The technically minded performance runner would want to be deeply interested in the inner workings of the human locomotor, and the numerical possibilities associated with the business of running and running performance. Through a series of articles, I hope to probe into and gain a deeper understanding of these possibilities. As Prof. di Prampero wrote in the Journal of Sports Medicine in 1986, man is the only machine to be able to move about and also understand how he does it at the same time.
One can draw interesting parallels between the power production processes at the cellular level in the human body and the 4 stroke combustion engine.
In the latter, a governing thermodynamic cycle requires that a mass flow of combustibles flow into a chamber as a "batch" process. A mix of gasoline and air is introduced into the combustion chamber, said mix is compressed to high pressures, said mix is then ignited by a spark plug consequently intiating the power stroke which delivers useful mechanical power to a flywheel. In the final stroke, exhaust products are expelled out of the combustion chamber.
Muscle is a chemical engine in the human locomotor. Electron microscopy has revealed, quite beautifully, that there exists a molecular "power-stroke" that is ultimately responsible for muscle contractions.
Very simplistically, the requirement to deliver contractile force causes a "spark" from an innervating motor unit strong enough to activate clusters of muscle fibers according to the size of the demand.
Substrates chemically combine in coupled reactions and the energy used to make ATP. All human movement is paid in ATP. At the muscle sacromere level, the hydrolysis of a molecule of ATP hydrolysis leads to the cross-bridging of the protein myosin over another protein actin causing contraction of a sacromere.
A great video shows this elaborate molecular "power-stroke" in actin-myosin overlap. For academic purposes, one can read about fascinating molecular motors. Research on motility within muscle has spanned several decades and we still only continue to learn about the molecular agents responsible for muscle contraction.
I. Cost of Transport
The cost of transport becomes a decision maker for vehicle purchase. For example, a 40mpg family sedan will consume approximately 7 liters of fuel per 100km. A figure like this is considered 'good' by today's standards and gets a strong weighting factor in purchase.
In the human locomotor, oxygen uptake reflects the quantity of ATP used when aerobic metabolism can provide all of the energy at a given steady state running speed.
Given the conditions that running is steady state and no accumulation of lactic acid takes place, the oxygen cost of sub-maximal running (ml O2/kg/min) above resting value is known to be a linear function of running speed. This oxygen cost, when expressed on a per minute basis, becomes the "metabolic power".
Metabolic power divided by speed of movement yields cost of transport.
COT = Metabolic Power Demand ÷ Running Speed
where units are :
Cost of Transport, COT = mlO2/kg/m
Metabolic Power Demand (net or gross) = ml/kg/min
Running Speed = m/min
Note : COT is also called Cost of Running or simply Energy to Run (ECOR, Cr, Er etc) in some works. If expressed as an energy cost (J/kg/m), the volume of oxygen uptake has to be converted to it's energy equivalent.
Net metabolic power demand and running speed assumes linearity to a good degree; the slope becomes COT. As science consuming readers, we might be able to hold confidence in the linearity between metabolic power demand and running speed upto maximum metabolic power because a large collection of published studies show this correlation (Fig 1).
The linear relationship essentially means that COT is independant of running speed. That is, regardless of the speed of running, the runner's energy expenditure per unit distance is constant.
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| Fig 1 : Data accumulated from 10 studies (n=130) for adults performing treadmill running (8-20 kph speeds) show the linear relationship between oxygen cost (ml/kg/min) and running speed (kmph). In this dataset, the average regression line approximates. Oxygen cost (ml/kg/min) = 2.203 + (3.163 x kph). If VO2 = A + B x Speed, A = 2.203 +/- 8.285 and B = 3.163 +/- 0.474. Males (71.5%), females (28.5%), trained (50%), untrained (1.5%) and unknown training status (18.5%). Reference [3]. |
Fig 2 shows COT values for several runners from a popular marathon in Geneva published in [7]. It is interesting to note that for the same sub-maximal running speeds, COT differs among the runners sometimes upto 20%!
