# Comparing cycling world hour records, 1967-1996: modeling with empirical data.

**ABSTRACT** The world hour record in cycling has increased dramatically in recent years. The present study was designed to compare the performances of former/current record holders, after adjusting for differences in aerodynamic equipment and altitude. Additionally, we sought to determine the ideal elevation for future hour record attempts.

The first step was constructing a mathematical model to predict power requirements of track cycling. The model was based on empirical data from wind-tunnel tests, the relationship of body size to frontal surface area, and field power measurements using a crank dynamometer (SRM). The model agreed reasonably well with actual measurements of power output on elite cyclists. Subsequently, the effects of altitude on maximal aerobic power were estimated from published research studies of elite athletes. This information was combined with the power requirement equation to predict what each cyclist's power output would have been at sea level. This allowed us to estimate the distance that each rider could have covered using state-of-the-art equipment at sea level. According to these calculations, when racing under equivalent conditions, Rominger would be first, Boardman second, Merckx third, and Indurain fourth. In addition, about 60% of the increase in hour record distances since Bracke's record (1967) have come from advances in technology and 40% from physiological improvements.

To break the current world hour record, field measurements and the model indicate that a cyclist would have to deliver over 440 W for 1 h at sea level, or correspondingly less at altitude. The optimal elevation for future hour record attempts is predicted to be about 2500 m for acclimatized riders and 2000 m for unacclimatized riders.

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- H.K. Epema, S. van den Brand, Wouter Gregoor, J.D.G. Kooijman, H.P. Pereboom, D.C. Wielemaker, C.-J. van der Zweep[Show abstract] [Hide abstract]

**ABSTRACT:**The current International Human Powered Vehicle Association world records for faired bicycles stand at 133.284 km/h for the 200m flying start speed record and 91.562 km for the hour record. Traditionally the recumbent bicycles that have been developed for breaking one of either of these records have been optimized around a specific, relatively small rider, enabling the overall size to be kept small. Creating the smallest frontal area possible and optimal aerodynamic shape were then the design goals. This paper discusses the development of the Velox recumbent bicycle, which has been designed using another approach. The power required to break either of the records depends mostly on air resistance. Therefore small riders have the advantage of allowing for smaller frontal areas, whilst larger riders are able to provide more power. Performance optimization, lead to a design based around an average 1.95m tall male rider for Velox. The aerodynamic shape of Velox was then developed around the above criterion and designed with CFD and validated with wind tunnel and road tests. Essential for the rider's performance is that the rider feels comfortable whilst riding the bicycle. Therefore the uncontrolled lateral dynamics and the required rider steer control input were investigated. The bicycle's geometry was optimized for low speed stability and the required control input.Procedia Engineering. 34:313–318. - [Show abstract] [Hide abstract]

**ABSTRACT:**Chronic exposure to a stressor elicits adaptations enhancing the tolerance to that stressor. These adaptive responses might also improve tolerance under less stressful conditions. For example, historically there has been much interest in the adaptive responses to high-altitude, or hypoxia, and their ergogenic potential under sealevel, or normoxic, conditions. In contrast, the influence of the adaptive responses to heat on exercise under cooler conditions has received relatively little interest. Heat acclimation/acclimatization (HA) is known to increase work capacity in hot environments. Yet, aerobic exercise performance can progressively deteriorate as ambient temperature increases beyond*10 �C, indicating a thermal limitation even under relatively cool conditions. The improved thermoregulatory capability induced by HA might attenuate this thermal decrement in a manner similar to that seen when exposed to hotter temperatures. Moreover, the suite of adaptations elicited by HA has the potential to increase maximal oxygen uptake, lactate threshold and economy, and thus may be ergogenic even under conditions where performance is not thermally limited. Indeed, evidence is now emerging to support an ergogenic effect of HA but the number of studies is limited and in some instances lack appropriate control, are confounded by methodological limitations, or do not address the mechanisms of action. Nevertheless, these tantalising insights into the ergogenic potential of heat will likely generate considerable interest in this new ‘hot topic’. Future research will need to employ well-designed studies to clarify the exercise conditions under which ergogenic effects of HA are apparent, to elucidate the precise mechanisms, and to optimise HA strategies for performance.Sports Medicine 06/2014; · 5.32 Impact Factor - SourceAvailable from: Julien D Périard[Show abstract] [Hide abstract]

**ABSTRACT:**PURPOSE: To determine the effects of heat-acclimatization on performance and pacing during outdoor cycling time-trials (TT, 43.4km) in the heat. METHODS: Nine cyclists performed 3 TTs in hot ambient conditions (TTH, ∼37ºC) on the first (TTH-1), sixth (TTH-2) and fourteenth (TTH-3) days of training in the heat. Data were compared to the average of two TTs in cool condition (∼8ºC) performed pre and post heat acclimatization (TTC). RESULTS: TTH-1 (77±6min) was slower (p=0.001) than TTH-2 (69±5min) and both were slower (p<0.01) than TTC and TTH-3 (66±3 and 66±4 min, respectively) without differences between TTC and TTH-3 (p>0.05). The cyclists initiated the first 20% of all TTs at a similar power output, irrespective of climate and acclimatization status; however, during TTH-1 they subsequently had a marked decrease in power output, which was partly attenuated following six days of acclimatization and further reduced after fourteen days. HR was higher during the first 20% of TTH-1 than in the other TTs (p<0.05), but there were no differences between conditions from 30% onward. Final rectal temperature was similar in all TTHs (40.2±0.4ºC, p=1.000) and higher than in TTC (38.5±0.6ºC, p<0.001). CONCLUSION: Following two weeks of acclimatization, trained cyclists are capable of completing a prolonged TT in a similar time in the heat compared to cool conditions, whereas in the unacclimatized state they experienced a marked decrease in power output during the TTHs.Medicine and science in sports and exercise. 06/2014;

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[Applied Sciences: Physical Fitness And Performance]

Medicine & Science in Sports & Exercise

Issue: Volume 31(11), November 1999, p 1665

Copyright: © 1999 Lippincott Williams & Wilkins, Inc.

