International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 4

Number 4

December 2010

383

1 INTRODUCTION

Rule 14 of International Regulations for Preventing

Collisions of Sea-72 applies to the navigation of

ships in sight of each other on reciprocal courses,

when they are meeting head-on. “…When two pow-

er-driven vessels are meeting on reciprocal or nearly

reciprocal courses so as to involve risk of collision

each shall alter her course to starboard so that each

shall pass on the port side of the other…” – this how

Rule 14 of COLREG states. It seems to be simple

and quite understandable! Statistics of ship colli-

sions, however, shows that regardless of simplicity

and clearness of the actions according to this Rule

more than 50 percent of collisions precisely occur

when vessels are meeting on reciprocal courses

(Karapuzov, A. I. & Mironov, A. I. 2005. Maneuver-

ing…). The points that on practice application of

Rule 14 becomes complicated as it doesn’t give ex-

act quantitative criteria both for definition of “head-

on situation” and minimum permissible “collision

approach situation” to execute maneuvering safe

passing clear of each other. As to the criteria of

clearing up head-on situation, Rule 14 contains only

the direction that “…Such a situation shall be

deemed to exist when a vessel sees the other ahead

or nearly ahead and by night she could see the mast-

head lights of the other in a line or nearly in a line

and/or both sidelights and by day she observes the

corresponding aspect of the other vessel…When a

vessel is in any doubt as to whether such a situation

exists, she shall assume that it does exist and act ac-

cordingly”. The use of such inexact notations as

“…nearly reciprocal courses…”, “…nearly in a

line…”, “…nearly ahead…”, “…corresponding as-

pect of the vessel…” as well as the absence of exact

quantitative criteria in Rule 14 don’t make it possi-

ble for navigators to judge the head-on situation in a

unique manner. By virtue of navigators′ subjective

perception of inexact notations, laid in Rule 14,

some of them consider the head-on situation as fall-

ing under Rule 14, and the others – under Rule 15

applying crossing situation. The lack of agreement

in navigators′ actions to different Rules of COLREG

in the same situation often leads to collisions. It can

be illustrated by some simple examples from prac-

tice (Snopkov, W. I. 2004. Ships′…). Fig. 1 shows

the case in which one of the navigator (navigator C)

has determined the situation as “head-on” falling

within the jurisdiction of Rule 14 in accordance with

which he changed the course to starboard and the

other one (navigator A) has determined the situation

as “crossing” falling within the jurisdiction of Rule

15 and considered it necessary to keep out of the

way of the ship on her own starboard and changed

the course to port. Further development of the situa-

tion doesn’t require any commentaries.

Figure 1. An example of dangerous situation development,

when on navigator considers that he acts under Rule 14, and

the other – under Rule 15

On Determination of the Head-on Situation

Under Rule 14 of Colreg-72

V.M. Bukaty & S.U. Morozova

Baltic Fishing Fleet State Academy, Kaliningrad, Russia

ABSTRACT: Analyzed one possible criteria of stating the fact of ships' meeting on reciprocal courses and

proved that none of them can be judged with confidence of head-on situation. So, in fact Rule 14 of COLREG

-1972 should be strictly adhered to: “ …When a vessel is in any doubt as to whether such a situation exists we

shall assume that it does exist and act accordingly…”, i. e. alter the course to starboard.

384

Russian commentaries to COLREG-72 don’t at

all consider the problem of quantitative criteria as

applied to Rule 14, i.e. of minimum permissible as-

pect of oncoming vessel when it is to be considered

as the vessel proceeding on reciprocal course head-

on. In Russian commentaries to COLREG-72, com-

plying with Rule 14, it is recommended in any doubt

to use Rule 14 for altering the course “ahead of time

and positively” to starboard.

Some foreign commentaries to COLREG-72,

based on the materials of judicial arbitrary docu-

ments, assume that in the same case when the differ-

ence in courses doesn’t fall outside the limit of 180

± half a point, Rule 14 shall be applied. If the differ-

ence in courses falls outside the limit of 180

± half

a point, Rule 15 is recommended to apply (Karapu-

zov, A. I. & Mironov, A. I. 2005. Maneuvering…).

