; flight planning -- by Jos Koot

(define (square x) (* x x))

(define pi 3.141592653589793)
(define (radian->degree r) (/ r pi 2/360))
(define (degree->radian d) (* d 2/360 pi))
(define (rnd x) (round (inexact->exact x)))
(define (xmodulo x y)
(cond
  ((<= 0 x y) x)
  ((< x 0) (xmodulo (+ x y) y))
  ((>= x y) (xmodulo (- x y) y))))

(define (navigate1 d gt wn ws as)
 (let*
  ((b (- gt wn -180))
   (b-radians (degree->radian b))
   (sin-b (sin b-radians))
   (a (radian->degree (asin (/ (* sin-b ws) as))))
   (th (xmodulo (+ gt a) 360))
   (gs (+ (* as (cos (degree->radian (- th gt))))
          (* ws (cos b-radians))))
   (th (+ gt a))
   (ft (/ d gs)))
  (list
   (rnd gs)
   (rnd a)
   (xmodulo (rnd th) 360)
   (rnd (* 60 ft)))))

(define (navigate2 d gt wn ws as)
 (let*
  ((b (xmodulo (- gt wn -180) 360))
   (cos-b (cos (degree->radian b)))
   (wsqr (square ws))
   (asqr (square as))
   (det (+ (square (* ws cos-b)) (- wsqr) asqr))
   (gs (+ (* ws cos-b) (sqrt det)))
   (a (radian->degree (acos (/ (+ asqr (square gs) (- wsqr)) (* 2 gs as)))))
   (a ((if (< b 180) + -) a))
   (th (+ gt a))
   (ft (/ d gs)))
  (if (or (< det 0) (< gs 0)) ('error 'navigate "STRANGE" det gs))
  (list
   (rnd gs)
   (rnd a)
   (xmodulo (rnd th) 360)
   (rnd (* 60 ft)))))

(display (navigate1 180 90 90 20 90)) (newline)
(display (navigate2 180 90 90 20 90)) (newline)

(70 0 90 154)
(70 0 90 154)