Data.Geo.Jord.Kinematics

Types and functions for working with kinematics calculations assuming a spherical celestial body.

In order to use this module you should start with the following imports:

import qualified Data.Geo.Jord.Geodetic as Geodetic
import qualified Data.Geo.Jord.Kinematics as Kinematics

All functions are implemented using the vector-based approached described in Gade, K. (2010). A Non-singular Horizontal Position Representation and in Shudde, Rex H. (1986). Some tactical algorithms for spherical geometry

The Track type.

data Track a

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

Constructors

Track

Fields

• trackPosition :: HorizontalPosition a

  horizontal position of the track.

• trackBearing :: Angle

  bearing of the track.

• trackSpeed :: Speed

  speed of the track.

Instances

Model a => Eq (Track a)

Defined in Data.Geo.Jord.Kinematics

Methods

(==) :: Track a -> Track a -> Bool

(/=) :: Track a -> Track a -> Bool

Model a => Show (Track a)

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Track a -> ShowS

show :: Track a -> String

showList :: [Track a] -> ShowS

The Course type.

data Course

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

Instances

Eq Course

Defined in Data.Geo.Jord.Kinematics

Methods

(==) :: Course -> Course -> Bool

(/=) :: Course -> Course -> Bool

Show Course

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Course -> ShowS

show :: Course -> String

showList :: [Course] -> ShowS

The Cpa type.

data Cpa a

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

Instances

Model a => Eq (Cpa a)

Defined in Data.Geo.Jord.Kinematics

Methods

(==) :: Cpa a -> Cpa a -> Bool

(/=) :: Cpa a -> Cpa a -> Bool

Model a => Show (Cpa a)

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Cpa a -> ShowS

show :: Cpa a -> String

showList :: [Cpa a] -> ShowS

timeToCpa :: Cpa a -> Duration

time to CPA.

distanceAtCpa :: Cpa a -> Length

distance at CPA.

cpaOwnshipPosition :: Cpa a -> HorizontalPosition a

horizontal position of ownship CPA.

cpaIntruderPosition :: Cpa a -> HorizontalPosition a

horizontal position of intruder at CPA.

The Intercept type.

data Intercept a

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

Instances

Model a => Eq (Intercept a)

Defined in Data.Geo.Jord.Kinematics

Methods

(==) :: Intercept a -> Intercept a -> Bool

(/=) :: Intercept a -> Intercept a -> Bool

Model a => Show (Intercept a)

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Intercept a -> ShowS

show :: Intercept a -> String

showList :: [Intercept a] -> ShowS

timeToIntercept :: Intercept a -> Duration

time to intercept.

distanceToIntercept :: Intercept a -> Length

distance travelled to intercept.

interceptPosition :: Intercept a -> HorizontalPosition a

horizontal position of intercept.

interceptorBearing :: Intercept a -> Angle

initial bearing of interceptor.

interceptorSpeed :: Intercept a -> Speed

speed of interceptor.

Calculations

course :: Spherical a => HorizontalPosition a -> Angle -> Course

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

positionAfter :: Spherical a => HorizontalPosition a -> Angle -> Speed -> Duration -> HorizontalPosition a

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' :: Spherical a => HorizontalPosition a -> Course -> Speed -> Duration -> HorizontalPosition a

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 :: Spherical a => Track a -> Duration -> HorizontalPosition a

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 :: Spherical a => Track a -> Track a -> Maybe (Cpa a)

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 :: Spherical a => Track a -> HorizontalPosition a -> Maybe (Intercept a)

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 :: Spherical a => Track a -> HorizontalPosition a -> Speed -> Maybe (Intercept a)

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 :: Spherical a => Track a -> HorizontalPosition a -> Duration -> Maybe (Intercept a)

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.

re-exported for convenience

data Duration

A duration with a resolution of 1 millisecond.

Instances

Eq Duration

Defined in Data.Geo.Jord.Duration

Methods

(==) :: Duration -> Duration -> Bool

(/=) :: Duration -> Duration -> Bool

Ord Duration

Defined in Data.Geo.Jord.Duration

Methods

compare :: Duration -> Duration -> Ordering

(<) :: Duration -> Duration -> Bool

(<=) :: Duration -> Duration -> Bool

(>) :: Duration -> Duration -> Bool

(>=) :: Duration -> Duration -> Bool

max :: Duration -> Duration -> Duration

min :: Duration -> Duration -> Duration

Read Duration

See duration.

Defined in Data.Geo.Jord.Duration

Methods

readsPrec :: Int -> ReadS Duration

readList :: ReadS [Duration]

readPrec :: ReadPrec Duration

readListPrec :: ReadPrec [Duration]

Show Duration

Show Duration as (-)nHnMn.nS.

Defined in Data.Geo.Jord.Duration

Methods

showsPrec :: Int -> Duration -> ShowS

show :: Duration -> String

showList :: [Duration] -> ShowS

data Speed

A speed with a resolution of 1 millimetre per hour.

Instances

Eq Speed

Defined in Data.Geo.Jord.Speed

Methods

(==) :: Speed -> Speed -> Bool

(/=) :: Speed -> Speed -> Bool

Ord Speed

Defined in Data.Geo.Jord.Speed

Methods

compare :: Speed -> Speed -> Ordering

(<) :: Speed -> Speed -> Bool

(<=) :: Speed -> Speed -> Bool

(>) :: Speed -> Speed -> Bool

(>=) :: Speed -> Speed -> Bool

max :: Speed -> Speed -> Speed

min :: Speed -> Speed -> Speed

Read Speed

See speed.

Defined in Data.Geo.Jord.Speed

Methods

readsPrec :: Int -> ReadS Speed

readList :: ReadS [Speed]

readPrec :: ReadPrec Speed

readListPrec :: ReadPrec [Speed]

Show Speed

Speed is shown in kilometres per hour.

Defined in Data.Geo.Jord.Speed

Methods

showsPrec :: Int -> Speed -> ShowS

show :: Speed -> String

showList :: [Speed] -> ShowS