If the officers of Titanic would have read this article a disaster could have been avoided. Don’t make the same mistake yourself. Well that is an excellent way to start an article, isn’t it? Today we are going to discuss “COLLISION HORIZONS”? And how they are useful to you, let’s find out.

You might have never heard of this term “collision horizon” before!! Yes, of course, how could you because I just invented it. Though there is no single definition of collision horizon here I give you the simple version of the general definition. Later on, you will understand what are the different versions of this definition

Collision Horizon is an area or limit on radar PPI which if breached by any pre-acquired target  collision is unavoidable no matter what action is taken by the target or own vessel.

“It’s impossible” that was the first reaction of one of  my teacher to whom I told it first. But later when I explained him a bit he said he will think about it. And that’s the least  I want you all to do about it. Just give it a thought.

The definition  seem simple enough right?  It’s just like a dead zone on radar that must not be breached by any pre-acquired target. If we can calculate collisions horizon  they have enormous applications like suppose you have an ARPA which shows no matter what you do target must not come in this area of PPI. Won’t it help you take better maneuver decisions? Also, the vessel can maneuver such as to minimize the area of collision horizon when another ship is in ROC range to avoid a close quarter situation. Well, it’s out of our interest but one military application may be that missiles are to maneuver like that increase this area of collision horizon to get maximum chances of hitting the target. So how do we find these collision horizons?

Well before we find out collision horizon we need to understand them first. Then we will go step by step to calculate these collision horizons. So let’s begin

RADAR PLOTTING – if you don’t know don’t worry

To understand this concept we have to do a little radar plotting. If you don’t know radar plotting don’t worry I will explain it along the way. If you already know  you can skip to the first example. For radar plotting, we require plotting sheet’s which look exactly like your radar PPI display to which you all are already familiar with. As the target is observed on radar at a certain point on PPI we measure it’s range and bearing and using appropriate scale we plot that target on our plotting sheets. And it’s conventional to call this target O. WHY? You will know “why” after some time. After some time(T) same target is observed again for its range and bearing and this point is also plotted on our plotting sheet and it’s called A. Then we join O and A. And if it is a relative plot (for the matter of this post we will only use relative plot), this vector OA or you can say line OA in direction O to A represents the relative line of approach. Which means if the own ship and vessel observed (called target) do not alter course and speed the target will continue to follow this line OA extended from A

Then we draw our heading vector such that such that its head meets the point O or we can say from O we draw reverse of our heading. And the length of this vector to be calculated like this. Suppose time difference between O and A is “t” minutes. Now say we have a speed through  water of “S” knots. Now how much distance own ship would have covered in “t” minutes with “S” knots. It would be equal to “Sxt/60”. We plot this OW  vector on our plotting sheet then WA vector will represent the true heading and speed through water of target vessel. Also, there is something called performance delay. Suppose our ship is altering course or speed  and helm/ telegraph moment is given at 0600 and ship settled on new course at 0606. Then our performance delay is 6 minutes. For practical purposes, it is assumed that vessel followed original course until half the time of performance delay i.e until 0603 and then  altered course instantaneously.

The First Example

Guys we will we take our discussion step by step starting from easy to difficult examples. So let’s take up the first example.

Ex 1 Course alteration

Target data

0600 050 12
0612 050 8

Suppose performance delay for own ship is 6 minutes for all course alterations. Own ship course and speed are 010 @ 9.5  knots

Now calculate the range at which no matter what alteration, of course, is done by own ship it will be impossible to maintain a CPA of 2 miles. Or another way o f saying it is, calculate the “course collision horizon” for CPA of 2 miles.

Let’s plot the position of the target on plotting sheet


Here each circular ring represents 2 nm distance.

STEP 1- First plot both O and A and extended this line so as to obtain relative line of approach. AC represents relative line of approach. Then plot WO “way of own ship”(that’s why we choose  O,W,A) and length WO equals distance traveled by own ship in 12 minutes. Then WA represents “way of another ship” i.e course and speed of target ship.

