Eur J Appl Physiol (2011) 111:357–366 DOI 10.1007/s00421-010-1410-1
ORIGINAL ARTICLE
The energetics of cycling on Earth, Moon and Mars Stefano Lazzer • Luca Plaino • Guglielmo Antonutto
Accepted: 15 February 2010 / Published online: 27 March 2010 Ó Springer-Verlag 2010
Abstract From 1885, technological improvements, such as the use of special metal alloys and the application of aerodynamics principles, have transformed the bicycle from a human powered heavy transport system to an efficient, often expensive, object used to move not only in our crowded cities, but also in leisure activities and in sports. In this paper, the concepts of mechanical work and efficiency of cycling together with the corresponding metabolic expenditure are discussed. The effects of altitude and aerodynamic improvements on sports performances are also analysed. A section is dedicated to the analysis of the maximal cycling performances. Finally, since during the next decades the return of Man on the Moon and, why not, a mission to Mars can be realistically hypothesised, a section is dedicated to cycling-based facilities, such as man powered short radius centrifuges, to be used to prevent cardiovascular and skeletal muscle deconditioning otherwise occurring during long-term exposure to microgravity.
Communicated by Susan Ward. This article is published as part of the Special Issue dedicated to Pietro di Prampero, formerly Editor-in-Chief of EJAP. S. Lazzer L. Plaino G. Antonutto (&) Department of Biomedical Sciences and Technologies, University of Udine, P.le Kolbe 4, 33100 Udine, Italy e-mail:
[email protected] S. Lazzer L. Plaino G. Antonutto School of Sport Sciences, University of Udine, Udine, Italy S. Lazzer L. Plaino G. Antonutto MATI (Microgravity, Ageing, Training, Immobility) Center of Excellence, University of Udine, Udine, Italy
Keywords Muscle exercise Cycling efficiency Cycling world records Microgravity Artificial gravity
Introduction The history of bicycle officially begun in 1815 when the Indonesian volcano Tambora exploded, expelling into the atmosphere the greatest known mass of dust and making the 1816 the ‘‘year without summer’’ in central Europe (Wilson et al. 2004). Starvation was widespread and horses were killed for lack of fodder, with the price of oats then playing the same role as the price of oil today. The consequence of the shortage of horses led Baron Karl von Drais, a German from Mannheim with a background of mathematics and mechanics studies, to develop his first two-wheeled ‘‘running machine’’ with a front steering wheel. News concerning von Drais’ vehicle were reported in the German newspapers in 1817, in those from the UK (cited as Hobby Horse) in 1818 and in those from the USA in 1819. In France, von Drais obtained a 5-year patent for what was locally known as velocipede or Draisienne. The next step in the bicycle’s development was the introduction of pedals, directly connected to the driving wheel. Pierre Michaux (from France) and Pierre Lallement (from USA) patented this improvement in 1866, and the new machine was called velocipede bicycle. From then, bicycle development was fast in Britain, where in 1874 the spoked wheel was patented. Together with this innovation, the front, steering and driving wheel became larger and larger to cover a longer distance per pedal revolution, and therefore to attain a greater speed. The final result of these improvements was the high-wheelers, bicycles covering a distance for each full turn of the cranks equivalent to that covered by a middle gear of a modern bicycle. However, high-wheelers were difficult
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and dangerous to ride, since the cyclists were seated on a saddle located over a 1.5-m diameter front wheel. In 1885, with the advent of the safety bicycle, patented by John Kemp Starley, rubber tyres, ball bearings, tilted steering axis, steel tubes ‘‘diamond’’ frame and a chain driven transmission system were introduced. The improvement mentioned above led to a reduction of the drive wheel diameter and bicycle design became very similar to that of the majority of the bicycles used nowadays. In 1888, John Boyd Dunlop patented the pneumatic tyre, thus allowing the achievement of greater speeds, or of the same speed with less effort, greater comfort and safety. From the first years of 1900 to the present day, the bicycle phenomenon grew up in many Western countries with highs (restriction of gasoline during wars) and lows (availability of mass production motorbikes and cars) with increasing production, and utilisation, at first for transport, subsequently for leisure, sport and racing. Therefore, due to the great popularity reached by cycling in the last century, we here propose a biomechanical and bioenergetics analysis of this kind of locomotion. This is done also in view of future applications of cycling in non-terrestrial environment such as the Moon or Mars.
