The calculation of the speed the ship travels through the channel is dependent on the ship speed (through the water) and the water speed and direction.
When a ship is moving towards the harbour with a certain speed in a certain direction, the real speed will be different because of the influence of the current.
- Given that you are navigating from point a to point c with fullmanuevering speed v
- The current is going from point c to point b with speed f
- The angle with which the vectors cut each other of at point b is denoted α
Then we can determine the actual speed, x, that the ship is moving with from point a to point b.
The first thing to do is split the vector from point c to point b in a horizontal and vertical part. Applying the sinus and cosinus functions you can determine the lengths of these new vectors.
Where β = 2π - α
Applying pythagoras: v2 = (x + f cos(β))2 + (f sin(β))2
This can be rewritten to:
- x = (v2 - (f sin(β))2)1/2 - f cos(β)
- x = - (v2 - (f sin(β))2)1/2 - f cos(β)
One of the two values above will be positive. This is the resulting speed x.