A few years ago we analyzed the grounding of the Ever Given in the Suez Canal just a few days after it happened. The results are presented in a 5 min video, with then 3 support videos one of which had to do with the effect of a following current on steerage, which was likely a factor in the event. See discussion of tides and currents about 6 min into a support video.
There we presented and discussed this diagram
It shows what we mean when we say steering is inhibited in a downbound vessel with following current.
When we turn left 30º relative to the water we do indeed do that. We see in on compass. But we do not see in on the water alone. Where we would see it is if we are turning to avoid a rock ahead. The current causes us to loose actual turning relative to that rock. In other words, the heading HDG (also called course through water, CTW) changes but the COG changes less, which is the issue at hand. On the other hand, sailing into the current the maneuvers are enhanced relative to the ground.
Yesterday we got a call asking if this reckoning could be generalized into a formula which motivated some work on the topic. The above diagram we got from qtVlm app using its simulator function plus a forces current function.
Here is the geometry
Vessel moving due west at 6 kts in a 3 kt following current. Then turns left 40º but only achieves a 27º turn in COG.
Here is the trig and formula for the angle loss (beta) as a function of the turn (alpha) and the ratio of current to speed, r = C/S
We can also make a plot of the values
For example, for r= 0.4, a 35º turn will lose 10º and you only make good 25º
Here are a couple examples from Excel
