International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 1
March 2010
69
1 INTRODUCTION
The practical use of Rule 14 article of COLREG-72
is complicated by non-indication of minimal admit-
ted distance till the oncoming vessel for the purpose
of the maneuver to keep well clear. The COLREG-
72 Comments together with ship's guide textbooks
recommend to start the maneuver «to act according-
ly to the existing situation» for this case. But ob-
scure maneuver start definition accompanied with
the nearest admitted head-on distance (i.e. ships
beam distance) at the keeping clear moment together
with other factors may be the common cause of dan-
gerous getting closer of ships which involve risk of
collision or ending with collision. Unrestricted meet-
ing distance between vessels before the maneuver
and uncontrolled beam distance at the clear moment
cause the vessels to take the clearing maneuver non-
simultaneously. More of this, if one of the vessels
watches the other have turned starboard, the former
often sustains the present course and speed until the
situation becomes threatening. But we should mind
that the vessels' head off angles defining depend up-
on the head-on distance. These angles should be as
such that at the moment of divergence the abeam
distance between the vessels has no less than pre-
scribed safe value. To fulfil such requirement navi-
gators have to solve the task on vessels meeting at a
fixed distance, that is to define their own vessels'
maneuvers so as the distance between the vessels at
the beam passage moment is no less than the pre-
scribed value. So far this task is solved by navigators
without any calculation but based upon their own
experience and ocular estimation together with
shaky ground of Rule 14 article of COLREG-72 as
quoted «acting accordingly the factors of existing
situation...».
2 ANALYTIC REVIEW
Taking into account the fact that a considerable
number of collisions take place at the meeting ves-
sels courses in particular (Karapuzov, A. I. &
Mironov, A. I. 2005. Maneuvering…) there was
suggested to bring under regulation navigators' ac-
tions at maneuvering for safe divergence. So we
made some attempts in our articles (Zelenkov, A. I.
1999. The Distance…; Karapuzov, A. I. 1986. De-
termination…) define the minimal admitted distance
between vessels approaching each other meeting on
the almost reciprocal course by the minimal nearest
admitted vessels' head-on distance criterion depend-
ing on rudder angle at the maneuver start. As the re-
sult we have deduced expression for defining mini-
mal admitted distance S
min
between the vessels at the
maneuver start and for defining necessary head-off
(turn) angles ΔC
A
and ΔC
B
for vessels A and B re-
spectively to provide the divergence at the сlosest
point of approach d
cpa
( Fig. 1):
+=∆
A
B
сpa
А
v
v
S
d
arctgС 1
min4
S
min
A d
cpa
ΔC
B
v
B
B
v
A
ΔC
А
O
l
A
l
B
Figure 1. For calculation of minimal admitted distance between
vessels approaching on reciprocal courses
Defining of Minimally Admitted Head-on
Distance Before the Ships Start Maneuvering
V. M. Bukaty & E. N. Dimitrieva
Baltic Fishing Fleet State Academy, Kaliningrad, Russia
ABSTRACT: Without stating the very fact of head-on situation, an attempt has been made to define the min-
imum admitted head-on distance between the ships in order to carry out safe maneuvering at a determined the
closest point of approach, taking into account the ships' maneuvering characteristics.
70
+=∆
B
A
сpa
B
v
v
S
d
arctgС 1
4
min
B
A
B
A
BA
SS
LL
llS ++
+
++=
2
11
min
where ν
A
and ν
B
- the vessel's speed at the turn mo-
ment; l
1A
and l
1B
- the vessels' advance at moments
of head-offs; S
A
and S
B
- the ways passed by the ves-
sels within the wheel orders fulfilment; L
A
and L
B
- the
vessels' lengths overall.
The above given task solution is eventually defec-
tive as in this regard the vessels were suggested to
turn from their courses immediately while proceed-
ing at rectilinear motion. As the result the distance,
between the vessels' fore ends at moment of the O
meeting point entry along with unaltered courses,
taken as d
cpa
, is not the nearest head-on distance as
the actual distance exceeds it. Such a deficiency has
been caused by consideration the vessels' motion
straight but through maneuverable path, i.e. turning
circle.
3 TASK SOLUTION
But starting from the rudder displacement (starboard
as required by the COLREG Rule 14 in this case)
the vessel is known to pass first so called «dead in-
terval» (that is considerable for heavy-tonnage ves-
sels) keeping the present course for a while. Than af-
ter declining the course to port that is called as the
reversed bias l
3
, the vessel will proceed to the turn-
ing circle (Fig. 2). In the theory of turning circle the
advance l
1
is called a distance for which the center
of gravity is shifted from putting the wheel to the
vessel's exit to the point at the curve of the turning
circle, that corresponds to the course alter through
90º. Meanwhile the forward bias l
2
(Snopkov, W. I.