STEP 2 – Taking W as center and OW as radius we draw a circle. All points on this circle represent all the possible course alteration our ship can make.


STEP 3-  Now from “A” we draw two tangents AT1 and AT2 to our circle. What do AT1 and AT2 represent? AT1 represents that if own ship alters course such that  new O(O’) goes to T1  then   AT1 will be the new line of approach. Similarly for AT2.  But they also represent something more significant that is whatever course we alter our relative line of approach can not fall outside of AT1 and AT2.

STEP 4 – Then transfer the AT1 and AT2 as tangents to our 2 miles CPA circle and where they cut our initial line of approach we get these two more points S1 and S2 . As S2 is far from center then S1 it is of no significance. Can you guess what is the importance of point S1? Actually it is the point where if own ships alters course from WO to WT1 instantaneously then target vessel will just touch our 2 miles CPA circle, means that 2 miles CPA can be maintained by course alteration by own vessel up to point S1 but after point S1 point whatever course alteration is done 2 miles CPA can not be maintained. It is our Course Collison horizon without taking performance delay into account.

Because course alterations can not be done instantaneously we have to take into account Performance Delay. We consider that until half the time of performance delay vessel was on original course and then changed course instantaneously. While traveling on initial line of approach it will be traveling with relative approach speed which is equal to  OA/(12/60) or OAx5.

Now if performance delay is 6 minutes then until 3 minutes target will travel along AC. And distance traveled equals  OA X 5 X (3/60)  which equals to (OA/4) or 1 mile.

STEP 5 – Now we cut an arc of 1 mile from S1 to the original line of approach and we get a point H. Point H represents that if the helm is given after point H. Then there is no course you can steer to maintain 2 miles CPA. This is our point of Course Collision horizon. As here no collision is happening here we can call it “Dangerous horizon” .

This is only one case we have considered. Now lets another case.

Ex. 2 Speed Alterations

All data is same as example 1 but the only difference is we have to find speed collision horizon.

Here is how it’s done.


Here the initial process is same. But  here instead of alteration, of course, we have to alter speed keeping the course same. WT1 and WT2 represent the maximum vessel can alter speed from initial WO. Similarly, AT1 and AT2 will represent the area between which the relative line of approach will lie or we can say AT1 and AT2 are limiting relative line of approach.


Similarly when we transfer these limiting lines as a tangent to our CPA circle of 2 miles. We get Point S1 and S2, as S1 is near to center we consider this to find our  speed collision horizon

As explained earlier we will calculate for half time for Performance delay how much distance is traveled. That is until half the time of performance delay own vessel traveled on the original relative line of approach and after that speed is altered instantaneously. We already know this value to be 1 mile. We cut 1 mile’s from S1 in a direction away from center on original approach line. And we get our “speed collision horizon”

NOTE: The position of S1 in this example will most probably be different from the position of  S1 in the first example and so the position of collision horizons.

Now we discuss the position of collision horizon if we can alter both course and speed.

EX 3- Alteration of both course and speed

All data is same as the initial example. Let’s see how it’s done.


This look weird right! But it’s not that difficult. Let’s see WT1 represents maximum speed own vessel can archive then taking WT1 as center a circle is drawn to represent all possible course alterations at that speed. Similar infinite concentric circles can be drawn cutting line T1T2

But for sake of simplicity I have only drawn only 3 co-centric circles. Here tangent from A to outer circle is not possible because point A lies inside the outer circle. So what does it mean? It means that no matter how much close target ship comes to 2 miles circle there will always be possible to maintain a CPA of 2 miles. Why? Because suppose if we target is at exactly at 2 miles and  we alter course such that  T1 comes to P which makes PA it’s relative line of approach which is exactly in opposite direction of the initial line of approach. It means target will start moving in opposite direction relatively. So it seems that there are no collision horizons in this case. Not so fast pal!

