INVITED REVIEW

Efficiency in cycling: a review

Gertjan Ettema Æ Havard Wuttudal Loras

Accepted: 2 February 2009 / Published online: 20 February 2009

� Springer-Verlag 2009

Abstract We focus on the effect of cadence and work rate

on energy expenditure and efficiency in cycling, and present

arguments to support the contention that gross efficiency can

be considered to be the most relevant expression of effi-

ciency. A linear relationship between work rate and energy

expenditure appears to be a rather consistent outcome among

the various studies considered in this review, irrespective of

subject performance level. This relationship is an example of

the Fenn effect, described more than 80 years ago for muscle

contraction. About 91% of all variance in energy expendi-

ture can be explained by work rate, with only about 10%

being explained by cadence. Gross efficiency is strongly

dependent on work rate, mainly because of the diminishing

effect of the (zero work-rate) base-line energy expenditure

with increasing work rate. The finding that elite athletes have

a higher gross efficiency than lower-level performers may

largely be explained by this phenomenon. However, no firm

conclusions can be drawn about the energetically optimal

cadence for cycling because of the multiple factors associ-

ated with cadence that affect energy expenditure.

Keywords Efficiency � Cycling � Energy expenditure �Cadence � Work rate

Introduction

The study of energy consumption in cycling has a long

history. Many factors affecting energy consumption have

been studied extensively, not the least cadence. Research

has also been directed towards other factors, including

those related to task variations (e.g., crank arm character-

istics, load, ring shape, body position), environmental

conditions (e.g., uphill cycling), and also subject charac-

teristics (e.g. patient groups, athletic level) in relation to

energy cost.

It is common practice to express the energy expenditure

as efficiency (i.e., the ratio of work generated to the total

metabolic energy cost). This is often done in order to

compare various studies that have been done at different

work rates, as a higher work rate typically requires a higher

energy consumption. Another reason is to get a better

insight into how external work rate affects the physiolog-

ical stress. Moreover, the efficiency measure may also

provide more insight into the mechanisms behind the

effects of various factors on energy consumption, and

thereby into the function of the metabolic processes

involved in work production. One of the major challenges

in studying physical activity is finding an accurate mea-

surement of the (external) work done (e.g., van Ingen

Schenau and Cavanagh 1990). Cycling, especially on a

cycle ergometer, is one of the few exceptions. Thus, it is

not surprising that many studies on the relationship

between efficiency and energy consumption have been

conducted within the context of cycling.

Efficiency in cycling has been studied for almost a

century (Benedict and Cathcart 1913), and di Prampero

(2000) recently provided an overview of this issue. The

discussion that will be developed in this review is based on

an old debate. It deals in essence with the definition of

efficiency and what may be termed ‘‘baseline subtraction’’

(i.e., the subtraction from the measured oxygen uptake of

that associated with the baseline condition—rest, unloaded

pedalling etc.). Baseline subtractions were used in early

G. Ettema (&) � H. W. Loras

Human Movement Science Programme, Faculty of Social

Sciences and Technology Management, Norwegian University

of Science and Technology, 7941 Trondheim, Norway

e-mail: gertjan.ettema@svt.ntnu.no

123

Eur J Appl Physiol (2009) 106:1–14

DOI 10.1007/s00421-009-1008-7

experiments (e.g., Benedict and Cathcart 1913; Dickinson

1929; Garry and Wishart 1931, 1934), but criticised much

later (e.g., Cavanagh and Kram 1985; Stainbsy et al. 1980;

van Ingen Schenau and Cavanagh 1990). Even so, various

definitions of efficiency and baseline subtractions are used

currently. The essence of the debate on the validity of base-

line subtractions relates indirectly to the fundamental laws

of thermodynamics and mechanics. These laws and their

direct consequences for treatment and interpretation of data

are not always followed strictly, or are not explicitly

clarified in the literature. This lack of clarity can lead to

misunderstandings. The principal aim of this paper is

therefore to present a review of the literature on the rela-

tionships among cycling efficiency, cadence and work rate.

We focus on gross efficiency because, in our opinion, this

is the most relevant efficiency measure for such consider-

ations, as we explain later. As a result, some of our

conclusions may differ from those expressed in the

literature.

We start with a brief overview of a number of principles

that originated from thermodynamics and classic mechan-

ics. In doing so, we clarify our standpoint on the use of

various definitions of efficiency. We then discuss a number

of detailed issues that relate directly to the calculation and

interpretation of efficiency, especially in cycling. Ee then

critically review the literature on efficiency in cycling and

its dependence on the two main variables, power and

cadence. Finally, the ‘‘trainability’’ of cycling efficiency is

briefly discussed. It is beyond the scope of this paper to

include comprehensive discussion of factors such as mus-

cle fibre type (Horowitz et al. 1994; Coyle 2005), bicycle

models (Minetti et al. 2001), crank systems (Zamparo et al.

2002), chain rings (Cullen et al. 1992; Hull et al. 1992),

crank inertial load in uphill cycling (Hansen et al. 2002),

foot position (Van Sickle and Hull 2007), and environ-

mental conditions (Ferguson et al. 2002; Green et al. 2000).

We hope that this analysis contributes to setting a

framework by which studies can be better compared,

and efficiency can be interpreted and discussed more

appropriately.

Mechanisms of energy conversion and efficiency

definitions, as applied to cycling

Thermodynamics and efficiency definition

The first law of thermodynamics, i.e., the law of conser-

vation of energy, states that the total energy of a system and

its surroundings is constant. Thus, in a system isolated from

its surroundings, the total amount of energy is constant and

no energy can be produced or lost, only transformed. By

using the terms energy loss and production, we implicitly

regard the human body (i.e., its locomotor muscles) as a

system that is not isolated. Indeed, energy from its envi-

ronment can flow into the system (metabolites and negative

work) and out (in the form of work and heat). The ther-

modynamic potential of a system, enthalpy (H) is the sum of

the internal energy of a system and the product of pressure

and volume. When considering energy changes in muscle

contraction, this can be simplified to that enthalpy change is

equal to internal energy change because muscle volume is,

practically speaking, constant. Enthalpy consists of two

forms, free energy (G) and entropy (S). The change in free

energy drives reactions: when doing work, one spontaneous

reaction occurs (ATP hydrolysis) and liberates energy (DG

is negative) that drives another reaction (work production,

DG is positive). However, not all free energy that is liber-

ated in the driving reaction is utilised in the driven reaction.