2004. Ships′…; Woytkunsky, Y. I. & Perschitz, R.
Y. & Titov, I. A. 1973. The Ships…) is the least dis-
tance from the previous course line to point on the
turning circle curve, corresponding to the course al-
teration by the same value. The distance from the
moment of the vessel's exit to the circulation start till
her turn to 180º is called the tactical diameter D
T
.
The advance l
1
value, forward bias l
2
and the tacti-
cal diameter D
T
are give in the vessel's maneuvering
fact sheet inevitably.
Figure 2. Center of vessel's gravity path on circulation
The following correlations are typical for vessels
of all types (Woytkunsky, Y. I & Perschitz, R.Y. &
Titov, I.A. 1973. The Ships…)
T
Dl ≈
1
;
T
Dl 5,0
2
≈
;
T
Dl 1,0
3
≈
(1)
The tactical circulation radius depends on the
rudder angle ψ and vessel's rate of sailing ν. Based
on field testing results Table 1 presents the follow-
ing data: tactical circulation radius, the advance, the
forward bias of «the Atlantic» type full-freezing
trawler (FFT) at full steam ahead (FSA), at half
steam ahead (HSA), at slow steam ahead (SSA),
for rudder deflection by 15º, 25º, 35º (Karapuzov,
A. I. 1984. Ships…).
Table 1. Circulation items of the «Atlantic» full-freezing trawl-
er (FFT) type
___________________________________________________
Rate of FSA HAS LSA
sailing 13 kts 10.5 kts 7 kts
___________________________________________________
Rudder angle
15
o
25
o
35
o
15
o
35
o
15
o
35
o
Circulation 2.35 1.73 1.51 2.16 1.40 1.99 1.25
tactical
radius, cab
Advance, cab 2.03 1.51 1.40 1.92 1.29 1.75 1.25
Forward bias, 1.27 0.97 0.93 1.08 0.80 1.02 0.71
cab
___________________________________________________
As we can see from the table in fact the forward
bias l
2
makes 50% of the tactical diameter D
T
on an
average
, and the advance is approximately equal to
the tactical diameter D
T
.
Suggested that the both vessels navigators having
known the tactical diameters of his vessel as well as
the oncoming vessel's one (e.g. these data could
have been included within the information transmit-
ted by AIS) began the passing maneuver in accord-
ance with COLREG Rule 14 with turning starboard
for the distance S
min
equal to sum of advances l
1A
+l
1B
of own (A) and oncoming (B) vessels (Fig. 3).
71
Figure 3. Scheme of vessels' manoeuvering at divergence as
per COLREG-72 Rule 14 at the minimal distance equal to ad-
vances sum
We can take adequately that vessels' turning ef-
fect centers, before they achieve the course altering
by 90º, move along curves coinciding with circles
which diameters are equal to tactical diameters D
TA
and D
TB
of vessels (indicated with dashed lines at
Fig. 3).Then as we can see from figure 3 D
TB
the
closest range d to which the vessels' centers of gravi-
ty will get closer, will be placed at straightway
crossing centers of circles with diameters D
TA
and
Consequently, taking into account the geomet-
rical configuration of the task coming from figure 3
we can write down as follows:
2
2
22
2
22
+=
++
ТBТAТBTA
DDD
d
D
(2)
Then we calculate the following from equa-
tion (2):
( )
+=−
+=
22
41,012
22
TBTATBTA
DDDD
d
(3)
However we have not considered the reduction of
the closest vessels' head-on range due to that while
turning circle there will be inevitably leeway angle β
which can be estimated on the approximate correla-
tion (Karapuzov, A. I. & Mironov, A. I. 2005. Ma-
neuvering…) by reason of its low values (order of
10º-15º):
T
D
L
9,0=
β
(4)
where L - the vessel's length.
While the vessel is sailing with leeway angle she
will occupy a lane which width S is found from the
expression:
S=Lsinβ+Bcosβ (5)
where B = the vessel's breadth.
Thus we can draw the following for defining the
closest point of approach d
cpa
between the two ves-
sels:
(
)
BA
сpa
SSdd +−=
2
1
(6)
where S
A
and S
B
- the A and B vessels motion
lane widths respectively.
Otherwise we can obtain from (3)-(5) as follows:
+−
−
+=
TB
B
B
TA
A
A
TBTA
cpa
D
L
L
D
L
L
DD
d
9,0sin(9,0sin(
2
1
22
41,0
(7)
where L
A
and L
B
- the vessels A and B lengths re-
spectively.
