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FA-69036 / Tide and marine navigation tables / Open access

Course to steer across a stream: Feasibility compares the whole drift with boat speed · case 01

A strong but fair stream is declared impossible to counter.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The test rejects drift>boat speed instead of only a cross component the boat cannot cancel.

THE FAILURE

The test rejects drift>boat speed instead of only a cross component the boat cannot cancel.

Unsuccessful approach: Testing the along-track component instead of the cross component rejects the wrong cases.

Case contract

Input [track, boat_speed, set, drift] with degrees true (set is the direction the stream flows toward) and knots. Cross-track stream c=drift*sin(set-track); heading = track+asin(-c/boat); SOG=boat*cos(asin(-c/boat))+drift*cos(set-track). Return None when |c|>boat or SOG<=0, else [heading mod 360 rounded to 0.1, SOG rounded to 0.01].

Why this case matters

Tide tables and passage plans turn published predictions into go/no-go decisions about depth, clearance and timing.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    track,bs,setd,drift=x
    rel=math.radians(setd-track)
    cross=drift*math.sin(rel)
    if drift>bs: return None
    a=math.asin(-cross/bs)
    sog=bs*math.cos(a)+drift*math.cos(rel)
    if sog<=0: return None
    return [round(math.degrees(math.radians(track)+a)%360,1),round(sog,2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [90, 6, 180, 1.5]', [90, 6, 180, 1.5], [75.5, 5.81]), ('course to steer across a stream [90, 6, 0, 1.5]', [90, 6, 0, 1.5], [104.5, 5.81]), ('course to steer across a stream [10, 5, 100, 2]', [10, 5, 100, 2], [346.4, 4.58]), ('course to steer across a stream [350, 5, 80, 2]', [350, 5, 80, 2], [326.4, 4.58]), ('course to steer across a stream [200, 4, 200, 3]', [200, 4, 200, 3], [200.0, 7.0]), ('course to steer across a stream [200, 4, 20, 3]', [200, 4, 20, 3], [200.0, 1.0])], [('course to steer across a stream [0, 5, 10, 7]', [0, 5, 10, 7], [345.9, 11.74]), ('course to steer across a stream [350, 5, 80, 2]', [350, 5, 80, 2], [326.4, 4.58]), ('course to steer across a stream [200, 4, 200, 3]', [200, 4, 200, 3], [200.0, 7.0]), ('course to steer across a stream [200, 4, 20, 3]', [200, 4, 20, 3], [200.0, 1.0]), ('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [120, 5, 300, 5.5]', [120, 5, 300, 5.5], None), ('course to steer across a stream [0, 5, 90, 0]', [0, 5, 90, 0], [0.0, 5.0])], [('course to steer across a stream [90, 4, 100, 4.5]', [90, 4, 100, 4.5], [78.7, 8.35]), ('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [120, 5, 300, 5.5]', [120, 5, 300, 5.5], None), ('course to steer across a stream [0, 5, 90, 0]', [0, 5, 90, 0], [0.0, 5.0]), ('course to steer across a stream [270, 8, 315, 2.5]', [270, 8, 315, 2.5], [257.2, 9.57]), ('course to steer across a stream [5, 6, 275, 1.2]', [5, 6, 275, 1.2], [16.5, 5.88]), ('course to steer across a stream [180, 3, 90, 2.9]', [180, 3, 90, 2.9], [255.2, 0.77])], [('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [270, 8, 315, 2.5]', [270, 8, 315, 2.5], [257.2, 9.57]), ('course to steer across a stream [5, 6, 275, 1.2]', [5, 6, 275, 1.2], [16.5, 5.88]), ('course to steer across a stream [180, 3, 90, 2.9]', [180, 3, 90, 2.9], [255.2, 0.77]), ('course to steer across a stream [300, 7, 120, 2]', [300, 7, 120, 2], [300.0, 5.0]), ('course to steer across a stream [5, 6, 90, 1.5]', [5, 6, 90, 1.5], [350.6, 5.94]), ('course to steer across a stream [355, 6, 260, 1.5]', [355, 6, 260, 1.5], [9.4, 5.68])], [('course to steer across a stream [0, 5, 10, 7]', [0, 5, 10, 7], [345.9, 11.74]), ('course to steer across a stream [300, 7, 120, 2]', [300, 7, 120, 2], [300.0, 5.0]), ('course to steer across a stream [5, 6, 90, 1.5]', [5, 6, 90, 1.5], [350.6, 5.94]), ('course to steer across a stream [355, 6, 260, 1.5]', [355, 6, 260, 1.5], [9.4, 5.68]), ('course to steer across a stream [90, 4, 100, 4.5]', [90, 4, 100, 4.5], [78.7, 8.35]), ('course to steer across a stream [90, 6, 180, 1.5]', [90, 6, 180, 1.5], [75.5, 5.81]), ('course to steer across a stream [90, 6, 0, 1.5]', [90, 6, 0, 1.5], [104.5, 5.81])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
course to steer across a stream [45, 5, 60, 7]None[23.8, 11.42]Failed
course to steer across a stream [90, 6, 180, 1.5][75.5, 5.81][75.5, 5.81]Passed
course to steer across a stream [90, 6, 0, 1.5][104.5, 5.81][104.5, 5.81]Passed
course to steer across a stream [10, 5, 100, 2][346.4, 4.58][346.4, 4.58]Passed
course to steer across a stream [350, 5, 80, 2][326.4, 4.58][326.4, 4.58]Passed
course to steer across a stream [200, 4, 200, 3][200.0, 7.0][200.0, 7.0]Passed
course to steer across a stream [200, 4, 20, 3][200.0, 1.0][200.0, 1.0]Passed

