Kayak Stroke Simulator
As always, I’ve been working on my forward stroke and wanted to better understand how certain aspects of technique affect speed and efficiency. I was curious about how changing the amount of force I applied at the start and end of my stroke affected how efficient my stroke was. Assuming I’m pulling just as hard on average, does it make any difference if I start pulling hard at the catch and taper off towards the end vs starting more gently and leaning into it harder towards the end when the blade exits?
I asked Claude.ai to help me develop a simulator where I could draw in a power curve (how the force from my paddle changed during my stroke) and have it estimate how fast I would go. The simulator below outputs a graph of speed over time starting from a standstill and proceeding for a few seconds until the speed leveled out. The resulting saw-tooth line shows the kayak accelerating when my paddle is in the water applying force, and decelerating when my blade comes out of the water as I switch to the other side.
Because moving your paddle blade in the water at different speeds changes how the blade interacts with that water, the simulator needed to account for some slippage differences at different forces and speeds. The force from a paddle blade is primarily pushed in the direction the blade is facing, so the simulator accounts for the blade angle throughout the stroke.
With your paddle at 90° to the water when viewed from the side, lower angles are when the blade power face is directed somewhat downwards and higher angles occur as the power face rotates up to start facing upwards. You can input the blade angle for the catch (start) and exit (end). Note that this is not accounting for a “cant” angle on the blade or a “high” or “low” angle stroke technique when viewed from the front or back. We are looking at the length of the blade and its overall angle relative to the water surface as seen from the side. For simplicity’s sake, the simulator assumes the “cant” and stroke angle is more or less constant throughout the stroke.
The Blade Drag Coefficient is essentially related to how big/wide the blade is. Smaller numbers indicate a smaller blade. The model assumes the paddle is being used in a technique that produces mostly drag. While this may seem like a big deal if you use a wing paddle or wing-paddle stroke technique, but really that would just change the drag coefficient to a lift coefficient. While they may have different numbers, the relative effect of increasing the drag coefficient is the same as increasing the lift coefficient. It may be best to just think about this as how well the paddle grabs the water, with grippier paddles having higher numbers.
Max Force is just an adjustment of where the top of the force curve is. It will raise or lower the force of the whole curve proportionally. If the whole power curve has all the points pushed all the way to the top, this means it is simulating the max force for the entire duration of the in-the-water part of the stroke.
Cadence is in strokes per minute with the strokes on both sides each being counted. One stroke on the left and one on the right is two strokes, but honestly, the model doesn’t distinguish between left and right; they are each just one more stroke.
Your paddle is only powering your forward while the blade is in the water. The Drive Fraction of the Cycle is measured as a ratio of how long the paddle is driving in the water compared to the time from the start of one stroke until the start of the next (water time plus air time). A Drive Fraction of 0.5 means the paddle is applying the force curve drawn above for half the time between the start of one stroke and the start of the next.
The model is pretty simplistic about the kayak. It is just looking at how much Mass (the boat plus paddler and anything else in the boat) is being moved and a basic Drag Coefficient. Lower coefficients are sleaker, faster boats; higher are at the slower end.
After the speed graph, you will find the Average Speed after it has come up to a more-or-less steady full speed. The Speed Swing shows how much the speed varies between the start and end of your stroke. Angle Efficiency shows how much you are losing when the paddle is not pulling straight back. Over All Efficiency includes any losses due to slippage. The Paddler Output Power is how hard you had to work as a paddler, and the Propulsive Power is how much actually went to moving the kayak forwards. Any difference between the two is due to moving extra water in such a way that it didn’t help you go forward.
This model is best at giving you a gist of what happens as you change different things about your stroke. If you happen to know precisely what your paddle drag coefficient is and have data on everything else, don’t expect this model to give you an accurate speed prediction. But if you want to know what happens when you add a little more oomph to the end of your stroke, this simulator may be fun to play around with.
There is a more detailed explanation below as well as some examples of interesting adjustments to try.
Physics model · interactive
Kayak Stroke Simulator
Draw a force curve for one paddle stroke, set blade angle and blade size, and see how the shape of the stroke — not just its total effort — changes boat speed and efficiency.
Stroke force curve
Drag the dots to shape applied blade force from catch to exit. Recovery (no force) follows automatically.
