# Cycling Aerodynamics and Physics · Triathlon Level 8: Expert

Triathlon · Level 8: Expert · Insporta Book (https://book.insporta.app/triathlon/level-8/cycling-aerodynamics-and-physics/)

Cycling Aerodynamics and Physics in Triathlon (Level 8: Expert) on Insporta: 100 sourced facts behind 10 tests. Covers: the cycling power equation; and more.

The physics behind bike speed: the power equation, air density, CdA in numbers, boundary layers and surfaces, how drag is measured, drafting, climbing and gradients, wind, kinetic energy and speed-power calculations.

## Test 1: The Cycling Power Equation

- 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)
- 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)
- Power is force times speed, so aerodynamic power scales with v cubed. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)
- Rolling resistance force is roughly constant, so the power it absorbs rises about linearly with speed. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- Air density (rho) depends on altitude, temperature, pressure and humidity, not on the rider. (Source: Martin et al., J Appl Biomech 1998)
- CdA combines a dimensionless drag coefficient with an area, so it is given in square metres. (Source: Debraux et al., Sports Biomech 2011)
- 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)

## Test 2: Air Density and Conditions

- The standard atmosphere gives about 1.225 kg/m3 at sea level and 15 C. (Source: International Standard Atmosphere (ISO 2533))
- Air density drops by about a tenth for each kilometre of altitude near sea level. (Source: International Standard Atmosphere (ISO 2533))
- Lower air density at Mexico City's altitude reduced drag enough to outweigh the lower oxygen availability. (Source: Crouch et al., Sports Eng 2017)
- 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)
- Density is inversely proportional to absolute temperature, so hot air offers slightly less drag. (Source: International Standard Atmosphere (ISO 2533))
- 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))
- Water vapour is lighter than the nitrogen and oxygen it displaces, so humid air is slightly less dense. (Source: International Standard Atmosphere (ISO 2533))
- 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)
- The drag force measured reflects both CdA and air density; separating them needs temperature, pressure and humidity. (Source: Debraux et al., Sports Biomech 2011)
- 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)

## Test 3: CdA in Numbers

- Wind-tunnel and track data put top time-triallists at roughly 0.20-0.23 m2. (Source: Crouch et al., Sports Eng 2017)
- An upright road position roughly doubles the drag area compared with the best time-trial positions. (Source: Crouch et al., Sports Eng 2017)
- 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)
- Cd reflects shape and flow behaviour; multiplied by frontal area it gives CdA. (Source: Debraux et al., Sports Biomech 2011)
- Measured projected frontal areas of riders in aero positions are typically around 0.3-0.4 m2. (Source: Debraux et al., Sports Biomech 2011)
- How smoothly air flows around the body, the Cd part, varies with posture, clothing and shape. (Source: Debraux et al., Sports Biomech 2011)
- 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)
- 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)
- Tunnels often quote drag force at a reference speed, which converts to CdA with density and speed. (Source: Debraux et al., Sports Biomech 2011)
- 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)

## Test 4: Boundary Layers and Surfaces

- 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)
- A turbulent layer resists separation, delaying it and producing a smaller low-pressure wake. (Source: Crouch et al., Sports Eng 2017)
- 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)
- At a critical Reynolds number the boundary layer becomes turbulent and drag drops sharply, the drag crisis. (Source: Crouch et al., Sports Eng 2017)
- It depends on speed, size and fluid viscosity and predicts whether flow is laminar or turbulent. (Source: Crouch et al., Sports Eng 2017)
- 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)
- 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)
- Kammtail designs cut off the tail where little flow benefit remains, saving weight and side force. (Source: Crouch et al., Sports Eng 2017)
- Each texture triggers transition at a particular Reynolds number, so suits are tuned to expected race speeds. (Source: Crouch et al., Sports Eng 2017)
- Fluttering material creates unsteady separated flow, increasing drag beyond its small area. (Source: Crouch et al., Sports Eng 2017)