2 CLEARING UP THE HEAD-ON SITUATION

ACCOUNTING MAST IN LINE

If the vessels are in sight of one another, then in day

time a trivial criterion of their meeting on reciprocal

courses might be an alignment of the oncoming ves-

sel’s masts, that can be seen with unaided eye or

through the binocular. In this case let’s consider this

criterion. An observer is known to think that he is on

a line of alignment (Fig. 2) until he deviates from it

so that the formed angle a between the directions to

leading beacons will not be larger than an angular

perceptibility of the observer’s eye. Then, Fig. 2

shows, that deviation W from the alignment axis will

be (Kolomijchuck.1975. Hidrography…)

Figure 2. On calculating of angular perceptibility of linear

alignment

dDD

)( +

(1)

where d - the distance between leading beacons; D -

the distance up to front leading beacons.

This, angle α determining an angular accuracy of

the observer position in line will be:

Or in view of (1) and accepting for an unaided

eye of the observer that β=ε=1′ we record in writing

)1(

′

= arc

arctg

(2)

According to (2) with the oncoming vessel’s

masts displacement equals 100 m, at a distance D =

= 4 miles, we receive α = 12.3

. For other values of

d and D, the meanings of angle α are given in Table

1. As the table shows, to detect the movement of on-

coming vessel proceeding on reciprocal course head-

on by its masts alignment with unaided eye prac-

tically impossible. This is true even for very

large vessels at close quarter distance as well. At

least the accuracy to establish such fact will contra-

dict with the accuracy the modern course indicatory

can provide. The observer will assume that the

vessels are proceeding on reciprocal courses head-

on, though in reality their courses can differ by some

degrees and even by some ten degrees (as to small

ships they can be at a considerable distance from the

observer). Probably, half a point difference in oppo-

site courses, considering as a criterion for ships in

head-on situation in the Foreign Commentaries to

Rule 14, as it was mentioned above, when observing

with an unaided eye is related to meeting distance in

1-2 miles with masts displacement of the oncoming

ship by a factor of 60-120 m., as Table 1 shows. But

they are closest point of approach close to last mo-

ment distances for maneuvering.

Table 1. Angular accuracy of defining oncoming masts align-

ment, degrees

___________________________________________________

Distance

between Distance up to front mast D, miles

masts

d, miles 1 2 3 4 5

___________________________________________________

20 15.2 28.4 39.0 47.2 53.4

40 7.8 15.2 22.1 28.4 34.0

60 5.3 10.3 15.2 19.8 24.2

80 4.0 7.8 11.5 15.2 18.7

100 3.2 6.3 9.3 12.3 15.2

120 2.7 5.3 7.8 10.3 11.0

140 2.4 4.6 6.7 8.9 9.7

160 2.1 4.0 5.9 7.8 8.6

180 1.9 3.6 5.3 7.0 8.6

200 1.7 3.2 4.8 6.3 7.8

___________________________________________________

Using a binocular or optical finding tube for ob-

servation can help to improve the situation and in-

crease the eye resolution (in our case to increase an-

gle β) in numbers equal to multiplicity of a binocular

and finding tube increase (Kolomiychuck. 1975. Hi-

drography…). But even if angle β is reduced by a

factor of 10 it will means according to (2), that the

385

angular accuracy of defining masts alignment is in-

creased by a factor of 10, as Table 1 shows. But it

doesn’t solve the problem of small-sized vessels nei-

ther in the maneuvering zone (distance of 4-8 miles),

nor in all the distances of close quarter (distance of 4

miles), to say nothing of the distances in the zone of

situation appraisal (8-12 miles). As a result, the fol-

lowing situation is possible (Fig. 3): the navigator of

a large ship observing the masts alignment of the

oncoming small ship has come to the conclusion

that it is proceeding on a reciprocal course head-on

(β<ε) and decided to act according to Rule 14, alter-

ing the course to starboard. The navigator of a

small ship, who has had the possibility to determine

the masts alignment of a large ship, come to the con-

clusion that the masts of an oncoming ship are not

in line (β> ε) and, accordingly, the ships are pro-

ceeding on reciprocal courses and he decided to

take head-on maneuvering under Rule 15, altering

the course to port and keeping out of the way of the

ship on his own starboard. As a result, there was a

situation schematically presented on (Fig. 1).