Publication Type: [Applied Sciences: Physical Fitness And Performance]

ISSN: 0195-9131

Accession: 00005768-199911000-00025

Keywords: AERODYNAMICS, BICYCLE, POWER OUTPUT, VELOCITY, DYNAMOMETER, MATH MODEL, PHYSIOLOGY, HYPOXIA, WORLD RECORDS

Comparing cycling world hour records, 1967–1996: modeling with empirical data

BASSETT, DAVID R. JR; KYLE, CHESTER R.; PASSFIELD, LOUIS; BROKER, JEFFREY P.; BURKE, EDMUND R.

Author Information

Exercise Science Unit, University of Tennessee, Knoxville TN; Department of Mechanical Engineering, California State University, Long Beach CA; Biomedical Sciences,

University Medical School, Foresterhill, Aberdeen, SCOTLAND; USOC Sports Sciences Division, Colorado Springs, CO; and University of Colorado at Colorado Springs, Colorado

Springs, CO

Submitted for publication September 1998.

Accepted for publication February 1999.

Address for correspondence: Dr. Chester Kyle, 9539 North Old Stage Rd., Weed, CA 96094; E-mail: kyle@snowcrest.net.

Abstract

BASSETT, D. R. JR, C. R. KYLE, L. PASSFIELD, J. P. BROKER, and E. R. BURKE. Comparing cycling world hour

records, 1967–1996: modeling with empirical data. Med. Sci. Sports Exerc., Vol. 31, No. 11, pp. 1665–1676, 1999.

Purpose: The world hour record in cycling has increased dramatically in recent years. The present study was

designed to compare the performances of former/current record holders, after adjusting for differences in

aerodynamic equipment and altitude. Additionally, we sought to determine the ideal elevation for future hour

record attempts.

Methods: The first step was constructing a mathematical model to predict power requirements of track

cycling. The model was based on empirical data from wind-tunnel tests, the relationship of body size to frontal

surface area, and field power measurements using a crank dynamometer (SRM). The model agreed reasonably well

with actual measurements of power output on elite cyclists. Subsequently, the effects of altitude on maximal

aerobic power were estimated from published research studies of elite athletes. This information was combined

with the power requirement equation to predict what each cyclist’s power output would have been at sea level.

This allowed us to estimate the distance that each rider could have covered using state-of-the-art equipment at

sea level. According to these calculations, when racing under equivalent conditions, Rominger would be first,

Boardman second, Merckx third, and Indurain fourth. In addition, about 60% of the increase in hour record

distances since Bracke’s record (1967) have come from advances in technology and 40% from physiological

improvements.

Results and Conclusions: To break the current world hour record, field measurements and the model indicate

that a cyclist would have to deliver over 440 W for 1 h at sea level, or correspondingly less at altitude. The

optimal elevation for future hour record attempts is predicted to be about 2500 m for acclimatized riders and

2000 m for unacclimatized riders.

The hour record is one of the most prestigious events in cycling, having been attempted by many of the best

racers in the world. Distances in this event have more than doubled since it was first established in 1876. Over the

first century, improvements in the hour record gradually began to reach a plateau (Fig. 1). During the past 14 yr,

however, dramatic improvements have been achieved. The more recent athletes have used radically different

body positions and cycling equipment, greatly reducing the aerodynamic drag forces. In addition, some of the hour

records were set in Mexico City (2300 m elevation), where the power requirement of track cycling is decreased

because of a 20% reduction in air density. However, this advantage is partially offset by a decline in power

output, due to decreased oxygen availability. Thus, it is unknown to what extent the improvements seen in recent

years are due to increased power outputs of the cyclists, as compared to technological improvements.

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Figure 1 The world cycling hour record from 1876 to 1998. The first record was set in 1876 by F. L. Dodds of

England, riding a high-wheeled bicycle. From 1888 until 1984, conventional track bicycles were used. Starting in

1984, aerodynamic improvements such as disk wheels, aero handlebars, and aerodynamic bicycles were introduced.

Sport scientists have attempted to determine which cyclist had the best hour record performance (after

correcting for equipment and elevation differences). Genzling (18) used a simple mathematical model to compare

hour records up until 1984 and concluded that the true hour record holder was Ferdinand Bracke. However,

Genzling’s estimate of Bracke’s power output (580 W) is very high, as is his estimate of Eddy Merckx’s power in

Mexico City (525 W). Peronnet et al. (30,31) conducted an analysis of hour record performances from 1942 to 1988

and concluded that Francesco Moser’s 1988 Stuttgart record was the best up to that time. Later, Keen (20) used a

rigorous scientific approach that combined empirical data collection and modeling, and found that Chris

Boardman’s 1993 performance exceeded those of two cyclists who came before him (Merckx and Obree).

To further extend this line of inquiry, we developed a mathematical model to predict the power requirements

of track cycling that accounted for most of the major variables. These included velocity, altitude, cycling

equipment, clothing, body position, height, weight, track circumference, and track surface. The effects of each

variable on the drag forces experienced by the cyclist were determined through: 1) extensive wind-tunnel testing

to determine the effects of specific variables on the drag coefficients, 2) empirically determined relationships

between body dimensions and frontal surface area and, 3) measurements of power output during actual track

cycling, using a crank dynamometer. The model was compared with direct field measurements performed on elite

trained cyclists, to ensure the model predicted the actual power requirement of track cycling reasonably well.

To determine the effects of altitude on power output, we estimated the reduction in power output at higher

elevations. The decline in maximal aerobic power ([latin capital V with dot above]O2max) with increasing elevation

was estimated from the results of scientific studies on elite runners or cyclists. Although this approach has been

used before (Peronnet et al. (30,31), Capelli and di Prampero (8)), previous studies used the altitude-related

decline in [latin capital V with dot above]O2max for average-fit males.

