The beguiling dream of capturing the force of gravity to assist forward motion when running has re-emerged in recent months. There have been two recent re-incarnations of the dream. Both attempt to overcome the problems of the Pose technique that had attracted enthusiastic followers but also critical analysis in the past decade. I discussed the benefits and problems of Pose in some detail on this site five years ago. The more recent versions avoid the unrealistic claim implicit in the Pose mantra ‘Pose, Fall, Pull’ that the Centre of Mass (COM) actually falls between mid-stance and lift-off from stance. This claim is simply contrary the evidence that the COM rises after mid-stance. This rise can easily be observed in video recordings of elite and recreational runners. Both of the recent versions of the theory accept this.
Nonetheless in common with Pose, the recent versions are both based on the argument that when the COM is ahead of the point of support in late stance, there is a torque acting on the body that tends to produce head-forwards and downwards rotation. Unfortunately neither of the new versions adequately addresses the fact than an oppositely direct torque acts prior to mid-stance, and both under-estimate the importance of the push that is required to overcome the braking that occurred during early stance and to get airborne.
Although both theories are flawed and neither provides grounds for claiming that gravity provides energy for forward propulsion, both provide a pointer to cues that might perhaps help a runner improve efficiency and decrease risk of injury. It is therefore potentially worthwhile to examine them in greater detail. However, if you are more interested in the practical conclusions than the detail, you can skip to the final section
Svein Kanstad a Norwegian coach has teamed up with an academic physiologist, Aulikki Kononoff, from University of Kuitpo in Finland to test and publish a creative new version of the hypothesis that gravitational torque acting after mid- stance can drive horizontal motion. As in the theory of Pose, they argue that due to the forward inclination of the body after mid-stance, there is a component of gravity that drives a head forward and down rotation, as illustrated in Figure 1.
Figure 1. Forces acting after Mid-Stance. vGRF = vertical Ground Reaction Force; hGRF= horizontal Ground Reaction Force. Force C1 directed along the line of action of total GRF propels the body forward and upward. Force C2, at right angle to GRF produces a torque which promotes head-forwards rotation around the point of support. Illustrative numerical values are based on the model I presented on this site in 2012
Kanstad’s theory is somewhat more sophisticated than Pose theory, insofar as he recognises that the leg extends during late stance so that there is no net fall of the centre of mass after mid-stance. Because of the leg extension, the situation is a little more complex than portrayed in figure 2 of their paper, which depicts a body rotating about a fixed point of support, with fixed length from point of support to COM. In reality, the distance from point of support to COM increases as the leg extends, thereby changing the moment of inertias (i.e. the body’s resistance to rotation) and furthermore, the point of support moves forwards in late stance. Nonetheless as discussed in the extensive comments section of my article ‘Running: a Dance with the Devil’, computation based on a reasonably realistic model confirms that angular rotation in a head-forwards direction does occur after mid-stance.
Kanstad and Kononoff accept that both energy and angular momentum must be conserved, in accord with the laws of physics. They argue that the angular momentum imparted in late stance is preserved during the airborne phase and then converted to forward linear motion at the next footfall, analogous to the manner in top-spin imparted to a tennis ball causes the ball to accelerate forwards as it rebounds off the ground.
In other words, instead of simply claiming that gravitational energy is captured by falling after mid-stance, they argue that gravity generates angular momentum as the body rises, and the associated head-forwards rotation of the body is converted to forward linear motion at the next footfall.
There are two flaws in their argument. First of all, while they state that the rotational motion imparted after mid-stance might provide propulsive power at the next footfall, they do not address the question of where the energy associated with this rotation comes from. It has certainly not been provided by gravity because the body actually rises after mid-stance. Gravity extracts kinetic energy from the body during this phase. When averaged over the entire gait cycle, the net contribution from gravity is zero.
The energy associated with the rotation imparted during late stance comes largely from a redistribution of the kinetic energy existing at mid-stance. A small fraction of the energy associated with forward motion of the body is transferred to the rotation. Rotation acts as a temporary store of energy derived from an energy source other than gravity.
With regard to determining the energy requirement of running, the re-redistribution of energy within the three interchangeable energy pools (kinetic, gravitational and elastic) does not result in any net increase in total energy over the gait cycle. There is however a loss of energy from these three pools due to several processes that dissipate energy. There is loss due to friction within the tissues of the body; loss due to air resistance; loss to due to failure to capture all of impact energy at footfall and loss of energy due to the braking that occurs during early stance. When running at constant speed, these losses are made-up by active contraction of muscles that consumes metabolic energy. Any suggestion that rotational energy derived from gravity might be a source of propulsive power is false. Muscle contraction must meet the costs, and the key issue in maximizing efficiency of running is minimising the losses.
