Roadbook
How race pacing works
How we predict your time, how the plan chooses your power on each part of the course, and what each number rests on.
How a plan is built
- Speed from power: the power at the wheel equals your speed times the forces against you: rolling resistance, gravity on the slope and air drag in the wind you meet. Your weight, drag area, rolling resistance and drivetrain losses come from your profile and the bike you choose.
- Your effort is a target normalized power: an average that weighs hard efforts more, so surges cost more than steady riding. Here it is worked out over the plan's pieces of road.
- The plan cuts the course into pieces of 200 m and chooses the power on each so the whole ride is as short as possible at your normalized power, with no piece over the climb cap. Extra watts buy the most time where you are slowest, on climbs and into the wind, so that is where the plan puts them.
- Weather: when the race weather forecast is open, each piece gets the wind against it and the air density at the time you get there. The plan is worked out three times, each time reading the weather at the times the last one predicted.
- Descents: you are not faster than your top speed or than the corners allow, and you brake for corners in time. Where that holds you back, the plan has you freewheel instead of pedalling for nothing.
- What it leaves out: riding in a group, getting tired over the day, stops, and the speed you carry from one piece into the next. Treat the time as a riding time for a steady day alone; the power targets are the useful part.
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.
| Number | Value | Basis |
|---|---|---|
| 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] |
| Harder uphill and into the wind | least time for your normalized power | Models of time trials found that riding a little harder on climbs and into the wind, and easier downhill and with the wind, saves time at the same effort, most for lower-powered riders. We let the plan choose each piece's power so the whole ride is as short as possible for your target normalized power. [2][3] |
| Climb cap | 110% of your target, adjustable from 100% to 130% | The time savings were modelled for power varied by ±10%. Whether a rider can tolerate more over a long ride is unclear, so we cap any piece at 10% over your target unless you choose otherwise. [3] |
| Default target | 70% of FTP, or 180 W without an FTP | FondoLab default for a ride of five hours or more. It is a starting point to change, not a prescription.
FondoLab default |
| Wind at rider height | 0.54 × the forecast wind at 10 m | FondoLab default: the textbook logarithmic wind profile over open farmland (roughness 0.1 m), from 10 m down to 1.2 m. Among trees and buildings the wind on the road is weaker still; on an exposed col, stronger.
FondoLab default |
| 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 |
| Descending | cautious 55 km/h, 17° lean · normal 65 km/h, 22° · confident 75 km/h, 27°; braking 3 m/s² | The speed a corner allows follows from its radius and how far the rider leans: tan(lean) = v² ÷ (g × radius). We read each corner's radius from the course every 25 m and brake for it in time. The top speeds, lean angles and braking are FondoLab defaults. [4] |
| Pieces and sections | 200 m pieces at a steady speed; sections split at 2% up and down, at least 1 km, at most 40 | FondoLab defaults. Short enough to follow the road, long enough that a power target can be held; sections short enough to fit on a stem card.
FondoLab default |
References
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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.
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Swain DP (1997). A model for optimizing cycling performance by varying power on hills and in wind. Medicine & Science in Sports & Exercise 29(8):1104–1108. doi:10.1097/00005768-199708000-00017
Mathematical model · A modelled 70 kg cyclist; no riders were tested. · Read by us: Abstract
Modelled what varying power, with the same average, does to time on hilly and windy courses.
- 10 km time trial with alternating 1 km uphill and downhill at 10%, 10% variation in effort: 22:47 with varied power versus 24:20 at constant power, 1 min 33 s faster.
- 40 km time trial with alternating 5 km headwind and tailwind at 16 km/h, 10% variation: 60:21 versus 60:50, 29 s faster.
- The time saved grew with the variation, the gradient and the wind speed, and was larger for weaker riders.
Conclusion: ride slightly harder uphill and into the wind, and compensate with less power downhill and with the wind.
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Atkinson G, Peacock O, Passfield L (2007). Variable versus constant power strategies during cycling time-trials: prediction of time savings using an up-to-date mathematical model. Journal of Sports Sciences 25(9):1001–1009. doi:10.1080/02640410600944709
Mathematical model (validated power model of Martin et al., 1998) · A modelled 70 kg cyclist on a 10 kg bike, at average powers of 164, 289 and 394 W; no riders were tested. · Read by us: Abstract
Repeated Swain's 1997 analysis with a newer power model.
- At 289 W average, varying power by ±10% with the terrain saved 126 s on Swain's hilly 10 km course and 51 s on his windy 40 km course.
- On a "standard" 40 km time trial, 10% variation saved 26 s.
- The largest savings were for the riders with the lowest average power.
The authors note that how much power variation a rider can tolerate during a time trial is still unclear.
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Sakai D, Uchida N, Enomoto S, Iwata S, Kawakami Y, Wesugi S (2020). Improving Road Bike Leaning Skills on Downhill Corners (Developing a System for Detecting Curvature Change Points and the Angle of a Road Bike while Riding). Proceedings 49(1):153 (13th Conference of the International Sports Engineering Association). doi:10.3390/proceedings2020049153
System development with a small field test (conference paper) · One expert rider on a campus downhill with corners of 30 and 50 m radius, speed held at about 25 km/h by an automatic brake, three runs. · Read by us: Full text (open access)
Describes downhill cornering as three skills: anticipating hazards and judging the situation, controlling the bike's lean, and controlling speed.
- The theoretical lean angle for a corner follows from speed and radius: tan θ = v² / (g R).
- The expert's measured lean followed the theoretical lean reasonably well, and he started leaning about 5 m before the start of the corner.
- An earlier study by the same group found that some beginners leaned their bikes more than the expert in the same corners, which the authors link to tyre slips and falls.