What power measures, and how it differs from speed
Cycling power is the rate at which a rider does mechanical work, measured in watts. Speed, by contrast, is simply distance covered per unit time and depends heavily on external conditions: the same power output produces very different speeds depending on gradient, wind and road surface. A rider climbing a steep hill at 10 km/h can be producing far more power than the same rider cruising on the flat at 30 km/h, because most of that power on the climb is going into lifting body and bike weight against gravity rather than into forward speed.
This is why power has become the preferred measure of effort in cycling training and racing: unlike speed, it is not distorted by hills, wind or drafting, so it reflects the rider's physiological output directly, comparable session to session and rider to rider once normalized for body weight.
The physics model: three resistive forces
A well-established physics model, validated against directly measured power in studies such as Martin and colleagues (1998), calculates the power required to ride at a given speed by summing three resistive forces and multiplying by speed, then dividing by drivetrain efficiency to account for friction losses in the chain and bearings. Gravity force is the combined mass of rider and bike times gravitational acceleration times the sine of the road angle. Rolling resistance is that same combined mass times gravitational acceleration times the cosine of the road angle times a rolling-resistance coefficient. Aerodynamic drag grows with the square of speed, which means the power needed to overcome it grows with the cube of speed.
Because the true drag and rolling parameters of a specific rider and bike are rarely known without dedicated testing, typical published values are commonly used as fixed assumptions in physics-model calculators: a rolling-resistance coefficient (Crr) of 0.005, representative of road tires on asphalt; an effective frontal area (CdA) of 0.32 square metres, representative of a road rider riding on the hoods; air density of 1.225 kg per cubic metre, the standard sea-level value at 15 degrees Celsius; and a drivetrain efficiency of 97.5%, in line with published chain-drive measurements. Still air is assumed, with no head- or tailwind.
- P = (F_gravity + F_rolling + F_aero) x v / 0.975
- F_gravity = (m_rider + m_bike) x 9.8067 x sin(atan(grade% / 100))
- F_rolling = (m_rider + m_bike) x 9.8067 x cos(atan(grade% / 100)) x 0.005
- F_aero = 0.5 x 1.225 x 0.32 x v^2 (v in m/s)
Why air resistance dominates at higher speeds
The table below shows model estimates for a 75 kg rider on a 9 kg bike on a flat road in still air, using the standard assumptions above. Note how the share of power spent overcoming air resistance climbs steadily with speed: aerodynamic drag force grows with the square of airspeed, so the power to overcome it grows with the cube, while rolling resistance stays nearly constant with speed.
| Speed | Estimated power | Share spent on air resistance |
|---|---|---|
| 20 km/h | ≈ 58 W | ≈ 59% |
| 25 km/h | ≈ 97 W | ≈ 70% |
| 30 km/h | ≈ 152 W | ≈ 77% |
| 35 km/h | ≈ 226 W | ≈ 82% |
| 40 km/h | ≈ 323 W | ≈ 85% |
Watts per kilogram as a comparison metric
Watts per kilogram divides power output by rider body weight, and it is the standard normalization used in cycling because climbing speed on steep gradients is governed largely by power relative to total system weight. On flat roads, by contrast, speed is governed largely by absolute power relative to aerodynamic drag, since gravity plays little role when the road angle is near zero. This is documented in the power-based training literature, notably Allen, Coggan and McGregor's Training and Racing with a Power Meter, which uses watts per kilogram as a standard axis for comparing rider performance across different body sizes.
Because sustainable watts per kilogram varies enormously with training background, duration of effort, age and many other individual factors, no single number defines a 'good' value across all riders; comparing an individual's own watts-per-kilogram figure over time, at a consistent effort duration, is generally more informative than comparing against other riders.
What is FTP?
Functional Threshold Power (FTP) is a concept from the power-based training literature, described in Allen, Coggan and McGregor's Training and Racing with a Power Meter, referring to the highest power output a rider can sustain in a quasi-steady physiological state for approximately one hour. It functions as an individual reference point: because riders vary enormously in absolute power capability, expressing a workout's target intensity as a percentage of a rider's own FTP allows training zones to be personalized rather than based on a fixed wattage that would be meaningless across different riders.
FTP is not a single fixed number for life -- it changes as fitness changes, which is why power-based training programs periodically reassess it. This article describes the concept only; specific field-test protocols for estimating FTP are not covered here, as testing methodology and appropriate intensity progression are best guided by a qualified coach or the source training literature.
Câu hỏi thường gặp
What is the difference between power and speed on a bike?
Power is the rate of mechanical work a rider produces, measured in watts, while speed is simply distance covered per unit time. Speed is heavily distorted by gradient, wind and drafting -- the same power output produces very different speeds on a climb versus a flat road -- which is why power is considered a more direct and comparable measure of physiological effort.
How is cycling power calculated from physics?
A standard physics model sums three resistive forces -- gravity, rolling resistance and aerodynamic drag -- and multiplies the total by riding speed, then divides by drivetrain efficiency. Typical published constants (a rolling-resistance coefficient of 0.005, a frontal area of 0.32 square metres, air density of 1.225 kg per cubic metre, and 97.5% drivetrain efficiency) are commonly used when a rider's own measured values are not available.
What is a good watts-per-kilogram value?
Watts per kilogram is power divided by rider weight, and it matters most on climbs, where speed is governed largely by power relative to total weight. Sustainable watts per kilogram varies enormously with training background, effort duration and age, so no single 'good' number applies to all riders; tracking an individual's own value over time at a consistent duration is more informative than comparing across riders.
What does FTP mean in cycling?
FTP, or Functional Threshold Power, is the highest power output a rider can sustain in a quasi-steady physiological state for roughly one hour, a concept described in the power-based training literature (Allen, Coggan and McGregor). It serves as a personalized reference point: training intensities are commonly expressed as a percentage of a rider's own FTP rather than as a fixed wattage.
Why does air resistance matter more at higher cycling speeds?
Aerodynamic drag force grows with the square of airspeed, and the power required to overcome it grows with the cube of airspeed, while rolling resistance stays roughly constant regardless of speed. In a standard physics model, air resistance accounts for roughly 59% of total power at 20 km/h but climbs to roughly 85% at 40 km/h, which is why aerodynamics dominates cycling performance at racing speeds.
Tài liệu tham khảo
- Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR. Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics 1998; 14(3): 276-291.
- Wilson DG. Bicycling Science, 3rd edition. MIT Press, 2004.
- Allen H, Coggan AR, McGregor S. Training and Racing with a Power Meter, 3rd edition. VeloPress, 2019.
- International Civil Aviation Organization (ICAO). Standard Atmosphere -- sea-level air density 1.225 kg/m^3 at 15 degrees Celsius.
- American College of Sports Medicine. ACSM's Guidelines for Exercise Testing and Prescription, 11th edition. Wolters Kluwer, 2021.