Mechanical work of cycling When cycling on flat terrain at constant speed in the absence of wind, the forces opposing the cyclist’s motion are (a) the rolling resistance given by the sum of the friction of the tyres on the terrain, of the bearings into the hubs and of the transmission gear, and (b) the air resistance. Therefore, Wc ¼ a þ bv2
ð1Þ
in which Wc (J m-1) is the mechanical work performed over unit of distance, v is the air speed and a and b, for a given set of environmental conditions, are constants. By towing the cyclist, the tractive resistance (RT, N) can be experimentally determined and it results that the force RT is conceptually and dimensionally equal to the mechanical work per unit of distance (Wc = RT). This being so, the constants a and b of Eq. 1 can be determined from the tractive resistance as a function of speed (di Prampero et al. 1979; Capelli et al. 1993). In fact, by setting RT as a function of squared speed, Eq. 1 can be represented by a straight line whose intercept on the y axis is the constant a, while its slope (DWcDs-2) is equal to b (Fig. 1). A different practical approach to determine the constants a and b consists in measuring, by means of load cells, the forces exerted on the pedals by the cyclist and deriving from these the mechanical work of cycling (Sargeant and Davies 1977; Sargeant et al. 1978).
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Fig. 1 Tractive resistance (RT, N) as a function of the square of the ground speed (s2, m2 s-2) for riding traditional (broken line; from di Prampero et al. 1979) or aerodynamic (continuous line; from Capelli et al. 1993) racing bicycles in the absence of wind in dropped posture. RT is also equal to the mechanical work per unit of distance (Wc, J m-1). The anthropometric data of the cyclist were: body mass 70 and 71 kg; stature 180 and 184 cm; body surface area 1.80 and 1.84 m2, respectively. The masses of their bicycles were 7 and 14 kg, respectively. Air pressure (PB) and temperature (T) were: PB = 755 and 758 mmHg (100.7 and 101 kPa), respectively; T = 15 and 11°C, respectively. Only regression line is shown. Traditional (broken line): RT = 3.2 ? 0.19s2 (r2 = 0.96, n = 33); aerodynamic (continuous line): RT = 2.4 ? 0.155s2 (r2 = 0.96, n = 19) (from di Prampero 2000, with permission)
The friction of the hubs of the wheels and of the transmission gear of high-quality modern bicycles is almost negligible (Kyle 1986). It follows that the rolling resistance is entirely determined by the kind of tyres and by their inflation pressure and by the characteristics of the terrain. The rolling resistance does not depend on the speed, but depends on the total moving mass (cyclist ? bicycle); therefore, it would be more useful to express it as a ‘‘coefficient of friction’’ (dimensionless) given by the rolling resistance divided by the total weight of cyclist plus bicycle. Coefficients of friction, assessed in different experimental conditions, are reported in Table 1 and the constant a can be easily calculated if the total weight is known. Table 1 also reports the minimal values of coefficients of friction valid for wheels of standard radius, tubular tyres inflated with high pressure air and moving on smooth terrain (asphalt surface). These values are about one-tenth with wheels of profiled mountain-bike tyres used off-road. The constant b (kg m-1) which links air resistance to squared speed (Eq. 1) is expressed by Eq. 2: b ¼ 0:5Cd Af qa
ð2Þ
in which Cd (dimensionless) is the drag coefficient, Af is the frontal area (m2) of the cyclist plus the bicycle and qa is
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Table 1 Coefficient of friction (a, dimensionless), coefficient of drag (Cd, dimensionless), fontal area (Af, m2) and constant b (kg m-1) for various types of bicycles, cyclist postures, types of tyres and wheels rolling on asphalt surface Tyres characteristics Width (cm) Pressure (MPa) Diameter (cm)
Constant b Coefficient of Coefficient Frontal friction, a of drag, Cd area, Af (m2) (kg m-1)
Mountain bike, knobby 26 in. tyre
5.4
0.32
65.9
0.0086
0.80
0.440
0.216
Mountain bike, knobby 29 in. tyre
5.8
0.32
74.1
0.0080
0.80
0.440
0.216
Touring bike, standard 28 in. tyre Road bike, 28 in. clincher tyre
3.5 2.3
0.45 0.71
69.0 66.8
0.0070 0.0039
1.00 0.72
0.450 0.433
0.276 0.191
Track pursuit bike, 28 in. tubular tyre 2.0
1.01
66.7
0.0030
0.65
0.390
0.155
Wheel diameter, together with tyre width and inflation pressures (1 MPa = 9.87 atm), is also indicated. Energy expenditure against the rolling resistance, per unit of distance, can be easily obtained by dividing the coefficient of friction (a) by the overall efficiency of cycling (g % 0.25), and multiplying it by the mass of cyclist plus bicycle (M, kg) an by g (9.81 m s-2). Drag coefficient (Cd), frontal area (Af) and constant b refer to a cyclist of 70 kg body mass and 175 cm stature (body surface area, Abs = 1.85 m2) at sea level (PB = 760 mmHg = 101.3 kPa) and at 20°C air temperature (data from Capelli et al. 1993; di Prampero et al. 1979; Kyle 1986; Olds et al. 1993, 1995; Pugh 1974; http://www.rouesartisanales.com)
