Passing Distance and CPA from Chart Plot

TL;DR — Closest Point of Approach (CPA) is the minimum predicted passing distance between own vessel and a target; risk of collision exists whenever compass bearing to an approaching vessel remains constant while range decreases (CBDR). Both manual radar plotting and ARPA-derived data are tools to quantify CPA and TCPA, but neither replaces a proper visual and radar lookout.

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What the Rule Says

Detecting Risk of Collision — Bearing Watch

The foundational method for determining whether a risk of collision exists is the compass bearing observation. If the compass bearing to an approaching vessel remains constant and the range is decreasing, risk of collision exists. This condition is known as Constant Bearing, Decreasing Range — CBDR. Bowditch Ch. 7 §704

This is not merely a navigational convenience; it is the practical implementation of the watchkeeper's duty. A single bearing observation is insufficient. The watchkeeper must take successive compass bearings over time and compare them. Only a series of bearings can confirm whether the bearing is steady, drawing forward, or drawing aft. Bowditch Ch. 7 §704

Safe Speed as the Governing Standard

Every vessel must at all times proceed at a safe speed so that she can take proper and effective action to avoid collision and be stopped within a distance appropriate to the prevailing circumstances and conditions. 33 CFR §83.06 The concept of CPA is directly tied to this requirement: if the predicted CPA is unacceptably close, the vessel is obligated to act — and that action must be taken at a speed that allows it to be effective.

Factors bearing on safe speed include the state of visibility, traffic density, maneuverability of the vessel with special reference to stopping distance and turning ability, the state of wind, sea, and current, proximity of navigational hazards, and the draft in relation to available depth of water. 33 CFR §83.06

For vessels with operational radar, additional factors apply: the characteristics, efficiency, and limitations of the radar equipment; constraints imposed by the radar range scale in use; the effect of sea state, weather, and other interference on radar detection; the possibility that small vessels, ice, and other floating objects may not be detected at adequate range; the number, location, and movement of vessels detected by radar; and the more exact assessment of visibility that radar range measurements can provide. 33 CFR §83.06

ARPA — Automated CPA and TCPA

An Automatic Radar Plotting Aid (ARPA) computes target tracks automatically and displays predicted CPA and TCPA. ARPA does not replace bridge watchkeeping; it supplements visual lookout. Bowditch Ch. 13 §1303

At the request of the observer, the following information must be immediately available from the ARPA in alphanumeric form for any tracked target: present range to the target; present bearing of the target; predicted target range at the closest point of approach (CPA); predicted time to CPA (TCPA); calculated true course of target; and calculated true speed of target. 33 CFR §164.38

ARPA must be capable of warning the observer with a visual and/or audible signal of any tracked target predicted to close to within a minimum range and time chosen by the observer. The target causing the warning must be clearly indicated on the display. 33 CFR §164.38

Within one minute of steady-state tracking, ARPA must present the relative motion trend of a target. Within three minutes of steady-state tracking, it must present the target's predicted motion — including CPA and TCPA — to specified accuracy values. 33 CFR §164.38 After a tracked target or own ship completes a maneuver, the system must again present a motion trend within one minute and full predicted motion within three minutes. 33 CFR §164.38

Manual Plotting — The Doubling-the-Angle Technique

For a single fixed object, bearings taken at two different times can produce a running fix. The doubling-the-angle technique uses two relative bearings: the distance run between the two observations equals the distance to the object at the time of the second bearing. Bowditch Ch. 7 §703 On the exam, this technique is applied to determine how far off a point of land or a buoy the vessel will pass — which is, in effect, a CPA calculation for a stationary object.

ARPA Installation Requirements

ARPA must be installed on: each self-propelled vessel (other than a public vessel) of 10,000 gross tons or more carrying oil or hazardous materials in bulk as cargo or residue on navigable waters of the United States, or which transfers such materials in any U.S. port; each tank vessel of 10,000 gross tons or more operating on navigable waters of the United States; each self-propelled vessel of 15,000 gross tons or more that is not a tank vessel and was constructed before September 1, 1984 (except on the Great Lakes and connecting waters); and each vessel of 10,000 gross tons or more constructed on or after September 1, 1984 (except on the Great Lakes and connecting waters). 33 CFR §164.38

Each vessel required to carry ARPA must also be fitted with a device to indicate speed and distance, either through the water or over the ground. Speed errors must not exceed 5 percent of vessel speed or 0.5 knot, whichever is greater. Distance errors must not exceed 5 percent of distance run in one hour or 0.5 nautical mile per hour, whichever is greater. 33 CFR §164.40

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Why It Matters on the Exam

OUPV and Master 100 GT written exams test CPA and passing distance from multiple angles:

Bearing observation questions present a scenario — vessel bearing 045° at 0800, bearing 043° at 0810, range decreasing — and ask whether risk of collision exists. The answer turns on whether the bearing is steady (CBDR = risk exists) or changing. Bowditch Ch. 7 §704

