Eur J Appl Physiol
DOI 10.1007/s00421-009-1008-7
INVITED REVIEW
Efficiency in cycling: a review
Gertjan Ettema Æ Håvard Wuttudal Lorås
Accepted: 2 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 efficiency. 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 expenditure 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 associated 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
G. Ettema (&) H. W. Lorås
Human Movement Science Programme, Faculty of Social
Sciences and Technology Management, Norwegian University
of Science and Technology, 7941 Trondheim, Norway
e-mail: [email protected]
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 characteristics, load, ring shape, body position), environmental
conditions (e.g., uphill cycling), and also subject characteristics (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 physiological 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 measurement 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
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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 baseline 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 relationships 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 considerations, 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 mechanics. 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 muscle 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 environmental 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 conservation 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
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regard the human body (i.e., its locomotor muscles) as a
system that is not isolated. Indeed, energy from its environment can flow into the system (metabolites and negative
work) and out (in the form of work and heat). The thermodynamic 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 liberated 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:
e¼
work
power
¼
energy cost 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 necessarily 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 maintain homeostasis should be considered as energy inflow, as
Eur J Appl Physiol
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 processes 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 abovementioned 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 fundamental 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 ¼
power
:
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 positive 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 presumption 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
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Eur J Appl Physiol
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 metabolic 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:
power
ework ¼
:
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.
Energy influx
internal
elastic
energy
neg. internal
work
external work
internal
movement
energy
neg. internal
work
pos. internal
work
muscle contraction
muscle contraction
pos internal work
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)
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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 conversion 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. sufficiently 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 measuring 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
Eur J Appl Physiol
as discussed previously, namely that this approach presumes 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 consumption 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 evidence 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. Furthermore, 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 segments’ 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; HintzyCloutier 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 values than true unloaded cycling, and discuss some reasons
for this.
Delta efficiency
It is only a small step from work efficiency to delta-efficiency (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 ¼
Dpower
;
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 baseline 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 increments) 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
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30
a
Gross efficiency (%)
Gross efficiency (%)
30
25
**
* *
20
15
*
**
*
*
10
b
25
20
Luthanen et al., (1987)
15
10
5
5
30
45
60
75
90
105
120
0
100
Cadence (rpm)
2500
30
2000
1500
Samozino et al. (2006)
Moseley and Jeukendrup (2001)
Luhtanen et al. (1987)
Gross efficiency (%)
Metabolic rate (W)
c
1000
Chavarren & Calbet (1999)
500
200
300
400
500
400
500
400
500
External power (W)
d
25
20
15
10
Moseley et al. (2004)
Sallet et al. (2006)
0
5
0
100
200
300
400
500
0
100
External power (W)
2500
30
e
2000
Gross efficiency (%)
Metabolic rate (W)
200
300
External power (W)
1500
1000
120
500
f
25
20
15
10
60
0
5
0
100
200
300
400
500
External power (W)
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
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0
100
200
300
External power (W)
offset (i.e., base-line metabolism) with increasing work
rate. Gaesser and Brooks (1975) considered this a calculation artifact and therefore rejected the use of gross
efficiency, a standpoint we dispute; it is rather a matter 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 interpretation, we wish to note once more that the problem
Eur J Appl Physiol
b 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 thin
horizontal 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 e
shows 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 Hallén (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)
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 interpretation of such efficiencies in depth. Cavanagh and Kram
(1985) refer to net-efficiency, delta-efficiency as conceptually 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 efficiency 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 efficiency in whole body movements seems a fruitless
exercise. Accordingly, in the remainder of this paper, we
will focus on gross efficiency in cycling, reflecting efficiency 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 performance 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 Hallén 2005). Some authors argue that this hampers
performance (e.g., Foss and Hallén 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 activation (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 contraction. 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 discrepancy 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; Lorås 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
123
External power (W)
Eur J Appl Physiol
500
a
400
300
200
100
0
0
20
40
60
80
100 120 140
Cadence (rpm)
2200
b
2000
Metabolic rate (W)
1800
1600
1400
1200
1000
800
600
400
200
0
0
25
Ca
50
den
ce
75
(rpm 100
)
125 0
100
200
300
400
500
wer (W)
External po
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
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 consideration 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
123
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 relationship is even more clearly demonstrated by plotting the
metabolic rate against work rate (Fig. 2c). A linear relationship 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; HintzyCloutier 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 sé, 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 variation 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 analysis), 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.
Eur J Appl Physiol
Table 1 Average values of the reciprocal slope of work rate–metabolic 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)
Luhtanen et al. (1987)
24.4
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). Measurements done in same lab as (b)
b
Data are from the same study as Ettema et al. (2009) and Lorås
et al. (2009), but not reported in these publications
Interestingly, the intercept of the two-dimensional regression 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 disproportional 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 importance 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 metabolic 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
123
Eur J Appl Physiol
RSep-mr values of a number of studies that reported metabolic 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 calculations 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 Hallén 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 (Böning et al. 1984; Coast and
Welch 1985; Francescato et al. 1995; Foss and Hallén
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 forcevelocity 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 activationrelaxation 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 metabolic 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
123
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 efficiency, indicating that we are not only dealing with
processes associated with work rate, but also other processes (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 efficiencies 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 differences can have a relatively large impact on the cadenceefficiency relationship. Furthermore, relatively small errors
in power measurements affect the efficiency value considerably (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.
Eur J Appl Physiol
In summary, because of the fundamental challenges of
discriminating the various mechanisms of energy expenditure and losses that relate differently to cadence (e.g.,
expenditure not directly associated to doing work, forcevelocity 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 improvement (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. Nevertheless, 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 difference 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 metabolic 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 challenged; 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 processes may be, for example, ventilation and circulation, but
also digestive processes. Energy loss associated with relative 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
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Eur J Appl Physiol
increase of internal work losses. Whatever the case, the
equation can be rewritten as follows:
E ¼ Ic þ kðq þ 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 accurately 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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