The difference is transferred as heat, leading to an increase

in S. Efficiency of an energy converting system is the ratio

of free energy outflow over the total free energy inflow.

In muscle contraction, the free energy outflow is work.

This efficiency ratio is also found by taking the energy

rate (power) for both nominator and denominator in this

equation:

e ¼ work

energy cost¼ power

energy rate

The energy cost is usually expressed as metabolic cost.

When discussing the ways in which efficiency can be

defined, it is important to have a clear system definition and

be aware of the fact that efficiency is a parameter

describing a quality of the energy flow that runs through

that particular system. In a previous paper (Ettema 2001),

we briefly touched on this issue. Here, it is taken as an

explicit departure point: the definition of what the energy

conversion system entails fully determines what is to be

considered as energy inflow (cost) and what as energy

outflow (work and heat). Thus, this system definition

determines the definition of efficiency. In our opinion,

unfortunately, an explicit and formal definition of the

energy conversion system is often lacking, which may lead

to confusion and misunderstanding for the reader.

The complication with locomotion of the (human) body

is that the energy transforming system and the physical

body may physically be overlapping, but are not neces-

sarily identical entities. In locomotion, one can define the

energy converting system as the total physiological human

body, and the object that work is done against as the

physical human body (mass). The energy inflow is then

contained in the food intake. This implies that the energy

required for swallowing and digestion is to be considered

in the calculations of efficiency. One could go as far as

arguing that all the energy consumption required to main-

tain homeostasis should be considered as energy inflow, as

2 Eur J Appl Physiol (2009) 106:1–14

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without this maintenance cost (i.e., the cost merely to stay

alive), it would be impossible to do work at all. This

maintenance entails far more than only the process of

digestion and is an ongoing process with, in principle, a life

long energy flow, leading to efficiency values equal to zero

for any activity. This line of thought is rarely followed,

however. Yet, it exemplifies problems that may arise when

interpreting the term efficiency and it shows how important

it is to define the system explicitly and accurately. If we are

more interested in how muscles generate work, and not in

the energy cost of food intake and other metabolic pro-

cesses in the body, we may define the system as the

musculoskeletal system of the body. In this case, the

energy inflow is defined as the energy from glycogen and

other substrates, but it does not include the abovemen-

tioned processes, nor the costs of supporting cardiac output

and ventilation, for example.

Net efficiency

Energy consumption is often calculated from oxygen

uptake and lactate production, the latter especially in case

of exercise performed above the lactate threshold. Often,

one is interested in the musculoskeletal system as the

energy conversion system. In such a case, it is common

practice to subtract all energy costs that are not related

directly to work production (e.g., associated with resting

metabolism) from the estimation based on oxygen uptake

and lactate production. Various methods and efficiency

definitions have been proposed to handle this challenge, but

none are without problems. The basic principle is that one

estimates the energy consumption of all processes that are

not part of the energy flow through the defined system of

interest (e.g., muscle; contractile element). This is referred

to as base-line subtraction (Gaesser and Brooks 1975;

Stainbsy et al. 1980). The main aim of base-line subtraction

is to establish a measure that refers to the efficiency of

muscle contraction in vivo. While this procedure may be

relatively simple in engineering, it is not so in biology

because of the many interactions and interdependences

between physiological systems. Perhaps the most funda-

mental of base-line subtractions is that of the resting

metabolic energy rate (e.g., Gaesser and Brooks 1975). The

reasoning is that the resting metabolic rate is needed to

maintain overall system homeostasis, irrespective of the

work being performed, and thus is not associated with

doing this work.

enet ¼power

metabolic rate� rest metabolic rate:

By using such subtraction, one implicitly assumes that

the processes related to resting metabolism are independent,

constant (Stainbsy et al. 1980) and, more importantly,

essentially isolated from the process of doing work (the last

issue not commonly being discussed in the literature). In

other words, the line of thought is that maintenance is, of

course, necessary to support a system in the first place, but

the energy flow otherwise is not related to that of doing

work in whatever form: one assumes that two independent

energy flows run in ‘parallel’, while not affecting or

relying on each other. One energy flow is that of the

musculoskeletal system as a work generator (assuming that

constitutes the defined energy transformation system), and

the other flow is that of system maintenance. It may be

incorrect to assume that the energy cost of base-line

processes is unaffected by the work rate during exercise (see

e.g., Cavanagh and Kram 1985; Stainbsy et al. 1980; van

Ingen Schenau and Cavanagh 1990). In fact, there is ample

evidence that this is not the case, especially at higher work

rates; various processes are affected, e.g., gastrointestinal,

splanchnic metabolism, general metabolic processes due to

temperature increase via the Q10 effect, and ventilation (e.g.

Stainbsy et al. 1980). On the other hand, gross efficiency

increases with work rate (see below) because of the

diminishing effect of offset (base-line) metabolism (at rest

or zero work rate) as work rate increases. In other words,

when studying the effect of work rate, the unqualified

use of gross efficiency seems rather meaningless when

attempting to enhance our understanding of the energy flux

process; gross efficiency will, of necessity, increase with

work rate. Refuting the use of net efficiency as a true

expression of efficiency does not mean that we disagree

about the existence of various energy consuming body

functions that have no, or little, direct bearing on

mechanical work production. Rather, we disagree with

the philosophy that these functions have no impact on work

production and that work production does not rely at all on

these processes.

