Cycling Aerodynamics and Physics

Martin's validated model sums aerodynamic, rolling, bearing and drivetrain losses, the gravity term on gradients and kinetic energy changes.

Source: Martin et al., J Appl Biomech 1998 · recall

Drag force = 0.5 x air density x CdA x v squared, so doubling air speed quadruples the force.

Source: Martin et al., J Appl Biomech 1998 · recall

Power is force times speed, so aerodynamic power scales with v cubed.

Source: Martin et al., J Appl Biomech 1998 · recall

Because aero power scales with the cube of speed, 2 x 2 x 2 = 8 times the power.

Source: Martin et al., J Appl Biomech 1998 · applied

At racing speeds on the flat, aerodynamic drag dominates; rolling resistance and drivetrain losses make up the rest.

Source: Martin et al., J Appl Biomech 1998 · recall

Rolling resistance force is roughly constant, so the power it absorbs rises about linearly with speed.

Source: Martin et al., J Appl Biomech 1998 · recall

The model explained about 97% of the variation in measured power, with errors of a few watts.

Source: Martin et al., J Appl Biomech 1998 · recall

Air density (rho) depends on altitude, temperature, pressure and humidity, not on the rider.

Source: Martin et al., J Appl Biomech 1998 · recall

CdA combines a dimensionless drag coefficient with an area, so it is given in square metres.

Source: Debraux et al., Sports Biomech 2011 · recall

1.1 cubed is about 1.33, so the aerodynamic part of the power demand rises by roughly a third.

Source: Martin et al., J Appl Biomech 1998 · applied

The standard atmosphere gives about 1.225 kg/m3 at sea level and 15 C.

Source: International Standard Atmosphere (ISO 2533) · recall

Air density drops by about a tenth for each kilometre of altitude near sea level.

Source: International Standard Atmosphere (ISO 2533) · recall

Lower air density at Mexico City's altitude reduced drag enough to outweigh the lower oxygen availability.

Source: Crouch et al., Sports Eng 2017 · recall

Drag falls with density, but maximal aerobic power also falls; the net effect depends on altitude and event length.

Source: Crouch et al., Sports Eng 2017 · applied

Density is inversely proportional to absolute temperature, so hot air offers slightly less drag.

Source: International Standard Atmosphere (ISO 2533) · recall

Going from 278 K to 308 K lowers density by about 10%, which cuts aerodynamic power at a given speed by the same share.

Source: International Standard Atmosphere (ISO 2533) · applied

Water vapour is lighter than the nitrogen and oxygen it displaces, so humid air is slightly less dense.

Source: International Standard Atmosphere (ISO 2533) · recall

For the same power and CdA, lower air density in the heat allows a higher speed, so splits are not directly comparable.

Source: Crouch et al., Sports Eng 2017 · applied

The drag force measured reflects both CdA and air density; separating them needs temperature, pressure and humidity.

Source: Debraux et al., Sports Biomech 2011 · recall

With power proportional to density x v cubed, speed rises by about the cube root of 1/0.9, roughly 3.5%.

Source: Martin et al., J Appl Biomech 1998 · applied

Wind-tunnel and track data put top time-triallists at roughly 0.20-0.23 m2.

Source: Crouch et al., Sports Eng 2017 · recall

An upright road position roughly doubles the drag area compared with the best time-trial positions.

Source: Crouch et al., Sports Eng 2017 · recall

0.5 x 1.225 x 0.01 x (11.1 m/s) cubed is about 8 W.

Source: Martin et al., J Appl Biomech 1998 · applied

Cd reflects shape and flow behaviour; multiplied by frontal area it gives CdA.

Source: Debraux et al., Sports Biomech 2011 · recall

Measured projected frontal areas of riders in aero positions are typically around 0.3-0.4 m2.

Source: Debraux et al., Sports Biomech 2011 · recall

How smoothly air flows around the body, the Cd part, varies with posture, clothing and shape.

Source: Debraux et al., Sports Biomech 2011 · applied

A few watts saved at race speed adds up; over 180 km a small CdA gain can be worth several minutes.

Source: Crouch et al., Sports Eng 2017 · applied

Per kilometre the time saved in seconds is larger when you are out there longer, even though the watt saving is smaller.

Source: Crouch et al., Sports Eng 2017 · applied

Tunnels often quote drag force at a reference speed, which converts to CdA with density and speed.

Source: Debraux et al., Sports Biomech 2011 · recall

Each 0.01 m2 is about 8 W at 40 km/h, so 0.02 m2 is worth roughly 16 W.

Source: Martin et al., J Appl Biomech 1998 · applied

Air right next to a surface is slowed by friction, forming a thin boundary layer whose behaviour shapes drag.

Source: Crouch et al., Sports Eng 2017 · recall

A turbulent layer resists separation, delaying it and producing a smaller low-pressure wake.

Source: Crouch et al., Sports Eng 2017 · recall

Like dimples on a golf ball, texture can trigger an earlier transition to turbulence on cylinders such as arms.

