LOAD · MOVEMENT · EFFORT
Rowing physics
Shaft bend describes loading. The force, its lever arm and the oar’s rotation determine how that loading becomes work and power.
Load and movement
At the catch, the shaft can bend before the oar has swept through much angle. There is load, but little sweep work has accumulated. Work increases as that load moves through the drive.
A short, sharp peak and a longer, steadier pull can reach the same maximum load while producing different amounts of work. Holding the oar under load without further sweep adds no sweep work, although shaft bending can store elastic energy.
Bend, moment and force
Force applied through a lever produces a turning effect, or moment, about the pin. Only the component of force perpendicular to the lever contributes to that turning effect.
Moment (N·m) = perpendicular handle force (N) × pin-to-hand distance (m)
Handle force (N) = moment (N·m) / pin-to-hand distance (m)
For example, 300 N·m through a 1.0 m lever corresponds to 300 N of perpendicular force. Through a 1.2 m lever, the same moment corresponds to 250 N.
Shaft stiffness
The shaft bends under load. Its stiffness, together with the positions where that bend is measured, determines the relationship between bend angle and moment. A calibrated Moment/Bend Factor expresses that relationship.
Moment (N·m) = Moment/Bend Factor (N·m/°) × bend (°)
A stiffer shaft requires more moment to produce the same bend angle.
Work and power
Work adds up the moment carried through each part of the drive. The sweep angle in this calculation is in radians.
Drive work (J) = ∫ moment (N·m) × dθ (radians)
Power (W) = positive drive work (J) / full stroke-cycle time (s)
The full stroke cycle includes drive and recovery. Work depends on both the load and the angle through which it acts; power also accounts for the time between catches.
The relationship between this effort and boat speed also depends on hull resistance, wind, current and crew movement.