Move the sliders to see how speed, body cross-section, drag coefficient and stroke change the hydrodynamic drag, required propulsion power, Reynolds number and 100 m time in real time.
Choose a stroke
Swimming speed v
m/s
Body mass m
kg
Height h
cm
Water temperature T
°C
While paused, moving a slider updates the results immediately.
Live underwater drag and power
0
Drag F_d [N]
0
Required power P [W]
0
Speed v [m/s]
0
Drag coefficient Cd
0
Energy/distance [kJ/100m]
The drag arrow grows with the square of speed, while required power rises with the cube of speed (double the speed → about eight times the power). Adjust speed, body size, and water temperature with the sliders, and choose a stroke with the buttons.
Results
Drag force FD
42.3
N
Propulsion power P
76.2
W
Reynolds number Re
3.1e6
—
Equivalent 100 m time
55.6
s
Specific power
1.09
W/kg
Drag
Power
Comparison
Theory & key formulas
\(F_D = \frac{1}{2}\rho C_D A v^2\)
\(P = F_D \cdot v = \frac{1}{2}\rho C_D A v^3\)
\(Re = \frac{\rho v L}{\mu}\)
What this simulator computes
🤩
Why does swimming feel so much harder than running, even at the same speed?
🎓
Because water is about 800x denser than air. Drag scales with density, so even at 1.5 m/s the resistive force is in the tens of newtons. Try sliding the speed from 1.0 to 2.5 m/s and watch the power soar — it grows with v cubed.
🤩
Then why is breaststroke so much slower than freestyle?
🎓
During the kick recovery the body presents a much larger frontal area, raising the effective drag coefficient. Switch the stroke selector and notice the FD jump — that is exactly why elite distance times differ so much between strokes.
🤩
Where would an engineer use this kind of model?
🎓
Sports engineers use it to size propulsion power for human-powered submarines, to set CFD boundary conditions, and to compare swimsuit designs before running expensive PIV tests.
Physical model
The total resistive force on a swimmer is dominated by pressure (form) drag, well captured by the quadratic drag law $F_D = \tfrac{1}{2}\rho C_d A v^2$ where $\rho$ is water density (about 997 kg/m³ at 25 °C), $C_d$ is the drag coefficient, $A$ is the frontal cross-section and $v$ is the swimming speed.
The mechanical power the swimmer must deliver to the water is $P = F_D\,v$, which scales with the cube of speed. This is why elite swimmers can only shave fractions of a second from world records: the metabolic cost rises explosively.
Real-world applications
Race-time prediction: coaches estimate the fastest sustainable speed for a given athlete by intersecting their available aerobic power with the cubic power curve.
Equipment design: swimsuit and goggle manufacturers test prototypes in a flume and back out an effective $C_d A$ to compare designs.
CAE setup: the simple quadratic-drag estimate gives a sanity check before launching multi-million-cell CFD simulations of the swimmer-water interface.
Common misconceptions
"Doubling the speed doubles the effort" — no, drag quadruples and required power grows 8x.
"A bigger swimmer is always faster" — larger frontal area increases drag, partially offsetting the higher power output.
"Reynolds number doesn't matter for swimmers" — flow is fully turbulent (Re ~ millions). Drag coefficient is roughly Re-independent in this regime, which is why the simple quadratic law works.
FAQ
Why is water resistance much greater than air?
Water density is roughly 800x that of air. Since drag scales linearly with density, swimming drag is dramatically higher than running drag.
How does stroke affect drag?
Freestyle has the lowest drag coefficient. Breaststroke has the highest because of the large frontal area during the kick recovery phase.
What power do elite swimmers produce?
100 m freestyle world records correspond to about 2.1 m/s. Estimated mechanical power output is 200-400 W depending on body size and efficiency.
How does body shape matter?
Smaller frontal cross-section lowers drag. A streamlined posture and narrow profile reduce A in the drag equation.
Enter swim speed (v) in m/s, typical range 1.2–2.5 m/s for competitive swimmers
Input frontal body cross-section area (A) in m², typically 0.04–0.06 m² depending on posture and body type
Set drag coefficient (Cd) based on stroke: freestyle ~1.05, breaststroke ~1.35, butterfly ~1.25
Click Calculate to compute hydrodynamic drag force, metabolic power output, Reynolds number, and projected 100 m race time
Worked Example
Elite freestyle swimmer at v=2.0 m/s, A=0.048 m², Cd=1.05, water density ρ=1025 kg/m³ (seawater). Drag force F_D = 0.5 × 1025 × 2.0² × 0.048 × 1.05 = 51.5 N. Propulsion power P = 51.5 × 2.0 = 103 W. Reynolds number Re = (1025 × 2.0 × 0.22)/0.001 ≈ 450,000 (turbulent boundary layer). Projected 100 m time = 100/2.0 = 50 seconds.
Practical Notes
Higher drag coefficient in breaststroke (~1.35) versus butterfly (~1.25) reflects greater frontal resistance despite similar velocities; adjust A to account for body roll angle
Reynolds number >100,000 confirms turbulent flow; skin friction drag dominates, so suit material and body hair removal yield measurable gains
Power estimates assume 100% propulsive efficiency; actual metabolic cost is 20–25% higher due to non-propulsive movements and internal losses
Test in pool conditions matching your training: chlorinated freshwater (ρ=1000 kg/m³) versus seawater alters drag by ~2.5%