FondoLab

Roadbook

How the rider profile works

How the profile estimates what you have not measured, and the research behind each number.

How a plan is built

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
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. [1]
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. [2]
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. [3]
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. [4]
Crr from a drum test Crr = watts ÷ (42.5 kg × 9.80665 m/s² × 28.8 km/h) bicyclerollingresistance.com tests one tyre loaded with 42.5 kg on a 77 cm drum at 28.8 km/h and reports the watts it takes to keep it rolling, as its methodology page says. Power is force times speed, so the watts give the Crr. A drum is smoother than a road and curved, so the number is good for comparing tyres; a ride test gives yours on the road. We link to that site and do not copy its numbers: you look your tyre up and type them in.
FondoLab default
Which number is used tested › entered › estimated FondoLab default. Your latest test wins, then the number you entered, then the estimate from research. You can pin an older test or your entered number instead; the profile always says which one is used. A tested Crr holds at the pressure it was tested at, and the profile says when the bike rides more than 0.5 bar away from it, rather than rescaling a measurement with an estimate.
FondoLab default
Virtual elevation slope = (wheel power ÷ speed − mass × acceleration) ÷ (mass × g) − Crr − ½ ρ CdA speed² ÷ (mass × g) The power equation, turned round: from your power and speed it gives the slope you must have been riding, second by second. Adding those slopes up gives a virtual elevation profile. With the right CdA and Crr it matches the road's, lap after lap. Wind, braking, a change of position or a tyre losing air show up in the profile, so it also shows where a run went wrong. Chung's method is not peer reviewed; the power equation it turns round was validated against measured road power. [5][6]
Fitting CdA and Crr least squares: the virtual elevation against your barometric altitude, each lap from its own start FondoLab's way of finding the best match: the virtual elevation is a straight-line sum in CdA and Crr, so the values that bring it closest to the road's, over every second of the laps you pick, follow in one step. Power meters on the road are sensitive enough to see modest changes in position and large changes in tyre pressure. [7]
When Crr is measured too speeds at least 8 km/h apart; Crr uncertain by at most 25%, counting one sample per 30 s; Crr 0.0015–0.020, CdA 0.12–0.6 Telling CdA from Crr needs extra information: drag grows with speed squared, rolling resistance does not, so laps at clearly different speeds separate them. Without that, Crr is held at your tyre's known Crr, or estimated from its pressure, and only CdA is measured; the result says so. The limits are FondoLab defaults. [5]
Air density temperature from your head unit or you; pressure from your weather-station reading, else the standard atmosphere at your altitude An error in air density moves the CdA almost one for one; in Chung's example 1% in density moved CdA by about 1.5%. The standard atmosphere can be a few percent off on a given day, so enter the air pressure where you rode if you can. [5]
Checks on a run braking: 3 s slowing faster than 1.0 m/s²; a lap more than 1 m off at its end; a fit more than 1 m off on average FondoLab defaults. Each is shown before you accept a result, so you can leave out the lap or ride again. Braking shows as a sudden drop in the virtual elevation, wind as profiles that change with speed. [5]
Threshold (MLSS) from VO2max and VLamax where glycolysis forms lactate as fast as oxygen can burn it; Ks1 0.0631, Ks2 1.331, 0.02049 mmol lactate per ml O2 over 0.4 of body mass, 11.7 ml O2/min per W Mader and Heck's model as Hauser et al. set it out: calculated from lab-measured VO2max and sprint-lactate VLamax, it came within 12 ± 20 W of the measured MLSS in 13 cyclists (r = 0.92). For their average rider our implementation gives 240 W against their 229 W calculated. This threshold is the FTP your profile uses. [8][9]
VLamax from blood lactate (peak lactate after the sprint − before) ÷ (20 s − alactic time, 3 s unless you give it) The lab method: a finger-prick before the sprint and the highest of several after it. With it, VLamax is measured rather than fitted to your powers, and its range closes. [8][9]
VO2max and VLamax from your four efforts energy balance of each all-out effort: aerobic (87% of VO2max, rising with τ 25 s, 1% of it lost per minute past 5 min) + phosphocreatine (12 ml O2/kg) + lactate (3.0 ml O2/kg per mmol/L, building up towards 18 mmol/L) FondoLab's own model, fitted to your 20 s, 3, 6 and 12 minute powers by least squares. No study we have read gives VLamax from power alone, so these constants are our choices, not findings: the share of VO2max and the phosphocreatine are set so that two INSCYD power-only tests come out within a few percent of what INSCYD reported. The ranges come from varying each of them, and your power meter by ±1.5%. A sprint-lactate VLamax or a lab VO2max takes the place of the fitted value.
FondoLab default
Fat and carbohydrate at a power carbohydrate share = (pyruvate glycolysis forms ÷ pyruvate the oxygen can burn)^0.743; fat: the rest of the oxygen; 747 ml O2 per g glucose, 2012 per g fat; rest 3.5 ml/kg/min In Mader's model fat covers the oxygen uptake glycolysis leaves uncovered, the pyruvate deficit, and falls to zero at the threshold; a higher VLamax means more carbohydrate at the same power. Taken as it is, the model gave 10 percentage points less carbohydrate than two INSCYD reports at every zone, so we raise its ratio to the power 0.743, a FondoLab calibration that meets both reports within 1.5 points and puts FatMax within 2%. Measured gas exchange gives more carbohydrate still: riders about as fit as the one INSCYD tested got 46, 51 and 76% of their energy from carbohydrate at 44, 57 and 72% of VO2max, where this split gives 27, 40 and 68%, and most trained men burn less fat at their peak than either. The oxygen per gram follows from the chemistry of burning glucose and palmitate; resting uptake is the conventional 1 MET, a FondoLab default. [9][10][11]
Critical power and W′ work = CP × time + W′, fitted to the 3, 6 and 12 minute efforts The classic two-parameter model, shown beside the threshold as a check that needs no model of metabolism. Critical power usually sits above the maximal lactate steady state, so it is not used as your FTP.
FondoLab default
When a fitness test is old after 90 days FondoLab default: fitness changes over a season, so test again every few months.
FondoLab default
Sweat rate from a weigh-in (weight before − weight after + drunk + eaten − urine) ÷ hours, 1 kg = 1 L Weighing yourself before and after exercise is the simplest accurate way to measure your own sweat rate, and sweat rates differ so much between people that plans should be built on your own. Breathing water and the mass of fuel burned are not subtracted, so the rate comes out a little high, as in the sources' own method. [12][13]
Results we ask you to check below 0.1 or above 3.5 L/h, or more than 5% of body weight lost Sweat rates above 3 L/h happen but are rare, in extreme heat, at high intensity or in large athletes. Outside these limits a typing mistake is more likely than a real result, so we ask before saving. [12]
Your sweat rate at any temperature the planner's average curve × your tests' mean ratio to it; a test a year old counts half FondoLab default. Sweat rises with temperature and effort. We keep the shape of the planner's temperature curve and let your tests set how high it sits. Effort and humidity are recorded with each test but not yet used, because we have not read a source to scale them by.
FondoLab default
Sweat sodium you had measured 100–3000 mg/L accepted; replaces light / average / salty Whole-body sweat sodium is typically about 230–1600 mg/L, and patches on the skin read higher. FondoLab cannot measure it; if you had a test done, enter its result and where it came from. [12]