The first aim of the present study was to determine the power requirements of track cycling using direct field

measurements, so as to permit comparisons of world hour record performances. These tests were conducted at

five different locations from near sea level to high elevation on four continents (2,3,5,20). We combined this

information with our estimates of the altitude-induced decline in power output, to compute what each cyclist’s

power output would have been if they had ridden at sea level. This allowed us to estimate the distance that each

rider could have covered using similar equipment at sea level. A secondary aim of the study was to predict the

ideal elevation for future hour record attempts.

METHODS

Theoretical model for predicting power required for track cycling.

The power required to cycle on a bicycle racing track depends upon many variables; some of the more

important ones are: speed; cyclist’s riding position and body size; type of bicycle; wheels, tires, and components;

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altitude, track design, and condition; and environmental conditions such as wind velocity, temperature, and

humidity, etc. Heretofore, estimates of the mechanical power required to cycle were based upon indirect

measurements such as oxygen uptake, laboratory ergometer studies, wind tunnel measurements, coast down tests,

towing tests, or upon theoretical models based upon these indirect measurements (7,9,21,23,24,28,34,35).

However, since the advent of the bicycle crank dynamometer, it is no longer necessary to use theoretical or

indirect estimates of the power required; it can be measured directly with accuracy.

Theoretical models, however, can still be very useful when researchers, coaches, or athletes want to estimate

the required power under a variety of conditions without direct measurement. Models can also be useful in

comparing past cycling performances for which power data are not available. It is the purpose of this section to

develop a model for cycling power versus speed on a track, using field power measurements conducted with an

SRM crank dynamometer system (described later). The tests were performed by Jeff Broker of USOC Sports

Sciences, on U.S.A. Team cyclists (2–5), and by Louis Passfield of the University Medical School in Aberdeen and

Peter Keen (20) of the British Cycling Federation on British Team cyclists. Hence, this study represents secondary

data analysis of existing data bases, which were collected by coaches and technical staff for the purposes of

preparing their athletes for national and international competition. Table 1 summarizes the resulting SRM power

data used for developing the model. The column labeled Power gives the average measured power required in W

to go 52.27 kph. This was the speed of Chris Boardman’s world hour record set in Bordeaux, France, July 23, 1993,

and it is used as a reference by Passfield and Peter Keen (20). The speed is also typical of National Caliber

individual pursuit racers and is the equivalent of 4 min and 35 s in a 4000-m pursuit. In this paper, speeds are

given in kilometers per hour (kph), because this is the most familiar form for velocity in bicycle racing.

Table 1. Power versus speed for track cyclists; all results at 52.27 kph.a The Lotus and SB2 are composite aero

bikes with disk or tri-spoke rear wheels and tri-spoke or bladed-spoked front wheels. The standard track bikes had

rear disks and tri-spoke or bladed spoke front wheels. The Merckx bike was a traditional track bike with

conventional wheels with steel spokes.

The power required by various cyclists to go 52.27 kph, as listed in Table 1, ranges from about 360 W to over

500 W. With such data scatter, one cannot expect a model to predict required power accurately under all

circumstances because the experimental results depend so much upon individual rider position, ambient

environmental conditions, and the condition of the track. In one example (tests 1, 2, and 3, Table 1), Louis

Passfield measured a cyclist using identical equipment in Manchester, England, which is near sea level, and on a

practice track in Duitama, Colombia, at an elevation of about 2500 m. The power required at altitude was actually

higher than the power at sea level (Fig. 2), although theoretically the wind resistance should be about 23% less at

2500 m. Passfield attributes the surprising result to a very rough track with tight curves. Wind conditions could

also have increased the required power. Another example would be the tests at Adelaide, Australia (test 14),

where required power is higher than expected. Despite the inherent certainty of errors, it will be well worthwhile

to examine mathematical models of cycling performance.

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Figure 2 Cycling crank power input measured by a crank dynamometer at sea level on the indoor track at

Manchester, England, and at about 2500 m on the outdoor track at Duitama, Colombia. The rider used the same

equipment at both locations (Table 1). Contrary to theory, the measured power at altitude was higher than the

power at sea level. Measurements by Louis Passfield.

Direct measurement of power.

For the data listed in Table 1, the measurement protocol used by all of the test directors was similar. The

SRM crank dynamometer (Schoberer Rad MeBtechnik, Welldorf, Germany) consists of an instrumented chainring

that transmits strain-gauge readings by telemetry to a handlebar microprocessor or to a central computer, along

with crank RPM and bicycle speed. From this, average power can be computed and stored.

The SRM system was calibrated before each set of tests. SRM power for 1-s intervals was averaged for each

lap. Passfield and Keen had the cyclists start at about 40 kph and increase their speed gradually (about 0.1 s

faster per lap) until they reached approximately 53 kph. The cyclists increased speed continuously, without resting

between laps. Broker had the cyclists ride steady lap speeds in 5-kph increments, starting at about 30 kph, and

increasing until about 50–55 kph. The cyclists rode at each speed for at least two laps and rested for two laps

between intervals. The speeds were ridden in a sequence which varied according to each rider’s preference.

Exponential equation.

The power/speed data points for each lap were plotted, and an exponential equation of the form P = Cvn was

fit to the data, where P is the crank power in W, C is a proportionality constant, V is the speed in kilometers per

hour (kph), and n is an exponent. The regressions for all of the data sets had a mean r2 value of 0.9754. The

exponential equations fit to each data set are given in Table 1. Typical curves and data points are shown in Figure

2.

Tests 4 through 8 in Table 1 were conducted by Louis Passfield at the indoor track in Manchester, England,

with similar bicycles but with five different cyclists. Using all data points from the five subjects gives an

exponential power equation of:

MATH 1

Equation 1

The mean height of the five subjects is 1.82 m and the mean mass 75.4 kg.