Internal work and work efficiency

Internal work is often defined as the work necessary to

move the body segments relative to the body’s centre of

mass, i.e., changing the relative kinetic and potential

energy of these segments. Often, this is redefined as posi-

tive work done to accelerate the limbs relative to the centre

of mass of the body (e.g., Cavagna et al. 2008). The

negative component, i.e., reduction of body-segment

movement energy relative to the centre of mass, is often

‘‘removed’’ from the calculations (by taking the absolute

values of their energy changes, e.g., Thys et al. 1996;

Willems et al. 1995). This approach implies the presump-

tion that this component is an energy loss (i.e., always

converted into heat, never into external work). There is no

basis for this presupposition. For cyclic movements such as

walking, running, and cycling it is obvious that, over an

Eur J Appl Physiol (2009) 106:1–14 3

123

entire movement cycle, the net change of this relative

movement energy equals zero. In other words, the total

internal work in cyclic movements equals zero. Neptune

and Herzog (1999) found that more negative work is done

on the crank with increasing cadence, particularly above

90 rpm. Thus, it is likely that more energy is lost by

decreasing mechanical effectiveness. It should be noted

that Neptune and Herzog (1999) did not link this increase

to internal work, but rather to muscle activation dynamics,

i.e. neuromuscular coordination aspects. The definition of

work efficiency is based on the assumption that the meta-

bolic cost for unloaded cycling (or any other activity) is not

utilized for doing external work. The rationale is well

explained by Whipp and Wasserman (1969) and illustrated

in their Fig. 1:

ework ¼power

metabolic rate�metabolic rateunloaded

:

The metabolic rate at unloaded cycling is the sum of the

resting metabolic rate and the metabolic rate required for

doing internal work. We do not agree with the use of work

efficiency as a measure for muscular efficiency, nor do we

support the notion that summation of internal and external

work is a valid estimate for muscular work. The reasons are

explained below.

When summating internal work and external work as the

total work done by a system (e.g., Minetti et al. 2001;

Winter 1979), two questionable steps are taken. Firstly, the

system definition is unclear, as an ‘internal’ energy con-

version is, in a way, regarded an outflow. For example,

Winter (1979) defined mechanical efficiency as the sum of

internal and external work divided by the metabolic cost.

However, he did not define the energy converting system

that this efficiency is a measure for. According to logical

semantics, the term ‘internal’ cannot appear in the

numerator in an efficiency definition. Secondly and more

importantly, one runs the risk of counting twice a part of

the work done, overestimating the calculated efficiency.

For example, applying this method, Widrick et al. (1992)

report mechanical efficiencies of above 40%, i.e. suffi-

ciently high to suggest a flaw. Furthermore, their data (see

Fig. 1 in Widrick et al. 1992) indicate a negative intercept

for the work rate—energy expenditure relationship. This

implies a negative muscular efficiency, if it is assumed that

the sum of internal and external work is a valid measure for

muscular work. The use of the misleading notion that

internal work is not related to doing external work has been

similarly criticized (e.g., Kautz et al. 1994; Kautz and

Neptune 2002). Figure 1 shows a conceptual diagram

explaining how, in principle, the various energy deposits

and work transitions are linked to each other. The changes

in the energy levels of the ‘‘internal energy depots’’ (elastic

energy and body-segment movement energy) are internal

or external work transitions, but not both at the same time.

The main message here is that often we do not have

information on one of the depots (elastic energy), but not

on the direct transition of muscle work to external work.

This lack of information makes it impossible to judge,

a priori, a reduction in body-segment movement energy as

a loss. We do not argue here that the measurements on

internal work, or better body-segment movement energy, is

pointless, but we do argue against the interpretation of this

measure as an ‘‘internal loss of energy’’, and against the

summation of internal and external work as a measure for

muscular work. For the same reason, we argue that the use

of work efficiency as a measure for muscular efficiency is

based on a flawed assumption.

A practical and at first sight elegant solution for mea-

suring the true metabolic cost of losses by doing internal

work is the measurement of the metabolic cost during

unloaded movements (e.g., Dickinson 1929; Whipp and

Wasserman 1969; Gaesser and Brooks 1975; Hagberg

et al. 1981; Hintzy-Cloutier et al. 2003; Nickleberry and

Brooks 1996). If one creates a condition in which no

external work can be done, all work done by the muscular

system is related to the body-segment movement energy,

and will be dissipated into heat. This is in essence a pure

base-line subtraction. The problem that arises is the same

internalmovement

energy

internalelasticenergy

muscle contractionpos internal work

neg. internal

work

pos. internalwork

neg.

inte

rnal

wor

k mus

cle

cont

ract

ion

exte

rnal

wor

k

Energy influx

External work

Fig. 1 Conceptual model for energy flow during exercise. The terms

‘positive’ (pos) and ‘negative’ (neg) indicate direction of energy flow

only. One of the main issues is that internal work, as described in the

literature, cannot be assumed to be loss of energy. Further, every

energy conversion (arrow) implies energy loss (as heat)

4 Eur J Appl Physiol (2009) 106:1–14

123

as discussed previously, namely that this approach pre-

sumes two independent energy flows. Furthermore, by

measuring the energy cost of the unloaded movement, not

only is all internal work dissipated into heat, but it must be

dissipated into heat because the circumstances do not allow

external work production. There is no reason to believe

that in the case where external work can be done, the same

internal work is not (partly) converted to external work.

Moreover, it appears that by moving the lower extremities

passively, i.e. by external forces, metabolic rate increases

significantly (Nobrega et al. 1994). This indicates that

other processes than simply the active limb movements

also affect metabolic rate. Unpublished data from our

laboratory indicate that muscle activity in unloaded cycling

is extremely low and can hardly account for the total

increase of metabolic rate that is usually observed in

unloaded cycling (e.g., about 200–450 W energy con-

sumption at 0 external work rate, at 60–120 rpm, Hagberg

et al. 1981; Sidossis et al. 1992). Two other processes that

at first sight are obvious candidates are the enhanced

heart—and ventilation rate. However, there is ample evi-

dence that these processes require comparatively little

additional energy consumption (e.g., McGregor and

Becklake 1961; Aaron et al. 1992; Kitamura et al. 1972)

and thus can hardly explain this phenomenon. Further-

more, doing more ineffective work due to coordination

challenges (Neptune and Herzog 1999) likely enhances

metabolic rate in passive cycling. This was substantiated

by Bell et al. (2003), who found considerable muscle

activity and a coinciding increase in metabolic rate during

pure passive cycling compared to other modes of passive

leg movements. In that study, subjects reported it was

difficult to relax completely in passive cycling. Thus, it

seems difficult to experimentally determine the energy cost

of true internal work (i.e., work that never appears as

external) in loaded cycling.

Another method to determine the costs of body seg-

ments’ movement energy changes is by extrapolating the

relationship between external work rate and energy cost to

a zero work rate (e.g., Hintzy-Cloutier et al. 2003). Such

an approach requires that the several work rates that are

used entail the same body segments’ movement energy.