Kanstad and Kononoff recommend that the runner should land with the foot as nearly under the COM as possible. They point out that this would decrease the amount of head-backwards rotation that might otherwise detract from the proposed (but illusionary) advantage of head forwards rotation. However, the second flaw in their argument is a serious under-estimate of the amount by which foot must be ahead of the COM at footfall.
The laws of physics demand that the foot must be placed appreciably ahead of the COM. Apart from the instant when the COM is directly above the point of support at mid-stance, the COM must be either before or behind the point of support throughout stance. The line from COM to point of support is angled either forwards when COM is behind the support producing a braking effect, or backwards when the COM is ahead of the point of support, producing forward and upwards acceleration (as shown in Figure 1). If there is no net change in pace over the gait cycle, the forward acceleration generated by the push when the COM is ahead of the point of support must be equal to the deceleration due to braking (if we ignore the effect of air resistance).
It would only be possible to abolish braking while landing with the foot under the COM if the duration on stance was zero, but this would require an infinite vertical ground reaction force. If there is to be no net generation of momentum in an vertical direction averaged over the gait cycle, the upwards impulse generated by upwards ground reaction force (GRF) during stance must equal the body weight which acts downwards over the entire gait cycle. Thus the average value of vertical GRF is body weight divided by proportion of the gait cycle on stance and this approaches infinity as duration on stance approaches zero. Therefore the foot must be on stance for an appreciable time. While on stance there must be appreciable but equal amounts of acceleration and deceleration. The deceleration occurs when the point of support is ahead of the COM between footfall and mid-stance. Therefore, the foot must land an appreciable distance in front of the COM.
Where should the foot land?
Although the issue of rotation is of trivial importance, the question of where the foot lands is actually of vital importance because it determines braking costs. It therefore warrants careful consideration. While the forward acceleration generated when the COM is ahead of the point of support must equal the deceleration occurring when the COM is behind, the proportion of stance time spent with the COM ahead of the point of support is not necessarily equal to the proportion when COM is behind the point of support, because the cumulative effect of acceleration or deceleration are determined by both duration and magnitude of the force. The force tends to be greater in early stance because there is substantial tension in the leg at footfall to prevent the knee buckling. Force plate data confirms the rapid rise in ground reaction force immediately after footfall. As a result, the duration between footfall and mid-stance is less than that between mid-stance and lift off, even though the net transfer of linear momentum over the gait cycle is zero when running at a steady pace.
Observation confirms these theoretical predictions. For example Cavagna and colleagues reported measurements of the braking time and the acceleration time during stance in sample of 10 runners at various speeds. At 10 Km/hour (2.8 m/sec) the average braking time was 0.125 sec and the acceleration time was .145 sec. From these numbers it can easily be shown that on average the COM advanced 35 cm from footfall to mid-stance (i.e. the COM was approximately 35 cm behind the point of support at footfall) and at lift-off it was 40 cm ahead of the point of support. (Note that to be precise we need to know how much the point of support moved forwards during stance but allowing a small movement of the point of support would make only a small change in these estimates of distance travelled during braking and acceleration.)
Cavagna also reported that the difference between braking time and acceleration time diminished as speed increased. This is almost certainly because at greater speed it is necessary to exert a stronger push against the ground after mid-stance, thereby reducing the difference between forces exerted during braking and acceleration phases. Cavagna reported that braking time and acceleration time were equal at paces above 15Km/hour. At 15Km/hour (4.15 m/sec) braking time and acceleration time were both 0.1sec. Thus the COM advanced by 41.5 cm in each half of the stance period.
However Cavagna provided no indication of the competence of these runners. His runners did not necessarily achieve optimal placement of the foot. Would they have been more efficient if the foot had landed less far in front of the COM leading to a shorter time on stance and less braking?
The key question is: what is the optimum time on stance? It is necessary to bear in mind that while less time on stance decreases braking costs, the need for a relatively longer airborne time demands a more powerful push, creating not only greater stress on the legs but also greater loss of energy at impact, as only about 50% of impact energy can be captured as elastic energy, so an extremely short time on stance is likely to be inefficient.
