Stroke rate 20 spmSpeed 0 km/hSplit --:-- /500 mPower 0 WDistance 0 mPhase readyHeading 0°FPS 0

Drag to look around, wheel or pinch to zoom. The blades dig in at the catch, push through the drive, and are feathered flat on the recovery.

Stroke rate 20 spm

Effort

Speed 0 km/h

English Rowing on the River Cam: Stroke Timing, Drag and Power

Row a single scull past willows, a boathouse and a stone bridge. Set stroke rate and effort, keep both oars in time, and see how drag ties speed to power. Virtual only.

Stroke

Live readouts

Boat speed over the last 40 s

Force on the boat through one stroke

2D plan of the river

Challenge

Experiment: stroke rate vs speed

Each row simulates 80 s at the current effort and port/starboard timing, then reports the cycle-averaged speed.

Independent numerical checks

Controls

Start rowing begins the stroke; Stroke rate and Effort change it live. Drag to orbit the camera, wheel or pinch to zoom, or choose Beside / Behind / Above.
Timing offset delays the starboard oar behind the port one; Balance gives one side more power. Either one makes the boat yaw (turn); foot steering damps it at the cost of extra drag.
Sync: on forces both oars together (offset and balance zero).

The science

Drag. A hull moving at speed v through water feels F_drag = ½ ρ C_d A v². For a single scull the effective product ½ ρ C_d A ≈ 3.6 kg/m (wetted area about 1.3 m², C_d ≈ 0.0055 including wave drag) so P = F v = 3.6 v³: doubling the power raises speed by only 26 %.

Oar as a lever. The rower pulls the handle (inboard 0.88 m from the gate) with force F_h; the blade is 2.0 m outboard. Torque balance about the gate gives a blade force F_b = F_h l_in/l_out = 0.44 F_h. For the system boat + rower + oars the only external horizontal force is the water force on the blades, so the propulsion is F_prop = η F_b cosθ with θ the oar angle from the perpendicular and η ≈ 0.85 for blade slip.

Stroke. Handle force is a half-sine over the drive (about 38 % of the cycle at 20 spm), zero on the recovery. The oar sweeps from +50° (catch) to −40° (finish). Surge: M dv/dt = F_port + F_stbd − k v|v|, M = 102 kg (boat 14 + rower 85 + oars 3). Yaw: I_z dω/dt = (F_port − F_stbd) a − c ω with oarlock offset a = 0.95 m: an oar that pulls early or harder turns the boat; the course correction costs k(1 + 2ψ²).

Checks. Constant force gives v(t) = √(F/k) tanh(t √(Fk)/M); at steady state the cycle impulse and energy of thrust equal those of drag, and the mean speed is close to √(F̄/k).

Simplifications. The mass of the rower is lumped with the hull (no momentum exchange between body and boat during the slide, which makes real boat speed surge within a stroke), no added water mass, blade slip a constant efficiency, wind and stream ignored, hull reflection is a mirror trick. Virtual only. Models built with Blender, scene by Three.js.