Resulting speed

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.