In cycling, this requirement is fulfilled by using the same

cadence. Furthermore, it is expected that the energy

cost—work rate relationship is linear, which has been

substantiated empirically in many studies (e.g., Bijker

et al. 2001, 2002; Chavarren and Calbet 1999; Hintzy-

Cloutier et al. 2003; Widrick et al. 1992; see also the

literature results gathered in this review, Fig. 2), although

it should be noted that for sustained work rates that

exceed the lactate threshold this relationship may become

nonlinear because of the influence of the so-called ‘‘slow

component’’ of oxygen uptake (e.g., Poole et al. 1994;

Whipp and Rossiter 2005). Hintzy-Cloutier et al. (2003)

found that the extrapolation method results in lower val-

ues than true unloaded cycling, and discuss some reasons

for this.

Delta efficiency

It is only a small step from work efficiency to delta-effi-

ciency (e.g., Bijker et al. 2001, 2002 ; Chavarren and

Calbet 1999; Coyle et al. 1992; Garry and Wishart 1931;

Marsh et al. 2000; Mora-Rodriguez and Aguado-Jimenez

2006; Nickleberry and Brooks 1996; Sidossis et al. 1992)

defined as:

eD ¼Dpower

Dmetabolic rate;

where Dpower and Dmetabolic rate stand for increment of

power and metabolic rate with increasing work rate. The

advantage of such a measure is that knowledge about

resting metabolic rate is not required, and the measure is

likely to be less affected by potential changes in the base-

line energy cost caused by work rate. However, the same

fundamental problem remains, namely, that implicitly one

assumes that the energy flow for the Dpower production is

independent of the energy flow for the first amount of

power produced. This is the same as stating that when

increasing work rate one turns on an ‘extra’ engine

(muscle, motor units) that runs independently from the

other engine(s) that produces the initial amount of power

production. Delta efficiency is not, by definition, an

integral measure for the entire energy conversion process.

It will be independent of the protocol (work rate incre-

ments) only if the metabolic cost–work rate relationship is

linear (e.g., Bijker et al. 2001, 2002; Chavarren and

Calbet 1999; see also Fig. 2). This implies that all ‘extra’

engines that are turned on with increasing work rate will

show the same efficiency. In that case, the efficiency of

one engine is equal to the efficiency of all engines when

they are considered together as one unit. In other words,

when using delta efficiency as a measure for muscular

efficiency, the a priori assumption is made that efficiency

is independent of work rate. Note that a linear relationship

does not imply that delta efficiency provides a valid

measure, and neither does the finding that the efficiency

value obtained are realistic (i.e., between say 20 and

25%). These findings merely hold this option open.

Nevertheless, theoretically impossible efficiency values

indicate a flaw in the calculations. For example, Bijker

et al. (2001, 2002) report a delta efficiency for running of

around 50%, which seems to be an unlikely, if not

impossible, true efficiency. Note that we do not claim that

the use of delta efficiency is meaningless; rather we claim

that it is not a measure for efficiency. Instantaneous

Eur J Appl Physiol (2009) 106:1–14 5

123

efficiency is the same as delta efficiency for an infinitely

small Dpower, and in fact a more accurate measure than

delta efficiency. However, the same problems apply to

instantaneous efficiency as for delta efficiency.

The use of gross efficiency

The curved work rate–gross efficiency relationship is a

consequence of the decreasing relative contribution of the

offset (i.e., base-line metabolism) with increasing work

rate. Gaesser and Brooks (1975) considered this a cal-

culation artifact and therefore rejected the use of gross

efficiency, a standpoint we dispute; it is rather a mat-

ter of interpretation of what a true measure is, and

that depends on the definition of the energy converting

system.

In a final remark on efficiency definitions and interpre-

tation, we wish to note once more that the problem

Luthanen et al., (1987)

** ** ** *

*

*

*

120

60

5

10

15

20

25

30

30 45 60 75 90 105 120

Cadence (rpm)

Gro

ss e

ffici

ency

(%

)

5

10

15

20

25

30

0 100 200 300 400 500

External power (W)

Gro

ss e

ffici

ency

(%

)

5

10

15

20

25

30

0 100 200 300 400 500

External power (W)

Gro

ss e

ffici

ency

(%)

0

500

1000

1500

2000

2500

0 100 200 300 400 500

External power (W)

Met

abol

ic r

ate

(W

)

5

10

15

20

25

30

0 100 200 300 400 500

External power (W)

Gro

ss e

ffici

ency

(%)

0

500

1000

1500

2000

2500

0 100 200 300 400 500

External power (W)

Met

abol

ic r

ate

(W)

Samozino et al. (2006)

Moseley and Jeukendrup (2001)

Luhtanen et al. (1987)

Chavarren & Calbet (1999)

Moseley et al. (2004)

Sallet et al. (2006)

a b

c d

e f

6 Eur J Appl Physiol (2009) 106:1–14

123

presented here is not new. For example, Cavanagh and

Kram (1985), and before them Stainbsy et al. (1980),

presented the problem of base-line subtractions and inter-

pretation of such efficiencies in depth. Cavanagh and Kram

(1985) refer to net-efficiency, delta-efficiency as concep-

tually flawed, and van Ingen Schenau (1998) argued

strongly against the subtraction of internal work. It seems,

however, that the use of these methods in the scientific

literature is continues unabated. In the remainder of this

review on efficiency in cycling, we will take gross effi-

ciency as the departure point, and discuss delta efficiency

with the critical note that we do not consider it to be a valid

measure for efficiency. Stainbsy et al. (1980) also indicated

that gross efficiency does not resemble muscular efficiency

(independently of how the muscle is defined as an energy

conversion system). In other words, for theoretical and

practical reasons, an attempt to determine muscular effi-

ciency in whole body movements seems a fruitless

exercise. Accordingly, in the remainder of this paper, we

will focus on gross efficiency in cycling, reflecting effi-

ciency of the entire human body in action.