air density (kg m-3). The latter is a function of barometric pressure (PB, Pa) and air temperature (T, K): qa ¼ q0 0:359PB T 1
ð3Þ -3
in which q0 (1.293 kg m ) is air density at PB = 101.3 kPa, T = 273 K and relative humidity = 0% (Weast 1988–1989). For practical purposes, the effects on air density from the environmental actual relative humidity can be neglected. Barometric pressure decreases as altitude (km above sea level) increases according Eq. 4: PB ðkPaÞ ¼ 101:3 e1:124 km
ð4Þ
Equations 2, 3 and 4 demonstrate that changes of the frontal area, the drag coefficient and the altitude may lead to changes of the constant b and, therefore, of the mechanical work Wc (see Eq. 1). A way to reduce Af is to assume a fully dropped posture on bicycles. Such is the case of the most recent models of racing bicycles on which the cyclist is forced to assume a posture compatible with the minimum value of Af (Capelli et al. 1993; Grappe et al. 1998) even if this leads to a minor, but significant, reduction of the maximal aerobic power _ 2 max ) (Welbergen and Clijsen 1990). The dropped (VO position also allows the cyclist to reduce the drag coefficient and, therefore, to further reduce his aerodynamic resistance (Capelli et al. 1993). An even greater reduction of Af (0.34 ± 0.02 m2), which would increase speed for a given metabolic power, is possible with recumbent bicycles where the rider is placed in a laid-back reclining position (Capelli et al. 2008). The use of aerodynamic fairings also leads to a reduction of Cd to values ranging from 0.09 to 0.11 (Gross et al. 1983). Another way to reduce air resistance is to follow another cyclist, thereby exploiting his wake (drafting). At high speeds, the reduction of power needed by the cyclists may reach about 30% (Kyle 1979; Olds 1998). For example, in 1973 the cyclist A. Abbott, by riding a special
bicycle into the draft of a dedicated car, has reached the speed of 223.13 km h-1 over the distance of 1.2 km. When a group of cyclists moves together, the reduction of the power needed by a single cyclist depends on the position he holds into the group. Broker et al. (1999) have demonstrated that during a team pursuit race, performed at 60 km h-1, the average mechanical power requested was equal to 607 W in the leading position, but went down to 430 W (70.8%) in second position and to 389 W (64%) in third and fourth positions. The human body surface (Abs) increases with its squared linear dimension, whereas body mass increases with the cube of the same dimension. Assuming that Af be a fraction of Abs (Swain et al. 1987; Capelli et al. 1998) and proportional to body mass (Heil 2002), Af can be calculated, for traditional road bike position (hands on the drops and full crouched posture), according to: Af ¼ 0:03608M 0:589
ð5Þ
in which M is the cyclist body mass (kg). For cyclists using aerodynamic handlebars, Af can be calculated according to Heil (2001): Af ¼ 0:0163M 0:762
ð6Þ
It follows that cyclist with greater body size has a minor Af per unit of body mass than those having a smaller body size. This will lead to a lower energy expenditure per unit of body mass or to a greater speed for the same power per unit of mass, thus giving an advantage to cyclists with greater body size. Obviously, this analysis is referred only to the air resistance, not taking into account the rolling resistance and the effects of gravity which are both _ 2 max proportional to the body mass. Moreover, since VO per unit of body mass [mlO2 (kg min)-1] tends to be lower in subjects with greater body mass (Astrand and Rodahl 1986), there should exist an optimum body size for cycling performances on flat terrain.
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The preceding analysis refers to cycling on flat terrain or on a bicycle track (velodrome). To evaluate the energy expenditure when cycling uphill or downhill, the mechanical work spent against (or provided by) the gravity must be taken into account. When moving uphill at constant speed, the mechanical work spent against gravity per unit of distance is given by Wc g ¼ Mghd 1 ¼ Mgd sin cd1 ¼ Mg sin c
ð7Þ
in which M (kg) is the mass, g is the acceleration of gravity (9.81 m s-2), d is the distance (m), h is the difference in height (m) that is also equal to the product of the distance times the sine of the angle between the terrain and the horizontal plane (c, deg). The sum of Eqs. 1–7 fully describes the mechanical work of cycling at constant speed and with no wind: 2
Wc ¼ a cos c þ bs þ Mg sin c
ð8Þ
where s (m s-1) is the speed with respect to the terrain. Obviously, the slope of the terrain (c, deg) affects the work spent against the rolling resistance. However, considering the slopes of the usual routes, the value of cos c is very close to 1. Moreover, the third term of Eq. 8 becomes negative when cycling downhill.