●

β>ε

β<ε

●

Figure 3. A navigator of small ship A sees the masts a large

ship C not in line, and he think the ships are proceeding on re-

ciprocal courses, and a navigator of large ship C sees the masts

of small ship A in line and he thinks the ships are proceeding

head-on

3 CLEARING UP THE HEAD-ON SITUATION

ACCOUNTING MASTHEAD LIGHTS AND

SIDELIGHTS

By night time the criteria for ships in head-on situa-

tion could be simultaneous visibility of sidelights or

masthead lights in line. As to the criterion of deter-

mining head-on situation by the alignment of mast-

head lights, it is evidently that it is not better than

the criterion of determining head-on situation by the

alignment of the masts. Both of them have the same

shortcomings. As to the criterion of clearing up the

head-on situation by the visibility of sidelights, in

our opinion, thought it is not perfect, it has some ad-

vantages in comparison with the criteria of clearing

up the head-on situation by alignments of masts or

masthead lights. The point is that in compliance with

Rule 21 to COLREG-72 “… Each sidelight shows

an unbroken light over an arc of the horizon of

112.5o and so fixed as to show the light from right

ahead to 22.5o abaft the beam on its respective side.

In Annex 1 to COLREG-72 it is defined more exact-

ly that.” In the forward direction, sidelights as fitted

on the vessel shall show the minimum required in-

tensities. The intensities must decrease to reach

practical cut-off between 1 degree and 3 degrees

outside the prescribed sectors.” It means that having

difference up to 180±3o in “nearly reciprocal cours-

es” approaching vessels can observe the sidelights of

one another: it will seem to them that they are pro-

ceeding on opposite courses, i.e. head-on. The same

situation can arise when two ships are approaching

each other “not head-on”, but on opposite course

(parallel course), in the case, when the course angle

of observed ship in visibility of sidelights (3 miles)

has the meaning up to 3o, i.e. when the distance be-

tween course lines is about 1,5 cables and there will

arise the risk of collision because of the hydrody-

namic interactions of the ships. These circumstances

could have been taken as more precise definition of

the notation “nearly reciprocal courses”. They are

supposed to be the courses, the differences of which,

is within the limit of 180 ±3o. However, the substan-

tial limitation, of criterion of the determination of

head-on situation by the visibility of both sidelights

is that it can be only applied at small distances be-

tween the ships because of their poor visibility.

As applied to clearing up the quantitative criteria

of meeting of the ships proceeding on reciprocal

(nearly reciprocal) courses head-on, we have put a

special emphasis on the fact that the above-

mentioned criteria could have been the same, that is

they could have been implemented only under per-

fect conditions of navigation, when no external fac-

tors influence upon ships′ movement and when the

ships could have been able to proceed without drift-

ing and sheering along the course line (Fig. 1,

Fig. 2). But the case it not often like this.

In practice in most cases of ship’s navigation, any

ship is exposed to winds and currents, and because

of that, first the ship, is moving with drift angle, that

is, not along the course line but on track line and, se-

cond, the ship lab ours yawing. As a result, the ships

can move head-on (move on reciprocal track lines),

though their courses difference can be other than

180

. Moreover, due to yawing it can be alternating,

either larger or smaller than 180

. By daytime for the

same reason, masts alignment of oncoming chip

can’t be observed, they can be either aligned or not

386

aligned, and at night time only one sidelight can be

observed – if the ship is moving with constant drift

angle and both sidelights can casually appear – if the

ship is moving with yawing (Fig. 4).

N N

COG

A C

Figure 4. Ships proceeding on reciprocal course

In case, ships are proceeding with drift angle, it

would be correctly to say, in our opinion that they

are meeting on reciprocal track angle.

