International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 4
Number 3
September 2010
309
1 INTRODUCTION
Earlier we were discussing non-traditional approach
to the earliest possible clearing up of the head-on
situation the essence of which is in defining the time
of simultaneous approach the same latitudes and
longitudes taking into account the fact that the in-
formation about ship’s movement was received by
means of Automatic Identification System (AIS)
(Bukaty, V. M. 2005. Research…; Bukaty, V. M.
2006. Non-traditional…)
2 FUNDAMENTALS OF METHOD
When using AIS at a given instant of time t
1
posi-
tions φ
g1
and λ
g1
speed v
g
and track angle TA
g
of a
given vessel and positions φ
o1
and λ
o1
, speed v
o
and
track angle TA
o
of an oncoming vessel (target). At
instant of time t
2
positions φ
g2
and λ
g2
of the given
vessel and positions φ
o2
and λ
o2
of the oncoming
vessel will be:
( )
ggggggg
TAtvTAttv coscos
11212
+=−+=
ϕϕϕ
(1)
( )
=−+=
mgggg
TAttv
ϕλλ
secsin
1212
=
mggg
TAtv
ϕλ
secsin
1
+
(1) (2)
( )
оо1оо12о1о2о
TAcostvTAcosttv +=−+=
ϕϕϕ
(3)
( )
=−+=
mоооо
TAttv
ϕλλ
secsin
1212
=
mооо
TAtv
ϕλ
secsin
1
+
(4)
In equations (1), (2), (3) and (4) t = t
2
- t
1
, φ
m
-an
average latitude between vessels .
If in a period of time t the vessels are in the same
position it will mean that φ
g2
= φ
o2
, λ
g2
= λ
o2
. Then
taking into account (1), (3) and (2), (4) we can put it
as:
(5)
In equations (5) we provided the value t with in-
dices “φ” and “λ” to indicate the time of vessels’
reach the same latitude and longitude.
Equations (5) follows:
oogg
go
TAvTAv
t
coscos
11
−
−
=
ϕϕ
ϕ
(6)
mo
o
gg
ot
TAvTAv
t
ϕ
λλ
λ
sec)sinsin(
11
−
−
=
. (7)
Possible Method of Clearing-up the Close-
quarter Situation of Ships by Means of
Automatic Identification System
V.M. Bukaty & S.U. Morozova
Baltic Fishing Fleet State Academy, Kaliningrad, Russia
ABSTRACT: The tonic discussed is an non-traditional approach to the earliest possible clearing up of the
head-on situation, consisting in defining the time of simultaneous approach to same latitudes and longitudes,
bearing in mind that the information about the ships' movement was received by means of Automatic Identifi-
cation System. If the time the ships proceed to these latitudes and longitudes is the same the collision of the
ships is unavoidable and by the time identified the head-on situation is immediately indicated. If the time is
different the ships will not be able to reach the same point and the collision will be avoided. The attempts
have been also made to evaluate the minimal admitted inequality of time when the ships' safe passage without
maneuvering is considered possible.
This method is rather attractive because it does not require any additional measurements and it is not neces-
sary to attract the Officer-in-Charge away from his main responsibility – to control the situation round the
ship.
310
If t
φ
= t
λ
, that is the vessels reach the same posi-
tion simultaneously, the collision is unavoidable.
The value of t
φ
= t
λ
then helps to obtain the time
of meeting. If t
φ
≠ t
λ
, the vessels are not able to reach
the same latitude and longitude simultaneously, that
is they are not able to be in the same position and
their meeting is impossible.
3 INDIVIDUAL CASES OF THE GIVEN
METHOD
The analysis of (6) and (7) shows:
1 In head-on situation when vessels run the longi-
tude they will reach the same latitude (meet) in
a period of time equal to:
o
g
go
vv
t
+
−
=
11
ϕϕ
ϕ
and they will reach the same longitude in a period
of time equal to:
0
0
=
λ
t
2 When vessels run the longitude the same track
one after another they will reach the same lati-
tude in a period of time equal to:
og
go
vv
t
−
−
=
11
ϕϕ
ϕ
and reach the same longitude in a period of time
equal to:
0
0
=
λ
t
However, if v
g
<v
o
, vessels will reach the same
latitude in a period of time equal to:
o
g
go
vv
t
−
−
−=
11
ϕϕ
ϕ
and reach the same longitude in a period of time
equal to:
0
0
=
λ
t
This will mean that the speed of the given vessel
is lower than the speed of the target vessel.