Although exponential equations are convenient for predicting power accurately over the range of the tests,

there is no real physical significance to the coefficient or the exponent. If the equation were modified to account

for changes in wind resistance, rider weight and height, track conditions, or other physical variables, it would

produce a purely empirical expression, which is difficult to interpret physically. The authors did develop an

exponential model, which matched experiment fairly well. However, the choice of coefficients was somewhat

arbitrary, so it will not be presented here.

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Power series equation.

The following power series equation does have a firm physical basis:

MATH 2

Equation 2

A1 is a constant expressing the static rolling resistance of bicycle wheels and tires (a bicycle wheel has a

frictional resistance to motion even when standing still). A2 is a constant related to the dynamic rolling resistance

(rotating bicycle tires, wheels, and bearings increase their frictional resistance as the speed increases). A3 is a

constant that is a function of the air density, the frontal area of the rider and bicycle, and the aerodynamic drag

coefficient (related to the shape of an object and the efficiency with which it moves through the air) (22,24).

The constant A1 may be derived from experimental data (24). Racing bicycle tire tests show that rolling

resistance increases with the weight on the tire, the steering angle, the roughness of the surface, and other

factors (24). There are several things that tend to cause rolling resistance on a bicycle racing track to be higher

than measured on a straight level test surface. 1) On a track, in the curves, the centrifugal force raises the weight

on the tire by over 1.5 times at racing speeds. 2) The steering angle of a bicycle at racing speed, oscillates

through about ± 3° with every pedal stroke, causing increased rolling friction due to tire scrubbing. Scrubbing

occurs, when the tire contact patch acquires a slip angle with the pavement as the bicycle turns. 3) Bicycle tracks

are always cambered (banked) even on the straights. The fact that the bicycle is almost never perpendicular to

the track means that a steering correction is required to hold the bicycle on a line, which causes added tire

friction. 4) Also, most racing tracks are not entirely smooth. Even though static rolling resistance can be as low as

0.22% of the down force applied to the tire (24), a more reasonable estimate for conditions on a bicycle track

would be an average of 0.35% of the applied force on the tire. This would give a value for A1 of (0.00953 Mt) W h·

(kg km)-1, where Mt is the total mass of the bicycle and rider in kilograms (we will assume the bicycle weighs 10.0

kg, because no direct measurements of the bicycle weights are available).

A2 is proportional to the increase in rolling resistance due to bearing friction, dynamic tire deformation, and

the windage of a spinning wheel. It has been measured for a 17-inch Moulton bicycle wheel with wheel covers by

Richard Moore of General Motors (27). Because no other reliable data are available, the constant derived from

Moore’s report shall be used, A2 = 0.00775 W·km-2·h-2 (2).

Using and the values for A1 and A2, one can now solve for A3 directly, based upon the average experimental

data. gives a power of 432 W at 52.27 kph. This gives a value for A3 of 0.002582. Substituting the values for the

constants in gives:

MATH 3

Equation 3

To be able to correct the equation for rider size, altitude, bicycle type, riding position, temperature, and

other variables requires further development. Neither A1 nor A2, which are related to tire rolling resistance,

require modification; however, A3, which is related to aerodynamic drag, should be adjusted for changes in

altitude, bicycle and component types, rider position, rider size, atmospheric conditions, etc.

Factors influencing aerodynamic drag.

Because A3 is a function of the aerodynamic drag of the bicycle and rider it may be expressed as (19,22,24):

MATH 4

Equation 4

where [rho] is the air density, Cd is the aerodynamic drag coefficient and Af is the frontal area of the bicycle

and rider.

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In the range of speeds in endurance track racing (50–60 kph), the drag coefficient of cyclists Cd is typically

constant as long as the rider position, equipment, and environmental conditions are constant. This was shown by

full scale tests in the General Motors Automotive wind tunnel, Warren, MI (4). For a fixed riding position, when the

air drag was plotted versus velocity squared in the range from 40 to 56 kph, the result was linear with the average

r2 = 0.998. We will discuss the influence of rider position and cycling equipment on the drag coefficient and

frontal area in more detail later. First, we will consider the effects of air density.

Air density.

Air density varies with altitude according to atmospheric temperature and pressure. The air density ratio may

be estimated from the following polytropic gas equation, which is used for calculating low level density variation

in the U.S. Standard Atmosphere (29):

MATH 5

Equation 5

where [rho] is the air density in kg·m-3, g is the acceleration of gravity 9.807 m·s-2 at sea level, n is a

polytropic gas coefficient, N = 1.235, z is the elevation above sea level in meters, R is the gas constant for air R =

287.1 Nm(kg·K)-1, and T is the absolute temperature in Kelvin T = 288°K (15°C). For example: z = 1829 m for

Colorado Springs and the density ratio would be [rho]2/[rho]1 = 0.836, compared with sea level. This means that

the density, and therefore the air resistance, should be about 16.4% less in Colorado Springs than at sea level for

the same rider and bicycle combination.

Frontal area.

Table 2 shows the frontal area and air drag of three cyclists measured in the Texas A&M wind tunnel in 1990

(23). The cyclists used road time trial bikes with triathlon aero bars, a rear disk wheel, and a bladed-spoked front

wheel. They wore one-piece Lycra cycle clothing with Giro aero helmets. The frontal area was measured by taking

telephoto photographs of the cyclists outdoors at a distance of 50 m, with a reference area held at the midpoint

of the crank. To find the frontal area, the photographs were cut out and the paper figures weighed on a laboratory

balance and compared with the weight of the reference area. Using the data in Table 2, Figure 3 shows a plot of

the air drag versus the frontal area of the bicycle plus rider (23). The linear regression shows that air drag

increases linearly with frontal area. The correlation is only fair with r2 = 0.524; however, the approach should still

be useful. Broker of the USOC Sports Sciences also measured the frontal area of cyclists (not including the

bicycle), along with the wind tunnel air drag (4) (see Table 3). Broker’s data also yields a linear relation for air

drag versus frontal area, with r2 = 0.572. We can assume then, with reasonable accuracy, that air drag is

proportional to frontal area.