4 CLEARING UP THE HEAD-ON SITUATION

WHEN USING RADAR

If the ships are proceeding with visual drift angle,

instantaneously received criterion for clearing up

head-on situation is not perceived at all. The only

things to be undertaken in this case is to solve this

problem in classic way, i.e. by relative plot ling

method, observing the oncoming ship’s alignment

changes and distance to it by the radar. However, it

should be implied that the question is about ships

movement on nearly reciprocal route angles with

relatively small course angles of each other and

nearly equals to drift angle. That’s why occasional

errors of measuring, especially of bearings will

greatly influence upon the results of relative plot-

ting. Really, assume that the ships are preceding at

speed of 10 knots on reciprocal courses with track

angles and at a distance of 5 miles the navigators,

observing with binocular or through optical finding

tube, sight masthead lights supposedly not in line. In

fact, it could be true, as under the condition of the

problem, the ships are proceeding with drift angle.

The navigator of A ship thinks that C ship is on his

starboard side, and the navigator of C ship think, that

A ship is on his portside. Nevertheless, the navigator

of A ship decided to define more exactly head-on

situation and he measured the bearing of C ship and

distance to it by radar, and three minutes later he re-

peated his measuring again. Under the condition of a

problem the C ship’s bearing must not change, but

due to occasional errors of gyrocompass (and with

probability of 95% they can reach values ±0,5

(Di-

rections on…1987) it turned out that at a distance

=5 miles, bearing B

was 89,5

in the first measur-

ing, and in the second measuring at a distance D

= 4

miles bearing was B

= 90,5

. Calculation of closest

point of approach by a formula:

BDD

cpa

∆

(3)

where ΔB = B

-B

, ΔD = D

–D

, which gives it ac-

curate to the component of 2

order infinitesimal

with minor values d

cpa

(Luschnikov, E. M. 2007.

Ships′...), and also relative plotting “made sure” the

navigator of A ship that C ship would be on his re-

ciprocal, but parallel course and pass his starboard at

a closest point of approach (CPA) d

cpa

= 3.5 cables

(Fig. 5). It is not excluded, that the navigator of C

ship also observed distance and bearings changes of

A ship and his results were that at a distance of 5

miles A ship’s bearing was equal to 270,5

and at a

distance of 4 miles it was equal to 269

, though, in

fact A ship’s bearing did not change and was equal

to 270

. As a result of relative plotting and the above

occasional errors in taking bearing, he “cleared up”

that A ship was proceeding reciprocal but parallel

course and it would pass on his port side at a close

quarter distance of 3.5 cables sufficient for safe

passing (Fig. 6). Both navigators could regard that

ships would pass at a sufficient distance, but actually

they were proceeding reciprocal track angles head-

on.

А B

true

LОD

cpa

seeming

LОD

Figure 5. Possible result of relative plotting aboard A ship,

when ships are proceeding on reciprocal track angles. The re-

sult was caused by random error in taking bearing

true

LОD

. B

seeming

LОD

cрa

Figure 6. Possible result of relative plotting aboard B ship,

when ships are proceeding on reciprocal track angles. The re-

sult was caused by random error in taking bearing closest point

of approach

We cannot ignore one more situation, under

which radar observation aboard A ship has showed

that at a distance of 5 miles A ship’s bearing is equal

to 269.5

, and at a distance of 4 miles it has

changed to 270.5

. In that case a relative plotting

387

showed that A ship was crossing C ship’s course and

would pass it at a closest point of approach of 3.5

cables (Fig. 7). A ship’s navigator thinking that both

ships, even if they are proceeding on reciprocal par-

allel courses, but at a short distance of closest point

of approach d

cpa

, and taking into consideration small

bearing changes of C ship (even 1

is a sign of risk

of collision) has decided to act in compliance with

Rule 14, altering course to starboard. But C ship’s

navigator, computing the situation of meeting on

crossing courses and A ship as being on his star-

board has decided to act in compliance with Rule 15

and keeping out of the way of A ship, turned port

side and as a result the situation of meeting has aris-

en which could lead to ships’ collision of which we

have mentioned earlier (Fig. 1) .

