfter t d computes the horizontal position of a track t after duration d has elapsed. For example:

>>> let p = Geodetic.s84Pos 53.321 (-1.729)
>>> let b = Angle.decimalDegrees 96.0217
>>> let s = Speed.kilometresPerHour 124.8
>>> Kinematics.trackPositionAfter (Kinematics.Track p b s) (Duration.hours 1)
53°11'19.367"N,0°8'2.456"E (S84)

cpa ownship intruder computes the closest point of approach between tracks ownship and intruder. The closest point of approach is calculated assuming both ships maintain a constant course and speed.

>>> let ownship = Kinematics.Track (Geodetic.s84Pos 20 (-60)) (Angle.decimalDegrees 10) (Speed.knots 15)
>>> let intruder = Kinematics.Track (Geodetic.s84Pos 34 (-50)) (Angle.decimalDegrees 220) (Speed.knots 300)
>>> let cpa = Kinematics.cpa ownship intruder
Just (Cpa { timeToCpa = 3H9M56.155S
          , distanceAtCpa = 124.231730834km
          , cpaOwnshipPosition = 20°46'43.641"N,59°51'11.225"W (S84)
          , cpaIntruderPosition = 21°24'8.523"N,60°50'48.159"W (S84)})

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. For example:

>>> let t = Kinematics.Track (Geodetic.s84Pos 34 (-50)) (Angle.decimalDegrees 220) (Speed.knots 600)
>>> let ip = Geodetic.s84Pos 20 (-60)
>>> Kinematics.intercept t ip
Just (Intercept { timeToIntercept = 1H39M53.831S
                , distanceToIntercept = 162.294627463km
                , interceptPosition = 20°43'42.305"N,61°20'56.848"W (S84)
                , interceptorBearing = 300°10'18.053"
                , interceptorSpeed = 97.476999km/h})

Returns Nothing if intercept cannot be achieved e.g.:

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

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

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.For example:

>>> let t = Kinematics.Track (Geodetic.s84Pos 34 (-50)) (Angle.decimalDegrees 220) (Speed.knots 600)
>>> let ip = Geodetic.s84Pos 20 (-60)
>>> let d = Duration.seconds 2700
>>> interceptByTime t ip d
Just (Intercept { timeToIntercept = 0H45M0.000S
                , distanceToIntercept = 1015.302358852km
                , interceptPosition = 28°8'12.046"N,55°27'21.411"W (S84)
                , interceptorBearing = 26°7'11.649"
                , interceptorSpeed = 1353.736478km/h})

Returns Nothing if given duration is <= 0 or interceptor and target are at the same position. Contrary to intercept and interceptBySpeed this function handles cases where the interceptor has to catch up the target.

A duration with a resolution of 1 millisecond.

A speed with a resolution of 1 millimetre per hour.