Navigational lines and maps

This is a facility whereby electronic lines can be drawn on the screen.  The position, length and orientation of the lines can be adjusted, thus making it possible to produce parallel indexing lines and to draw navigational limits in channels, traffic separation schemes, poor-response coastlines etc.  It is also possible to indicate points of interest such as isolated rocks and buoys with symbols.

These allow the observer to prepare and store the pattern at a convenient time when passage planning and subsequently to recall it when required.  It is possible to move the map around the screen in order to align it with displayed radar echoes. The facility is generally used in association with automatic ground-stabilization.

The potential point of collision

The potential point of collision (PPC) is that point toward which own ship should steer at her present speed (assuming that the target does not manoeuvre) in order for a collision to occur.

The reason for displaying the PPC’s is that they assist in developing a collision avoidance strategy by showing the observer, at a glance, the courses, which are completely unacceptable, because they intersect a collision point. 

They do not give any indication of miss distance (other than in the zero case) and any attempt to extrapolate the clearing distance either side of the point is dangerous.  A safe course is one which, among other things, results in passing at a safe distance, which implies knowledge of clearing distance. 

Safe and effective use of PPC does depend upon a thorough understanding of the factors, which affect their location and movement.

The concept of collision points

When two ships are in the same area of sea, it is always possible for them to collide.  The point(s) at which collision can occur may be defined and depends upon:

The speed ratio of the two ships,

The position of the two ships.

Considering any two ships, usually one is moving faster than the other; the possibility that one is at exactly the same speed as the other and will maintain that ratio for any period of time is quite unlikely, though it may also happen.

The ship which is the faster of the two will always see displayed one and only one collision point, since it can pursue the target if necessary. 

The ship, which is the slower of the two, may see displayed two collision points, both of which must be on the target track. 

One exists where the slow ship heads toward the target and intercepts it, while another exists where the slow ship heads away from the target but is struck by it. 

Alternately there may be no way for the slower ship to collide with the faster (even though the faster may collide with the slower) because it is just not fast enough to reach the target

Note A critical in-between case of one collision point exists where the slow ship can just reach the track of the fast ship.

It is important to realize that collision points exist, whether an actual collision threat exists or not.  The only significance is that in the event of an actual collision threat, the collision points are the same for both ships. 

The behaviour of the collision point when the target ship’s speed changes

If the speed ratio is infinitely large, e.g. when the target is stationary, then obviously the collision point is at the position of the target.  If the observing ship maintains speed while the target begins to increase speed, the collision point will begin to move along the target track.  When the target speed has increased to that of the observing ship, the secondary collision point will appear at infinity.  Further increase of the target speed will move the primary and secondary collision points toward each other (not necessarily by equal amounts); eventually, own speed in comparison to target speed may be so slow that the two points will merge and then disappear. 

The behaviour of the collision point when the target changes course

If the two ships have the same speed, the collision point moves on a locus, which is the perpendicular bisector of the line joining the two ships.  The greater the aspect, the farther away the collision point will be. Theoretically, the limiting aspect in this case is 90˚, but then the collision point would be at infinity and hence an aspect of some 85˚ plus is considered the practical limit.

For a slower observing ship

When the observing ship is slower than the target, two collision points exist. And they are seen to be on the circumference of a circle whose centre and radius are dependent of the speed ratio; the circle is always on the ‘observing ship’ side of the unity speed ratio locus.  A limiting aspect can be defined which is also dependent on the speed ratio.  A slower own ship will mean that a target will have a smaller limiting aspect angle.

Aspects greater than the limit pose no hazard since the observing ship can never catch up with the target.

When the observing ship is the faster, the circle of collision points lies on the target side of the equal-speed locus.  As the aspect increases, the collision point moves farther away from the observing ship.  There is no limiting aspect and collision is always possible.

This is effectively a limiting course for the observing ship, if the actual heading is to the remote side of this line, all collision points appear on the one bow.  If own heading is inside this limiting direction, the collision point will move across the heading marker as the target changes aspect.


Own Ship on course of 000° (T) and at a speed of 10 knots, observes as follows:

            Time     Bearing Range

            0923    037° (T)           10.3 NM

            0929    036°(T)            8.5 NM

            0935    034°(T)            6.7 NM

Find the PPC.





If vessel alters course to port (O’) then there would be collision at point P1.

And if she alters course more to port nearly same as that of the target then too there would be collision at P2

How to draw:

Draw the normal plot. Extend the line WA to beyond the plot.

From centre C, draw a line to A and extend it beyond the plot.

Draw an arc – centred on W, with radius as WO so as to cut the new line CA extended.