We know we can’t we alter course speed instantaneously but if can 2 miles circle would have been our collision horizon. That collision horizon would have no meaning because it’s just like saying that if we alter course when the range is less than 2 miles we won’t be able to maintain a CPA of 2 miles. That’s obvious, right. But courses and speed can’t be altered instantaneously so we have to consider performance delay. We follow the same procedure as explained in previous examples we assume half the time of performance delay vessel was on the original relative line of approach and we calculate that distance, which comes out to be 1 mile. From 2 miles CPA circle we cut an arc of 1 mile on the original relative line of approach and this point (H) will be our collision horizon. How? Because  we can say even  if we start altering course and speed such that PA will be our relative line of approach after point H then vessel we go beyond S which is at 2 miles circle before changing the relative line of approach so our 2 miles CPA limit is breached.

NOTE: In this example, we can’t draw a tangent from A. but in certain conditions, it will be possible to draw tangent to from A. Then our limiting line of approach will be AT1 and AT2. and rest of the procedure followed would be same. But did you notice that the limiting line of approach  forms  when the vessel is at its maximum speed? This is of great significance while determining the action to avoid collision. And it is called most effective action. And my next article will be about most effective action. Stay tuned for that.

Action by target vessel

Now you know the rules of the game and ready to  discuss action by target vessel here assuming own ship maintain course and speed. I am going to do a little fast forward here because action by target vessel will just alter the  position of A in our plot. Also, it is of little significance as we are not going to keep our course and speed same when on a collision course with the target.

Now let’s start with an example

EX 4  Course and speed alteration by target vessel

Data is not required to understand the plot so we will go without data


Here in this example, A will move along the circle drawn taking W as center and WA as a radius as the target will alter its course. Also, A will move along AW extended as target alter’s speed and maximum deviation from the initial line of approach WL1 is obtained when  the vessel is at a reverse speed(for speed collision horizon). We transfer these tangents to our 2 miles CPA. Similar to  previous examples, we account for performance delay of the target vessel and calculate the position of collision horizon. Here H is the “Course collision horizon” and H1 is the “Speed collision horizon ”. Here it is assumed that target is already at its maximum speed.

Can you tell me what will be the collision horizon if target vessel can alter both course and speed?

It will still be H. why? Because even if the target vessel can alter both course and speed still its limiting line of approach will be OT2 and OT1. In most of the cases limiting line of approach is obtained by course alteration’s unless you are doing a speed say 5 knots and maximum reverse you can go is 6 knots

Ex 5 Both ships altering course and speed

Now here we do the real deal. This seem’s like a practical situation . What will happen when both ships are altering course and speed.  Let’s check it out.


This plot looks pretty horrible, isn’t it? Well, I will explain everything in a minute. First, you see just our old beloved OAW triangle. Now if you can see it then we draw a circle taking W as a center and WO as radius this represents all possible course alterations for the own vessel. Similarly, we draw a circle whose center is W and passes through A to represent all possible alteration of course of target vessel marked “orange” in the plot. Own ship and target ship can also alter their speeds here we assume that vessels are already at their maximum speed and only can reduce speed to make things little simple, it means  that  these circles can reduce their radius too. You can work out this example assuming vessels can increase speed, there will be no difference as far as this discussion is concerned.

Now you can see as we alter course O will travel along the smaller circle  and as target alter course A will travel along the bigger circle. And OA will represent our line of approach. here the best case scenario would be when target ship alter’s course such that A goes to B and new target course will be WB and new relative line of approach will be OB. Which reverses its line of approach and hence collision horizon shift at 2 miles CPA(without considering performance delay). And there will always exist a way to reverse our initial line of approach no matter what course and speed own ship or the target are doing. So  whenever both ships can alter course and speed the collision horizon will be always at the range for what you are finding the collision horizon.

Now we draw a tangent(red) from A to our black circle and transfer it to 2 miles CPA circle. And we do the same for the pink and yellow circle. Let’s see what they signify.