Therefore, calculating COT yields an excellent barometer by which to judge different runners just as fuel consumption guides vehicle purchase.
Runners with a low COT have greater margin to push speed leading to superior performance to cover a given distance. Following that thought, we might consider that the hypothetical runner with a superior COT would be the one to break the marathon sub 2 hour barrier.
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| Fig 2 : Energy cost of running (COT) at constant speed on flat terrain as a function of speed. Filled symbols refer to the two less economical and open symbols to the two most economical among 36 subjects taking part in the “Marathon International de Genève”. Reference [7]. |
II. Influencing Factors of COT
A) Substrate Use
It is essential to know in what proportions the human locomotor uses fats and carbohydrates to fuel exercise in order to derive the energy equivalents of their associated consumptions. Metabolic substrate use is dependant on intensity of run and variable of interest is decide fat-carb use and aerobic and anaerobic regime of operation is the respiratory exchange ratio.
For example, if the intensity is low enough in constant speed running and respiratory exchange ratio (RER) is 0.7, the human locomotor is known to operate in a predominantly aerobic fashion oxidising fats (palmitate). Based on this knowledge, a calorific equivalent of 19.6 J/mlO2 is used for this operational regime.
However, when exercise intensity increases and RER approaches 1, fraction of glucose (carbs) aerobically metabolised must be account for. Glucose yields 21.1 kJ/mLO2 and is therefore volumetrically 7% more energetic than fats. (diesel automobile enthusiasts will fondly remark that diesel fuel is volumetrically more efficient than petrol and that we ought to use diesel more!).
Under the simplifying assumption of zero anaerobic contribution, an average value of 20.9 J/mlO2 is used in literature to account for both fats and glucose oxidation, although this average value corresponds to a RER = 0.96.
Beyond a respiratory exchange ratio = 1, the human locomotor is anaerobic and equivalency value of 20.9 J/mlO2 without inclusion of the energy contribution of lactate introduces an error into the calculations. Therefore, improper assumptions about substrate use can lead to error-prone estimates of energy production depending on training status of the runner.
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| Fig 3 : The red lines indicate the corrected VO2 equivalent of running as a function of running intensity in sloped and level running conditions when blood lactate contribution is accounted for. Black lines neglect this contrbution. In this particular study on trained runners, the difference of neglecting lacate contribution amounted to a mean value of 0.02 mlO2/kg/m for level running and 0.03 mlO2/kg/m for sloped running. Reference [11]. |
Aerobic Regime
The shape of the aerobic COT in relation to running intensity has been reported to mildly curvilinear that tends to flatten out with intensity. The net oxygen consumption in the following relation is dependant on subject and assumes that during locomotion, the resting metabolism remains unchanged.
Aerobic COT = [Net Oxygen Consumption x Calorific Equivalent] ÷ Speed
Aerobic COT = J/kg/m
Net Oxygen Consumption = ml/kg/min [Reported to be between 3.5-5 ml O2/kg/min]
Calorific Equivalent = J/ml
Caloric Equivalent of Aerobic Metabolism (Fat & Carb) = 20.9 J/mlO2 (average value)
Speed = m/s
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| Fig 4 : Non-linear increase of aerobic COT in several non-athletic male subjects (n=29) while running indoors. Reference [4]. |
Anaerobic Regime
When the energy demand exceeds the locomotor's aerobic capacity, the fraction of energy production from anaerobic sources come into the picture. A byproduct of anaerobic metabolism is lactate, therefore measurements of blood lactate ([bLA]) in standardized laboratory protocols constitute a valid cardiorespiratory assessment of exercise intensity. Not accounting for [bLA]'s energy contribution (what literature calls "oxygen debt") may have varying degrees of error based on the subject measured on and the exercise intensities (Fig 3).
The precise shape of the anaerobic COT in relation to running intensity has been reported to be sharply curvilinear. The net increase in blood lactate (net bLA) is multiplied by an equiavalent of 60 J/kg/mM or 3 mlO2/kg/mM to determine the net energetic value of lactate. When divided by the overall distance covered, one gets the net anaerobic COT.
