FondoLab

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Gearing

Speed in a gear at a cadence, and the steepest climb your power turns it on.

Your numbers
Fine-tuning

Sensible defaults; change them if you know better.

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GearingFondoLab

10.9

km/h

Per pedal turn
2.26 m
Gear inches
28.4
Steepest
8.4%

34×32 at 80 rpm is 10.9 km/h. With 220 W you can keep that cadence up to 8.4%.

34×32 at each cadence
rpmkm/hSteepest
608.111.5%
709.59.7%
8010.98.4%
9012.27.3%
10013.66.4%
11014.95.7%

How we got this

The formula with your numbers in it, then every constant we used and where it comes from.

The working

  1. Wheel: 622 + 2 × 28 = 678 mm; development = 34 ÷ 32 × π × wheel = 2.26 m
  2. Speed = 2.26 m × 80 rpm × 60 = 10.9 km/h
  3. Rider and bike: 80.5 kg
  4. Drag area: 0.256 m², estimated from your position and 72 kg
  5. Rolling resistance: Crr 0.0051, estimated from 6 bar
  6. Drivetrain loss: 2.5%
  7. Air density: 1.204 kg/m³ at 0 m and 20 °C
  8. Steepest: the gradient where holding that speed takes 220 W.

The numbers and their sources

A number marked FondoLab default is our judgement, not a study's finding; we say so rather than borrow authority.

NumberValueBasis
Wheel size 622 mm rim (700c) + 2 × tyre width 622 mm is the rim's ISO size. Taking the tyre's height as its width is a FondoLab approximation; measure your wheel's roll-out for a bike computer.
FondoLab default
Power and speed rolling + gravity + air drag, less drivetrain losses The standard model of road cycling power, which predicted measured road power with a standard error of 2.7 W. We leave out its smallest terms, wheel bearings and the energy to speed the wheels up, and ride each piece at a steady speed. [1]
Air density pressure of the standard atmosphere at the road's elevation, temperature from the forecast The gas law: thinner air at altitude and in the heat means less drag. Without a forecast we use the standard atmosphere's temperature too. Humidity changes it by under 1%, so we leave it out.
FondoLab default
Drag area by position upright 0.270 · drops 0.243 · aero bars 0.211 m² Measured in a wind tunnel for one 72 kg rider with his bike. He wore an aero helmet and a racing suit and his legs were still, so a rider in a jersey and road helmet will usually be a little higher. Measure your own CdA if you can and enter it instead. [2]
Drag area on the hoods 0.256 m² FondoLab default, halfway between upright and the drops. We have not read a study that measured the hoods on its own.
FondoLab default
Scaling for your size × (your weight ÷ 72 kg) to the power 0.594 The frontal area of rider and bike grows with body mass to the power 0.594, measured from photos of 21 male racers. We assume the drag coefficient stays the same, which is our assumption, not a finding. [3]
Rolling resistance from tyre pressure Crr = 0.1071 × kPa^−0.477, between 1.5 and 12 bar Fitted to coast-down measurements of one tyre on a smooth indoor floor. Real roads are rougher and modern tyres differ, so treat it as a starting point: if you know the Crr of your tyres, enter it. [4]
Default drivetrain loss 2.5%, adjustable FondoLab default. A clean, oiled derailleur drive lost under 2% at high power in the lab, more at low power, and adjacent gears differed by 1–3%. 2.5% allows for a real ride's mix of gears and chain condition. [5]

References

  1. Martin JC, Milliken DL, Cobb JE, McFadden KL, Coggan AR (1998). Validation of a mathematical model for road cycling power. Journal of Applied Biomechanics 14(3):276–291. doi:10.1123/jab.14.3.276

    Validation study (model against measured road power) · Road cycling on a flat course with a bicycle-mounted power meter, itself validated against a laboratory ergometer. · Read by us: Abstract

    Derived a mathematical model of the power needed to ride a road bike, determined each of its parameters, and compared its predictions with power measured on the road.

    • Measured power was highly correlated with the model's (R² = 0.97) and not different from it.
    • The standard error between modelled and measured power was 2.7 W.

    The model is the standard one for road cycling, used by later pacing studies such as Atkinson et al. (2007). We have read the abstract only, so the terms we use are listed on the method page in our own words, not attributed to the paper beyond its validation.