The mechanical efficiency of cycling The value of the mechanical efficiency (g) of cycling or of pedalling on a cycloergometer is not very far from 0.25, depending on the pedalling frequency (fp, Hz), and it is maximal for fp of about 1.0 Hz. Since the observations of Dickinson (1929), a series of data (Banister and Jackson 1967; Gaesser and Brooks 1975; Seabury et al. 1977; Coast and Welch 1985; Luhtanen et al. 1987; Ericson 1988; Francescato et al. 1995; Zoladz et al. 1998) has constantly shown that as the mechanical power increases from 50 to 300 W, the optimum fp increases accordingly from 0.7 to 1.0 Hz; moreover, g is equal to 0.25 at the optimum fp. These data demonstrate that even remarkable changes of fp, above or below its optimum value, determine small changes of g. For example, for a mechanical power of 100 W, associated with an optimum fp of 0.75 Hz, g decreases to 0.24 if fp is equal to 0.55 or to 0.95 Hz, and to 0.22 if fp is equal to 0.45 or to 1.15 Hz (Fig. 2). In a similar way, for a mechanical power of 300 W, associated with an optimum fp of 1.0 Hz, g decreases to 0.24 if fp is equal to 0.7 or to 1.6 Hz, and to 0.22 if fp is equal to 0.45 or to 1.9 Hz (Fig. 2). This also demonstrates that for high values of mechanical power, the relationship between g and fp is rather flat, probably explaining why during real competitions fp is maintained at values higher than those corresponding to the maximal value of g.
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At the same speed, by increasing fp, a reduction of the average force exerted by the cyclist on the pedals is attained. This will probably lead to a reduction of the lactic component of the energy expenditure. A lower involvement of anaerobic lactic metabolism probably compensates for the decrease of g caused by the increased fp. This explanation, based on bioenergetics reasons, appears plausible, but other factors, such as the muscular activation strategy and/or effort perception, may play a role into the choice of the best fp in real competitive conditions (Marsh and Martin 1993, 1995, 1998).
Bioenergetics of cycling The metabolic energy expenditure of cycling is evaluated by introducing the mechanical efficiency g into Eq. 1: Cc ¼ Wc g1 ¼ ða þ bv2 Þg1
ð9Þ
by putting a = ag-1 and b = bg-1 Eq. 9 becomes: Cc ¼ a þ bv2
ð10Þ -1
in which Cc (J m ) is the energy cost of cycling (above the resting condition) per unit of distance and, once again, for a given set of environmental conditions, and a and b are constants. In particular, a represents the metabolic energy spent, per unit of distance, against the rolling resistance, while b represents the metabolic energy spent, per unit of distance, against the aerodynamic forces. The mechanical power Pc or the metabolic power E_ c needed to proceed at constant speed s (m s-1) in respect to the terrain is given by the product of Wc (Eq. 1), or Cc (Eq. 10), times the speed s. Therefore, if the wind is null and v is equal to s: Pc ¼ Wc s ¼ as þ bs3
ð11Þ
and E_ c ¼ Cc s ¼ as þ bs3
ð12Þ
If Cc is expressed in J m-1 and s in m s-1, Pc and E_ c are expressed in W. However, for practical reasons, Cc is often expressed in mlO2 m-1, and in this case since s is expressed in m min-1, E_ c will result in mlO2 m-1. Obviously, it is possible to convert the ‘‘physiological’’ units of measurement into units of the International System (SI), since 1 l of oxygen provides 20.9 kJ of energy [or 468.2 kJ mol(O2)-1]. An approach similar to the one used to determine the constants a and b of Eq. 1 can be used to determine the constants a and b of Eq. 10 (Capelli et al. 1993, 1998). In this case, the dependent variable is the energy cost per unit of distance (Cc) (Fig. 3). Cc is generally calculated by _ 2, dividing the oxygen consumption at steady state (VO
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Fig. 2 Pedal frequency (fp, Hz) as a function of the mechanical power output (w_ e , kW) in cycling. Iso-metabolic power _ 2, lines (O2 consumption, VO kW or ml s-1) are also drawn, thus allowing the assignation of a given efficiency value (g) to any given point of the plane. The points characterised by the same g are joined by isoefficiency functions. This figure was compiled mainly from the data of Banister and Jackson (1967) and Seabury et al. (1977) (from di Prampero 2000, with permission)
Fig. 3 Energy cost of cycling at constant speed (Cc, J m-1) as a function of the square of the ground speed (s2, m2 s-2) for a traditional racing bicycle in the absence of wind. The cyclist is (mass 77.5 kg; stature 1.95 m; body surface area 2.09 m2) in dropped posture. Bicycle mass is 10.6 kg; PB = 755 mmHg (100.7 kPa); T = 26°C. The regressions are described by: Cc = 16.7 ? 0.84s2; r2 = 0.99, n = 9 (from Capelli et al. 1998, with permission)