SHA-256 / c6398cff21f83e2ad9e47bd199ef220239d637284b955300c3223672caba2631

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    track,bs,setd,drift=x
    rel=math.radians(setd-track)
    cross=drift*math.sin(rel)
    if abs(drift*math.cos(rel))>bs: return None
    a=math.asin(-cross/bs)
    sog=bs*math.cos(a)+drift*math.cos(rel)
    if sog<=0: return None
    return [round(math.degrees(math.radians(track)+a)%360,1),round(sog,2)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [90, 6, 180, 1.5]', [90, 6, 180, 1.5], [75.5, 5.81]), ('course to steer across a stream [90, 6, 0, 1.5]', [90, 6, 0, 1.5], [104.5, 5.81]), ('course to steer across a stream [10, 5, 100, 2]', [10, 5, 100, 2], [346.4, 4.58]), ('course to steer across a stream [350, 5, 80, 2]', [350, 5, 80, 2], [326.4, 4.58]), ('course to steer across a stream [200, 4, 200, 3]', [200, 4, 200, 3], [200.0, 7.0]), ('course to steer across a stream [200, 4, 20, 3]', [200, 4, 20, 3], [200.0, 1.0])], [('course to steer across a stream [0, 5, 10, 7]', [0, 5, 10, 7], [345.9, 11.74]), ('course to steer across a stream [350, 5, 80, 2]', [350, 5, 80, 2], [326.4, 4.58]), ('course to steer across a stream [200, 4, 200, 3]', [200, 4, 200, 3], [200.0, 7.0]), ('course to steer across a stream [200, 4, 20, 3]', [200, 4, 20, 3], [200.0, 1.0]), ('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [120, 5, 300, 5.5]', [120, 5, 300, 5.5], None), ('course to steer across a stream [0, 5, 90, 0]', [0, 5, 90, 0], [0.0, 5.0])], [('course to steer across a stream [90, 4, 100, 4.5]', [90, 4, 100, 4.5], [78.7, 8.35]), ('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [120, 5, 300, 5.5]', [120, 5, 300, 5.5], None), ('course to steer across a stream [0, 5, 90, 0]', [0, 5, 90, 0], [0.0, 5.0]), ('course to steer across a stream [270, 8, 315, 2.5]', [270, 8, 315, 2.5], [257.2, 9.57]), ('course to steer across a stream [5, 6, 275, 1.2]', [5, 6, 275, 1.2], [16.5, 5.88]), ('course to steer across a stream [180, 3, 90, 2.9]', [180, 3, 90, 2.9], [255.2, 0.77])], [('course to steer across a stream [45, 5, 60, 7]', [45, 5, 60, 7], [23.8, 11.42]), ('course to steer across a stream [270, 8, 315, 2.5]', [270, 8, 315, 2.5], [257.2, 9.57]), ('course to steer across a stream [5, 6, 275, 1.2]', [5, 6, 275, 1.2], [16.5, 5.88]), ('course to steer across a stream [180, 3, 90, 2.9]', [180, 3, 90, 2.9], [255.2, 0.77]), ('course to steer across a stream [300, 7, 120, 2]', [300, 7, 120, 2], [300.0, 5.0]), ('course to steer across a stream [5, 6, 90, 1.5]', [5, 6, 90, 1.5], [350.6, 5.94]), ('course to steer across a stream [355, 6, 260, 1.5]', [355, 6, 260, 1.5], [9.4, 5.68])], [('course to steer across a stream [0, 5, 10, 7]', [0, 5, 10, 7], [345.9, 11.74]), ('course to steer across a stream [300, 7, 120, 2]', [300, 7, 120, 2], [300.0, 5.0]), ('course to steer across a stream [5, 6, 90, 1.5]', [5, 6, 90, 1.5], [350.6, 5.94]), ('course to steer across a stream [355, 6, 260, 1.5]', [355, 6, 260, 1.5], [9.4, 5.68]), ('course to steer across a stream [90, 4, 100, 4.5]', [90, 4, 100, 4.5], [78.7, 8.35]), ('course to steer across a stream [90, 6, 180, 1.5]', [90, 6, 180, 1.5], [75.5, 5.81]), ('course to steer across a stream [90, 6, 0, 1.5]', [90, 6, 0, 1.5], [104.5, 5.81])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
course to steer across a stream [45, 5, 60, 7]None[23.8, 11.42]Failed
course to steer across a stream [90, 6, 180, 1.5][75.5, 5.81][75.5, 5.81]Passed
course to steer across a stream [90, 6, 0, 1.5][104.5, 5.81][104.5, 5.81]Passed
course to steer across a stream [10, 5, 100, 2][346.4, 4.58][346.4, 4.58]Passed
course to steer across a stream [350, 5, 80, 2][326.4, 4.58][326.4, 4.58]Passed
course to steer across a stream [200, 4, 200, 3][200.0, 7.0][200.0, 7.0]Passed
course to steer across a stream [200, 4, 20, 3][200.0, 1.0][200.0, 1.0]Passed

SHA-256 / b9653ba0084e3c48e534cb826aa38047998cbfb27eebea31a5f76965a13ef749

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

A deterministic toy model with stipulated rules and constants; not certified hydrographic software or a substitute for official tide tables. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:07.727191+00:00.

Case digest / 35a9b1d476476a9f93b9c6939e4136bee8e47bf7afb4fbe2ee0595fb34d5c49a