Data.Geo.Jord.Kinematics

Types and functions for working with kinematics calculations assuming a spherical earth model.

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 position, bearing and speed.

Constructors

Track

Fields

• trackPos :: a

  position of the track.

• trackBearing :: Angle

  bearing of the track.

• trackSpeed :: Speed

  speed of the track.

Instances

Eq a => Eq (Track a)

Defined in Data.Geo.Jord.Kinematics

Methods

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

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

Show a => Show (Track a)

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Track a -> ShowS

show :: Track a -> String

showList :: [Track a] -> ShowS

(NTransform a, Show a) => IsGreatCircle (Track a)

GreatCircle from track.

Defined in Data.Geo.Jord.Kinematics

Methods

greatCircle :: Track a -> GreatCircle

greatCircleE :: Track a -> Either String GreatCircle

greatCircleF :: MonadFail m => Track a -> m GreatCircle

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

IsVector3d Course

Defined in Data.Geo.Jord.Kinematics

Methods

vec :: Course -> Vector3d

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

Eq a => Eq (Cpa a)

Defined in Data.Geo.Jord.Kinematics

Methods

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

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

Show a => Show (Cpa a)

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Cpa a -> ShowS

show :: Cpa a -> String

showList :: [Cpa a] -> ShowS

cpaTime :: Cpa a -> Duration

time to CPA.

cpaDistance :: Cpa a -> Length

distance at CPA.

cpaPosition1 :: Cpa a -> a

position of track 1 at CPA.

cpaPosition2 :: Cpa a -> a

position of track 2 at CPA.

The Intercept type.

data Intercept a

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

Instances

Eq a => Eq (Intercept a)

Defined in Data.Geo.Jord.Kinematics

Methods

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

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

Show a => Show (Intercept a)

Defined in Data.Geo.Jord.Kinematics

Methods

showsPrec :: Int -> Intercept a -> ShowS

show :: Intercept a -> String

showList :: [Intercept a] -> ShowS

interceptTime :: Intercept a -> Duration

time to intercept.

interceptDistance :: Intercept a -> Length

distance at intercept.

interceptPosition :: Intercept a -> a

position of intercept.

interceptorBearing :: Intercept a -> Angle

initial bearing of interceptor.

interceptorSpeed :: Intercept a -> Speed

speed of interceptor.

Calculations

course :: NTransform a => a -> Angle -> Course

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

position :: NTransform a => Track a -> Duration -> Length -> a

position t d r computes the position of a track t after duration d has elapsed and using the earth radius r.

    let p0 = latLongHeight (readLatLong "531914N0014347W") (metres 15000)
    let b = decimalDegrees 96.0217
    let s = kilometresPerHour 124.8
    let p1 = decimalLatLongHeight 53.1882691 0.1332741 (metres 15000)
    position (Track p0 b s) (hours 1) r84 = p1

position84 :: NTransform a => Track a -> Duration -> a

position using the mean radius of the WGS84 reference ellipsoid.

cpa :: (Eq a, NTransform a) => Track a -> Track a -> Length -> Maybe (Cpa a)

cpa t1 t2 r computes the closest point of approach between tracks t1 and t2 and using the earth radius r.

    let p1 = decimalLatLong 20 (-60)
    let b1 = decimalDegrees 10
    let s1 = knots 15
    let p2 = decimalLatLong 34 (-50)
    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 r84
    fmap cpaTime c = Just (milliseconds 11396155)
    fmap cpaDistance c = Just (kilometres 124.2317453)

cpa84 :: (Eq a, NTransform a) => Track a -> Track a -> Maybe (Cpa a)

cpa using the mean radius of the WGS84 reference ellipsoid.

intercept :: (Eq a, NTransform a) => Track a -> a -> Length -> Maybe (Intercept a)

intercept t p r computes the minimum speed of interceptor at position p needed for an intercept with target track t to take place using the earth radius r. 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 on the great circle of target and behind as the minimum speed would be target speed + epsillon

    let t = Track (decimalLatLong 34 (-50)) (decimalDegrees 220) (knots 600)
    let ip = (decimalLatLong 20 (-60))
    let i = intercept t ip r84
    fmap interceptorSpeed i = Just (knots 52.837096)
    fmap interceptTime i = Just (seconds 5947.698)

intercept84 :: (Eq a, NTransform a) => Track a -> a -> Maybe (Intercept a)

intercept using the mean radius of the WGS84 reference ellipsoid.

interceptBySpeed :: (Eq a, NTransform a) => Track a -> a -> Speed -> Length -> Maybe (Intercept a)

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

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

interceptBySpeed84 :: (Eq a, NTransform a) => Track a -> a -> Speed -> Maybe (Intercept a)

interceptBySpeed using the mean radius of the WGS84 reference ellipsoid.

interceptByTime :: (Eq a, NTransform a) => Track a -> a -> Duration -> Length -> Maybe (Intercept a)

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

    let t = Track (decimalLatLong 34 (-50)) (decimalDegrees 220) (knots 600)
    let ip = (decimalLatLong 20 (-60))
    let d = seconds 2700
    let i = interceptByTime t ip d r84
    fmap interceptorSpeed i = Just (knots 730.959238)
    fmap interceptorBearing i = Just (decimalDegrees 26.1199030)
    fmap interceptPosition i = Just (decimalLatLong 28.1366797 (-55.4559475))
    fmap interceptDistance i = Just (metres 1015302.3815)
    fmap interceptTime i = Just (seconds 2700)

interceptByTime84 :: (Eq a, NTransform a) => Track a -> a -> Duration -> Maybe (Intercept a)

interceptByTime using the mean radius of the WGS84 reference ellipsoid.