Or, if v
g
=v
o
, vessels will reach the same latitude
in a period of time equal to:
∞=
ϕ
t
and reach the same longitude in a period of time
equal to:
0
0
=
λ
t
.
This will mean that that the speeds of vessels are
equal.
3 In head-on situation when vessels run the lati-
tude they will reach the same longitude (meet)
in a period of time equal to:
m
og
go
vv
t
ϕ
λλ
λ
sec)(
11
+
−
=
and reach the same latitude in a period of time
equal to:
0
0
=
ϕ
t
4 When vessels run the latitude the same track
one after another they will reach the same lon-
gitude in a period of time equal to:
mo
g
go
vv
t
ϕ
λλ
λ
sec)(
11
−
−
=
and reach the same latitude in a period of time
equal to:
0
0
=
ϕ
t
However, if v
g
< v
o
m
o
g
g
o
vv
t
ϕ
λλ
λ
sec)(
11
−
−
−=
and they will reach the same latitude in a period
of time equal to:
0
0
=
ϕ
t
It will mean that the given vessel is moving more
slowly than the target vessel.
Or, if v
g
=v
o
∞=
ϕ
t
and they will reach the same longitude in a period
of time equal to:
0
0
=
λ
t
This will mean that that the speeds of vessels are
equal.
5 When vessels run different longitudes on recip-
rocal tracks they will reach the same latitude in
a period of time equal to
311
o
g
go
vv
t
+
−
=
11
ϕϕ
ϕ
and they will reach the same longitude in a period
of time equal to:
∞=
λ
t
6 When vessels run different longitudes on the
same track they will reach the same latitude in a
period of time equal to:
og
go
vv
t
−
−
=
11
ϕϕ
ϕ
and they will reach the same longitude in a period
of time equal to:
∞=
λ
t
However, if v
g
<v
o
, vessels will reach the same
latitude in a period of time equal to
o
g
go
vv
t
−
−
−=
11
ϕϕ
ϕ
and they will reach the same longitude in a period
of time equal to
∞=
λ
t
It will mean that the given vessel is moving more
slowly than the target vessel.
If v
o
=v
g
, vessels will reach the same latitude in a
period of time equal to:
∞=
ϕ
t
and they will reach the same longitude in a period
of time equal to:
∞=
λ
t
This will mean that that the speeds of vessels are
equal.
7 When vessels run different latitudes on recipro-
cal tracks they will reach the same longitude in
a period of time equal to:
m
og
go
vv
t
ϕ
λλ
λ
sec)(
11
+
−
=
and they will reach the same latitude in a period
of time equal to:
∞=
ϕ
t
8 When vessels run different latitudes on the
same track they will reach the same longitude
in a period of time equal to:
mo
g
go
vv
t
ϕ
λλ
λ
sec)(
11
−
−
=
and they will reach the same latitude in a period
of time equal to:
∞=
ϕ
t
However, if v
g
<v
o
, vessels will reach the same
longitude in a period of time equal to:
m
og
g
o
vv
t
ϕ
λλ
λ
sec)(
1
1
−
−
−=
and they will reach the same latitude in a period
of time equal to:
∞=
ϕ
t
It will mean that the given vessel is moving more
slowly than the target vessel.
If v
g
=v
o
, vessels will reach the same longitude in
a period of time equal to:
∞=
λ
t
and they will reach the same latitude in a period
of time equal to:
∞=
ϕ
t
This will mean that that the speeds of vessels are
equal.
