Walking on a boat, with and without drag

A person of mass m_p walks from one end of a boat of mass m_b and length L to the other. On frictionless water the boat slides back a distance m_pL / (m_p + m_b) and stays there. Add a linear drag force F = −k v_b and the boat drifts back to where it started, while the centre of mass of the system moves.

No dragmomentum of boat + person stays zero

Linear drag

0.00 s

Person mass m_p kg

Boat mass m_b kg

Boat length L m

Walking speed (relative to boat) m/s

Time to start and stop walking s

Drag coefficient k N·s/m

No drag

Predicted boat shift m_pL/(m_p+m_b):

Simulated boat shift:

Centre of mass shift:

Linear drag

Boat shift at the end of the run:

Furthest the boat moved:

Centre of mass shift:

Net drag impulse −k∫v_b dt must vanish, so ∫v_b dt = Δx_b → 0.