Table 2. Frontal area and air drag of three cyclists (24).All cyclists had round tube triathlon bicycles with aero

bars, rear disk wheels, and front aero blade spoked wheels.

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Figure 3 The air resistance of three cyclists versus the total frontal area of the cyclist plus the bicycle.

Measurements by C. R. Kyle, at the Texas A&M wind tunnel, 1990 (23).

Table 3. Frontal area and air drag of five cyclists (4).Cyclists had composite track bikes with airfoil shaped tubing,

aero bars, rear disk wheel, and aero blade spoked wheels.

Air drag will change with body size and riding position, as shown by Swain et al. (34,35). Both rider size and

riding position will significantly affect the frontal area but will also influence the drag coefficient. As a cyclist

changes position, two things happen; the frontal area changes, and at the same time the drag coefficient also

changes because the new pattern of airflow is not geometrically similar to the previous condition. This means it is

not possible to separate the effects of drag coefficient and frontal area where rider position is concerned. Any

changes therefore should be lumped into one factor (often called the drag area CdAf). However, by selecting one

cycling position as a standard, we can handle the effects of body size and riding position separately. For

simplicity, as a standard we will use the triathlon racing position (elbows on triathlon aero bars, arms inside the

projected frontal body area, torso flat, head tucked low between shoulders). See Figure 4 for the common cycle

racing positions.

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Figure 4 Bicycle racing positions. From the 1890s until 1986, cyclists used the same traditional crouched racing

position. Starting in 1986, aero bars (invented by Peter Pensayres and used in the Race Across America in 1986)

allowed cyclists to rest on their elbows while maintaining a low aerodynamic riding posture. Graham Obree of

Scotland pioneered two unique riding positions, which he used to set hour records in 1993 and 1994 (the Obree

position and the Superman position).

The effect of body size on frontal area.

To be able to estimate a riders’ frontal area easily, by utilizing their height and weight, we can adapt the

expression of Dubois and Dubois (16) for human body surface area:

MATH 6

Equation 6

The surface area As is in m2, H is the height in m, and M is the mass in kg. Using data from Wright et al. (41)

and Kyle (23) (Tables 2 and 4), Figure 5 shows a linear relation between the surface area of cyclists to the total

frontal area of the cyclists plus bicycle, for a yaw angle of 0°. The regression equation in Figure 5 gives an r2 =

0.757. In other words, the total frontal area of cyclists plus bicycle, in the standard time trial aero racing position,

is proportional to the surface area of the cyclists with reasonable accuracy. Applying the regression equation to

gives an expression for the total frontal area in terms of the cyclist height and mass:

Table 4. Total frontal area and surface area of cyclists (41).

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Figure 5 The total cyclist projected frontal area (body plus bicycle) plotted against the cyclist’s body surface area.

The cyclists in the lower curve (Wright et al. (41) and Kyle (23)) used standard aero bars, whereas those in the

upper curve (Capelli et al. (9)) used the older traditional racing position.

MATH 7

Equation 7

Also shown in Figure 5 are the data of Capelli et al. (9) for elite racing cyclists using standard racing bicycles.

Capelli et al. plotted frontal area versus body surface area and obtained a reliability coefficient of r2 = 0.401. The

riders in Capelli’s study apparently did not use aero bars, and thus the frontal areas were significantly higher than

in the present study. However, it can be seen from Figure 5, that the slope of the linear regression curves is very

similar. Both Capelli et al. and Swain et al. note that the ratio of body surface area to frontal area favors larger

subjects who have a lower frontal area related to their body size than do smaller subjects, and unless this is

taken into account, any performance model will tend to overestimate the power required of larger subjects to

overcome wind resistance. accounts for this difference.

In the present study, the average cyclist size is height = 1.82 m and mass = 75.4 kg, the average frontal area

is Af = 0.344 m2, and the density correction for Manchester is 0.994. Using equations 4 and 7, can now be

modified for changes in wind resistance due to rider size, altitude, equipment type, position, etc., as follows:

MATH 8

Equation 8

where K is a factor which allows adjustment for track roughness or other external conditions and K1 is an

aerodynamic factor which incorporates a correction for altitude (the density ratio), and corrections for rider

position, bicycle type, components, clothing, helmets, etc. No effect of winds will be included in either of the

factors K or K1 because on an oval racing track the effect of wind is unpredictable. K1 can be expressed as:

MATH 9

Equation 9

where Kd is the density ratio compared with sea level (equation 5), Kpo is the effect of position, Kb is the

effect of the bicycle and components, Kc is the effect of clothing, and Kh is the effect of the helmet. Table 5 lists

a few of the more important factors affecting aerodynamic drag. The correction factors listed in Table 5 were

obtained by tests of bicycles, cyclists, wheels, and helmets in the General Motors wind tunnel (Warren, MI, 1994–

1996, [ref. 4 and internal reports]). Obviously, by improving position, bicycles, wheels, components, clothing,

helmets, etc., a time trial bicycle can be much faster. The factors listed in Table 5 are valid in the range of

racing speeds from 50 to 60 kph.

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Table 5. Correction factors to cycling aerodynamic drag (4).The above correction factors to the aerodynamic drag

assume an average air drag for a rider and bicycle of approximately 2.5 kg (24.5 N) at 48 kph. By multiplying the

above factors together, an overall correction K1 may be obtained.

Table 1 shows the result of using this model in predicting power measurements from five locations:

Manchester England; Duitama, Colombia; Bordeaux, France; Colorado Springs, CO; and Adelaide, Australia (see

Table 6 for track specifications). The Manchester track was used as a reference K = 1.0, and the correction factors

in Table 5 and altitude corrections were applied. The absolute power prediction error is shown in Table 1.