Efficiency in cycling

Here, we are concerned with the literature on efficiency in

cycling, particularly regarding the influence of work rate

and cadence. This paper does not aim to discuss perfor-

mance enhancement in competitive cycling by optimisation

for energy expenditure in cycling. Nevertheless, it appears

that one tends to freely choose a pedalling rate that is

somewhat above the energetically optimal one (e.g., Foss

and Hallen 2005). Some authors argue that this hampers

performance (e.g., Foss and Hallen 2005; Hansen and

Ohnstad 2008). Others use this finding to argue that the

human body apparently does not ‘care’ about minimising

energy expenditure (e.g., Redfield and Hull 1986), or

consider other optimisation criteria, such as muscle acti-

vation (e.g., Neptune and Hull 1999). While we do not take

a stand on this issue in this paper, the findings summarised

here may be of relevance for its ultimate resolution.

Cadence and work rate

The two most obvious variables that may affect efficiency

are cadence and work rate. Cadence is often thought of a

rather simple and straightforward ‘gear between force

(torque) and velocity (angular velocity) of muscle con-

traction. Thus, the energetically optimal cadence is likely

to be found at a muscle contraction speed that is close to

maximal power and efficiency in isolated muscle (i.e.,

around 0.3 of maximal force and contraction velocity; e.g.,

see Barclay et al. 1993). Kohler and Boutellier (2005)

argued that the freely chosen cadence may not follow the

principle of minimising energy cost because of the dis-

crepancy between velocities giving maximal power and

efficiency. However, their analysis does not account for a

number of processes that are affected by cadence as well.

For example, because of activation-relaxation dynamics,

relatively more time is consumed at higher cadences by the

activation and relaxation process. Furthermore, inertial

effects by rotating lower limb masses lead to a change from

muscle performance to performance on the pedals (e.g.,

Ettema et al. 2009; Kautz and Hull 1993; Kautz and

Neptune 2002; Loras et al. 2009). Ettema et al. (2009)

demonstrated that details in cycling technique change with

cadence. In other words, the concept of treating choice of

cadence as a mere ‘gearing’ between force and velocity of

muscle contraction may be attractive, but it probably does

not fully hold.

To summarize the extensive literature on efficiency in

cycling and the effect of work rate and cadence, we plotted

the results of a large (but certainly not complete) set of

studies that report gross efficiency in cycling. The studies

include untrained up to elite and professional cyclists

(including world top), different exercise protocols, and

Fig. 2 Overview of literature data explored in this review and used in

the quantification of efficiency. The different symbols indicate

different studies. Figures a–d show the mean values at a particular

cadence or external power for each study. a Gross efficiency against

cadence. *: Dickinson (1929), net efficiency for comparison. b Same

data against external power. A low efficiency (Luhtanen et al. 1987) is

indicated. Two values at high power are boxed (Lucia et al. 2002

(open circle); Coyle 2005 (filled circle)] and discussed in more detail

in the text. c Metabolic rate against external power, based on same

data as in a and b. Boxed values are same as boxed in b. Data by

McDaniel et al. (2002) are shown in grey squares for comparison. A

few studies, with somewhat different findings, are indicated in the

legend and discussed in the text. d Same data as in b, but depicting a

possible error of measurement of 5%. Thick curve is the average

curve, based on the regression line in b. Thin curves indicate ranges if

both metabolic rate and external power have deviation (error) of 5%,

but in opposite directions. A thick vertical error bar indicates the

same range if only one of the measures has a 5% deviation; the thinhorizontal arrows indicate the efficiency difference following from

this error. Filled marker represents the highest power in the study by

Luhtanen et al. (1987). Its deviation from power measures in other

studies is discussed in the text. e, f Same diagrams as c and d,

respectively, but now showing all reported values for different

cadences at one particular power. Thin curves are identical to figures

c and d, and thick curves are those based on all values. Inset in eshows data from Chavarren and Calbet (1999), indicating effect of

cadence (60–120 rpm). Studies presented in the figure: Cannon et al.

(2007), Chavarren and Calbet (1999), Coyle et al. (1992), Coyle

(2005), Delextrat et al. (2003), Foss and Hallen (2004), Gaesser and

Brooks (1975), Hansen et al. (2002), Hintzy et al. (2005), Hopker

et al. (2007), Horowitz et al. (1994), Lucia et al. (2002, 2004),

Luhtanen et al. (1987), Moseley and Jeukendrup (2001), Moseley

et al. (2004), Mora-Rodriguez and Aguado-Jimenez (2006); Mourot

et al. (2004); Nickleberry and Brooks (1996); Sallet et al. (2006);

Samozino et al. (2006); Sidossis et al. (1992); Unpublished data—

Elite; Unpublished—Trained; Widrick et al. (1992); Zameziati et al.

(2006)

b

Eur J Appl Physiol (2009) 106:1–14 7

123

various procedures to calculate metabolic rate and external

power. However, all studies used respiratory exchange

ratio values to convert oxygen uptake rate to metabolic

rate. Where the anaerobic contribution was considerable,

either the relevant data points were not considered in the

original reports or lactate levels were taken into consider-

ation and converted to metabolic rate, according to, for

example, di Prampero (1981). To avoid over-representation

of studies that examined a matrix of cadence and work rate,

we averaged their results according to cadence and work

rate before entering them into the figures (Figs. 2a–d).

Thus, per study, one single data entry for each work rate

and each cadence was used. All separate combinations of

cadence and power are shown in Fig. 2e, f.

Figure 2a shows the data according to cadence. Even

though most studies report a clear negative effect of

cadence on gross efficiency, the overall picture shows a

minimal effect. The inter-study variation is much larger

than any visible trend, and some studies show the opposite

(positive) effect or an inverted u-shape with an optimal

cadence. The inter-study variation may easily be thought to

be caused by methodological differences. However, when

plotting the same pool of data against external power, a

different picture is shown. A very consistent relationship

between work rate and efficiency is found. This relation-

ship is even more clearly demonstrated by plotting the

metabolic rate against work rate (Fig. 2c). A linear rela-

tionship is found, which is not unexpected but merely

reflecting what various studies have reported explicitly

(e.g., Anton-Kuchly et al. 1984; Bijker et al. 2001, 2002;

Chavarren and Calbet 1999; Coast and Welch 1985;

Francescato et al. 1995; Gaesser and Brooks 1975; Hintzy-

Cloutier et al. 2003; McDaniel et al. 2002; Moseley et al.