References

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Chung R (2012). Estimating CdA with a power meter. Technical presentation with notes, self-published. Read it

    Method description with worked examples (not peer reviewed) · Field rides recorded with power meters, mostly by the author and other experienced riders; a few laps of a 3.1 km loop in Paris as the main example. · Read by us: Full text

    Describes the virtual elevation method, now called the Chung method. From power, speed, total mass, air density and guesses for CdA and Crr, the power equation gives the slope at each moment, and adding up the slopes gives a "virtual" elevation profile. On laps of a loop, which start and end at the same height, the CdA that makes every lap end where it started is the estimate.

    • The course need not be flat and speed need not be constant; varied speed and some elevation change help. Hold one position, do not brake, and test with as little wind as possible.
    • Wind, braking, a change of position or a tyre losing air all end up in the virtual elevation, so the profile also shows where a run went wrong: braking as a sudden jump, wind as profiles that change with speed.
    • Without a known Crr the method gives good relative accuracy (changes in CdA) more easily than absolute CdA. Same tyres, pressure, road and day keep Crr constant.
    • When Crr is known, the author reports agreement with wind-tunnel and classic field tests within ±1%. Experienced users report a spread as low as 0.3% between repeated estimates; the classic constant-speed method has given about 1.3%. These are reported results, not a controlled study.
    • In the author's example, a 1% error in air density moved the CdA estimate by about 1.5%, a 1% error in Crr by about 0.3%.
    • Comparing estimates across different days is not recommended, because conditions cannot be kept the same.
    • Separating CdA and Crr needs extra information, such as two runs up the same hill at different power with a known height gain.

  6. 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.