seeming

LОD

cpa

C B

true

LОD

А D

Figure 7. Possible result of the plotting on C ship when two

ships are proceeding on reciprocal track angles. The result was

caused by random errors in taking bearings

Thus, we have made sure that neither visual nor

radar observation permit to determine with confi-

dence the fact of ships’ approaching on reciprocal

courses (with track angles). That’s why in this case

of uncertainty, for want of something better, we

should comply with Rule 14 of COLREG :

“…When a vessel is in any doubt as to whether such

a situation exists she shall assume that it does exist

and acts accordingly…”, i.e. alter course to star-

board in due time. But the whole problem lies in that

every navigator has his own degree of doubt…

5 CLEARING UP THE HEAD-ON SITUATION

WHEN USING AUTOMATIC

IDENTIFICATION SYSTEM

During the past few years many ships are being

equipped with new technical aids to navigator, in

particular, automatic information systems (AIS).

They allow the ships’ meeting within the range of

VHF coastal station (about 20 miles) to exchange in-

formation about current positions of the ships, their

speed, track angles, etc. That’s why it is interesting

to clear up their capabilities in order to determine

head-on situations.

Ships’ coordinates related to the same time and

received from AIS allow determining the distance

between ships and an oncoming vessel’s bearing.

Actually, if at some instant of time t

we received

coordinates φ

and λ

of our ship and coordinates

and λ

of the oncoming vessel, distances D

and

between ships and the oncoming vessel’s bear-

ings B

and B

at those instants of time can be de-

termined by formulae:

(

)

( )

ϕλλϕϕ

cos−+−=

(4)

cos)(

аrctgB

ϕϕ

ϕλλ

−

(5)

( ) ( )

ϕλλϕϕ

cos−+−=

(6)

cos)(

аrctgB

ϕϕ

ϕλλ

−

(7)

where φ

- an average latitude between vessels .

To simplify these judgments, assume, that navi-

gator takes place near Equator and φ

=0. In this case

difference of distances and difference of bearings

are:

( ) ( )

(

)

(

)

bobo

λλϕϕ

−+−−

−−+−=∆

(8)

=∆B

−

)(

аrctg

ϕϕ

λλ

)(

аrctg

ϕϕ

λλ

−

(9)

Knowing the difference of distances and differ-

ence of bearings and taking info account the most in-

teresting for practice the occurrence of small dis-

tances of close quarter approaching of ships we can

use formula (3), to find the distance of close quarter

approaching or we can determine it using method of

relative plotting.

Root-mean-square errors of distances measuring

and measuring of bearings m

can be found by

formulae, following from equations (6) and (7)

(Bukaty, V. M. 2005. Research…)

ϕλ

(10)

ϕλ

(11)

where m

φλ

- a root-mean-square error of determining

ships’ coordinates (the errors is considered to be

identical by latitude and longitude).

For larger simplicity of judgment, assume, the

ship are approaching one another meridian so that

longitudes difference will equal 0

and latitudes dif-

ference at the instant of time t

, will be 5′. Assume,

that at the instant of time t

it will be 4′, i.e. at the in-

388

stant of time t

the distances between ships are 5

miles and at some instant of time t

– 4 miles. Dis-

tances difference is 1 mile. Taking into account that

AIS transmits the positions received from receiver-

indicator NSS we calculate root-mean-square errors

of determining distances and bearings by formulae

(10) and (11). Assume NSS is working in the usual

condition. Root-mean-square coordinates errors are

a factor of m

φλ

= ± 20-25 m, and double errors (with

probability 95%) will be a factor of ± 40-50 m (IMO

Resolution A.953(23). 2003). According to (10) and

(11) at instant of time t

with probability of 95% dis-

tance error

between ships is ± 0.5

, and error of on-

coming ship’s bearing is ± 0.44

. At instant of time

the error of bearing determination is ± 0.55

, and

the error of distance determination is just the same.