2004; Widrick et al. 1992). As stated before, the curved

work rate–gross efficiency relationship is a consequence of

the offset (y-intercept) of the work rate–metabolic rate

relationship. Note, that this offset does not, per se, indicate

any fixed baseline energy cost that, physiologically, is

independent of work rate. The rather surprising aspect of

the result is the high consistency between the various

studies regarding the work rate–metabolic rate relationship,

where it seems to be lacking as a function of cadence.

Although one should be cautious with the interpretation of

correlations here, that between metabolic rate and external

power amounts to 0.97 (n = 93, p \ 0.0001; 26 studies, 29

conditions/subject groups, meaning that 94% of the varia-

tion among all (mean) energy expenditure values for all

these situations is explained by absolute work rate. This

outcome is only slightly more ambivalent when separate

data for all different cadences at the same power output

were entered (in 9 studies), as shown in Fig. 2e. Also when

converting the data to work rate-efficiency curves, only

small differences with the original calculations occur

(Fig. 2f), with the correlation being reduced to 0.95

(r2 = 0.91). In other words, factors other than work rate,

including cadence, explain less then 10% of the variation in

energy expenditure. Adding cadence as a dependent factor,

the explained variance is increased to 94% (cadence

explains about 10% on its own). These findings, both

correlation values as well as the absolute cost-work rate

relationship, agree well with McDaniel et al. (2002)

(redrawn in grey in Fig. 2c, but not included in the anal-

ysis), who looked at cadence, work rate and movement

speed (by altering crank length). In their study, 95% of all

variation in metabolic cost, including all experimental

conditions, was explained by work rate. In the present data

pool, cadence and power are correlated to some extent

(r = 0.171, p \ 0.019; Fig. 3a), which complicates the

interpretation somewhat as these two factors share some of

their variance. Still, both factors seem reasonably evenly

spread over all data considered in this overview (Fig. 3a).

Therefore, it is unlikely that this correlation between work

rate and cadence has a strong effect on the findings.

025

5075

100125 0 100 200 300 400 500

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

0

100

200

300

400

500

0 20 40 60 80 100 120 140

Cadence (rpm)

Ext

erna

lpow

er(W

)

External power (W)

Cadence (rpm)

Met

abol

ic r

ate

(W)

a

b

Fig. 3 a Cadence plotted against work rate for all data considered in

this overview (see Fig. 2). b Energy expenditure plotted against work

rate and cadence (same data as in Fig. 3a and Fig. 2e and f. Coloured

mesh is the two-dimensional linear regression (red marker indicates

extrapolated intercept at zero load and zero cadence). Markers

distinguish data below (filled) and above the mesh (open). The

regression is described by: Metabolic rate = 39.7 (±29.3) ? 2.84

(±0.34) 9 rpm ? 3.73 (±0.08) 9 External Power

8 Eur J Appl Physiol (2009) 106:1–14

123

Interestingly, the intercept of the two-dimensional regres-

sion at zero work rate and zero cadence (Fig. 3b), which

would be the theoretical value for energy expenditure while

sitting still on a bicycle, reaches a value of 40 W (not

statistically significant from zero). This value is too low,

but still physically possible, despite the rather large

extrapolation range from the experimental data. Overall, it

seems that the very original findings by Fenn (1924) on

isolated muscle also apply to the entire human body in

cycling in a very consistent manner.

In the literature data in Fig. 2c, some deviations appear: in

two cases the offset in metabolic rate is somewhat higher

(Chavarren and Calbet 1999; Samozino et al. 2006), and in a

few others the metabolic rate increases exponentially at high

work rates (Luhtanen et al. 1987; Moseley and Jeukendrup

2001; Moseley et al. 2004). The higher offset cannot be

explained, but the exponential increase may be because the

subjects exercised above lactate threshold and approached

their maximal work capacity. In such an instance, one may

expect that an increase in work rate requires a dispro-

portional amount of metabolic input (e.g., because of

deterioration of coordination). In the case of Luhtanen et al.

(1987), where the highest three work rates were at and above

anaerobic threshold, this leads to a negative relationship

between gross efficiency and work rate (Fig. 2b). Note that

for all data presented in Fig. 2, the metabolic rate was based

not only on aerobic, but also on anaerobic contributions if

relevant. Still, the estimates of the anaerobic contribution are

bound to be less accurate than the aerobic counterpart. The

curvilinear increase of metabolic rate with work rate is likely

related to the slow component of O2 uptake that emerges at

intensities above lactate threshold (e.g., Poole et al. 1994;

Whipp and Rossiter 2005). That is, for constant work-rate

exercise, VO2 shows a further slow increase (after a delay of

2–3 min). Thus, some of the differences between studies

may be due to the emergence of the VO2-slow component

especially at high work rate (e.g., Luhtanen et al. 1987;

Moseley and Jeukendrup 2001; Moseley et al. 2004).

Clearly, both work rate and exercise duration are of impor-

tance when comparing efficiency results. The studies

discussed in this paper tend to have relatively short time

periods of measurement at constant work rates (2–3 min.).

Thus, the impact of the VO2-slow component is likely not

more than moderate.

Coyle and coworkers (e.g., Coyle 2005; Sidossis et al.

1992) report that gross efficiency is independent of work

rate. This seems in contradiction with the current overview

of the literature that includes their publications. However,

considering Fig. 2, it becomes clear that the impact of work

rate on gross efficiency diminishes strongly from about

150 W. And, as mentioned above, a negative trend can be

discerned in some studies, but these they are explained (at

least partially) by relatively high work rates close to the

individual’s maximum.

In summary, absolute external power determines not

only metabolic rate, but also gross efficiency in a more

consistent manner than cadence does.