Source: Crouch et al., Sports Eng 2017 · recall

At a critical Reynolds number the boundary layer becomes turbulent and drag drops sharply, the drag crisis.

Source: Crouch et al., Sports Eng 2017 · recall

It depends on speed, size and fluid viscosity and predicts whether flow is laminar or turbulent.

Source: Crouch et al., Sports Eng 2017 · recall

On bluff shapes at cycling speeds, a smooth surface may keep a laminar layer that separates early, increasing drag.

Source: Crouch et al., Sports Eng 2017 · applied

Their 2014 tests found shaved legs reduced drag by a few percent, estimated at about 50-80 seconds over 40 km.

Source: Specialized Win Tunnel, 2014 · recall

Kammtail designs cut off the tail where little flow benefit remains, saving weight and side force.

Source: Crouch et al., Sports Eng 2017 · recall

Each texture triggers transition at a particular Reynolds number, so suits are tuned to expected race speeds.

Source: Crouch et al., Sports Eng 2017 · applied

Fluttering material creates unsteady separated flow, increasing drag beyond its small area.

Source: Crouch et al., Sports Eng 2017 · recall

Tunnels control air speed and yaw, making small differences measurable and repeatable.

Source: Debraux et al., Sports Biomech 2011 · recall

Riding at steady speeds on an indoor track with power measurement allows CdA to be estimated with little wind.

Source: Debraux et al., Sports Biomech 2011 · recall

If CdA and Crr are correct, the modelled elevation profile matches the real road; the values are tuned until it does.

Source: Chung, Estimating CdA with a power meter (2012) · recall

CFD solves flow equations numerically, allowing many shapes to be screened before physical testing.

Source: Crouch et al., Sports Eng 2017 · recall

Measuring air speed and density on the bike removes some of the guesswork about wind in field tests.

Source: Debraux et al., Sports Biomech 2011 · recall

Gusts, traffic and small position changes make field results less precise unless tests are repeated carefully.

Source: Debraux et al., Sports Biomech 2011 · recall

How quickly speed falls when coasting on a flat surface reflects combined aerodynamic and rolling resistance.

Source: Debraux et al., Sports Biomech 2011 · recall

Equipment ranking can change with yaw, so results are reported across a range of wind angles.

Source: Crouch et al., Sports Eng 2017 · recall

Returning to a baseline checks for drift in conditions and rider position over the session.

Source: Debraux et al., Sports Biomech 2011 · recall

Absolute CdA varies by method; within-method comparisons of set-ups are more reliable than cross-method totals.

Source: Debraux et al., Sports Biomech 2011 · applied

Wheel-following at short gaps reduces the trailing rider's drag by roughly a third or more.

Source: Kyle, Ergonomics 1979 · recall

The trailing rider raises pressure behind the leader, reducing the leader's drag by a few percent.

Source: Blocken et al., J Wind Eng Ind Aerodyn 2013 · recall

Riders in the middle and rear of a large peloton experienced only a small fraction of solo drag.

Source: Blocken et al., J Wind Eng Ind Aerodyn 2018 · recall

The low-speed wake behind a rider mixes out with distance, so the shelter weakens.

Source: Crouch et al., Sports Eng 2017 · recall

At the long gaps required, the wake has largely recovered, so the remaining benefit is small but not zero.

Source: Crouch et al., Sports Eng 2017 · recall

Blocken showed a vehicle behind a rider raises pressure behind them, reducing drag, which can matter in time trials.

Source: Blocken et al., J Wind Eng Ind Aerodyn 2016 · recall

In a crosswind the wake is displaced sideways, which is why echelons form diagonally across the road.

Source: Crouch et al., Sports Eng 2017 · recall

On steep climbs speed is low and gravity dominates, so aerodynamic shelter saves little power.

Source: Martin et al., J Appl Biomech 1998 · applied

The leader's drag is close to that of a solo rider while followers ride in their wake.

Source: Blocken et al., J Wind Eng Ind Aerodyn 2013 · applied

Lower drag means less mechanical power is required to hold the same speed.

Source: Martin et al., J Appl Biomech 1998 · recall

Gravitational power = mass x g x speed x sine of the slope angle.

Source: Martin et al., J Appl Biomech 1998 · recall

1 kg x 9.81 x 4.17 m/s x 0.08 is about 3.3 W.

Source: Martin et al., J Appl Biomech 1998 · applied

Velocita Ascensionale Media is the vertical ascent rate in metres per hour, a proxy for climbing power per kilo.

Source: Crouch et al., Sports Eng 2017 · recall

At low climbing speeds, almost all power goes into lifting mass, so W/kg sets speed.

Source: Martin et al., J Appl Biomech 1998 · recall

Unless climbs are long and steep, time spent at speed makes aerodynamics the bigger factor.

Source: Crouch et al., Sports Eng 2017 · applied

Speed rises until the drag and rolling forces equal the component of gravity pulling downhill.

Source: Martin et al., J Appl Biomech 1998 · recall

The downhill force grows with mass but drag depends on CdA and speed, so the heavier rider reaches a higher balance speed.

