Capstan rope traction: top view (2D)

The capstan equation T_load / T_tail = e^(mu theta) follows from a force balance on a small rope element: friction adds dT = mu T dtheta over each wrapped angle, so tension grows exponentially along the contact arc. Every extra turn multiplies holding capacity by e^(2 pi mu); that is why a few turns let a hand hold a heavy load.

What this 2D view adds

• A top-down picture of the drum with the rope coloured by its local tension.
• Three graphs: tension along the contact arc, capacity against turns and against friction.

Honest simplifications

Ideal flexible rope, constant coefficient of friction, no rope stiffness or heating. The slip speed shown when the load exceeds capacity is an illustrative relation from the 3D lab, not a calibrated friction law. Shares its physics module with the 3D page, so both give identical numbers.