  2. Blocken B, Defraeye T, Koninckx E, Carmeliet J, Hespel P (2013). CFD simulations of the aerodynamic drag of two drafting cyclists. Computers & Fluids 71:435–445. doi:10.1016/j.compfluid.2012.11.012

    Wind-tunnel measurements with computer simulations (CFD) · One rider (183 cm, 72 kg) in a large wind tunnel, in an aero helmet and a tight long-sleeved suit, on a racing bike with disc wheels, legs and wheels not moving. Two taller riders (81 kg) for the drafting measurement. · Read by us: Full text (authors' preprint)

    Drag area (CdA) measured in the wind tunnel for the rider and bike together, in three positions:

    • Upright: 0.270 m²
    • Dropped, arms straight: 0.243 m²
    • Time-trial position on aero bars: 0.211 m²

    The rider's body alone accounted for 0.193, 0.167 and 0.134 m² of these; the bike makes up the rest.

    Riding close behind another rider cut the trailing rider's drag by about 27% upright, 23% on the drops and 14% on aero bars at a 1 cm gap, less at larger gaps. The leading rider also gained 1–3%.

    Limits the authors name: the legs and wheels were still, and pedalling disturbs the flow. Their rider wore an aero helmet and a racing suit, so a fondo rider in a jersey and a road helmet will usually measure higher.

  3. Heil DP (2002). Body mass scaling of frontal area in competitive cyclists not using aero-handlebars. European Journal of Applied Physiology 87(6):520–528. doi:10.1007/s00421-002-0662-9

    Cross-sectional measurement study · 21 competitive male cyclists (mean 74 kg, 1.82 m, 24 years), photographed on their own bikes on stem, hoods, drops and aero positions with drop handlebars. · Read by us: Abstract

    Projected frontal area grows with body mass, but less than in proportion to it:

    • The body's frontal area scaled with body mass to the power 0.720.
    • Rider and bike together scaled with body mass to the power 0.594.

    So a rider twice as heavy does not present twice the frontal area. The study measured frontal area from photos, not drag; drag area also depends on the drag coefficient, which the study did not measure.

  4. Grappe F, Candau R, Barbier B, Hoffman MD, Belli A, Rouillon JD (1999). Influence of tyre pressure and vertical load on coefficient of rolling resistance and simulated cycling performance. Ergonomics 42(10):1361–1371. doi:10.1080/001401399185009

    Field measurement study (coasting deceleration) · One rider and bike coasting in a level indoor hallway, at five tyre pressures and four loads. · Read by us: Abstract

    The coefficient of rolling resistance (Crr) fell as tyre pressure rose, following Crr = 0.1071 × P^−0.477 with P in kPa (r² = 0.99):

    • 150 kPa (1.5 bar): Crr 0.0101
    • 1200 kPa (12 bar): Crr 0.0038, 62% lower

    Carrying 15 kg more raised Crr by about 11% (0.0035 to 0.0040).

    These numbers come from one tyre on a smooth indoor floor. Rough roads, and tyres of other widths and constructions, give other values; the relationship with pressure is what carries over.

  5. Kyle CR, Berto F (2001). The mechanical efficiency of bicycle derailleur and hub-gear transmissions. Human Power 52:3–11. Read it

    Laboratory dynamometer study · Eleven transmissions, including a Shimano 27-speed derailleur drive and eight hub gears, driven by a motor at 75 rpm and 50–370 W, chains oiled. Not riders. · Read by us: Full text (open access)

    Efficiency rose with power for every transmission. A derailleur drive went from about 91% at 50 W to over 97% at 370 W as measured; corrected for the test rig's own losses (2 to 2.5%), it was over 98% at the highest load, in line with earlier work that found over 98% with a 52/15 at 200 W.

    • Hub gears were generally about 2% less efficient than derailleur gears.
    • Adjacent gears often differed by 1–3%, up to 4% in the 27-speed, so a poor gear choice can cost about 2%.
    • Average efficiency fell as the gear ratio rose.

Read more: How much power does your drivetrain lose?

A clean derailleur drive delivers about 98% of your power to the wheel. What costs you the rest, and the default FondoLab uses.

On your race

Race pacing: this physics on your own course, with race-day wind and air

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