mlO2 min-1) by the corresponding speed, the limit of which _ 2 max of the cyclist. Nowadays, poris imposed by the VO table gas exchange analysers allow the experimenters to measure Cc even in actual competition conditions since these small and light equipment (e.g. K4, Cosmed, I) neither interfere with cycling nor they are cumbersome to significantly modify Af (Kawakami et al. 1992; Lucia et al. 1993). Mechanical and metabolic (aerobic) powers of cycling are affected by altitude. In fact, the constants b (Eq. 11) and b (Eq. 12) decrease with increasing altitude. Consequently, by increasing altitude, the E_ c necessary to proceed at a
given speed will be lower or, conversely, a given E_ c will allow the cyclist to reach a higher speed. The effects of altitude on cycling performances may be calculated, pro_ 2 max of the cyclist and the amount of the vided that the VO decrease of this variable with altitude are known (di Prampero et al. 1979; Peronnet et al. 1989; Capelli and di Prampero 1995; Bassett et al. 1999). In 1979, di Prampero et al. demonstrated that (a) the optimum altitude for an aerobic cycling performance should be located at about 4,000 m a.s.l. and (b) in one ideal indoor velodrome in which an air–vacuum could be produced, an elite cyclist could reach the speed of 580 km h-1 if he could pedal wearing a special suit allowing him to breathe at 150 mmHg of oxygen inspiratory pressure. Coming to a more realistic condition, the maximal speed (s) which a cyclist may maintain for 1 h depends essentially on his _ 2 max and the fraction of it (F B 1) which the cyclist is VO able to sustain during the full hour (Capelli and di Prampero 1995). At sea level (sl), this condition is described by _ 2 max ¼ assl þ bs3sl E_ c ¼ F VO
ð13Þ
The decrease of barometric pressure, due to altitude (a), _ 2 max and the constant b. Therefore, affects both VO _ 2 max ¼ asa þ kbs3a AF VO
ð14Þ
in which A and k are constants taking into account the _ 2 max and b. By combining Eqs. 13 effects of altitude on VO and 14: Aðassl þ bs3sl Þ ¼ asa þ kbs3a
ð15Þ
After considering that the metabolic power utilised against non-aerodynamic forces is essentially the same at sea level and in altitude (Aassl = asa), and therefore
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neglecting this term, and rearranging Eq. 15, the following equation is obtained: p ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 sa s1 ð16Þ ðAk1 Þ sl ¼
_ 2 max , F and the energetic cost of cycling (Cc) are VO known:
which allows to calculate the increase of speed at any altitude by knowing A and k. _ 2 max with altitude (described by the The decrease of VO constant A) is rather well-known from published data and for non-athletic subjects (Cerretelli 1981). In athletes, this decrease is even greater (Ferretti et al. 1997). Assuming that air temperature and posture of the cyclist (i.e. Af and Cd) on the bicycle are the same at sea level and in altitude, it follows that k results from the ratio of altitude barometric pressure to that prevailing at sea level (Eqs. 3, 4). Consequently, the ratio sa s1 sl can be calculated for any altitude. For example, at Mexico City (2,230 m a.s.l.) sa s1 sl ¼ 1:04. It means that the present 1 h best performance holder (Chris Boardman, 56.375 km, Manchester, UK, 1996) could cycle in Mexico City 58.63 km in 1 h. According to the calculations of di Prampero et al. (1979), the best altitude for 1-h record would be 3.8 km, corresponding to that of the velodrome located in Alto Irpavi (La Paz, Bolivia). In that location, the ratio sa s1 sl ¼ 1:046 thus allowing, at least theoretically, C. Boardman to reach the distance of 58.97 km in 1 h. It must be said that these calculations are based on the following assumptions: (a) _ 2 max at altitude (constant A) should that the decrease of VO be the same in middle level athletes and in elite athletes _ 2 max which an and (b) the fraction (F, Eqs. 13, 14) of VO elite athlete can sustain during 1 h is the same in altitude and at sea level. To complete the analysis of the bioenergetics of cycling by considering the slope of the terrain, Eq. 10 must be modified as follows:
Obviously, this approach does not take into account the actual ‘‘strategy’’ of the race, which can include sprints and consequents peaks of metabolic energy expenditure, or other race behaviours carried out to decrease the energetic expenditure, like cycling following another cyclist to exploit his draft. More interesting could be the maximal performances in short distance races. In these events, the maximal metabolic power that can be utilised by the cyclist strongly depends on the duration and therefore on the distance of the race. Considering exclusively track races, and with no wind, the metabolic power E_ c , needed to cover the distance d in the performance time tp and therefore at the speed s ¼ dtp1 , is given by the equation:
Cc ¼ a cos c þ bv2 þ ðMg sin cÞg1
ð17Þ
With the usual assumption that the wind is null, and air speed (v) is equal to ground speed (s), the metabolic power is described by
_ 2 max Cc1 s ¼ F VO
E_ c ¼ Cc dtp1 ¼ adtp1 þ bðdtp1 Þ3
ð19Þ
ð20Þ
Often the races start from a standing still position. In this case, Eq. 20 must be modified taking into account also the energy (Ektot) needed to accelerate the cyclist ? bicycle from zero to the final speed: Ektot ¼ 0:5Mðdtp1 Þ2 g1
ð21Þ
That, per unit of mass M and of distance d, becomes: Ek ¼ Ektot M 1 d1 ¼ 0:5dtp2 g1
ð22Þ
which is true if and only if the final speed is equal to the average speed, a fact that is not possible. However, for practical purposes and as a first approximation, Eq. 22 represents a sufficiently accurate estimate of Ek (Capelli et al. 1998). Consequently, for cycling races starting form a standing still position, Eq. 20 becomes: E_ c ¼ adtp1 þ bðdtp1 Þ3 þ Ek dtp1 ¼ adtp1 þ bd3 tp3 þ 0:5d2 tp2 g1
ð23Þ
The meanings of the above symbols are the same as in Eqs. 8 and 12.
Equations 20 and 23 demonstrate that, for every d, E_ c increases as tp decreases. In other terms, the shortest tp, or the fastest speed, on a given distance, will be reached when E_ c will be equal to maximal metabolic power (E_ max ) that the cyclist will be able to maintain along the entire race. According to Wilkie (1980):
Maximal performances
_ 2 max VO _ 2 max ð1 ete =s Þste1 E_ max ¼ AnSte1 þ VO
E_ c ¼ a cos cs þ bs3 þ ðMgs sin cÞg1
ð18Þ
The speed reached using a given metabolic power can be easily calculated from Eq. 18 knowing the anthropometric, mechanical and environmental parameters requested to solve this equation. For endurance races, under aerobic conditions and on flat terrain, a simple approach to calculate the speed s is given by the following equation, if
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ð24Þ _ 2 max is expressed in W, te is the exhaustion in which VO time, AnS is the maximal anaerobic capacity deriving from the complete utilisation of the anaerobic alactic energy sources (i.e. hydrolysis of phosphocreatine) and lacticrelated sources (net production of lactic acid from
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glycogen). The third term of Eq. 24 takes into account the _ 2 shows an fact that at the beginning of muscular work VO exponential time course with s as time constant. As a first approximation, Eq. 24 correctly describes E_ max and te if the duration is comprised between 50 s and 15 min. If te is shorter than 50 s, AnS will not be completely tapped and if te is longer than 15 min the aerobic power will be signifi_ 2 max . With the constraints mentioned cantly lower than VO _ above, if VO2 max , AnS and s are known the relationship between E_ max and te can be analytically described. On the other hand, if Cc is known, also the relationship between E_ c and tp for a given distance d can be analytically described according to Eqs. 20 and 23. Moreover, it can be reasonably assumed that the best performance time on a given distance and for a given cyclist coincides with his exhaustion time (tp = te). In this case, it is possible to calculate his best time of performance as the time for which E_ max of Eq. 24 is equal to E_ c of Eq. 20 or 23 (Fig. 4). This approach was originally proposed by di Prampero (1986, 1989) for athletics track middle distance races, and later on it has been applied rather satisfactorily by di Prampero et al. (1993) and Peronnet and Thibault (1989). In 1998, Capelli et al. have applied this analysis to track cycling, starting from standing still position, of a group of middle level amateur cyclists. The theoretical times, calculated as described above for every distance and every cyclist, have been compared to the actual seasonal best performance times of the same subjects over the same distances. The results indicate that theoretical times and actual times are very similar: the average ratio between these two groups of results is equal to 1.035 ± 0.058 (Capelli et al. 1998). Studies concerning maximal cycling performances, such as records or the use of bicycles in an extreme environment like high altitude, induce to hypothesise its beneficial utilisation in the extra terrestrial environment, characterised by microgravity or weightlessness.