AnaerobicLa COT = [Net bLA x O2 equivalent x Caloric Equivalent of Carb. Oxid.] ÷ Distance
where units are :
Anaerobic La COT = Anerobic Lactate COT, ml/kg/m
Net bLA rise = mM/l
O2 Equivalent of bLA accumulation = ml/mM/kg. This is between 2.7 and 3.3 mlO2/mM/kg (swimming to running) .
Caloric Equivalent of Carb. Oxidatation (glucose) = 21.131 J/mlO2
Distance = m (running time x speed)
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A third contribution to energy supply comes from anaerobic alactic stores, or the cleavage of phospocreatine PCr but this is only prominent in short distances under maximal running conditions. For example, in the 400m sprint, 10-12% of total energy has been reported to come from this contribution. However, in long distance running, this contribution maybe conveniently neglected.
AaerobicaLa COT = [PCr x O2 equivalent x Caloric Equivalent of PCr] ÷ Distance
The metabolically derived COT, COTm is a summation of anerobic and aerobic contributions.
COTm (J/kg/m) = Aerobic COT + Anaerobic La COT
COTm from a large number of studies done on athletic subjects approach the value of 0.9 kcal/kg/km or 3.7 J/kg/m in indoor conditions without environmental influences. Under the same conditions, the non-linear shapes of the aerobic and anaerobic COT combine to produce a net linear shape in COTm as shown in Fig 1.
B) Environmental Conditions : Accelerated Running
The above discussion is valid for indoor settings. In an outdoor running environment, the influence of air resistance starts to play a substantial role in fast running. Furthermore, accelerated running out of block starts such as track running incurs a kinetic cost of accelerating the body from zero to final speed in the acceleration phase.
The energy cost of overcoming wind resistance is particularly appreciable beyond 5 m/s. For a man of 1.75m and 70kg in mass, wind resistance only accounts for 6.5% of the total cost although it can and have been known to affect speeds significantly in short distance track races.
Even under still wind conditions, runners "create" their own wind by virtue of moving speed. Speeds approaching the sub-2 hour marathon barrier (5.8 m/s) under still wind conditions will require +8% higher energy compared to running with no air resistance (Pugh, 1970).
C) Environmental Conditions : Slope of Terrain
A strong environmental condition known to affect COT is the slope of the running surface. Fig 5 distills the work of some prominent researchers on slope effects. Recall that Minetti's regression 5th order equations for slope effects on running cost are also reflected in the GOVSS power calculation algorithm.
So we see that upto a slope of 2%, COT is linear. Running on a slopes of 3-5% will require upwards of 10J/kg/m! Therefore, higher work loads can be accumulated under hill running in a given amount of time compared to flat running and this has implications for training. On the other hand, in a race or long hiking situation on very steep terrain, the runner is faced with how to minimize energy costs of travel. There is advantages in traversing up a zigzag path to artifically flatten the slope.
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| Fig 6 : COT along the direction of motion as a function of the incline of the terrain. COT is independant of speed and only depends on slope. Reference [7]. |
D) Environmental Conditions : Heat and Humidity
The running machine faces a substantial reduction in work capacity in hot and humid climates. The reasons are seen below.
Considering the running locomotor and the ambient surroundings (ground + air) as a thermodynamic system, heat production is a function of energy cost, speed and weight :
Heat Production = COTm x Speed x Weight
where units are :
Heat production = Watts
COTm = Joules/kg/m
Speed = m/s
Weight = kg
On the other hand, heat dissipation is a function of surface area (or mathematically the square root of body surface area). Heat dissipated by means of conduction, radiation and evaporation added to the storage of heat within the body must balance heat production.