## Test 5: Measuring Aerodynamic Drag

- Tunnels control air speed and yaw, making small differences measurable and repeatable. (Source: Debraux et al., Sports Biomech 2011)
- 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)
- 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))
- CFD solves flow equations numerically, allowing many shapes to be screened before physical testing. (Source: Crouch et al., Sports Eng 2017)
- 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)
- Gusts, traffic and small position changes make field results less precise unless tests are repeated carefully. (Source: Debraux et al., Sports Biomech 2011)
- How quickly speed falls when coasting on a flat surface reflects combined aerodynamic and rolling resistance. (Source: Debraux et al., Sports Biomech 2011)
- Equipment ranking can change with yaw, so results are reported across a range of wind angles. (Source: Crouch et al., Sports Eng 2017)
- Returning to a baseline checks for drift in conditions and rider position over the session. (Source: Debraux et al., Sports Biomech 2011)
- 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)

## Test 6: The Physics of Drafting

- Wheel-following at short gaps reduces the trailing rider's drag by roughly a third or more. (Source: Kyle, Ergonomics 1979)
- 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)
- 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)
- The low-speed wake behind a rider mixes out with distance, so the shelter weakens. (Source: Crouch et al., Sports Eng 2017)
- 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)
- 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)
- In a crosswind the wake is displaced sideways, which is why echelons form diagonally across the road. (Source: Crouch et al., Sports Eng 2017)
- On steep climbs speed is low and gravity dominates, so aerodynamic shelter saves little power. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- Lower drag means less mechanical power is required to hold the same speed. (Source: Martin et al., J Appl Biomech 1998)

## Test 7: Climbing, Weight and Gradients

- Gravitational power = mass x g x speed x sine of the slope angle. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)
- At low climbing speeds, almost all power goes into lifting mass, so W/kg sets speed. (Source: Martin et al., J Appl Biomech 1998)
- Unless climbs are long and steep, time spent at speed makes aerodynamics the bigger factor. (Source: Crouch et al., Sports Eng 2017)
- Speed rises until the drag and rolling forces equal the component of gravity pulling downhill. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)
- 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)
- 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)

## Test 8: Wind on the Bike

- Drag depends on the velocity of the air relative to the rider, which includes any wind. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)
- 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)
- Larger side areas produce more side force and steering torque when gusts hit. (Source: Crouch et al., Sports Eng 2017)
- 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)
- 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)
- Drag differences scale with air speed squared, so an aero advantage grows into a headwind. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)

## Test 9: Kinetic Energy and Speed Changes

- Kinetic energy = 0.5 x mass x v squared. (Source: Martin et al., J Appl Biomech 1998)
- Every brake application dissipates kinetic energy, which the rider must pay back in power when accelerating. (Source: Martin et al., J Appl Biomech 1998)
- Smooth cornering preserves speed, reducing the repeated cost of accelerating back to race pace. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)
- 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)
- Repeated slowing and accelerating makes power bursts and handling more important relative to pure aero. (Source: Crouch et al., Sports Eng 2017)
- Brief accelerations cost both kinetic energy and cubic aerodynamic power; the gain is often small. (Source: Martin et al., J Appl Biomech 1998)
- Riders at the rear brake more and must accelerate harder, so the concertina effect stretches the group. (Source: Crouch et al., Sports Eng 2017)
- 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)

## Test 10: Speed and Power Calculations

- 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)
- Five hours at 1% faster saves about 1% of 300 minutes, roughly 3 minutes. (Source: Martin et al., J Appl Biomech 1998)
- (36/40) cubed is about 0.73, and 0.73 x 250 is about 182 W. (Source: Martin et al., J Appl Biomech 1998)
- Time saved per watt is larger at lower speed and accumulates over a longer ride. (Source: Crouch et al., Sports Eng 2017)
- Work = power x time: 200 J/s x 3,600 s = 720,000 J. (Source: Martin et al., J Appl Biomech 1998)
- 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)
- 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)
- With efficiency around 20-25%, most energy leaves as heat, which the body must dissipate. (Source: Martin et al., J Appl Biomech 1998)
- A 4% power-equivalent saving gives roughly a third of that in speed, about 1.3%. (Source: Martin et al., J Appl Biomech 1998)
- 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)

Sources: Peer-reviewed sports engineering and physiology literature, with published test data and standards for settled facts

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