A nomogram for your holidays at the sea

At a traffic boat on the Lake of Zurich

In the harbor we see the boats fastened to the jetty. What may be the force this ship may pull on the rope while swinging in the waves? You see that the rope is wound around the bollard with two 8-shaped loops. The loose end seems to be fixed somewhere by a thin rope holding only about 50kg.

According to the sketch in the nomogram the enlacement angle created by the 8-loops is about 2 x 500° = 1000°. The friction factor µ may be 0.3 (dry textile rope on cast iron). This creates an amplification factor of about 200. Hence the ship may pull at most with 50 × 200 = 10'000 kg.

But we see that these bollards will only allow a 400° enlacement for an 8-loop. And of course during a storm everything is wet and hence the friction factor will be only 0.15. Hence in our imagination we put 3 additional loops on the bollards thus getting 5 × 400° = 2000° enlacement.

2000 x 0.15 is the same as 1000 x 0.3, hence the amplification is 200 again.

Quieted in our heart we take a fine gelati and a cafe coretta (obviously we are in Italy).