I like the topic, but the question is a little bit specious. A sprinter have to bounce forward... What are the sprinter characteristics that influence the predominance of these models? My point of view. It is a matter of personal optimization. The leg stiffness have to be high enough to guarantee higher force applications and better energy conservation. Hip extensor have to work at a level of force-velocity that is in equation with the timing of the load applied to the hip. I think the natural orientation of the trunk and hip, and the relative location of the foot during the contact are the key visual variables of this individual optimization.

I suppose that manipulating the task constraints (e.g. horizontal/vertical work and contact time) and compare the relative performance in a group of sprinters could help understand individual limits.

Fabrice, I agree, elite sprinters need to have short contact time to bounce forward and to have a high stride frequency, why is possible by increasing the leg stiffness. Further, for each specific angle at the touch-down, there is an optimal value of leg Stiffness. The best sprinter are able to find naturally (or with training??) this angle. So, they all are a stiff spring. But I'm not sure that there all are able to have high work of hip extensor, which depend primarily of the strenght of the gluteus maximus as well as the biceps femoris, the semi membreanosus and tendinosus. Mickael Johnson was for me the best example of "the scooter model" with a large part of his propulsion developed by a huge work of the hip extension.

To resume, I think that the capacity to produce a high level of work with the hip extensor allows to increase the amplitude of the stride, whereas producing high level of Leg stiffness allows to increase the stride frequency.

Finally, the velocity is the product of thestride frequency by the amplitude, so a sprinter which is able to product high work of the hip extensor with long lower-limb and at the same time to bounce as a ball on the ground will be the greater sprinter ever.

This Man exists!

A few years ago, an article was published in Scientific American that concluded that the compliance of the track needed to match that of the leg to give optimal stride length for the desired velocity. This is why some tracks favour sprinters and others distance runners.

The sprinter who will win the most races will have the skill to adapt his leg stiffness and side length according to the track. He can do this through practise on the race track and choice of shoes.

An interesting discussion!

Another aspect is that stride frequency and stride length change over time -- mostly increasing from the start. While frequency slows down after a peak, excellent sprinters are able to keep speed by further increasing stride length.

Here are two papers on the man you mentioned:

What gives Bolt the edge-A.V. Hill knew it already!

Ralph Beneke, Matthew J D Taylor

Journal of biomechanics, 05/2010;

https://www.researchgate.net/publication/44578074_What_gives_Bolt_the_edge-A.V._Hill_knew_it_already!

How fast could Usain Bolt have run? A dynamical study

H K Eriksen, J R Kristiansen, Ø Langangen, I K Wehus

Am J Phys. 2009; https://www.researchgate.net/publication/228567239_How_fast_could_Usain_Bolt_have_run_A_dynamical_study

Article What gives Bolt the edge-A.V. Hill knew it already!

Article How fast could Usain Bolt have run? A dynamical study

Graham,

I agree, different surfaces need different stiffnesses to optimize the stride cycle. One interesting paper explains very well the neural feedback necessary for this adaptation:

Robust passive dynamics of the musculoskeletal system compensate for unexpected surface changes during human hopping.

van der Krogt MM, de Graaf WW, Farley CT, Moritz CT, Richard Casius LJ, Bobbert MF.J Appl Physiol. 2009 Sep;107(3):801-8.

http://www.ncbi.nlm.nih.gov/pubmed?term=farley%20leg%20stiffness%20surface

Michael,

thank you for the references and comments. Indeed, with fatigue, the central nervous system is not able to maintain a high strides frequency and best elite sprinters compensate by lengthening their strides. Especially after 7s-sprint, all sprinters decelerate, but the slope of the deceleration is very slight for sprinter with high level of leg stiffness.

One other difficulty for sprinter is the contradiction between having a high level of explosive power for starting (0-30m), which necessitates high muscular mass and power, as well as a low position of the center of mass (best sprinters in the 60m are generally small) and being very stiff in the second and third parts of the 100m, which necessitates plyometric qualities.

To be powerful and stiff are generally contradictory.

I'm not sure if the bouncing-ball model is appropriate for sprinting. I think they key lies more in power-generation. The theoretical treatment by Beneke and Taylor addresses this idea nicely. The interesting thing is that Bolt actually has a much lower stride frequency than other competitors. This would suggest that stride frequency itself is not necessarily the most important component, but rather it is the power generated per-step which determines how quickly you get to the finish line. This power could come from different sources throughout the stride, but certainly hip power would play a critical role.