Stroke & hull parameters
Blade angle: 0° = power face down, 90° = power face straight back, 180° = power face up.
Boat speed over time
Details about the Model
What the model is trying to simulate
At its core, this is a 1D point-mass dynamics model of a kayak: it treats the boat as a single mass being pushed by a repeating stroke and slowed by drag. Everything you can adjust — force curve shape, blade angle, blade size — feeds into one differential equation:
m dv
dt
= F(t)·sin(θ(t)) − k·v2
Each stroke cycle alternates a drive phase (where your drawn force curve is active, redirected by blade angle) and a recovery phase (zero propulsive force). The model integrates this numerically, cycle after cycle, until boat speed settles into a repeating steady-state pattern — a little surge during each drive phase, a little decay during recovery. Two add-on layers sit on top of that core:
- Blade angle decomposes your applied force into a forward-propulsive piece and a wasted vertical piece via sin(θ), where 0° = power face down, 90° = power face straight back, 180° = power face up.
- Blade slip estimates how much of your power gets spent accelerating water backward rather than moving the boat, based on a quadratic force-slip relationship borrowed from propeller and oar theory: F = kblade·s2, where s is slip velocity.
What it's good for
This is best used as an intuition-building tool, not a predictive one. It's well suited to:
- Comparing shapes of effort against each other under matched constraints — e.g., front-loaded vs. even vs. back-loaded curves at the same max force, same cadence, same blade — to see how timing alone changes average speed and efficiency.
- Demonstrating why nonlinear drag punishes uneven pacing: because drag scales as v2 (and drag power as v3), speed fluctuation itself is costly, independent of total effort.
- Demonstrating why blade slip punishes force spikes doubly: slip scales as the square root of force, so wasted power scales close to F1.5 — concentrating force into a peak costs more than spreading it out, even before accounting for drag.
- Exploring qualitative equipment and technique tradeoffs — blade size vs. slip, angle consistency vs. peak force — in a way that's fast to iterate on and cheap to be wrong in.
What it's not good for
Every physical simplification here was made for tractability, not accuracy, and several are worth being explicit about:
- No wave-making drag. Real hull resistance grows steeply near a kayak's "hull speed" as bow and stern wave systems interact; this model's drag stays smoothly quadratic at any speed, so it will overestimate achievable speed at the high end.
- No unsteady or added-mass effects. Accelerating a blade (or the boat) through water costs more than steady-state drag alone accounts for — this is ignored entirely.
- One continuous propulsion train, not alternating left and right strokes — there's no yaw, no wobble, no catch-timing offset between sides.
- Blade angle and slip are modeled as independent, multiplicative effects. In reality a badly angled blade doesn't just lose a force component — it tends to slip and ventilate differently too, and the two interact.
- The force curve is a free input, not derived from a muscle force-velocity relationship or realistic joint mechanics — the model has no opinion about what a human body can actually produce moment to moment.
- Recovery phase is metabolically free in the model, which it isn't in a real body.
Settings worth trying
- Isolate the drag-smoothing effect: set blade angle catch/exit both to 90° (removes angle effects) and blade drag coefficient high (around 150, minimizing slip losses), then compare Front-loaded vs. Even at the same max force. The speed difference you see comes almost entirely from the v2 drag nonlinearity.
- Isolate the slip effect: drop blade drag coefficient to its minimum (around 15, a "small blade") and compare the same two presets — the efficiency gap should widen noticeably, since a small blade punishes spikes harder.
- Bad angle, good pacing vs. good angle, bad pacing: try catch = 20°, exit = 160° (a poorly angled stroke throughout) against catch = 80°, exit = 100° (well-angled) — see which dominates: shape of effort or blade angle.
- Cadence vs. duty-cycle tradeoff: push cadence to 100 with a short drive fraction (around 0.3) vs. cadence 45 with a long drive fraction (around 0.6) at the same max force — a real analogue of a "quick, punchy" stroke vs. a "long, sustained pull."
- Push mass and drag together: a heavier "boat" (a loaded touring kayak, mass around 130 kg) with high hull drag vs. a light, low-drag racing setup — see how much curve shape still matters when the hull itself dominates the outcome.
