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In an episode in the tv series "I shouldn't be alive", crew members of a yacht racing team got caught in a violent storm and found themselves stranded in the Gulf of Mexico after their boat capsized. Drifting for two three days, they spotted an oil rig in a distance and decided to swim towards it. However, the ocean current that brought them near also carried them away.

Let's assume that the oil rig is of a distance 5km away and within the reach of an average strong swimmer under calm water condition. If the current speed is significant but not more than half the swimmer's average speed, there is a fair chance of reaching the rig provided that the swimmer is able to judge the current speed and direction and set his course in a direction such that the resultant path forms a straight line between his initial position and the rig itself.

Mathematically speaking, the resultant velocity (speed and direction) is the trigonometric sum of two velocity components: the current velocity and the swimmer's velocity. So my question is, how can a swimmer estimate the current velocity while floating in the sea.

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Typically, if you are out in the open ocean and do not have a GPS device you don't have any useful way to measure velocity*

This may not be a problem though, as what you are wanting is not your velocity, but an indication that you are heading in a straight line to the destination (if we assume a constant current)

To do this, what you need is something to allow you to measure parallax - in this case the obvious would be a front leg and a back leg of the oil rig. When you first start swimming, check frequently to see if you are moving left or right with respect to your target. Correct your angle by 10 degrees in the opposite direction to your perceived drift (left or right) and keep swimming. You want to reduce the side drift to zero - as this will indicate you are moving directly towards your target.

Where you have varying current, for example between two islands, you would use a different tactic as the current would be strongest mid-channel so you would have to point higher in the middle.

*If you are out for many days and have an accurate chronometer, you can get a reasonable idea as to your longitude, but that seems out of scope for this question

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I think using parallax to maintain course is a very brilliant idea! But that can only be done if there are two prominent objects positioned one behind the other along the line of sight. Not sure if there are other solutions, this is useful though. – Question Overflow Sep 18 '12 at 7:31
Yes - without parallax, you are in trouble. Ancient Polynesians used to be able to track wave/ripple patterns to identify their location - not certain that skill is easy to acquire though :-) – Rory Alsop Sep 18 '12 at 10:06

You cannot estimate the current speed and direction on the open ocean without a fixed reference or navigation aid. But you can watch a star behind the rig to make sure your track is toward the oil rig.

If you can swim faster than the current, you can always swim directly toward the oil rig and get there. You'll just have a curved track and will get to enjoy a little extra exercise.

If you cannot swim faster than the current, you will have to anticipate (swim upstream at a certain angle), and even that may not be good enough depending on your initial position.

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