Table 6. Characteristics of cycling tracks.Elevations were determined from the Defense Mapping Agency

Operational Navigation Charts, which include the elevation for all airports of the world (39). The nearest airport to

the cities above were used as benchmarks.a Site of Ritter’s (1968) and Merckx’s (1972) records.b Site of Moser’s

1984 records.

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Except for Duitama, Colombia (test 3), and Adelaide, Australia (test 14), the absolute error of prediction was

no higher than 7.7% and averaged 3.9% (SD 2.9), which is reasonable considering the data variability. Neither

Duitama nor Adelaide were included in the average. In the case of the outdoor track at Duitama, Colombia, the

required power was an extraordinary 25% higher than estimated by the model, which, as mentioned, could have

been caused by a rough track with tight turns or variable windy conditions (in Fig. 2, the data scatter outdoors at

Duitama was greater than indoors at Manchester). Another possibility would be an instrument calibration error,

but Passfield took pains to calibrate the SRM before each series of tests. In the case of the sea-level indoor track

at Adelaide, the required power was 13% higher than calculated by the model. There seems to be no reasonable

explanation for this discrepancy, except perhaps the team was inexperienced and may have used inefficient riding

positions or riding techniques.

In the field measurements by Peter Keen of Chris Boardman in Bordeaux (20), Keen had Boardman ride in the

standard aero position as well as in the Graham Obree position (arms folded against the body with the shoulders

resting on the hands; see Fig. 4). The required power decreased from 409 W to 393 W at 52.27 kph. This

represents about a 4% drop in wind resistance (K1 = 0.96). He also had Boardman ride a standard track bike with

drop bars and wire-spoked wheels similar to the one Eddy Merckx rode in his 1972 hour record set in Mexico City

(49.431 km). In this test, the required power was 473 W, which is equivalent to an increase in wind resistance of

18% (K1 = 1.18).

Power required for the hour record.

Chris Boardman set the current world hour record of 56.375 km at Manchester in 1996 using a new

Lotus/Merckx aero bike and the Superman position (arms extended forward in diving posture with the head tucked

between the arms—the elbows and hands are far forward of the steering axis; see Fig. 4). Wind tunnel data show

that the Superman position, on an aero bike, lowers the overall wind resistance about 5% compared with the

standard aero position (Kpo = 0.95) (4). Also an efficient composite aero bike would lower the wind resistance

about 7% compared with a standard track bike (Kb = 0.93) (4). The density ratio for Manchester is Kd = 0.994. This

gives a combined K1 = 0.994 × 0.95 × 0.93 = 0.878. According to the model, the required power would be 452 W

at 56.375 kph. In a personal communication to Craig Turner, Peter Keen estimated that Boardman produced about

442 W during his latest hour record (37); so in this case, the model predicts high by about 2%.

Effects of altitude on power output.

The percent decline in [latin capital V with dot above]O2max at various elevations is shown in Figure 6.

Measurements were made at sea level and within 2–7 d after arrival at altitude. The average sea level [latin

capital V with dot above]O2max (mL·kg-1·min-1) values were 74.4 (Daniels and Oldridge (13)), 72.0 (Dill and Adams

(15)), 69.8 (Chapman et al. (10)), 63 (Buskirk et al. (6)), 65 (Pugh (32)), and 66.2 (Faulkner et al. (17)). Chapman

et al. (10) used an inspired O2 concentration of 18.7% at sea level (simulating an elevation of 1000 m). The other

studies were conducted at elevations ranging from 2270 to 4300 m. An equation describing the relationship

between altitude and maximal aerobic capacity is:

Figure 6 The decrease in maximal oxygen uptake versus altitude for elite athletes. The upper curve is for athletes

who have trained for several weeks at altitude and who are acclimated. The lower curve is for athletes who have

spent only 1–7 d at altitude before the measurements were taken. Adapted from E. T. Howley. Effects of altitude

on physical performance. In:Encyclopedia of Physical Education, Fitness and Sports: Training, Environment,

Nutrition, and Fitness, G. A. Stull and T. K. Cureton (Eds.). Reston VA: AAHPERD, 1980, p. 180. Copyright 1980 by

AAHPERD; reprinted by permission.

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MATH 10

Equation 10

where Y is the percent of [latin capital V with dot above]O2max measured at sea level and X is the altitude in

kilometers. This equation predicts a [latin capital V with dot above]O2max in Mexico City (2338 m) that is 85.3% of

the sea level value, or a 14.7% decline.

Only studies on highly trained athletes were examined, because the altitude-related decline in [latin capital V

with dot above]O2max in this group may differ from that of normal individuals. In trained individuals, their greater

maximal cardiac output values tend to reduce red blood cell transit time in the pulmonary capillary. This makes it

difficult to saturate the blood with oxygen, particularly at altitude where the partial pressure of oxygen is reduced

(14). In other words, athletes function on a steeper portion of the oxyhemoglobin dissociation curve, and they are

more likely to desaturate when the inspired PO2 is reduced. Lawler et al. (25) and Martin and O’Kroy (26)

demonstrated that when exposed to hypoxic conditions (13% O2), the decline in [latin capital V with dot

above]O2max is almost twice as great for trained athletes, compared with untrained men. These investigators find

a strong, inverse linear relationship between maximal aerobic power and the change in [latin capital V with dot

above]O2max upon exposure to reduced oxygen (r = -0.91 to -0.94). Hence, there is good evidence that elite

cyclists undergo a greater decline in [latin capital V with dot above]O2max upon exposure to altitude than ordinary

subjects.

The relationship given by is for the effects of acute exposure, wherein [latin capital V with dot above]O2max

was measured within several days of arriving at altitude. However, the acclimatization response to high altitude

must also be considered. Merckx set his hour record a few days after arriving in Mexico City, whereas Moser

trained for a month in Bogota (3000 m elevation) before his records (11) and Ritter trained for three weeks in

Mexico City before his ride (O. Ritter, personal communication).