You all have some very good points, and each factor that has been discussed clearly has some relationship with overall speed over distance, or power generation per unit of time. I have a little difficulty with the bouncing ball analogy myself, from a physics stand point bouncing a ball is a very inefficient system. Energy is lost on each bounce and the ball soon loses all kinetic energy unless more is added into the system, as well as the fact that the motion is primarily dedicated to elevation off the ground. Sprinting is most efficient when power is generated along a horizontal vector, or parallel to the ground. The amount of energy or power put into the system at the start, or the amount of energy above that which is required to overcome inertia is critical, as I'm sure you all know, the best sprinters can usually continue to bring energy into the system created by the running movement for a short period of time and the best sprinters have the ability to conserve as much of that energy as possible as their contact point with the ground changes.

The key to conserving that energy is in shortening the amortization phase following foot strike and that is usually done by having a very fast swing phase with the free moving leg which certainly speaks to the idea of frequency in stride, of course if you have not maximized your kinetic energy via the initial push off, then you will never see your full potential in reference to power generation regardless of your stride frequency. Based on the mechanical factors of leg length, torso length, relative ROM , elasticity, strength, and stability of the articulations involved, I would say that the ideal stride would be different for each runner. In evaluating the relative power generation and subsequent conservation of kinetic energy within the system, each individual runner would have an optimal stride length, thereby giving them an optimal stride frequency at a given velocity.

If you are maximizing your initial push off and overcoming inertia with a net power gain into the system, then bringing in more energy into that system via maximum velocity of the leg in swing phase while reducing your net kinetic loss with shortening you time with ground contact, then you will run your fastest time. In reference to the "stiff leg" concept, there is clearly a balance between shock absorption based on maximum stress load on non-contractile connective tissue structures and maximizing energy conservation with the least number of degrees of flexion at each articulation, that balance again I would suspect is different with each runner, but certainly is an argument for maximizing the relative strength and elasticity of those non-contractile structures. Nice to have this thread out there, very interesting thought process...

...and just an additional thought on the leg stiffness issue, the ability to conserve energy in the system by transferring it from the contact leg (stance phase) to the free moving or swing phase leg is dependent on the eccentric loading of the connective tissue structures in the contact leg, thereby requiring a certain degree of deflection in order to load those structures which would dictate that a completely stiff leg would actually inhibit some of that energy conservation. Just an additional thought to consider...

Gabriel

I fully agree with your comment. A too short eccentric time did not allow to store elastic energy in the tendinous-muscular system. That's why recent researches propose to use another index which take into account this biais during jump such as drop jump:. the Reactivity strenght index

RSI= height/ contact time

WIth this index, a strategy which consists in having a very short contact time and so a too short eccentric time to allow a storing of elastic energy implies a low performance and so a bad RSI value despite the same motor strategy increases dramatically the leg stiffness index. But during sprinting, I'm not convinced that such a strategy (low eccentric time) would be possible contrary to a jumping task.

Ebben WP, Petushek EJ. (2010) Using the reactive strength index modified to evaluate plyometric performance. J Strength Cond Res. 2010 Aug;24(8):1983-7.

http://www.ncbi.nlm.nih.gov/pubmed/20634740

Sean,

thank you for this interesting answer and debate on Usain Bolt. But I think that his anthropometric characteritic (tall guy with a high value of skellic index, meaning long lower-limb) constraints him to have such a stride: long amplitude with high power developped by the extension of the hip, rather than bouncing with high frequency. But the bouncing model allows to discriminate elite sprinters from skilled sprinters. Indeed, values of leg stiffness is 2 times higher in the first population, showing his important role during sprinting especcially during phase 2 (constant velocity) and 3 (decceleration).

Leg strength and stiffness as ability factors in 100 m sprint running.Bret C, Rahmani A, Dufour AB, Messonnier L, Lacour JR.J Sports Med Phys Fitness. 2002 Sep;42(3):274-81.

http://www.ncbi.nlm.nih.gov/pubmed?term=bret%20leg%20stiffnes

Choukou MA, Laffaye G, Heugas-De Panafieu AM.Sprinter's motor signature does not change with fatigue.Eur J Appl Physiol. 2012 Apr;112(4):1557-68. Epub 2011 Aug 19.

http://www.ncbi.nlm.nih.gov/pubmed/21853307

Gabriel,

wow! What for a long and interesting point of view. You have right with assumption on the bouncing ball. It is not the best metaphor to explain the transfer of energy during a running cycle.

You are right when you say that for each sprinter has a specific signature. We have published a paper on this idea (http://www.ncbi.nlm.nih.gov/pubmed/21853307).