In the study of Weyand, in which nine of the 10 runners studied were competitive athletes, all except one of the 10 spent appreciably less time on stance, at comparable paces, than the average runner in the study by Cavagna. As they approached their top speed, all of Weyand’s runners decreased time on stance towards a limit of 0.1 sec (total for both acceleration and deceleration). It is possible that 0.1 sec on stance is the optimum duration for efficient capture of impact energy as elastic energy.
The shorter stance times achieved by the runners studied by Weyand suggest that on average Cavagna’s runners spent too long on stance for optimum efficiency. Possibly they simply lacked the power to get airborne, but it is also possible that a mental focus on landing with the foot more nearly under the body might have helped reduce stance time. While the recommendation of Kanstad and Kononoff (and many other coaches) to land with the foot as nearly under the COM as possible is advice to aim for something impossible, it is nonetheless is likely to be a useful cue for runners who tend to spend too long on stance.
The Virtual Pivot Point Model
The second these recent versions of the ‘gravitational torque’ theory is the Virtual Pivot Point (VPP) model described by Mick Wilson in a post on 15th Oct 2015. on Lee Saxby’s ‘Born To Run’ web- site. Mick Wilson is a Senior Lecturer in the Department of Sport and Exercise Sciences at Northumbria University
A key feature of the VPP model is that the tension in the muscles of the trunk, especially the hip extensors and flexors is adjusted to ensure that the ground reaction force is directed along a line joining the point of contact of foot with the ground to a fixed point (the VPP) high in the runners torso (Figure 2). During early stance, when the point of support is ahead of the VPP the direction of action of GRF is upwards and backward. The torso is tilted forwards a little due to the momentum of the torso when the forward movement of the foot is arrested. The hip extensors act to prevent buckling at the hip. By late stance the direction of action of GRF is upwards and forwards. The torso now tends to incline backwards relative to the thigh and the hip flexors contract to resist this. The action of hip extensors in early stance and flexors in late stance stabilises the body, preventing it buckling at the hip, and keeping it upright. It is reasonable to propose that these actions of hip extensors and flexors play a cardinal role in keeping the body upright.
Figure 2. The Virtual Pivot Point Model. The combination of gravity and GRF results in a force acting along the line of GRF and a component at right angles to GRF which exerts a rotational effect. VPP = Virtual pivot point; COM = Centre of Mass; GRF = Ground Reaction Force.
In early stance, the force aligned with GRF arrests the descent of the body and also has a braking effect, while the ‘rotational’ component at right angles to GRF creates a head-backwards rotation.
In late stance, the force aligned with GRF propels the body upwards and forwards, while the ‘rotational’ component at right angles to GRF creates a head-forwards rotation.
Furthermore, the variation of inclination of torso relative to hips from a slight forward lean in early stances results in the direction of action of GRF passing forwards of the COM to pass through the VPP, in early stance, while it passes behind the COM in late stance to the same pivot point in upper torso in late stance. Although in the VPP model the line of action of GRF does not pass through the COM (as was assumed by Kanstad and Kononoff), the direction of action of GRF is nonetheless upwards and forwards in late stance. As in the Kanstad model (and also in the Pose model) there is a torque that tends to produce acceleration in ahead forward and down direction during later stance. Similarly, an oppositely directed rotation will be generated when the COM is behind the points of support in early stance. The main difference between the models is that at any particular point in time after mid-stance, the inclination of GRF is a little less forwards that would be the case in the Kanstad and Pose models.
Unlike Kanstad, Wilson makes no attempt to explain how this rotation might be converted to forward motion. Furthermore, Wilson does not specifically claim that the head forward rotation induced after mid-stances exceeds the head-backward rotation induced before mid-stance. However these limitations do not matter, because, as in the Kanstad model, gravity can provide no additional energy while the COM rises after mid-stance. The energy associated with any rotation generated by gravitational torque after mid-stance is largely derived by redistribution of the energy in the pool of kinetic and elastic energy existing at mid-stance. There is one slight difference. In the VPP model, the direction of action of GRF is long a line that passes behind the COM. If this is in fact the case, the active contraction of muscles responsible for generating GRF will contribute directly to the energy associated with rotation. But gravity does not contribute.