Cycling on the Moon and Mars Since the early years of the Space Era, it was clear that prolonged exposure to microgravity induced a series of consequences at the cardiocirculatory level which were globally defined as Cardio Vascular Deconditioning (CVD) (Antonutto and di Prampero 2003). Therefore, scientists have studied and tested different countermeasures to prevent both CVD and reduced exercise capacity. Since the countermeasures used nowadays are only partially effective, the only way to prevent at the same time the decay of the cardiovascular function and of the musculoskeletal system could perhaps be ‘‘artificial gravity’’. By re-creating in space an acceleration vector mimicking gravity, hydrostatic gradients in the
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Fig. 4 The metabolic power (E_ c , W) required in track cycling to cover the distances of 1, 2 or 3 km from a standing still position, as a function of time, is indicated by three steep functions (triangles). The maximal metabolic power (E_ max , W) that an elite athlete could maintain at a constant level during an all-out effort of the duration reported on the same time axis is also indicated (filled circles). The best performance time over the three distances for the same athlete is given by the time value at which the appropriate E_ c function crosses the E_ max function. E_ c was calculated by inserting into Eq. 23 the appropriate distances and the values of a and b for a 70 kg, 1.75 m athlete riding a standard racing bicycle on a linoleum-covered track in the absence of wind at PB = 760 mmHg (101.3 kPa) and T = 20°C and assuming g = 0.25. E_ max was obtained from Eq. 24, assuming _ 2 max ¼ 2:0 kW, 76.5 mlO2 (kg min)-1, s = 10 s [Wilkie 1980; VO above resting] and the maximal capacity of the anaerobic energy stores (AnS) = 140 kJ (corresponding to 90 mlO2 kg-1) (from di Prampero 2000, with permission)
circulatory system of the astronauts are restored together with gravity proprioception during exercise. To this aim, short radius centrifuges located on board of the space stations have been proposed by several authors (Burton 1994; Cardus 1994; Burton and Meeker 1997; Vil-Viliams et al. 1997). These systems need an external power supply and their mechanics is not easily compatible with an exercising subject. To overcome these drawbacks, in 1991, Antonutto et al. proposed the Twin Bikes System (TBS) consisting of two coupled bicycles ridden by two astronauts, counter-rotating along the inner wall of a cylindrical Space module. However, the small inner diameter of the Space module (about 4 m) strongly limits the practical application of this idea. CVD is not limited to space flight, but it would likely be present also in astronauts living in manned bases on the Moon or Mars. Indeed, on these celestial bodies, the acceleration of gravity is substantially smaller than on Earth, amounting to 1.62 m s-2 (0.165 g) and to 3.72 m s-2 (0.379 g) on Moon and Mars, respectively. Consequently, the hydrostatic component of the blood pressure (DP = qgh) is proportionally reduced. Table 2 reports the arterial blood pressures at the carotid bifurcation and at feet level of standing astronauts living on Lunar
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Table 2 Arterial blood pressure (mmHg) at the carotid bifurcation and at the feet of standing astronauts of average stature, for an arterial pressure of 100 mmHg in the aortic bulbus on Moon, Mars and Earth Head (mmHg)
Feet (mmHg)
Head feet-1
g (m s-2)
Moon
97
113
0.86
1.62
Mars
92
130
0.71
3.72
Earth
80
180
0.44
9.81
outwards, in order to compensate for it the cyclist must lean inwards so that the vectorial sum of ac and the constant acceleration of gravity lies in the plane which includes the centre of mass of the system and the points of contact between wheels and terrain (Fig. 6). So, the resulting vector (g0 ) can be calculated by simple geometry as g0 ¼ ðg2cb þ a2c Þ0:5
or Martian, bases assuming their stature to be 175 cm and an arterial blood pressure of 100 mmHg in their aortic bulbus. Since these values are quite different from those corresponding on Earth, the astronauts will likely undergo CVD. To avoid this, we propose that astronauts living for long periods on Lunar or Martian bases undergo exercise daily, riding a bicycle along a curved path (di Prampero et al. 2009). With this in mind and considering the dimension of the lunar station proposed by Grandl (2007), the effects of cycling on a circular track with a radius of 25 m (Fig. 5) will be discussed below. To be operational on Moon or Mars, these tracks must be enclosed in appropriate structures within which the air is maintained at a predetermined pressure and temperature. Hence, they will here be defined ‘‘track tunnels’’. Cycling along a curved path induces a centrifugal acceleration vector given by ac ¼ v2 R1
ð26Þ