Several authors have studied the time course of the physiological response to training at high altitude. Dill

and Adams (15) studied high school champion runners at 3100 m and found that [latin capital V with dot

above]O2max was decreased by 17.6% after 2 d and 15.6% after 16 d. Buskirk (6) studied Penn State trackmen at

4000 m and found that [latin capital V with dot above]O2max was decreased from sea-level values by 29% on the

2nd day, 29% on the 21st day, and 26% on the 48th day. Pugh (32) studied six international middle-distance

runners in Mexico City and found a reduction of 14.6% on the 2nd day and 9.5% on the 27th day. Daniels and

Oldridge (13) found a 14.3% drop in world-class runners within 1–2 d of arrival in Mexico City. By the 5th week of

alternating high and low-altitude exposure, they still had a 9.2% drop in [latin capital V with dot above]O2max.

Faulkner et al. (17) studied elite runners in Mexico City and found a 17% decline initially and a 13% drop after 34

d. Taken together, these studies suggest that high-altitude training enables athletes to regain some of the decline

in [latin capital V with dot above]O2max they experience soon after arriving at altitude. For acclimatized subjects,

the equation expressing this relationship is:

MATH 11

Equation 11

where Y is the percent of [latin capital V with dot above]O2max measured at sea level and X is the altitude in

kilometers (see Fig. 6). This equation predicts a 10.7% decline in [latin capital V with dot above]O2max for Moser

and Ritter at 2338 m versus the 14.7% decline computed for Merckx (using .

The contribution of anaerobic energy sources during an hour record event is probably negligible (1). Thus, we

ignored the anaerobic contribution in our calculations, although it would be necessary to consider it in track

cycling events of short duration (9). Coyle et al. (12) have shown that highly trained cyclists ([latin capital V with

dot above]O2max = 68.6 mL·kg-1·min-1) can maintain power outputs that are near maximal (89% [latin capital V

with dot above]O2max) for approximately 1 h. Hence, we assumed that any decline in [latin capital V with dot

above]O2max with altitude would be accompanied by an equivalent decline in mechanical power output. This is

supported by research showing that the efficiency of cycling is unchanged at altitude (33,40) and that fractional

utilization of [latin capital V with dot above]O2max is not impaired (13).

For the hour records set in Mexico City, we took the estimated power outputs and adjusted them upward to

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reflect the power output of each cyclist at sea level. The estimated sea-level power outputs were then plugged

back into the mathematical model. This allowed us to estimate the distance that each cyclist could have covered

at sea level, using standardized equipment.

RESULTS

Table 7 gives an estimate of the power required for previous world hour records from 1967 to 1996. Height

and weight for each cyclist are listed along with the correction factors to account for cycling aerodynamic drag.

The right-hand column shows the predicted power outputs for each cyclist during his hour record ride, based on

the mathematical model we have presented. In the case of Boardman, the power measurements by Peter Keen are

used (20,37). In all others, the model was used to predict the power required.

Table 7. Power required for cycling 1-h records.a Sea level record in 1988.b Height and weight for Bracke are

estimated; values for other cyclists were obtained from published news reports or personal communication.

In Table 8 the power outputs have been corrected to sea level, and the distances have been calculated at

Manchester using Boardman’s equipment (K1 = 0.878). This model predicts that Rominger had the highest power

output of all time, based upon his distance 55.291 km and the equipment that he utilized. The estimate of his

power is probably somewhat high (460 W), but it should be definitely be greater than Boardman’s. Our model

estimated Boardman high (452 W), so if one corrects Rominger by the same ratio (442/452), it would give 450 W

for Rominger.

Table 8. Power and distance, normalized to Manchester, all cyclists using Boardman’s equipment and position.1988

sea level record.Distance, original record distance.P, power required at the track elevation.Psl, power corrected

to sea level.Dsl, estimated distance at Manchester, using Boardman’s equipment and position K1 = 0.878.f Power,

450 W and 460 W, respectively.

DISCUSSION

The hour records in Mexico City were characterized by lower power outputs than those at sea level. For the

most part, this is due to the decrease in maximal aerobic power at altitude. However, because the Mexico city

tracks were outdoors, the riders there may have faced mild wind conditions, causing our estimates of power to be

low. Until Moser’s sea level record at Stuttgart in 1988, no one had surpassed Bracke in total power output. Moser

trained specifically for the hour record (more so than his predecessors) and training methods have continued to

improve since then. With Indurain and those following, power outputs increased again.

After adjusting all of the hour records to sea level, using Boardman’s latest equipment and position on the

bike, some general conclusions can be drawn. Comparing past records on equal terms, the model shows that all of

the historic performances until Rominger, would have been reasonably close, 52.4–54.3 km, with Obree’s first

record (1993) a little lower (51.8 km). Obree’s second record (1994) was within the range of the others (52.7 km).

Comparing all record holders, we estimate that Rominger would be first, Boardman second, Merckx third, and

Indurain fourth. Because Merckx raced outdoors, his 1972 performance is all the more impressive when compared

with the recent indoor records.

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Some of the older record holders, Merckx, Bracke, Moser, Ritter, and even Indurain, were capable of quite

remarkable sea-level power levels for 1 h. The model predicts that all five racers would have been within 1.6 km

of each other (52.4–54.0 km), racing under equivalent conditions. Both Boardman and Rominger would have been

faster (56 to 57 km).

Effects of altitude on performance.

Using the present model, the advantage of riding in Mexico City (2338 m) is estimated to be worth 1.68 km·h-

1, compared with sea level, and for Colorado Springs (1829 m) 1.58 km·h-1. In fact, this is similar to the

advantage obtained by two cyclists (Francesco Moser and Jeannie Longo) who made hour record attempts in close

succession at sea level and altitude using similar equipment (8). The performance advantage in Moser’s case was

about 1.8 km·h-1 when comparing his Mexico City records with those in Milan. Longo derived a 1.5-km advantage in

Mexico City (vs Stuttgart and Moscow) and a 1.2-km advantage at the lower elevation of Colorado Springs (vs

Milan) (see Table 9).