Another misleading feature of Wilson’s account of the VPP model is his claim that the forwards and upwards GRF is generated purely by elastic recoil, so that an active push is not necessary. This could only be the case if the kinetic energy associated with downward movement at footfall could be captured as elastic energy and subsequently released with 100% efficiency. In fact, only about 50% of the kinetic energy of downwards motion at footfall can be recovered. Although Wilson acknowledges the fact that the COM rises after mid-stance, he actually appears to deny that any active muscle contraction is required to generate GRF. Thus he very seriously underestimates the work that must be done when running. But could this under-estimate be a virtue? This question leads us to the issue of what useful lessons might be learned from these two recent versions of the gravitational torque theory.
What useful practical lessons might be learned?
Why does the claim that gravity provides forward propulsion continue to attract attention? Many recreational athletes appear to benefit from the mental image created by the notion that gravity provides forward propulsion. As mentioned in my discussion of the theory of Kanstad and Knononoff, at least part of the benefit comes from the encouragement to land as nearly under the COM as possible. Although impossible to achieve, this advice discourages over-striding and tends to promote a short time on stance. However, the advice to land nearly under the COM is not specific to theories claiming that gravity provides forward propulsion.
In a more subtle way, the illusion that gravity might provide propulsive power tends to discourage a conscious focus on pushing against the ground. A short time on stance is only possible if there is a strong push, but perhaps paradoxically, for most athletes, conscious focus on the push is counter-productive. It is likely to lead to delay on stance – the opposite of what is required. Effective push-off from stance requires precise timing. For most runners, this precision is best achieved automatically. A cue that minimises potentially harmful conscious interference with the precision of timing is likely to be beneficial.
While a cue that promotes an automatic rapid lift off from stance is likely to be beneficial, I would prefer to employ a cue that is based on sound science rather than one based on illusionary theory. One consequence of spending a short time on stance is a relatively long airborne time associated with a relatively large amount of flexion and hip and knee of the swinging leg. I find that conscious focus on the swing rather than the push can be the most effective way to minimise harmful conscious interference with the precision of timing of the push.
The focus on an upward and forward swing of the thigh should be combined with a focus on a sharp swing of the arm in a downwards and backward direction. Our brains are wired to produce coordinated oppositely directed movements of the leg and arm. Because the brain can apply more finely tuned control of our arms and hands than to our legs and feet, more precise control can be achieved by placing the main focus on the arm swing. Precision in timing of the flexion of the hip is necessary to ensure that the swing does not lead to over-striding .
The required mental image of the swing is cultivated by the swing drill. However the swing drill does not involve getting airborne and hence does not help develop the association of a conscious swing with a forceful non-conscious push of the stance leg. For this, I find the Pose Change of Support (CoS) drill is effective. This drill entails alternating shift of stance from one leg to the other without forward motion. The mental focus is on a precise flexion of knee and hip of the ‘swing’ leg as it lifts off from stance; not on driving the other leg downwards.
Although CoS is a Pose drill, you do not have to invest faith in the claim that gravity provides forward propulsion to benefit from it. In fact CoS is similar to the major form of the ‘Hundred Up’ drill developed by WG George, the world’s fastest miler in the nineteenth century. While similar to Pose CoS, the ‘Hundred Up’ places emphasis on flexion of the hip to bring the knee to the level of the hip. This makes the drill quite effortful, but I do not think it is essential to lift the knee to hip height. The greatest focus should be on precise timing. George did place emphasis on the well-controlled swing of the arms, which helps promote precise timing. I recommend raising the arm somewhat higher and closer to the chest during the forward arm swing than is depicted in George’s model (Figure 3) as I believe bringing the arm close to the chest promotes better control of the swinging leg and minimises risk of over-striding.
In conclusion, in my opinion Pose and its more recent re-incarnations encourage a helpful focus on an effective swing without over-striding, while minimising the risk of harmful conscious interference in the essential push. I do not consider that it is necessary to invest faith in an illusory horizontal propulsive effect of gravity in order to achieve this helpful focus on the swing.
How much does this matter during every day running? For an athlete who suffers repeated injury, careful analysis of running form to identify possible errors is crucial and conscious focus on cues promoting good style is an essential part of correcting errors. Even when not dealing with injury, I think it is worthwhile to consciously attend to form during at least a small portion of each training session. During long races, conscious focus on a precise and firm downwards and backwards swing of the arm at lift-off from stance can play an important part in preventing a loss of power when tiredness builds up. I recommend including a short period of the CoS drill, together with conscious attention to arm action, in the warm-up to all training sessions.