Heat Production = Heat Lost in (Conduction + Evaporation + Radiation) + Heat Stored in Body
The technical issues that lead to an impact on running speed are the following :
1. The running locomotor's aerobic capacity or VO2max could shrink, hence there is a derate in aerobic potential.
2. The running locomotor faces a cardiovascular drift running in the heat.
3. Heat production is constrained by speed and weight
4. Heat dissipation is constrained by body surface area, temperature and relative humidity
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| Fig 7 : Heat production (W, Y-axis) as a function of running velocity (X-axis) and COT. Iso-temperature lines are shown in bold. Reference [12]. |
Ultimately, what this entails is a substaintial % decrease in sustainable speed in hot, humid environment dictated by the need to be able to cool the body. This leads to the following realities :
1. Distance runners are smaller than middle-distance runners to limit heat production, because weight has a 2-fold effect on heat production compared to heat dissipation.
2. Long distance running speed is temperature derated in hot climate because the running locomotor seeks to maintain heat balance without letting core body temperature rise to dangerous levels. For example, marathons in temperatures of 20± 25°C are 6%±10% slower than marathons in temperatures of 10±12°C.
3. Increasing age possibly has a multiplicative effect on COT degradation as well as the effect of the ability to shed weight.
Noakes et.al published an interesting graph indicating speed cutoffs to maintain estimated heat balance. Observe that for heavier runners, the speed derate are higher. These are only indications, rather than absolute values as they mentioned in their paper.
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| Fig 8 : Illustration of the derate in running speeds where heat production and maximum heat dissipation are in balance. Illustation provided are indications, not absolute values. Reference [13]. |
E) Environmental Conditions : Altitude
It is known that COT falls with rising altitude. Overground sea-level oxygen cost of running has been reported by Daniels et.al to be 4.5% greater than that measured at an altitude of 2,300m.
This has been attributed to the a) greater reliance on carbohydrate at high altitude for the same absolute running speed, which serves to explain the lower metabolic cost since the oxygen uptake for metabolising carbohydrate is lower than that for fats and b) lower work of ventilation due to lesser resistance to breathing [8]. However, since carbohydrate stores are low and due to low partial pressures of oxygen at great heights, these advantages are negated and the human runner has to compromise on work intensity to survive over long high altitude distances.
F) Other Contributers to COT : Training Status, Mass and Size
Training status has the ability to affect the Overall COT. Though literature is filled with estimates ranging from 6-24% reduction, an estimate of 8% can be expected in beginner runners on a 10 week training program, anywhere between 2-7% in endurance runners and about 7.5% after 9 weeks on an explosive training regimen. However, all of these estimates are subject to the specific protocol administered and calculations used.
Humans adapt with running training. They lose fat mass, build muscle and may alter their biomechanics in a way that elicits more tendon contribution in energy storage. Certainly the fat mass loss with training is something all runners are familiar with. Loss of fat around distal areas of the limb possibly lead to higher reductions in COT. The reduction of every 100 grams of mass from around the feet can lead to nearly 1% reduction in COT. This reduction is fairly consistent across a range of running speeds.
A Size-Independant Cost of Transport by dividing COT by the product of mass and height did not solve the interdependancies of mass to oxygen consumption. Alternative hypothesis suggest that the larger the body dimension, the larger the amount of energy stored and released through the stretch-shortening cycle of the leg extensor muscle (see below).
Under the dictation of some of the above influencers, a correction to the laboratory estimate COTm can be written as :
COT = COTm + Correction Due to Combination of (Wind + Altitude + Slope) Effects
III. Predicting Time For Covering Distances
Maximum Running Speed (m/s) = Maximum Metabolic Power ÷ Overall COT
Maximum Running Speed = m/s
Maximum Metabolic Power = W/kg or J/kg/s
Overall COT = J/kg/m
Since operating at the maximum metabolic power results in fatigue in the locomotor within approximately 7 minutes (runner dependant), the following equation allows the prediction of time to cover short distances upto 3000m :
Best Short Distance Running Time (s) = Distance ÷ Maximum Running Speed
Best Endurance Speed (m/s) = Highest Fraction of Maximum Metabolic Power ÷ Overall COT
Best Long Distance Running Time (s) = Distance ÷ Best Endurance Speed
IV. Towards Optimizing Cost of Transport
Fascinatingly, both mechanical engine and human locomotory movements exhibit a "non-linear" shape to cost of operation.