Reciprocal slope of work rate–metabolic rate

relationship (delta efficiency)

As we dispute the idea that delta efficiency reflects true

efficiency, we will refer to it here as the reciprocal slope of

work rate–metabolic rate relationship (RSep-mr). The data

in Fig. 2c show a RSep-mr of 25.5% (26.1% when using all

data separately, Fig. 2e). These values are similar to Bijker

et al. 2001, 2002. Coyle (2005) reports delta efficiency to

be very similar to gross efficiency in cycling (around 21–

23%) for one of the world top cyclists. This would imply

that the corrected baseline approaches zero or is negligible

with regard to total metabolic rate, which may in fact be the

case as these efficiencies were recorded at extremely high

work rates. Sidossis et al. (1992) find that delta efficiency

deviates from gross efficiency mainly at high cadence

(100 rpm). This is explained by that the base-line meta-

bolic rate (i.e., at zero work rate) depends on cadence. The

literature data in the present paper indicate that most, if not

all, studies have very similar RSep-mr values (Fig. 2c),

the overall value being close to 26%. Table 1 shows the

Table 1 Average values of the reciprocal slope of work rate–meta-

bolic rate relationship (RSep-mr) calculated from (and reported by) a

number of studies on cycling

Source RSep-mr

Chavarren and Calbet (1999) 22.2

Gaesser and Brooks (1975) 26.2

Hansen et al. (2002) 24.4

Luhtanen et al. (1987) 17.8

Moseley and Jeukendrup (2001) 25.5

Moseley et al. (2004) 21.5

Nickleberry and Brooks (1996) 25.0

Samozino et al. (2006) 21.6

Sidossis et al. (1992) 22.1

Widrick et al. (1992) 25.4

Zameziati et al. (2006) 27.6

Zamparo et al. (2002) 23.4

Unpublished—elitea 22.7

Unpublished—trainedb 27.4

Mean 23.8

Standard deviation 2.6

a Cyclists from the national Norwegian team (time trial). Measure-

ments done in same lab as (b)b Data are from the same study as Ettema et al. (2009) and Loras

et al. (2009), but not reported in these publications

Eur J Appl Physiol (2009) 106:1–14 9

123

RSep-mr values of a number of studies that reported meta-

bolic rate at various work rates. Most of these values are

not taken from the original papers, but calculated from the

data collected for this review. Thus, for all studies the same

algorithm was used. Some studies show substantially lower

reciprocal slopes than the average, but none much higher.

This is explained by the different weighting in the calcu-

lations of these studies: the studies with the higher slopes

have more data points. Thus, it seems more appropriate to

conclude that the RSep-mr as found in the literature averages

around 23–24% rather than 26%.

Is there an energetically optimal cadence?

When considering overall effectiveness for the entire

human body (i.e. total energy cost in relation to external

power), most studies that looked at a rather wide range of

cadences and are represented in the analysis in this review

report that the lowest pedalling rate is most effective

(Chavarren and Calbet 1999; Gaesser and Brooks 1975;

Lucia et al. 2004; Nickleberry and Brooks,1996; Samozino

et al. 2006; Sidossis et al. 1992; Widrick et al. 1992). Two

studies claim the highest rate to be most effective, and 2

others an optimal cadence (Foss and Hallen 2005; own

unpublished data). Other studies (e.g., Coast et al. 1986)

also find an optimal cadence with regard to efficiency. In

most of these studies, the optimal cadence lies between 60

and 80 rpm. These contradictory results may, in part, be

explained by the interaction between work rate and

cadence. In short, when an optimal cadence is found, it

increases with work rate (Boning et al. 1984; Coast and

Welch 1985; Francescato et al. 1995; Foss and Hallen

2004; Gaesser and Brooks 1975; Seabury et al. 1977), and

the impact of cadence on efficiency seems most remarked

at lower work rates (Chavarren and Calbet 1999; Samozino

et al. 2006; Widrick et al. 1992). Also di Prampero (2000),

in his review, concluded that efficiency in cycling is

affected by cadence and the optimum by work rate.

Extrapolations from cadence studies to the force-

velocity relationship of muscle should, however, be made

with caution. Indeed, Hill (1934) warned against this in his

critical comments on Garry and Wishart (1931, 1934). Not

only muscle shortening velocity, but also activation-

relaxation dynamics are strongly affected by cadence.

McDaniel et al. (2002) attempted to distinguish between

these two factors by manipulating crank length. They found

that pedal speed (marker for muscle shortening speed) and

power (work rate) were the main determinants for meta-

bolic rate, not cadence (marker for activation-relaxation

dynamics). Marsh et al. (2000) found no effect of cadence

on delta efficiency, where values were around 23–26%.

This does not contradict findings about optimal cadence

with regard to energetic cost. For the sake of argument, if

one assumes that resting metabolic rate and the cost of limb

movements is (physically) independent of work rate, delta

efficiency is a measure of the increasing cost directly

linked to increasing muscle work. Marsh et al. (2000)

basically substantiated that the impact of increasing work

rate is independent of movement speed. Chavarren and

Calbet (1999), however, report a significant positive effect

of cadence on delta efficiency. Their work rate–metabolic

rate data are redrawn in Fig. 2e, inset. Although the trend

of a changing slope is evident, it is small considering the

range of cadence (eD = 21.5% at 60 rpm to near 24% at

120 rpm). On the other hand, Chavarren and Calbet (1999)

report a stronger negative effect of cadence on gross effi-

ciency, indicating that we are not only dealing with

processes associated with work rate, but also other pro-

cesses (e.g., force-velocity properties, activation-relaxation

dynamics, energy flow associated with internal work,

ventilation and circulation).

In early work, Dickinson (1929), but also Garry and

Wishart (1931, 1934), studied the relationship between

cadence and efficiency, basing their analysis on Hill’s

force-velocity equation. (Note that they expressed speed in

terms of time of contraction.) Dickinson (1929) established

efficiency for maximal efforts (i.e., well over the lactate

threshold, and with no steady state) by including oxygen

uptake during recovery. She subtracted resting metabolism

(i.e., calculated net efficiency). We calculated gross effi-

ciencies from these original data, leading to values around

4–9%. These extremely low values occur because of the

long period of oxygen uptake measurement (30 min) in

relation to the exercise period (1–10 min), once more

clearly addressing the practical and theoretical challenges

around true efficiency of work production. Some of

Dickinson’s original data are re-plotted in Fig. 2a against

cadence. The optimal frequency lies around 35 rpm (all

data to the left that are omitted were lower). This is rather

striking as these measurements were made at a high work

rate. On the other hand, the data are not out of the ordinary

compared to the more recent studies accounted for in Fig. 2.

Furthermore, Dickinson calculated net efficiency, assuming

a constant and work independent of resting metabolism.