where gcb is the acceleration of gravity on the celestial body considered (gMoon = 1.62 m s-2 and gMars = 3.72 m s-2). It can therefore be readily calculated that for v ranging from 10 to 15 m s-1 (36–54 km h-1) and R = 25 m, g0 ranges from 4.32 to 9.14 m s-2 on the Moon and from 5.46 to 9.74 m s-2 on Mars, i.e. from 44 to 99% of the Earth gravity (Fig. 7). So, a cyclist riding a bicycle on a circular track will generate in its curved parts a force acting in the head to foot direction which can be expected to mimic, to a certain extent, the effects of Earth gravity on the cardiovascular system. Indeed, it can be calculated that, under these conditions, and assuming v = 10 m s-1 the arterial pressure prevailing at the carotid bifurcation, assuming an average aortic systolic pressure of 100 mmHg, would amount to 91 mmHg on the Moon and to 89 mmHg on Mars. By increasing speed, these blood pressure values 1m
ð25Þ
where v is the ground speed and R is the radius of curvature of the cyclist’s path. Since ac is applied horizontally
4m
ac = v2 * R-1 g’ = (a c2 + gcb2)0.5
ac gcb ac R = 25 m
gcb 1m
g’
g’ slow speed high speed
Fig. 5 Schematic view of a cycling ‘‘track’’ tunnel positioned around the Lunar Base (R = radius of track tunnel = 25 m). After Grandl (2007), modified by di Prampero et al. (2009) (with permission)
123
R R
Fig. 6 Schematic frontal view of a cyclist pedalling on the curved path of a ‘‘Lunar or Martian track tunnel’’. To compensate for the outwards acceleration (ac) itself a function of the radius of gyration (R) and of the ground speed (v), ac = v2R-1, the cyclist leans inwards so that the vectorial sum (g0 ) of ac and the gravity on the celestial body (gcb) lies in the plane that includes the centre of mass (grey circles) and the points of contact between the wheels and the terrain. The two values for v result in progressively larger ac (and hence g0 ) values. In addition, the angle between g0 and the vertical increases with ac, so that the track must be appropriately constructed to avoid skidding (from di Prampero et al. 2009, with permission)
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365
Power (W) 800 600 400 200 v (m · s-1 ) 0 0
5
g‘ (m · s-2) 15
10 Moon
15
20
systems proposed so far (Clement 2005), is that of combining at the same time muscular exercise and artificial gravity, without any additional needs for external power to set the system in motion. However, for these scenarios to become operational, it is mandatory to know the ‘‘doses’’ of g0 necessary to avoid CVD, and to maintain muscle mass, aerobic and anaerobic powers and bone density during prolonged exposure to the Lunar or Martian acceleration of gravity, both in terms of intensity with respect to the Earth acceleration of gravity, and in terms of duration (per day) and frequency (per week) of the exposure.
Mars
Acknowledgments In this Review article is partially reported the content of papers written by di Prampero and his co-workers during the long and happy years of cooperation they spent together.
10
References 5 v (m · s-1) 0 0
5
10
15
20
Fig. 7 Upper panel The mechanical power (W) when riding a standard racing bicycle in dropped posture in air at sea level (760 mmHg) and 20°C is plotted as a function of the speed (m s-1). Power was calculated according to W = Rrv ? kv3 in which the rolling resistance is Rr = 5.8 J m-1 and aerodynamic constant is k = 0.193 N s2 m-2 for a typical cyclist. Lower panel The vectorial sum (g0 ) of the outward acceleration (ac = v2R-1) and the acceleration of gravity (gcb) is calculated according to g0 ¼ ða2c þ g2cb Þ0:5 and is reported as a function of the speed on the Moon (gMoon = 1.62 m s-2) and on Mars (gMars = 3.72 m s-2). R is the track tunnel radius equal to 25 m (from di Prampero et al. 2009, with permission)
become progressively closer to those prevailing on Earth, which will be attained for v of about 15 m s-1. In view of the biomechanical characteristics of cycling, the speed and mechanical power values necessary to achieve sufficiently large values of the vector simulating gravity (g0 ) can be easily calculated (Fig. 7). The mechanical power necessary to achieve a given speed and hence a given g0 can be reduced, if necessary, by lowering the air density in the track tunnel. It should also be pointed out that the astronauts will be in the position of performing several ‘‘sprints’’ in the track tunnel, a fact which will help maintaining a reasonable level of ‘‘explosive power of the lower limbs’’ (Antonutto et al. 1999), once again depending on the number, duration and intensity of the daily sprints. This state of affairs will also lead to daily loading of the weight-bearing bones, thus helping to maintain their density close to the optimal level. Thus, one non-negligible advantage of the proposed track tunnels, as compared to the majority of the artificial gravity
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