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.

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

position using the mean radius of the WGS84 reference ellipsoid.

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)

cpa using the mean radius of the WGS84 reference ellipsoid.

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 "behind" the target

    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 52.633367756059)
    fmap interceptTime i = Just (seconds 5993.831)

intercept using the mean radius of the WGS84 reference ellipsoid.

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 returned by intercept

interceptBySpeed using the mean radius of the WGS84 reference ellipsoid.

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)

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

interceptByTime using the mean radius of the WGS84 reference ellipsoid.