Consider that the fuel combusting mechanical engine has a speed and torque dependant optimum fuel efficiency. Driving a car "too slow" or "too fast" introduces a bigger penalty on brake fuel consumption than a more optimum cruise speed somewhere in between. Therefore, an "island" that contains the optimum fuel consumption is by design placed at mid-engine speeds and high torque.
Consider that the fuel combusting mechanical engine has a speed and torque dependant optimum fuel efficiency. Driving a car "too slow" or "too fast" introduces a bigger penalty on brake fuel consumption than a more optimum cruise speed somewhere in between. Therefore, an "island" that contains the optimum fuel consumption is by design placed at mid-engine speeds and high torque.
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| Fig 9 : Optimum island for specific brake fuel consumption in an engine. Reference [1] |
Similarly, when COT data is collected for several runners, an optima for low COT shows up at a specific value of running speed. For example, in the data below, minimum COT appears to be around 11.1 kph. Therefore, just like the mechanical engine, there is an optimal movement load and speed for lowest costs.
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| Fig 10 : Optimal speed to minimize COT in 9 trained runners. Reference [2] |
At a kinematic level, speed is determined by the product of stride frequency and stride rate. The running locomotor attains a minima in COT at an optimum stride frequency that varies from individual to individual.
A set of data from 12 subjects in Fig 8 show a U shaped profile in COT with respect to stride frequency. A similar behavior is also seen in cyclists, where the optimum pedaling frequency for low metabolic cost is around 60rpm. Yet, cyclists impose a self selected 90rpm possibly to reduce torque demand and muscular effort.
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| Fig 11 : Relation between cost of transport (COT) and stride frequency for 12 physically fit and experienced runners. Reference [5]. |
Scientists tell us that metabolic cost is primarily linked to the cost of producing muscular force. So could optimal movement speed be governed by the force and speed of muscular firing?
For example, it is known muscles are governed fundamentally by force-length and force-velocity relationships. At a whole body level, it is also known that human runners incur the least operational cost at an optimally selected stride frequency. These relationships are fundamentally non-linear in nature and subject to inter-individual differences.
Secondly, operating the locomotor with a shorter ground contact time involves fast fiber contractions (faster muscle firing) leading to higher energy costs. This explanation has served very well in understanding why smaller animals have higher metabolic costs and COTs.
The practical takeaway from this discussion is that a self imposed step frequency may or may not necessarily correspond to the optimum required to achieve minimum metabolic cost and minimum COT. There is some trainability value in this aspect.
V. Apparent Efficiency of Running
In addition to the costs of transport, knowing efficiency as it relates to the maximum extractable work for a given metabolic input is also required to analyze the performance of any engine.
What's the efficiency of running?
At this juncture, we need to define the apparent efficiency of running. The apparent efficiency can be seen as the end result of all possible losses and energy saving mechanisms during complete cycles of running motion.
Apparent Efficiency = Total Mechanical Work Done / Metabolic Cost
where total mechanical work done = external work + internal work
Apparent efficiency can be either expressed as "gross" or "net" depending on whether the energy cost of vital functions that are not directly related to exercise (e.g. the O2 consumption of the brain, of the gut, kidneys and internal organs, as well as the minor fraction due other organs' metabolism) is included in the metabolic cost (the denominator).
Apparent Efficiency (Gross) = Total Mechanical Work Done / Gross Metabolic Cost
Where Net Metabolic Cost = Observed Metabolic Cost - Resting Metabolic Cost
Resting Metabolic Cost = Approx. 300 mlO2/min (≈ 1.5 kcal/min or ≈ 100 W) for an adult man of about 70 kg body mass and is essentially unaffected by the exercise.
Muscular contractions require splitting of ATP, the energy currency in the body. To synthesize ATP can take several substrate routes but if we assume exercise to be fundamentally aerobic, then the amount of oxygen processed in unit time becomes a proxy for the power of cellular energy production.