Table 9. Hour records of two cyclists at sea level and altitude.Sources: 1. UCI Record Book (38); 2. Conconi (11);

3. The Guardian (London) (36).

In 1995, Capelli and di Prampero (8) noted that their mathematical model predicted a performance advantage

for Moser and Longo that was twice as great as what they actually experienced. A contributing factor to this

difference could have been wind on the outdoor tracks of Mexico and Colorado Springs. However, it is likely that

the principal difference was due to two factors. First, the tests cited in the present paper show that the

mechanical power required to drive a bicycle is a function of the velocity raised to an exponent of about 2.6,

whereas it would be a function of the velocity cubed if aerodynamic forces were considered alone. Because Capelli

and di Prampero did not have the benefit of crank dynamometers, their model used velocity cubed as a

proportionality factor, and thus the model would have overestimated the importance of lower air resistance. A

second reason might be that Capelli and di Prampero (8) assumed the [latin capital V with dot above]O2max

decline in Mexico City to be about 8.8%, similar to that reported by Peronnet et al. (30,31). However, in elite

athletes the value may be slightly greater than this, even if they are well acclimated.

Optimal elevation for hour record attempts.

The optimal elevation for hour record attempts was predicted from the model, with Boardman as the subject,

using his latest equipment and the superman position on an indoor track to avoid wind (see Fig. 7). The optimal

altitude for Boardman, when acclimatized, would be about 2500 m, where theoretically he could attain a distance

of about 58.1 km in 1 h. At higher or lower elevations, his speed would decrease. If he were not acclimatized,

then the speed would be about 57.2 km·h-1 at an optimal elevation of about 2000 m. Coincidentally, these two

elevations bracket Mexico City (2338 m); so, according to our model, there would be little reason to attempt the

hour record at a higher elevation. The theoretical optimal elevation of 2500 m is less than reported by other

investigators. Peronnet and coworkers (30,31) predict about 4000 m as being optimal as do Capelli and di

Prampero (8). That elevation is slightly higher than the altitude of the Alto Irpavi velodrome (La Paz, Bolivia, 3658

m), where Capelli and di Prampero estimate that Rominger’s performance would equal 60.1 km·h-1 (8). Our model

predicts that Rominger’s distance would be about 1.5 km less than this at La Paz.

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Figure 7 The theoretical distance Christopher Boardman could cycle in 1 h at various elevations. The upper curve

assumes Boardman is acclimated and reaches a maximum of 58.1 km at about 2500 m. The lower curve assumes

Boardman has not trained at altitude and reaches a maximum of 57.2 km at about 2000 m.

It is interesting to compare the theoretical performances of Rominger and Boardman at Mexico City and La

Paz, Bolivia, on an indoor track. In theory, at Mexico City (2338 m), Rominger and Boardman should be able to go

about 59.1 km (411 W) and 58.1 km (395 W) respectively. At La Paz, Bolivia (estimated elevation of 3658 m), they

should go about 58.6 km (359 W) and 57.5 km (345 W), which is greater than they could manage at sea level but

less than at Mexico City.

Limitations of the model.

The model’s estimate of power seems to be accurate to within an absolute error of about 4%. So power

figures within about 4% of each other can be considered equivalent. In estimating the elapsed time to go a certain

distance, the absolute error would be less, about 1.6%. However, even after attempting to account for as many

factors as possible, it is apparent that generalized models have their limitations. On the other hand, specific SRM

tests can be used to predict performance very accurately, provided a reliable measure of the cyclist’s endurance

power potential is available (ergometer data, field performance data, [latin capital V with dot above]O2max data).

Another limitation to the model, is the considerable variability between individuals for the percent decline in

[latin capital V with dot above]O2max at altitude. For each of the studies shown in Figure 6, the standard

deviations are about 5%. The average percent decline in [latin capital V with dot above]O2max in Mexico City is

14.7% for unacclimatized athletes. This means that two-thirds of the athletes will experience a decrease between

9.7% and 19.7% (14.7 ± 5%). The entire range in [latin capital V with dot above]O2max decrement for all three

studies done in Mexico City was from 4.6% to 25.1% (13,17,33). Further, J. T. Kearney of the USOC Sports Sciences

(personal communication, August, 1998) found that Lance Armstrong, the former professional road race champion,

showed no decline in [latin capital V with dot above]O2max at the elevation of Colorado Springs (1829 m). Thus,

even though one can predict the decline in power output that Ritter, Merckx, and Moser might have experienced

in Mexico City, it is uncertain how any particular cyclist would respond to 2300-m elevation. However, by

estimating the [latin capital V with dot above]O2max decline on the basis of studies of highly trained athletes, one

can improve on the statistical accuracy of prediction.

In summary, by using field crank dynamometer measurements, the present study extended the mathematical

modeling approach used in previous studies that compare hour record performances. After adjusting for

differences in altitude and aerodynamic factors between cyclists, several conclusions can be drawn. The earlier

record holders who used traditional round tube track bicycles (Bracke, Ritter and Merckx) averaged sea level

powers of about 402 W. However, Merckx’s 1972 performance (429 W) stands out above the others. The next series

of record holders, who all used various aerodynamic improvements (Moser, Boardman, Obree) averaged sea level

powers of about 403 W, or about the same. The aerodynamic improvements during this era resulted in a record

distance increase of about 10%. The last three challengers (Indurain, Rominger, and Boardman) averaged 446 W, a

large increase in power compared with the previous record holders. During this period, the available bicycle

aerodynamic improvements did not change as markedly. The increased power of these cyclists, resulted in a

distance increase of about 7%. In other words, since Bracke’s era, about 60% of the improvement in the hour record

distance has come from aerodynamic advances and about 40% from higher power outputs. The combination has

produced the recent meteoric rise in the hour record. Finally, future hour records at altitude should be possible,

especially if the current champions use indoor velodromes at higher elevations, where the conditions of the track

are constant.