An important consequence of the analysis of cadence and

work rate effects on efficiency is that power differences

may be a confounder in experimental studies on cadence. In

experimental testing, relatively small differences in external

power that are related to cadence may occur. These dif-

ferences can have a relatively large impact on the cadence-

efficiency relationship. Furthermore, relatively small errors

in power measurements affect the efficiency value consid-

erably (see below, Fig. 2d). An error of 5% at 285 W

(14.25 W) gives an efficiency error of 1% (Fig. 2d). In other

words, it is important that possible systematic errors in

power linked to cadence are eliminated.

10 Eur J Appl Physiol (2009) 106:1–14

123

In summary, because of the fundamental challenges of

discriminating the various mechanisms of energy expen-

diture and losses that relate differently to cadence (e.g.,

expenditure not directly associated to doing work, force-

velocity characteristics of muscle), as well as accuracy

issues, a true cadence-efficiency relationship has still not

been established. Overall (Fig. 3b), there seems to be a

small negative effect of increasing cadence on efficiency.

Do elite athletes have high efficiencies and does

training improve efficiency?

Lucia et al. (2002) reported rather high gross efficiency

values for some top cyclists. The average for the group

amounted to 24.5% (with a peak individual value at

28.1%). Jeukendrup et al. (2003) argued that these results

were extremely high from a theoretical point-of-view and

must have been affected by errors in the measurements (see

also below, next section). They furthermore concluded that

if these data were correct, ‘‘some interesting physiological

adaptations may exist…’’. Coyle (2005) reported an

increase in efficiency over a period of 7 years of training

and competing in one of the most outstanding cyclists of

modern times from about 21–23%. Coyle proposed that

biochemical adaptations may have caused this improve-

ment (i.e., a greater contribution from aerobically-efficient

type I fibres). When considering these data and their

placement within the data derived from the literature

(Fig. 2b, c; data enclosed in a grey square; only overall

average is shown for both studies), these values do not

seem extraordinary, although Lucia et al. (2002) appear to

show a slightly high efficiency value. This is supported by

values from Sallet et al. (2006) on elite and professional

riders who score even higher efficiencies at powers above

400 W (data most to the left in Fig. 2b, c). The main reason

why gross efficiency is relatively high is likely because of

the high work rate. Also the improvement in efficiency

reported by Coyle (2005) may be explained by an increased

power at which these values were determined. Neverthe-

less, the studies by Sallet et al. (2006) and Lucia et al.

(2002) show metabolic rates below the regression line in

Fig. 2c, which may indicate either measurement error or,

indeed, some physiological changes that enhance efficiency

above the increase that is directly linked to that for the

work rate. It is interesting to note that the same group

(Lucia et al. 2004) report a lower efficiency is reported

(23.4 vs. 24.5%) at a slightly lower power (366 vs. 385 W).

How accurate are efficiency measurements?

Irrespective of definitions and concepts, a framework for the

accuracy of efficiency measurements can be established. It

seems reasonable to allow for a 5% error in biological

measurements with regard to studies on cycling efficiency.

Figure 2d shows the ranges of efficiency calculations that

arise from 5% error in both metabolic rate and external

power going in opposite directions. The vertical bar shows

the range near 300 W if only one of these measures has that

same error. Only one data point falls clearly outside the

range of 5% error (filled circle). This is the result from

Luhtanen et al. (1987) at the highest work rate, which was,

as mentioned earlier, well above the lactate threshold and

thus bound to result in a lower efficiency. Thus, the dif-

ference between studies may be partly explained by

differences in (systematic) errors. This merely strengthens

the notion that cycling is an extremely consistent exercise

model with regard to the relationship between metabolic

rate and external power. Thus, the situation presented in

Fig. 2c may constitute a very solid framework for the

interpretation of past, present and future studies.

Conclusion

We conclude this review by putting what was discussed

earlier into a simple theoretical framework. In the tradition

of Fenn (1924), one can factorise the metabolic costs as

found in cycling (Fig. 2): E = I ? kW, where E is meta-

bolic costs, I is the constant intercept (maintenance), k a

constant (reciprocal delta efficiency), and W the external

work done. When using delta efficiency as a measure for

muscular efficiency, one assumes that the intercept of the

work rate-metabolic rate relationship is not associated with

muscular contraction and all energy increase is linked to

the work accomplished. This is, of course, a tempting

thought, but the physiological basis for it can be chal-

lenged; the only matter that is clearly established is a very

consistent linear work rate-metabolic rate relationship. The

equation is likely better rewritten as E = Ic ? k(Iw ? W),

with Iw = qW. In other words, total metabolic rate is built

up from a constant rate (Ic), a work related rate (kW), and a

component of energy consumption that is not directly

associated with the work conversion process (muscle

contraction) but changes linearly with it (Iw). These pro-

cesses may be, for example, ventilation and circulation, but

also digestive processes. Energy loss associated with rela-

tive movements of segments (note once more, not the

entire internal work) would logically be accounted for by

the Ic component: losses associated with internal work do

not depend on external work rate, but more likely on

cadence (i.e., the amount of kinetic energy changes of the

moving limbs). Indeed, both Sidossis et al. (1992) and

Chavarren and Calbet (1999) clearly show that with

increasing cadence only Ic increases in a more or less linear

fashion (see Fig. 2e, inset). It is tempting, but likely

incorrect, to conclude that this increase is solely due to

Eur J Appl Physiol (2009) 106:1–14 11

123

increase of internal work losses. Whatever the case, the

equation can be rewritten as follows:

E ¼ Ic þ kðqþ 1ÞW :

While the efficiency of the pure work production system (a

precise definition of this system is not presented here) is

k-1, the measured efficiency is {k(q ? 1)}-1. Somewhat

speculatively, one can argue that if all non-associated

energy costs (Ic and kqW) could be accounted for accu-

rately in measurements, one should obtain a muscular

efficiency of close to 30%. As delta efficiency reported in

the literature is about 26% or less, one can conclude that q

must be about 0.1–0.15. This is, of course, based on the

assumption that muscular efficiency in vivo and in isolated

muscle are similar. However, we cannot take this as a

departure point if we want to gain knowledge about muscle

efficiency in vivo through experimentation. As long as we

do not have better knowledge about the value for q, or

about the validity of the entire equation for that matter, the

use of delta efficiency (or any other efficiency) in the

search for muscular efficiency is fruitless. As many new

methods are being developed that can monitor energy

consumption locally in the body under in vivo conditions,

the future holds a number of challenges that may be

realised.

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