The process leading to the splitting of ATP in the isolated muscle comprises two steps and each of these steps have an associated efficiency.
What's the efficiency of running?
At this juncture, we need to define the apparent efficiency of running. The apparent efficiency can be seen as the end result of all possible losses and energy saving mechanisms during complete cycles of running motion.
Apparent Efficiency = Total Mechanical Work Done / Metabolic Cost
where total mechanical work done = external work + internal work
Apparent efficiency can be either expressed as "gross" or "net" depending on whether the energy cost of vital functions that are not directly related to exercise (e.g. the O2 consumption of the brain, of the gut, kidneys and internal organs, as well as the minor fraction due other organs' metabolism) is included in the metabolic cost (the denominator).
Apparent Efficiency (Gross) = Total Mechanical Work Done / Gross Metabolic Cost
Apparent Efficiency (Net) = Total Mechanical Work Done / Net Metabolic Cost
Resting Metabolic Cost = Approx. 300 mlO2/min (≈ 1.5 kcal/min or ≈ 100 W) for an adult man of about 70 kg body mass and is essentially unaffected by the exercise.
Muscular contractions require splitting of ATP, the energy currency in the body. To synthesize ATP can take several substrate routes but if we assume exercise to be fundamentally aerobic, then the amount of oxygen processed in unit time becomes a proxy for the power of cellular energy production.
The process leading to the splitting of ATP in the isolated muscle comprises two steps and each of these steps have an associated efficiency.
1. ATP-synthesis/energy liberation from decomposition of nutritients : Phosphorylative coupling
2. Energy liberation during ATP-splitting/ATP Hydrolysis : Mechanical coupling
Overall muscle contraction efficiency = Phosphorylative coupling efficiency x Mechanical coupling Efficiency
A range of reported values for phosphorylative coupling efficiency and mechanical coupling have been reported in literature (Fig. 12) Certaintly, it appears that aerobic work is more efficient overall with the ATP resynthesis efficiency being as high 64% which when multiplied with a modest 40% for ATP hydrolysis efficiency yields an overall efficiency = 25.6%. On the other hand, anaerobic muscle efficiency maybe somewhat lower at 21.5% as reported by Margaria.
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| Fig 12 : Components in ATP turnover efficiency in human muscle. Reference [6]. |
However, running is not purely contraction movement, rather a mixture of positive work (the push-off) where ATP is split to apply force against the terrain and negative eccentric work (the landing) that dissipates energy while the terrain applies force on the body. It is then the apparent efficiency of positive-negative work that deserves attention.
Researchers discovered several decades ago that the summation of the theoretical oxygen requirement to power the different parts of the body during endurance running is over-estimated by approximately 50% when they compared theory to empirical data from level running experiments. In other words, the apparent work efficiency of whole body running was greater than the 25% efficiency for isolated muscle contraction.
How much greater? 40% or more for level running (Fig 13, 14).
Scientists agree that a reason for high apparent efficiency has partly to do with the fact that during the landing phase of running, passive, elastic elements that are connected to muscle bellies in the human body absorb some of the elongation of the muscle, store and release energy into the next phase of the cycle.
How much greater? 40% or more for level running (Fig 13, 14).
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| Fig 13 : Values of mechanical efficiency from several studies. |
Scientists agree that a reason for high apparent efficiency has partly to do with the fact that during the landing phase of running, passive, elastic elements that are connected to muscle bellies in the human body absorb some of the elongation of the muscle, store and release energy into the next phase of the cycle.
In other words, the human runner can activate "pre-stretch" in series connected elastic elements in the musculotendon unit just before touchdown, thereby storing energy which is then re-used for powering the next takeoff. The reduction in oxygen consumption is explained by the reduction in concentric response from the muscle and the lowered speed of contraction.
What this simply means is that work done by tendons does not have to be performed by muscles - therefore, tendons reduce muscle work, and therefore metabolic cost, during running.