  7. Lim AC, Homestead EP, Edwards AG, Carver TC, Kram R, Byrnes WC (2011). Measuring changes in aerodynamic/rolling resistances by cycle-mounted power meters. Medicine & Science in Sports & Exercise 43(5):853–860. doi:10.1249/MSS.0b013e3181fcb140

    Field measurement study · Eight experienced road cyclists (six men, two women) on their own road bikes, on a flat 200 m stretch of smooth asphalt in calm wind (under 1 m/s). · Read by us: Abstract

    Riders held constant speeds at power steps of 50 W (100–400 W for men, 100–300 W for women). Drag force (power divided by speed) was plotted against speed squared: the slope gives aerodynamic resistance, the intercept rolling resistance.

    • Aerodynamic resistance was significantly higher on the brake hoods than on the drops (0.175 vs 0.155, about 11% less on the drops).
    • Rolling resistance was significantly higher at 60 psi (414 kPa) than at 120 psi (828 kPa): 5.6 vs 4.2 N.

    The authors conclude that commercial power meters are sensitive enough to detect modest changes in position and large changes in tyre pressure in the field.

  8. Hauser T, Adam J, Schulz H (2014). Comparison of calculated and experimental power in maximal lactate-steady state during cycling. Theoretical Biology and Medical Modelling 11:25 (erratum 2016). doi:10.1186/1742-4682-11-25

    Validation study (model against measured MLSS) · 13 men, 24 ± 5 years, 72.9 ± 6.8 kg, VO2max 60.4 ± 8.6 ml/kg/min, VLamax 0.91 ± 0.18 mmol/L/s, on a cycle ergometer in the lab. · Read by us: Full text (open access), and the erratum

    Calculated power at the maximal lactate steady state (MLSS) from VO2max, measured in a ramp test with gas analysis, and VLamax, measured from blood lactate before and after a 15 s all-out sprint, with Mader and Heck's model of oxidative phosphorylation and glycolysis. Compared it with MLSS found by constant-load rides.

    • Calculated MLSS 229 ± 47 W, measured 217 ± 51 W: a mean difference of −12 ± 20 W, r = 0.92.
    • VLamax = (peak lactate after the sprint − lactate before) ÷ (sprint time − alactic time), the alactic time lasting until power falls 3.5% from its peak.
    • Oxidative phosphorylation VO2ss = VO2max ÷ (1 + Ks1 ÷ ADP²), Ks1 = 0.0631; glycolysis VLass = VLamax ÷ (1 + Ks2 ÷ ADP³), Ks2 = 1.331.
    • Lactate elimination is proportional to oxygen uptake: 0.02049 mmol lactate per ml O2, over a distribution volume of 0.4 of body mass.
    • Oxygen uptake at a power: VO2ss = (P × 11.7 + body mass × VO2rest) ÷ body mass. No value for VO2rest is given.
    • MLSS is where glycolytic lactate formation equals its maximal elimination, solved numerically.
    • The 2016 erratum corrects equation 7 (ADP from VO2ss) to use Ks1. Combining equations 3 and 4 gives ADP³ = (Ks1 × VO2ss ÷ (VO2max − VO2ss))^1.5; we use that form.

    The authors put the 12 W gap down to the day-to-day variability of VO2max and VLamax. VO2max and VLamax were measured in the lab, not estimated from power.

  9. Wackerhage H, Gehlert S, Schulz H, Weber S, Ring-Dimitriou S, Heine O (2022). Lactate thresholds and the simulation of human energy metabolism: contributions by the Cologne Sports Medicine Group in the 1970s and 1980s. Frontiers in Physiology 13:899670. doi:10.3389/fphys.2022.899670

    Narrative review (history and method) · Not a study of riders: it reviews the Cologne group's lactate testing and Mader's model of energy metabolism. · Read by us: Full text (open access)

    Explains, in English, the Cologne group's work on lactate thresholds and Alois Mader's mathematical model of energy metabolism during exercise, which is driven by VO2max and the maximal rate of lactate formation, VLamax.

    • VLamax is estimated from the rise in blood lactate after an all-out sprint, divided by the sprint time less the time phosphocreatine covers. It is hard to measure well: the sprint must switch glycolysis fully on while keeping oxidation low.
    • Oxidative ATP resynthesis follows ADP with a second-order Hill equation, glycolysis with a third-order one.
    • The maximal lactate steady state lies where glycolytic pyruvate formation equals the maximal rate of pyruvate oxidation. Below it, fat oxidation covers the "pyruvate deficit"; at and above it fat oxidation falls towards zero.
    • A higher VLamax puts the 4 mmol/L threshold at a lower power at the same VO2max; in the review's simulation about 110 W lower.
    • The simulations shown use 40% of body mass as active muscle; most of the full model's constants are not given in the review.