Doubling-the-angle questions give you two relative bearings and the distance run between them, then ask for the distance off at the time of the second bearing. The rule: distance run between bearings equals distance off at the second bearing, provided the first bearing is exactly half the second. Bowditch Ch. 7 §703

ARPA data questions ask what information the system must provide on demand. The six required alphanumeric readouts — present range, present bearing, predicted CPA range, TCPA, true course of target, true speed of target — are a direct exam target. 33 CFR §164.38

Safe speed questions ask which factors must be considered. The exam distinguishes between factors applicable to all vessels and the additional factors that apply only when radar is operational. Know both lists. 33 CFR §83.06

ARPA timing questions ask how quickly the system must produce a motion trend (one minute) versus full predicted motion (three minutes) after acquisition or after a maneuver. 33 CFR §164.38

ARPA installation threshold questions ask which vessel types and tonnages require ARPA. The 10,000 GT threshold for tank vessels and hazmat carriers, the 15,000 GT threshold for pre-1984 non-tank vessels, and the Great Lakes exception are all testable. 33 CFR §164.38

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Common Pitfalls

Confusing CPA with TCPA. CPA is a distance — the predicted minimum range at the closest point of approach. TCPA is a time — the predicted elapsed time until that closest point is reached. The exam will use both terms and expects you to keep them distinct. 33 CFR §164.38

Assuming a changing bearing means no risk. A bearing that is drawing slowly aft while range decreases rapidly can still result in a dangerously close CPA. The bearing observation establishes risk of collision; it does not by itself establish a safe passing distance. Bowditch Ch. 7 §704

Treating ARPA as a substitute for lookout. ARPA supplements visual lookout; it does not replace it. Small vessels, ice, and other floating objects may not be detected by radar at adequate range. 33 CFR §83.06 Bowditch Ch. 13 §1303

Misapplying the doubling-the-angle rule. The technique requires the first relative bearing to be exactly half the second. If the bearings given do not satisfy that relationship, the rule does not apply directly. Bowditch Ch. 7 §703

Forgetting the speed/distance device requirement. Candidates sometimes know the ARPA installation thresholds but overlook that a speed and distance indicator is also mandatory on every vessel required to carry ARPA. 33 CFR §164.40

Overlooking the Great Lakes exception. The ARPA requirement for vessels of 10,000 GT or more constructed on or after September 1, 1984, and for pre-1984 vessels of 15,000 GT or more, does not apply when operating on the Great Lakes and their connecting and tributary waters. 33 CFR §164.38

Applying only the "all vessels" safe speed factors when radar is in use. When a vessel has operational radar, the six additional radar-specific factors must also be considered. Listing only the general factors is an incomplete answer. 33 CFR §83.06

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Quick Check

Q1 — You observe a vessel bearing 278° at 0900 and 278° at 0912. Range has decreased from 6.0 nm to 4.2 nm. What is the situation?

Risk of collision exists. The compass bearing is constant and the range is decreasing — CBDR. A steady bearing with decreasing range is the canonical indicator of risk of collision. Bowditch Ch. 7 §704

Q2 — What six items of alphanumeric data must an ARPA provide on demand for any tracked target?

Present range to the target; present bearing of the target; predicted target range at CPA; predicted time to CPA (TCPA); calculated true course of target; calculated true speed of target. 33 CFR §164.38

Q3 — Your vessel is on course 090° at 12 knots. A target bears 045° relative. When the target bears 090° relative, you have run 3.0 nm since the first bearing. How far off will the target pass?

3.0 nm. The first relative bearing (045°) is exactly half the second (090°), so the doubling-the-angle rule applies: distance run between the two bearings equals distance off at the time of the second bearing. Bowditch Ch. 7 §703

Q4 — How quickly must ARPA present a motion trend after a tracked target completes a maneuver, and how quickly must it present full predicted motion?

Motion trend within one minute; full predicted motion (including CPA and TCPA to specified accuracy) within three minutes. 33 CFR §164.38

Q5 — A 12,000 GT tank vessel is operating on Lake Erie. Is ARPA required?

No. The ARPA requirement for tank vessels of 10,000 GT or more does not contain a Great Lakes exception in the text of 33 CFR §164.38(b)(2) — that exception applies to the categories in §164.38(b)(3) and (b)(4). A 12,000 GT tank vessel operating on the Great Lakes is still subject to §164.38(b)(2), which requires ARPA for each tank vessel of 10,000 GT or more operating on navigable waters of the United States without a Great Lakes carve-out. 33 CFR §164.38

Q6 — Name three factors applicable only to vessels with operational radar when determining safe speed.

Any three of the following: the characteristics, efficiency, and limitations of the radar equipment; constraints imposed by the radar range scale in use; the effect of sea state, weather, and other interference on radar detection; the possibility that small vessels, ice, and other floating objects may not be detected at adequate range; the number, location, and movement of vessels detected by radar; the more exact assessment of visibility that radar range measurements can provide. 33 CFR §83.06