This fact is empirically supported, with many studies showing that runners perform the work of running with an efficiency that exceeds that of isolated muscle (Cavagna et al., 1964; Heglund et al., 1982; Minetti et al., 1999). These observations support the idea that tendons do much of the work ‘for free’, thus increasing the apparent efficiency. This does not violate the principle of the second law of thermodynamics, as some people mistakenly claim.
VI. Spring Mechanics and Efficiency
Human locomotors naturally oscillate like a bouncing ball in order to run forward. As discussed in another post, human running can be approximated very well by a linear spring-mass model. However, because some energy is lost at each step due to friction and heat (attenuation), muscles need to constantly add some energy to the system to power forward movement.
Inspite of this little complication, the relation of COT to speed, stride frequency and the elastic behavior of the human running motion can all be fascinatingly tied up to support the metabolic cost of force production hypothesis.
The empirical finding on a treadmill was that humans chose a self-selected stride frequency corresponding to one which minimized metabolic energy expenditure, maximises apparent work efficiency and which corresponds closely to the calculated natural frequency of the "spring" (assuming damped harmonic motion).
The beautiful plot in Fig. 9 reveals more details. At low, medium and high running speeds (5.3 kph - 11.1 kph), human runners' freely chose a running cadence that corresponded to the minimum metabolic cost and maximum apparent efficiency.
This was despite the fact that mechanical power was greater at low cadences due to higher vertical work against gravity and lower at higher cadences due to a minimzation in vertical work done. In other words, these studies suggest that the running locomotor is somewhat blind to mechanical power minimization and instead the goal is to optimize cadence around the point where work efficiency is highest and metabolic cost lowest.
One also notices in Fig 9 that the apparent work efficiency increases as the speed increases, the magnitude is more than double (50%) of the metabolic efficiency of converting chemical energy to work in isolated human muscle (25%).
What this simply means is that work done by tendons does not have to be performed by muscles - therefore, tendons reduce muscle work, and therefore metabolic cost, during running.
This fact is empirically supported, with many studies showing that runners perform the work of running with an efficiency that exceeds that of isolated muscle (Cavagna et al., 1964; Heglund et al., 1982; Minetti et al., 1999). These observations support the idea that tendons do much of the work ‘for free’, thus increasing the apparent efficiency. This does not violate the principle of the second law of thermodynamics, as some people mistakenly claim.
VI. Spring Mechanics and Efficiency
Inspite of this little complication, the relation of COT to speed, stride frequency and the elastic behavior of the human running motion can all be fascinatingly tied up to support the metabolic cost of force production hypothesis.
The empirical finding on a treadmill was that humans chose a self-selected stride frequency corresponding to one which minimized metabolic energy expenditure, maximises apparent work efficiency and which corresponds closely to the calculated natural frequency of the "spring" (assuming damped harmonic motion).
The beautiful plot in Fig. 9 reveals more details. At low, medium and high running speeds (5.3 kph - 11.1 kph), human runners' freely chose a running cadence that corresponded to the minimum metabolic cost and maximum apparent efficiency.
This was despite the fact that mechanical power was greater at low cadences due to higher vertical work against gravity and lower at higher cadences due to a minimzation in vertical work done. In other words, these studies suggest that the running locomotor is somewhat blind to mechanical power minimization and instead the goal is to optimize cadence around the point where work efficiency is highest and metabolic cost lowest.
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| Fig 14 : The ratio of imposed step frequency and freely chosen cadence approaches 1 at the point where metabolic cost is minimized and apparent efficiency is maximized. Reference [9]. |
One also notices in Fig 9 that the apparent work efficiency increases as the speed increases, the magnitude is more than double (50%) of the metabolic efficiency of converting chemical energy to work in isolated human muscle (25%).
Conclusion
The human engine is likened to a mechanical engine, where molecular motors power the strokes responsible for movement while converting only a portion of the input energy to actual work. This post explored two key areas which influence human running performance - the cost of transport and the apparent efficiency.
Cost of transport is driven by metabolic substrate use and the effect of environment upon cost.