9 When vessels meet head and head on reciprocal
arbitrary tracks, they will reach the point of
meeting in a period of time equal to:
m
og
go
g
og
g
o
g
TAvv
t
TAvv
t
ϕ
λλ
ϕϕ
λ
ϕ
secsin)(
cos)(
11
1
1
+
−
=
+
−
=
=
=
10 When the vessels run the same arbitrary tracks
they will reach the point of meeting in a period
of time equal to:
=
−
−
=
g
og
go
TAvv
t
cos)(
11
ϕϕ
ϕ
=
m
og
go
g
TAvv
t
ϕ
λλ
λ
cossin)(
11
−
−
=
However, if v
g
<v
o
, vessels will reach the point of
meeting in a period of time equal to:
312
=
−
−
−=
g
og
go
TAvv
t
cos)(
11
ϕϕ
ϕ
=
mg
og
go
TAvv
t
ϕ
λλ
λ
secsin)(
11
−
−
−=
It will mean that the given vessel is moving more
slowly than the target vessel.
If v
g
=v
o
, vessels will reach the point of meeting in
a period of time equal to:
∞=
ϕ
t
∞=
λ
t
This will mean that that the speeds of vessels are
equal.
11 When vessels run reciprocal arbitrary parallel
tracks, they will reach the same latitude in a pe-
riod of time equal to:
go
g
go
TAvv
t
cos)(
11
+
−
=
ϕϕ
ϕ
and they will reach the same longitude in a period
of time equal to:
mg
og
go
TAvv
t
ϕ
λλ
λ
secsin)(
11
+
−
=
,
however, there is always inequality t
φ
≠ t
λ
.
12 When vessels run the same arbitrary parallel
tracks the times of their reach to the same lati-
tude and the same longitude in general case is
calculated by formulas (6) and (7). Here we can
speak about different combinations of values t
φ
and t
λ
depending on relation of speeds (v
g
<v
o
,
v
g
>v
o
, v
g
=v
o
), vessels’ position at the time in-
stant t
1
(φ
g1
> φ
o1
or φ
g1
< φ
o1
, λ
g1
> λ
o1
or λ
g1
<
λ
o1
) and values of track angles TA.
In this case negativity of one of the times and
positivity of another or negativity of the both
times mean that vessels will never reach the same
latitude (-t
φ
) or the same longitude (-t
λ
), or will
never reach the same latitude or the same longi-
tude (-t
φ
and -t
λ
)
13 When vessels run arbitrary tracks the time of
their approach to the same latitude and the
same longitude is calculated by formulas (6)
and (7). If t
φ
= t
λ
, it will mean that vessels are
going to meet; but if t
φ
≠ t
λ
they will not meet.
14 When vessels run arbitrary tracks there can be
situations when t
φ
=0 and t
λ
≠ 0, or vice versa, t
λ
= =0 and t
φ
≠ 0, though vessels can simultane-
ously be at the same point. For example, it can
happen when vessels at starting position are on
the same latitude or the same longitude. Thus,
if φ
g1
= φ
o1
, λ
g1
≠ λ
o1
or φ
g1
≠ φ
o1
, λ
g1
= λ
o1
and
vessels run crossing tracks, (6) and (7) follow:
in the first case
m
oogg
1g1o
,0
sec)TAsinvTAsinv(
tt
ϕ
λλ
λ
ϕ
−
−
=
=
;(8)
in the second case
0t,
TAcosvTAcosv
t
oogg
1g
1
o
=
−
−
=
λ
ϕ
ϕϕ
, (9)
In both cases t
φ
≠ t
λ
, but meeting of vessels is not
improbable. For example, if φ
g1
= φ
o1
= 0
O
,
v
g
=v
o
, TA
g
= TA
o
± 90
O
, it is clear that vessels will
meet despite the fact that t
φ
≠ t
λ
. In this case we
can clear up the situation in the following way.