  10. van Loon LJC, Greenhaff PL, Constantin-Teodosiu D, Saris WHM, Wagenmakers AJM (2001). The effects of increasing exercise intensity on muscle fuel utilisation in humans. Journal of Physiology 536(1):295–304. doi:10.1111/j.1469-7793.2001.00295.x

    Laboratory study (stable isotope tracers, indirect calorimetry and muscle biopsies) · 8 trained male cyclists, 22 years, 74.5 kg, VO2max 5.48 L/min (about 74 ml/kg/min), Wmax 413 W, after an overnight fast and a standard evening meal, on a cycle ergometer. Small sample; no women. · Read by us: Full text

    Measured how much of the energy came from fat and from carbohydrate, and from which stores, at rest and in three consecutive 30 minute stages at 40, 55 and 75% of Wmax, which were 44, 57 and 72% of VO2max.

    • Carbohydrate gave 44% of the energy at rest, 46% at 44% of VO2max (1.44 g/min), 51% at 57% (2.04 g/min) and 76% at 72% (3.91 g/min).
    • Fat oxidation rose to 0.79 g/min at 57% of VO2max and fell to 0.51 g/min at 72%: from 50% of the energy to 24%.
    • Muscle glycogen gave 35%, 38% and 58% of the energy at the three intensities, and blood glucose 10%, 13% and 18%.
    • Plasma lactate rose substantially only at the highest intensity.
    • The stages followed each other without a break; in four riders who repeated each intensity on its own, fat oxidation was much the same.

  11. Maunder E, Plews DJ, Kilding AE (2018). "Contextualising maximal fat oxidation during exercise: determinants and normative values". Frontiers in Physiology 9:599. doi:10.3389/fphys.2018.00599

    Narrative review with pooled normative values · Pooled step tests on a cycle ergometer after an overnight fast, by group; the largest is 201 endurance-trained, lean men. Fewer data for women. · Read by us: Full text (open access)

    Pools measurements of the highest rate at which people burn fat during exercise (MFO) and the intensity where it happens (Fatmax), and what changes them.

    • Endurance-trained, lean men: MFO 0.53 ± 0.16 g/min (20th–80th percentile 0.40–0.67) at 56 ± 8% of VO2max (49–63%). Recreationally active men: 0.46 g/min at 51%; recreationally active women: 0.35 g/min at 50%.
    • Across seven studies, MFO was on average 28% higher in men (0.56 vs 0.44 g/min); Fatmax was a little higher in women.
    • 75 g of glucose 45 minutes before exercise lowered MFO from 0.46 to 0.33 g/min and Fatmax from 60 to 52% of VO2max in trained men.
    • Total carbohydrate storage is typically under 740 g, about 80% of it in muscle and 10–15% in the liver, with about 4 g as blood glucose.
    • Muscle glycogen at the start, diet, training status and the test protocol all change the values, and the test is only moderately repeatable.

  12. Baker LB (2017). Sweating rate and sweat sodium concentration in athletes: a review of methodology and intra/interindividual variability. Sports Medicine 47(Suppl 1):111–128. doi:10.1007/s40279-017-0691-5

    Narrative review · Athletes across many sports, in the lab and the field. The author is at the Gatorade Sports Science Institute. · Read by us: Full text, first third (open access)

    Sweating rate and sweat sodium vary widely between athletes and within the same athlete from day to day.

    • Whole-body sweating rate typically ranges from about 0.5 to about 2.0 L/h. More than 3 L/h happens but is rare, in extreme heat, at high intensity, or in large athletes.
    • Sweating rises with ambient temperature and with exercise intensity, through the heat the body has to lose.
    • Whole-body sweat sodium is typically about 10–70 mmol/L, roughly 230–1600 mg/L. Local patches read higher (about 10–90 mmol/L).
    • The simplest accurate way to measure your own sweating rate is to weigh yourself before and after exercise.

  13. Sawka MN, Burke LM, Eichner ER, Maughan RJ, Montain SJ, Stachenfeld NS (2007). American College of Sports Medicine position stand. Exercise and fluid replacement. Medicine and Science in Sports and Exercise 39(2):377–390. doi:10.1249/mss.0b013e31802ca597

    Position stand · Expert synthesis for people exercising in general, not cyclists specifically. · Read by us: Abstract only

    The goal of drinking during exercise is to prevent excessive dehydration, defined as losing more than 2% of body weight to a water deficit, and excessive changes in electrolyte balance, both of which compromise performance.

    • Start exercise well hydrated.
    • Sweat rates vary a lot between people, so drinking plans should be individual; weighing before and after exercise estimates sweat rate.
    • Drinks containing electrolytes and carbohydrate can have benefits over water alone in some circumstances.

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