But I don't think that ldecreasing the amortization phase would be a good motor strategy to be highly efficient. Indeed, this phase is necessary for two reasons:

- first to control the dynamic balance of the athlete, by pushing backward, sprinter creates a momentum that creates a rotation of the trunk. To stop this rotation, he uses the free segments (arms and free leg) and so it is necessary to put his foot in front of his body after an elevation of the knee

- secondly, the leg has not to be considered as a simple solid but a real spring which is able to store elastic energy during this eccentric phase (amortization) and to restitute it during the concentric phase (push-off phase). Elite sprinters are able to adapt the value of stiffness to each angle without control strategy (see Blum et al. Swing leg control in human running. http://www.ncbi.nlm.nih.gov/pubmed/20498515)

Guillaume, first off; I would like to thank you for starting this thread. It is a very interesting thought process and I all too infrequently have the opportunity to engage in this type of discussion at this level with well informed people. I fully agree with your take on this, and would reinforce the need for an eccentric loading phase as both a period of energy storage and as part of a dynamic balancing strategy.

I do have to differ on the idea of the shortened amortization phase, however, as technically the amortization phase is not a synonym for the eccentric phase, it is actually defined as the time between the eccentric and concentric phases of a dynamic movement. It is the time that it takes to transfer the energy loaded into the connective tissue structures (including bone) during the eccentric loading and transfer that energy into a concentric movement. During that time, the mechanical change in direction, there is of course a dynamic stabilization strategy at work as the athlete works to stabilize the center of gravity/mass and initiate concentric recruitment of new motor units, however during this time, from a physics perspective, there is a net energy loss from the system.

When the time between the eccentric loading and the initiation of the concentric recruitment (amortization phase) is short, there is a greater conservation of energy and a more efficient transfer of energy from the eccentrically loaded structures to the newly activated concentrically moving structures. When this process is repeated at the greatest level of efficiently, there is minimal loss of energy when a sprinter moves from foot strike or deceleration to push off and swing phase of the other limb.

http://www.ncbi.nlm.nih.gov/pubmed/17530275

this study is one of many that discusses this issue. Keeping the amortization phase short is about transitioning from eccentric loading to concentric work as quickly as possible, which as you know is a guiding principle in plyometric training and I believe applies to sprinting as well. Thanks again for the intellectual exercise...

Guillaume, I enjoyed the paper on a sprinter's motor signature and how it relates to fatigue. I found the point that leg stiffness actually increased with fatigue to be very poignant and I have seen this phenomenon happen in practical applications. It certainly speaks to the need for deflection of connective tissue structures during the eccentric/deceleration phase in order to store energy for conservation. Great article, thanks!

Guillaume,

I didn't see the full paper, but Bret et al suggest that concentric half-squats are the best predictors of sprint performance, not leg stiffness, although they acknowledge that it plays a role. I can believe that leg stiffness during hopping might have some diagnostic value when it comes to screening athletes, but I think the analogy fails when applied to running.

I do totally agree with you that Bolt is constrained by his anatomy. The amazing thing, however, is that he is anatomically strange, as compared to almost all other successful sprinters, and he is also the fastest. Put another way, I don't think he is the fastest because he is the tallest and heaviest, since these would generally be disadvantageous. There is something else going on.

Thank you for adding to the thread, Gabriel. This is a fantastic discussion, and it has certainly become very complex! I think there are two separate ideas being floated, and I will attempt to paraphrase here. It seems that on the one hand we are considering a sprinter to be similar to a bouncing ball in the sense that they "conserve" energy by converting from kinetic- to spring- energy and back. On the other hand, there is the notion that there is a loading (eccentric) and unloading (concentric) of the structures of the body.

Assuming I've stated the ideas correctly, I would argue that semantically, the notion of energy conservation is a bit misleading. From either perspective, muscles are required to be active in order to either change stiffness or eccentrically activate (depending on your perspective). This means that in order to 'load' body structures, the athlete is expending energy to do so. I don't think this can be considered as energy conservation in this case.

What I do completely agree with is the idea that: athletes perform best when they can generate large eccentric activity during the braking phase of stance, generate large concentric activity during the acceleration phase of stance, and do it all very quickly (i.e. reducing this transition, or amortization time). To me, this is still all about power generation. Higher eccentric activity means higher muscle forces, means that when the athlete generates positive power, it will also be higher.

Sean, thanks for your response. I would agree that the braking phase is vital for storing energy from the deceleration in preparation for the concentric phase of push off and swing phase of the opposite leg. The greater the eccentric load, the greater the potential for power generation during the concentric phase, all vital for generating that positive power. However, I would ask you to reconsider that the idea of energy conservation does apply to sprinting.

The body is a closed system, and as any closed system, when energy is applied to it for the purpose of doing work, the ability to conserve that energy does relate to the amount of work that can be done. During the initial push off, the power generation of the contractile tissue (muscle) does certainly generate the initial energy in the system, although some models would include ground contact forces as a function of friction that allows us to overcome inertia and that one could argue energy transfer from the ground, I don't think it's necessary to go there in this discussion.