The errors of distance determination as above indi-

cated are not great and they may be ignored. But the

point is that bearings defining within the distances

of maneuvering zone end practically the same

whether we use AIS or radar observation. The rela-

tive plotting may show the same results and the

same situations of approaching ships as we have

considered above when writing about radar observa-

tions.

If necessary to consider an example when the dis-

tance differences between ships at the time of meas-

uring is equal to 2 miles (measures are being done

every 6 minutes at the same ships’ speed), then for

the distance of 5 miles (1

measure) the error of

bearing measuring would be the same ± 0.44

, and

for the distance of 3 miles (2

measure) it would be

± 0.73

according to (11). It won’t improve the situa-

tion, more than likely; deteriorate it i.e. the seeming

approaching situation might happen not to be in ac-

cordance with the truth. In this example AIS fails to

gain even to radar observation, where the error of

taking bearing can be considered as independent of

distances between ships.

It is of interest to examine AIS scope for much

earlier ships’ approaching situation. Suppose, that

under the conditions of previous example ships

started using the information of AIS at a distance of

20 miles. It means the errors of distance determina-

tion will not be changed and can as before be ig-

nored because of their infinitesimal, and errors of

bearing determination will reduce to one-quarter,

adding a factor of ± 0.1

according to (11). But, in

spite of the above, owing to distances increasing to

one-fourth, closest point of approach will increase

being equal to 6.6 cables as to (3). Owing to random

errors of taking bearings we, as a matter of fact, re-

ceive the same variants of approaching situation

from AIS, as we have considered them from radar

observations.

Thus, the use of AIS, taking positions from SNS,

funning in operation condition in order to clear up

the situation when ships are meeting on nearly recip-

rocal courses cannot solve the problem. And we can

repeat again and again the recommendations of Rule

14 that when the vessels are meeting on nearly recip-

rocal courses and if there is any doubt as to whether

such a situation exists we shall assume that it does

exists and other the course to starboard in due time.

If the information is entered into AIS from NSS,

running in differential condition, the random error of

ships’ positions with arability of 95% could be taken

as equal to 10 m (IMO Assembly Resolution. 2003).

Here according to (11) root-mean-square of bearing

error will equal to ± 0.1

when the distance between

ships is 5 miles and about ± 0.25

when the distance

is 20 miles.

6 CONCLUSION

Correspondingly, closest point of approach at the

same distance difference of 1 mile, as in previous

examples, will be equal to 0.7 cables in the first case

and 3.3 cables in second one according to (3). Such

a small closest point of approach of 5 miles at a

starting distance would indoubtly indicate that the

ships are meeting on reciprocal course (head-on sit-

uation). At a starting distance when the ships are 20

miles apart and the information about ships’ position

is entered info AIS from NSS, operating in differen-

tial condition, a seeming closest point of approach

(3.3 cable) is such that it is able to lead a navigator

into error as to the approaching situation. Thus, AIS,

having received ships’ positions from NSS, operat-

ing in the differential condition, allow a navigator to

make proper judgment about the ships’ meeting on

reciprocal courses even at such a small distance dif-

ference between them at the time of measuring as 1

mile.

REFERENCES

Bukaty, V. M. 2005. Research Investigations of Automatic In-

formation Systems′ Means for Increasing Ships′ Safe Pass-

ing. Report on SIW/BSAFF, edited by Bukaty V. M.

No.2004-03. Kaliningrad. – 26 p.

Directions on Arranging Pilot Service aboard Sta-going Ships

of Fishing Fleet USSR. 1987. Leningrad, Transport

Karapuzov, A. I. & Mironov, A.W. 2005. Maneuvering of

Large-tonnage Ships. Novorossiysk, NGMA.

Kolomiychuck, N. D. 1975. Hidrography. Moskva, GUNIO

MO SSSR

Lushnikow, E. M. 2007. Ships′ Navigation Safety. Kaliningrad,

BSAFF.

Snopkov, W. I. 2004. Ship′s Navigation: Text-book Sunct-

Petersburg, Professional.

IMO Assembly Resolution A.953(23) 5th Dec. 2003. World-

wide Radionavigational System.