Source: Martin et al., J Appl Biomech 1998 · recall

Aero power scales with the cube of air speed, so at climbing speeds it becomes a small share of total power.

Source: Martin et al., J Appl Biomech 1998 · recall

At high descending speeds, aero position saves the most time; at slow climbing speeds, power and breathing matter more.

Source: Crouch et al., Sports Eng 2017 · applied

Mass matters most where gravity dominates; on flats and descents it has little or even a slightly negative effect.

Source: Martin et al., J Appl Biomech 1998 · applied

Drag depends on the velocity of the air relative to the rider, which includes any wind.

Source: Martin et al., J Appl Biomech 1998 · recall

Because drag rises steeply with air speed and more time is spent on the slow headwind leg, the losses outweigh the gains.

Source: Martin et al., J Appl Biomech 1998 · applied

Time saved per watt is greater at low speeds, so modest extra power on slow sections improves total time.

Source: Swain, Med Sci Sports Exerc 1997 · applied

At moderate yaw the rim can act like a sail, producing lift with a forward component that reduces net drag.

Source: Crouch et al., Sports Eng 2017 · recall

Larger side areas produce more side force and steering torque when gusts hit.

Source: Crouch et al., Sports Eng 2017 · recall

If the air moves at the same speed as the rider, relative air speed and hence drag approach zero.

Source: Martin et al., J Appl Biomech 1998 · recall

With lower rider speed, the crosswind component makes up a larger share of the relative wind, raising yaw.

Source: Crouch et al., Sports Eng 2017 · recall

Drag differences scale with air speed squared, so an aero advantage grows into a headwind.

Source: Martin et al., J Appl Biomech 1998 · applied

Apparent wind is the vector sum of true wind and the air flow created by the rider's own speed.

Source: Crouch et al., Sports Eng 2017 · recall

Slightly easing on the fast tailwind leg costs little time, allowing more power where it buys more time.

Source: Swain, Med Sci Sports Exerc 1997 · applied

Kinetic energy = 0.5 x mass x v squared.

Source: Martin et al., J Appl Biomech 1998 · recall

Every brake application dissipates kinetic energy, which the rider must pay back in power when accelerating.

Source: Martin et al., J Appl Biomech 1998 · recall

Smooth cornering preserves speed, reducing the repeated cost of accelerating back to race pace.

Source: Martin et al., J Appl Biomech 1998 · applied

0.5 x 80 x (11.1 squared - 5.6 squared) is about 3.7 kJ, before drag losses.

Source: Martin et al., J Appl Biomech 1998 · applied

Momentum carries the rider into short rises, which is why keeping speed into a rise is efficient.

Source: Martin et al., J Appl Biomech 1998 · recall

A spinning wheel adds rotational energy, but the extra is modest and matters only when speed changes often.

Source: Martin et al., J Appl Biomech 1998 · recall

Repeated slowing and accelerating makes power bursts and handling more important relative to pure aero.

Source: Crouch et al., Sports Eng 2017 · applied

Brief accelerations cost both kinetic energy and cubic aerodynamic power; the gain is often small.

Source: Martin et al., J Appl Biomech 1998 · applied

Riders at the rear brake more and must accelerate harder, so the concertina effect stretches the group.

Source: Crouch et al., Sports Eng 2017 · recall

Because drag power rises with the cube of speed, riding unevenly at the same average speed requires more energy.

Source: Martin et al., J Appl Biomech 1998 · applied

Because power grows with roughly the cube of speed on the flat, speed moves by about a third of any power change.

Source: Martin et al., J Appl Biomech 1998 · applied

Five hours at 1% faster saves about 1% of 300 minutes, roughly 3 minutes.

Source: Martin et al., J Appl Biomech 1998 · applied

(36/40) cubed is about 0.73, and 0.73 x 250 is about 182 W.

Source: Martin et al., J Appl Biomech 1998 · applied

Time saved per watt is larger at lower speed and accumulates over a longer ride.

Source: Crouch et al., Sports Eng 2017 · applied

Work = power x time: 200 J/s x 3,600 s = 720,000 J.

Source: Martin et al., J Appl Biomech 1998 · recall

Burning 4.18 kJ of food energy to do about 1 kJ of work at ~24% efficiency makes the numbers nearly equal.

Source: Martin et al., J Appl Biomech 1998 · recall

Only about a fifth to a quarter of metabolic energy becomes power at the pedals; the rest is heat.

Source: Coyle et al., Med Sci Sports Exerc 1992 · recall

With efficiency around 20-25%, most energy leaves as heat, which the body must dissipate.

Source: Martin et al., J Appl Biomech 1998 · recall

A 4% power-equivalent saving gives roughly a third of that in speed, about 1.3%.

Source: Martin et al., J Appl Biomech 1998 · applied

Speed scales with the cube root of power/CdA, so a 10% CdA cut gives about 3.5% more speed.

Source: Martin et al., J Appl Biomech 1998 · applied