Today I am gooing to show you how you can determine the risk of collision without any navigational aid. Even radar and compass are not necessary. let’s begin.

For modern shipping to survive an effective ship handling is necessary. Navigation is one of the most important aspects  of ship handling. Can you imagine, what would the world’s first ship be like?  Or for example what is that property of an object that makes it ship. That’s a difficult question to answer because it will depend on person to person. Anyways I think that the first ship was a wooden log floating in water having just enough buoyancy to carry a person or two. And one of our ancestors must have used it for crossing a river or a lake. Though he was not aware of navigational techniques. And like that, our first passenger ship was born. Ta-da. But the point is navigation is the first and most important aspect of ship handling!!!

Not much longer after the compass was invented it would have been discovered that if an object is at constant bearing and its range is decreasing it will eventually collide with us.  And primary focus of navigation is to avoid collisions. So to determine the risk of collision with a target it is necessary to determine its range and bearing. And today we are going to talk about this.Now bearing determination is not a difficult job if you have a compass. You can just put your azimuth circle on the compass and observe the target from sight vane and note down its compass bearing. And if we take subsequent bearings of the same target we can determine if its bearing is constant or not. Easy job right!! .

Now my question is can you determine the targets bearing without a compass? The answer is “NO” we can’t and it’s self-explanatory.

But can you determine that bearing is constant or not without a compass?

The answer is “YES” you can.  But how?

Let’s see how. Say you put you azimuth circle on the stand of your compass but without a compass card inside say only a flat glass is there. Then you observe the target from the sight vane and draw a line in the direction of the target on the glass with help of a marker. We know that this line represents the bearing of the target but we just don’t know its numeric value. And if we repeat the same experiment again and again at specific time intervals we can determine if the bearing is constant or not.

Even the use of azimuth circle can be omitted if we can take a simple small piece of cardboard and make a slit on it. And revolve this cardboard around the binnacle( where we usually revolve azimuth circle ). And we can determine if the bearing is constant or not.

Now, what about range how we find out the range of a target without radar or any other aid. First of all, do you think that it is possible? If yes take some time and try to find out a way to do that before reading further and let me know in comment section.

Here I am going to discuss with you a way to find the range of target without radar or any other aid. I call this method horizon method. Let’s look at it, and you will surely find it interesting


Here in above figure if observer’s eye is at “O” then “OP” is its line of sight and “x” is the minimum distance observer can see. “e” is the height of any cardboard which is placed over this giant box.

We can calculate this “x” with help of little trigonometry


So, did you found it interesting? By seeing this mathematical model many of you would have already  guessed the method to find out the range. if you are feeling little confused don’t worry  let me show you how its done.

We can do this by a simple technique.For this, we make a plate of cardboard or other hard material of a known height say “s”. By using one of our azimuth circle’s sight vane of height “e” (known)  base of the target is observed over the sight vane (not inside of it as generally done while taking the bearing) and cardboard such that top of cardboard just touches the base of the target ship. And the range is calculated according to the formula proved below. The figure shown below is not to scale.

The h= height of eye above sea

e= height of sight vane of azimuth circle

s=height of custom made cardboard

r=distance between sight vane and custom made cardboard.

b= diameter of azimuth circle/compass binnacle

x= range of target from azimuth circle/compass binnacle


Now assuming the earth is a flat surface for the range of the target. From the above figure, we can say that


where h is in meters

The above formula has some inherent limitations. And more accurate ranges can be obtained by radar only.It will be cool to experiment though at sea find the range of a target  by above formula and by radar and then compare both to check the accuracy of this formula.

let us discuss the limitations of horizon method and this formula.


  1. h is the height of binnacle above sea level which can not be determined accurately at sea by seafarers so it will cause an error in the range obtained
  2. The minimum and maximum detection range will depend on upon height of cardboard (here “s”) and diameter of binnacle(here “b”) . So depending on how much observer chooses “s” to be and  it will vary max. and min.  detection ranges.
  3. The accuracy by which you can measure “r”, “s” and “b” also affect the range obtained.
  4. Error due to refraction of light. here it is assumed that light travel in a straight line. it may not be the case in reality

Overall you can say it can provide a rough estimation of the range of  the target. But do we actually need the range of the target to determine the risk of collision? “NO” we don’t we just need to know that range is decreasing or not. It may be possible that value of range provided by this method is erroneous but it can certainly determine range is decreasing or increasing. And the best part is you don’t even have to look at the formula. It’s simple if “r” is increasing(distance between sight vane and cardboard ) then range is increasing and if “r ” is decreasing then range is decreasing.

So, you can know if the range is decreasing or not and bearing is constant or not and hence determine the risk of a collision without the aid of any navigational equipment. Isn’t it awesome guys.

let me know in the comment’s my mistakes and any suggestions!!!


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