The diameter tactical D
Tψ
at the arbitrary rudder
angle ψ is connected with diameter tactical during
rudder deflection full helm (ψ=35º) D
T35
by correla-
tion (Karapuzov, A. I. & Mironov, A. I. 2005. Ma-
neuvering …)
35
509,0
1.6
T
T
DD
−
=
ψ
ψ
(8)
Using this connection between diameter tactical
and rudder angle we can attempt to define the rudder
angle necessary for divergence at the prescribed
nearest distance. However if rudder angles are small
so the vessel's circulation diameter is larger and con-
sequently the nearest distance between vessels is
larger at the distance accepted by us for divergence
that is equal to vessels' advances sum. In this case
we can agree to limit the rudder angles to 15º on
both vessels.
For instance, we calculate the closest point of ap-
proach between vessels of FFT the «Atlantic» type
that proceed at full steam in reciprocal to each oth-
er's courses. According to the table 1 data the at the
rudder angle of 15º D
T
=436 m (2.35 cab.). The ves-
sel's length is 82.2 m, breadth is 13,6m. According
to (7) we obtain d
cpa
=337.5 m ≈ 1.8 cab. Thus if two
FFT the «Atlantic» type vessels start divergence
maneuvering simultaneously at the following dis-
tance between them
S
min
= l
1A
+ l
1B
(9)
according to COLREG Rule 14, having displaced
rudder starboard 15º, they will get closer at the di-
vergence distance no more than 1,8 cab. that corre-
sponds to mutual vessels' position abeam. After this
maneuver the vessels can set their previous courses
since theoretically the head-on distance is sufficient
for safe divergence, the more so the vessels will
make the same course for some time passing the
72
dead interval. At least the closest point of approach
will not exceed the hydrodynamic coupling distance
that amounts to no more than half of lesser vessel's
hull width at parallel reciprocal courses (Snopkov,
W.I. 2004. Ships′…).
We draw the attention that if the distance exceeds
S
min
(9) at the divergence maneuver start, the nearest
vessels' approach distance will not increase really
provided turning to previous courses are carried out
at the moment of mutual abeam vessels' position. It
is determined by the fact that while displace the rud-
der to the previous courses accounting the dead in-
terval and reversed bias the abeam distance between
vessels will be sustained approximately the same as
it was at the mutual abeam position of vessels at the
circulation curve. To increase the vessels' closest of
point approach in any case it is necessary to make
turns to the previous courses after the vessels' mutu-
al abeam position, for example, when courses are al-
tered to 90º. In this case upon the vessels' returning
to their previous courses they will diverge at the
abeam distance approximately equal to fore biases
sum. For the case with FFT the «Atlantic» type ves-
sels this would mean that they diverge at the abeam
distance amounting according to the table 1 d
cpa
≈
2.5 cab.
4 CONCLUSION
Our suggested divergence maneuver regimentation
at approaching of vessels on reciprocal courses we
find advantageous as it complies with the common
sense: the more heavy-tonnage the vessels are the
more is the closest point of approach between them
during the divergence. For example, at full steam
while rudder displacement the vessels 200m long
and 20 m wide will have the circulation diameters of
order 0.5 mile (Karapuzov, A. I. & Mironov, A. I.
2005. Maneuvering…) While rudder displacement
to 15º the circulation diameters will make up 1 mile
according to (8). Therefore in our opinion the ves-
sel's closest point of approach should make up about
1 mile which is crucially sufficient for safe vessels'
divergence maneuver according to our suggested
maneuver regimentation of vessels' minimal distance
that is equal to doubled sum of vessels advances, on
condition that the rudder displacement is 15º, turning
to previously set courses after the vessels turn is to
90º on circulation path.
REFERENCES
Karapuzov, A.I. 1984. Ships Maneuvering Safety Issues during
the Joint Trawling. Moscow: The Light and Food Industry.
Karapuzov A.I. 1986. Determination of Ships Maneuvering
Stages at Reciprocal Counter-Courses to Provide Safe
Clearance. Proceeding “Navigation and Fishing Safety”, ed.
81. Leningrad: Transport.
Karapuzov, A. I. & Mironov, A.W. 2005. Maneuvering of
Large-tonnage Ships. Novorossiysk, NGMA
Snopkov, W. I. 2004. Ships′ Navigation: Text-book. Sunct-
Petersburg, Professional.
Voytkunsky, Y.I. & Pershitz, R.Y. & Titov, I.A. 1973. The
Ship’s Theory Reference-book. Leningrad: Shipbuilding
Zelenkov, A. I. 1999. The Distance Determination for Maneu-
vering Start while ships’ Clearing at Sharp Steering Angles.
VO “Marine Technical Information Advertisement”, MMF
EI, series “Navigation”, ed. 7 (362). VO “Marine Technical
Information Advertisement”.