Name the points of intersection O’ and O’’.

Join WO’ and WO’’. These are the new course to steer for collision to occur.

Draw parallel line to WO’ and WO’’ from C, so as to cut the extended line WA.

Measure off the Bearing and distance of points P1 and P2 from C.

These are the two PPCs.

The predicted area of danger (PAD)

The shortcomings of collision points can be listed as follows:

Inaccuracies in data acquisition are likely to displace the points.

No account is taken of the dimensions of the ships involved.

They offer no quantitative indication of miss distance, which is the essential data required for collision avoidance.

The logical development is to construct, around the PPC, a plane figure which is associated with a chosen passing distance and in the calculation of which due margin of safety can be allowed for the effects of data inaccuracies and the physical dimensions of the vessels involved. 

The area within the figure is to be avoided to achieve at least the chosen passing distance and is referred to as a predicted area of danger or PAD. It is essential that the user has a thorough understanding of the principles underlying the presentation with particular reference to the location, movement, shape and change of shape of the PAD.  As will be seen from the following explanation, this is not a simple subject.

In the case of the collision point there is a course which intercepts the target’s track at the given speed ratio, whereas in the predicted area of danger there are generally two intersection points.  One of these is where the observing ship will pass ahead of the target and the other where the observing ship will pass astern of the target.  The angle subtended by these two limiting courses will depend upon:

The speed ratio.

The position of the target.

The aspect of the target.

As shown in the case of the collision point, a faster observing ship must always generate a single cross-ahead and cross-astern position.  A slower observing ship produces much more complex possibilities and, depending on the three variables noted above, these might include:

Two cross ahead and two cross-astern points.

One cross ahead and two cross-astern points.

Two cross-astern points.

No hazard.

In the case of the single or primary collision point, the position at which the observing ship will cross ahead of the target is always farther from the target than the collision point, while the cross-astern point is always nearer to the target.

In the case of a slower observing ship, where there is a secondary collision point, the second cross-ahead position is nearer to the target and the associated cross-astern position more remote from it.

To indicate limits within the ‘cross-ahead/cross astern’ arc, it is necessary to draw a bar parallel to the target’s track and at the intended miss-distance closer to the observing ship’s position.

The limits defined by the arc and the bar are such that, if the observing ship were to cross those limits, then it would be at a less distance than the desired miss-distance from the target.

The PAD in practice

In order to produce an acceptable system for practical operation, these limits are normally encapsulated by a symmetrical figure such as an ellipse or a hexagon.

In the case of the ellipse, the major axis is equal to the difference between the cross-ahead and cross-astern distances as measured from the target, while the minor axis is equal to twice the intended miss-distance.  In the case of the hexagon, it is drawn from a rectangle and two isosceles triangles.  The base of the triangle is always twice the miss-distance and the vertical height is one quarter of the distance. It should be noted that the collision point is not necessarily at the centre of either of the traditional figures.

In many cases the stylized figures do not follow the limits exactly, but any bias is on the safe side.

Changes in the shape of the PAD

Due to the lack of symmetry in the geometry, which generates the area, the cross-ahead and cross-astern positions do not move symmetrically about the collision point when the miss-distance is changed.  The cross ahead position usually moves more markedly than the cross-astern position, showing the movement of the two collision points, where the primary movement is much slower than the secondary.  The overall result is an asymmetrical growth of the area with the cross-ahead position moving rapidly away from the collision point.

The movement of the PAD

As in the case of the collision point, when a danger area is violated by the heading marker the danger area will continue to move down the heading marker with the cross-ahead and cross-astern points on opposite bows.  The shape of the danger area may change but it will never move off the heading marker.  In the case of a slower ship, where either of the two predicted areas is violated, the other will move in toward the target and eventually merge with the one on the heading marker.

In the limiting case where the observing ship’s heading marker just touches the limit of either of the predicted areas of danger, the limit will remain in contact with the heading marker, although the shape of the area may change considerably.

In the non-collision case where the heading marker does not violate one of the danger areas, the areas themselves will move across the screen, changing in shape and position.   In the case of the dual areas of danger, although the movement will generally be the same as that shown for the dual collision points, a special case can arise when two danger areas may merge.  This special case indicates the possibility of two cross- astern positions existing but no cross-ahead position.  It is also possible that cross- astern positions may exist and an area of danger be drawn, which does not embrace an actual collision point.

Special cases

In some cases, for example, an end on encounter, a cross-ahead and cross-astern position is not valid.  In this context it is necessary to consider a pass-to-port and pass-to-starboard as defining the limits of the miss distance.  In the practical case, this results in the generation of a circle about the target’s position.