H1 – where red line intersects the relative line of approach it is the “course collision horizon” for own vessel means any alterations after this point won’t be able to maintain a CPA of 2 miles. It also represents a general collision horizon as alteration of speed can not alter the relative line of approach more than this.

H2 – where the pink line intersects the relative line of approach- similarly it is the “speed collision horizon” for own ship. That after point H2 any speed alteration will not be able to maintain a 2 miles CPA.

H3- where the yellow line intersects the relative line of approach –H3 represent speed collision horizon of the target means after H3 whatever alteration of speed, will be done by target a CPA of 2 miles can not be obtained.

H4 – green point on 2 miles CPA circle – it is the collision horizon if both ships can alter course and speed. Also in this, it is course collision horizon of the target ship.

Real-life example

Here is a situation.

0600 050 0.8
0603 050 0.4

Here performance delay is 2 minutes for all alterations of course and speed. (for simplicity)

Own ship data

Length: 190 m                   Co- 210

Breadth: 32 m                   Speed- 8.5 knots

Target ship data

Length: 190 m

Breadth : 32 m

We assume that own ship only takes action. Target ship is either unmanned or OOW is sleeping. Let’s find out the collision horizon

We have all the data we require, now we do the plotting.


Let’s analyze this baby, here you see that I have also taken into account the dimension both vessels. Similar to previous examples we draw a circle using W as center to check all possible alteration of our own vessel. Then from “A” we draw tangent to this circle and we transfer this tangent to the edge of own ship because we want target vessel to just keep clear of this edge and at the end of this tangent I have drawn target vessel. In this example, this tangent should touch the right edge of the target vessel because we want right edge of the target to keep clear of the left edge of own ship. If performance delay is 2 minutes then  target vessel will travel on initial approach line till 1 minute. Relative approach speed is (OA/3)x60 = 8 knots. With 8 knots target will move on its initial relative line of approach till 1 minute which is 8x(1/60)=0.133 miles. And as calculated from plot the distance between C to S is 0.12 miles. Please note that S is the point of collision horizon without performance delay. Now we add 0.12 + 0.133= 0.253. And we mark a point H to represent this collision horizon. So before point H, we must give a helm to avoid collision with the target vessel. Any action taken after target vessel has crossed point H collision will be unavoidable. Now let’s discuss why collision horizon is necessary and its limitations.


  1. All calculations dependent on Performance delay which is highly variable and depends on characteristics of vessel, weather conditions, loaded or ballast, etc. and that might never be calculated up to the precision required for collision horizon calculations.
  2. It must be noted that while calculating general collision horizon vessels must be on collision course. If not say CPA is 1 mile the collision horizon for 1 mile CPA can be calculated
  3. The assumption that current is affecting both own vessel and target vessel in the same way, can induce high errors in calculations for collsion horizon. So while calculating collision horizons SOG and CMG to be used.
  4. Collision horizon for each target will be different so in the case of multiple target situations there may be information overload.

5.At this point, it seems that entire concept is theoretical with no practical application.


Titanic, I assume everybody must have seen this movie more than just “painting scene”.No doubt it was a beautiful love story, ok let’s not drift from the topic. Now  do you think it would have been less disastrous if Titanic would have collided head on to iceberg instead sideways? I think yes because on ship’s in forward part there is collision bulkhead and it is the strongest part of the ship. If it would have collided head on only fore peak tank would be damaged and flooded. Instead in a sideways collision more  tanks flooded and ultimately the ship sank. OOW took that action because he thought he can avoid the collision and ended up banging the iceberg sideways. I bet he was not aware of collision horizons. But if he would have been able to determine that iceberg is at a certain distance  and no matter what action is taken collision is imminent. He might have taken the right decision of a head on collision. His failure was that he was unaware about performance delay of titanic i.e. he didn’t know that titanic will turn very slow because it is very large. So it look like that collision horizons have some practical importance in close quarter situations. I am finishing this discussion with you with a question but I will continue my research on this topic.






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