Once the body has overcome inertia and motion is generated, there is energy in the system, ie: the body. As the body is in free flight there is some loss of kinetic energy via frictional forces from the fluid medium we live in, air, however this loss is not significant without wind shear forces added to it. So that is to say that there is energy in the system which is waiting for a place to go, at this point, free flight, the forward momentum is now due to the inertia created from the initial push off and once swing phase is complete, there is no contact point for power generation. At foot strike, the energy in the system is loaded into the limb and some of that force is dispersed and refracted into the ground, these ground reaction forces allow for the storage of energy during the eccentric loading phase and of course if the amortization phase is short enough this energy can be conserved and transferred to the concentric phase. When this happens MORE work can be done then can be done purely from the contractile power generation of the concentric phase, we all know this, that's why we even discuss the eccentric loading as part of power generation. If there was no energy conservation, then with each foot strike, there would be a total loss of energy from the system, and the subsequent concentric movement would rely entirely on power generation from the muscle contraction and the amount of work able to be done would be limited.

That is why sprinters accelerate for a time during the initial part of the race, every contact point with the ground allows them to add energy into a system that is in motion and that has some conservation of that energy, otherwise there would be no ability to accelerate, as each contact point would only allow for the athlete to generate power to put towards the work (sprinting) from the generation of energy via there mms contraction. If they were limited by this and could not couple energy in the system from conserved energy, they would run at a constant rate for a time then decelerate due to fatigue.

This idea is easily demonstrated by the fact that a person sprinting cannot stop immediately when the race is over. Inertia continues to move the system forward because energy is conserved within the system and although there is no more need for generation of a concentric movement to push off and add more energy into the system, it still takes time and effort to disperse the energy that has been conserved.

Gabriel, I think we may differ semantically on the meaning of 'conservation'. I would take even one more step back from the model of the sprinter and consider Newton's Laws. You seem to be saying that conservation of energy allows the sprinter to continually move forwards, and also is what prevents them from coming to an immediate stop at the end of the race. I think what you are referring to here is momentum and not conservation of energy. Momentum is always conserved, and in the absence of external forces, an object will continue moving with a given momentum indefinitely. This is why the sprinter continues moving even after the race is finished. They have momentum that must be counteracted in order to reduce their velocity.

From an energetics perspective, the picture is a little different. The sprinter accelerates by, ultimately, converting chemical energy from their cells into kinetic energy. The ground has no energy to give, it is completely inert in this case. As the sprinter moves along, they alternately 1) brake and 2) accelerate their body. During both of these phases energy is expended. The sprinter must convert chemical energy into kinetic energy in order to brake, and again to accelerate. So, while there is some kinetic energy that resides in the runner during their entire race, there is a constant 'flow' of energy into the ground (braking) and into the runner (acceleration) with each step. Ultimately, both of these 'flows' begin in the runner's chemical stores. So, by this description, I don't really see a sprint as a situation where there is conservation of energy.

One could argue, and some have, that during braking some energy is temporarily stored in the musculo-tendinous structures of the body as they are stretched eccentrically. Essentially, some of the chemical energy from the sprinter is converted to spring-energy which is released during the acceleration phase. This likely does happen, however, I would argue that the amount of energy stored is probably trivial compared to the total energy required to complete a sprint. Animals with very long, very stretchy tendons can store huge amounts of energy, but we humans are not really built to do this.

So, to me it seems that the sprinter must be constantly generating power, both eccentrically and concentrically, in order to sustain their locomotion. The more effectively they can do this, the better they will be at sprinting.

Guillaume,

I would suggest that high speed locomotion performance is best explained with a combination of the models you describe.

A spring mass system offers a partially effective model to describe real function but one key problem with it is that it predicts much higher braking impulses than we see in athletes upon landing. Use of a stiffer spring (as is associated with better runners) then requires very short contact lengths and unachievably short contact times if excessive braking forces are to be avoided.

The modification of a spring mass model by adding a power generator at the top of the spring (functioning like the hip extensors) allows much better prediction of a normal ground force profile and explains how higher speeds can be achievable in humans. Using a stiffer leg spring facilitates faster travel, but to use a stiffer spring without generating excessive braking force on landing requires higher hip extensor power output. As such these qualities are coupled in athletes and need to be developed together; leg stiffness (driven predominantly by ankle and also some knee function) and extensor power (driven by hip extensors).

Jon

Jon's combination of the models was very articulate. Nicely done.

From my perspective, I would still equate "leg stiffness (driven predominantly by ankle and also some knee function)" with eccentric power generation since this makes the sprinter "active" in my mind instead of a "passive" spring.

Agreed Sean, briefly eccentric into isometric muscle action combined with tendon extension will drive the spring like response

thank you Jon and Sean for theses very interesting point of view in the understanding of this simple spring mass model.