The learning process in endurance running is mostly about finding how to strike a balance between this need to achieve speed on one hand and minimizing cost of transport and maximizing efficiency on the other. It boils down to the cost of producing force at the molecular level and researchers are only beginning to understand that there maybe a tradeoff between force and efficiency, i.e some fundamental mechanistic limitations prevent muscles being both powerful and efficient at the same time [10].
Numerous technologies are available today to aid the human runner to find their "pace"; these however are simply aids and the best runners still appear to run mostly by "feel". We know very little about how the human locomotor judges and acts upon internal and external feedback signals by way of sensory control systems but the fact is that it happens. So it becomes essential to investigate what those effort governance theories are and what the supporting observations might be. This aspect will be tackled in a future post.
Cost of transport is driven by metabolic substrate use and the effect of environment upon cost.
The learning process in endurance running is mostly about finding how to strike a balance between this need to achieve speed on one hand and minimizing cost of transport and maximizing efficiency on the other. It boils down to the cost of producing force at the molecular level and researchers are only beginning to understand that there maybe a tradeoff between force and efficiency, i.e some fundamental mechanistic limitations prevent muscles being both powerful and efficient at the same time [10].
Numerous technologies are available today to aid the human runner to find their "pace"; these however are simply aids and the best runners still appear to run mostly by "feel". We know very little about how the human locomotor judges and acts upon internal and external feedback signals by way of sensory control systems but the fact is that it happens. So it becomes essential to investigate what those effort governance theories are and what the supporting observations might be. This aspect will be tackled in a future post.
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[10] Barclay, C. (2017). The basis of differences in thermodynamic efficiency among skeletal muscles. Clinical and Experimental Pharmacology and Physiology, 44(12):1279-1286
[11] REIS, Victor Machado, OLIVEIRA, Diogo Roberto, CARNEIRO, André Luiz, FERNANDES, Hélder Miguel, & SCOTT, Christopher. (2016). Inclusion of blood lactate O2 equivalent in the VO2-intensity regression at level and 10.5% grade running. Revista Brasileira de Educação Física e Esporte, 30(2), 255-261. https://dx.doi.org/10.1590/1807-55092016000200255
[12] Arsac, L. M., Deschodt-Arsac, V., & Lacour, J. (2013). Influence of individual energy cost on running capacity in warm, humid environments. European Journal of Applied Physiology, 113(10), 2587-2594. doi:10.1007/s00421-013-2696-6
[13] Dennis, S. C., & Noakes, T. D. (1999). Advantages of a smaller bodymass in humans when distance-running in warm, humid conditions. European Journal of Applied Physiology, 79(3), 280-284. doi:10.1007/s004210050507
[8] Fletcher JR and MacIntosh BR (2017) Running Economy from a Muscle Energetics Perspective. Front. Physiol. 8:433. doi: 10.3389/fphys.2017.00433
[9] Cavagna, G. The Resonant Step Frequency in Human Running. Pflügers Archiv. 1997; 6:678–684
[10] Barclay, C. (2017). The basis of differences in thermodynamic efficiency among skeletal muscles. Clinical and Experimental Pharmacology and Physiology, 44(12):1279-1286
[11] REIS, Victor Machado, OLIVEIRA, Diogo Roberto, CARNEIRO, André Luiz, FERNANDES, Hélder Miguel, & SCOTT, Christopher. (2016). Inclusion of blood lactate O2 equivalent in the VO2-intensity regression at level and 10.5% grade running. Revista Brasileira de Educação Física e Esporte, 30(2), 255-261. https://dx.doi.org/10.1590/1807-55092016000200255
[12] Arsac, L. M., Deschodt-Arsac, V., & Lacour, J. (2013). Influence of individual energy cost on running capacity in warm, humid environments. European Journal of Applied Physiology, 113(10), 2587-2594. doi:10.1007/s00421-013-2696-6
[13] Dennis, S. C., & Noakes, T. D. (1999). Advantages of a smaller bodymass in humans when distance-running in warm, humid conditions. European Journal of Applied Physiology, 79(3), 280-284. doi:10.1007/s004210050507
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