By calculated value t
λ
, if t
φ
=0, or by calculated
value t
φ
, if t
λ
= 0, are calculated by the formulas:
tt
1t
2
t
TAcostv
λ
ϕϕ
+=
, (10)
m
secTAsintv
tt
1t2t
ϕλ
ϕ
λ
+=
(11)
Then t
φ
and t
λ
are calculated by formulas:
oo
1t2t
TAcosv
t
ϕϕ
ϕ
−
=
; (12)
m
oo
1o2t
secTAsinv
t
ϕ
λλ
λ
−
=
(13)
If calculated values t
φ
(12) or t
λ
(13) are equal to
earlier calculated values t
φ
(8) or t
λ
(9), the ves-
sels are going to meet. Otherwise they will not
meet. For example, if φ
g1
=φ
o1
=0
O
, λ
g1
=0
O
, λ
g2
=
=0
O
10′E, φ
m
=0
O
, v
g
=v
o
=10 kts, TA
g
=45
O
,
TA
o
=315
O
, according to (8) t
φ
=0, t
λ
= 42 min 25.6
sec. In accordance with this value t
λ
according
formula (10) φ
o2
= 0
O
05′N. Then according to
(13) we have t
λ
=42 min 25.6 sec. As t
φ
= t
λ
, the
vessels in the given example are going to meet.
Similar example can be given for the case when t
φ
≠ 0, and t
λ
= 0. If φ
g1
=0
O
05′N, φ
o1
= 0
O
05′S, λ
g1
=
λ
o1
= 0
O
, φ
m
= 0
O
, v
g
=v
o
=15 kts, TA
g
=135
O
,
TA
o
=45
O
, according to (8) and (9) t
λ
=0, t
φ
=
=28min17.1sec. In accordance with this value t
φ
by formula (11) is calculated λ
o2
=0
O
05′E. Then
according to (13) we have t
λ
=28min 17.1sec. As
t
φ
=t
λ
, the vessels in the given example are also
going to meet.
313
4 CONCLUSION
It follows from the our analysis that:
1 The sign of the situation when vessels are meet-
ing is the equality of the time of their reach to the
same latitude or the same longitude in general
case (t
φ
=t
λ
), or equality of uncertainty
0
0
of one
of the times of their approach the same latitude or
longitude when the vessels run the latitude or
longitude respectively
2 The sign of the situation when vessels run recip-
rocal parallel tracks in general case is inequality
of times of their reach to the same latitude and
longitude, both values of times being positive.
The sign of the situation when vessels run recip-
rocal parallel tracks in particular case is infinity
of times of their reach to the same latitude and
longitude when running the latitude or longitude
the target vessel is overtaking. If they are equal to
infinity, vessels are moving at the same speed. At
the same time if t
φ
or t
λ
are positive, the vessel
is the given vessel is overtaking. If t
φ
or t
λ
are negative, the target vessel is overtaking. If t
φ
= ∞ and t
λ
=∞, vessels are moving at the same
speed.
3 The sign of the situation when vessels run the
same parallel tracks in general case is inequality
of times of their reach to the same latitude and
longitude. If both values of the times are positive,
the given vessel is overtaking. If they are nega-
tive, the target vessel is overtaking. If they are
equal to infinity, vessels are moving at the same
speed. At the same time if t
φ
or t
λ
are positive,
the vessel is the given vessel is overtaking. If t
φ
or t
λ
are negativ, the target vessel is overtak-
ing. If t
φ
= ∞ and t
λ
= ∞, vessels are moving at
the same speed.
Realization of the non-traditional approach to
clearing up the situation when vessels are meeting is
possible with the help of automatic calculating de-
vice, information to which comes from AIS and re-
sults are presented in the form of messages on the
display of ECDIS and in the form of warning sound
signals about the threat of collision.
Non-traditional approach is in no way considered
to be an alternative for the traditional way of as-
sessment of head-on situation based on radar or AIS
data and on making up relative plotting which al-
lows to define a distance and shortest time of vessels
meeting. We consider it to be an addition to the tra-
ditional method allowing to assess head-on situation
in due time at distance between ships equal to oper-
ating distance of AIS (about 20 miles) without
measurements and relative plotting, and consequent-
ly without distracting Officer of Watch from control-
ling the situation round the ship.
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, 2005. – 26 p.
Bukaty, V. M. 2006. Non-traditional Approach to Clearing- up
the close-quarter Situation of the Ships. Materials of the 5
th
International Conference “Safety at Sea Management and
Training Specialists”. 8-9 November, 2005. – p.37-40. Ka-
liningrad: BSAFF.