The Mechanics of Efficient Running « Canute’s Efficient Running Site

This is a version of my original post on the Mechanics of efficient Running posted on 29th December 2007, updated as I have obtained more information from comments, observations or reading.

This version was updated on 1st January 2008; details of the changes are listed at the end of the article.

This page has been substantially extended by a series of articles under the tile ‘Running: a dance with the devil’ posted in March 2008.  That series attempts to cover the main physical, biological and psychological  aspects of running.

 

The Mechanics of Efficient Running

This article is a speculative account of how to run with minimal consumption of energy and minimum risk of injury per kilometre. We will start by addressing the question of how to run at constant velocity on the flat in the absence of wind resistance, and subsequently consider how to adapt to wind resistance and hills.

The first principle is that according to Newton’s first law of motion, no propulsive force is required to maintain a constant velocity on a horizontal surface in the absence of wind resistance. The practical consequence is that muscular effort to drive the body forwards is likely to waste energy and increase the risk of injury.

However, it would be misleading to imply that no muscular effort is required. If the feet were fixed to the ground, forward momentum and gravity would combine to cause the runner to crash face-down, so it is necessary to move the legs forward alternately in such a way as to arrest the tendency to fall. In contrast to walking, while one leg is swinging forwards (‘the swing phase’), the other leg is on the ground (stance phase’) for only a part of the time. Thus, for a substantial portion of time the runner’s body is airborne. The effort to become airborne and the impact with the ground at foot strike, create risk of injury. The art of efficient running entails swinging the leg forward in a way that uses minimum energy with minimal risk of injury.

To understand how this is done requires an understanding of what muscular actions are required and what muscular actions are to be avoided. Learning how to do it requires acquisition of the correct sequence of movements, which can be facilitated by use of a specific drill (the swing drill, described in a separate article), and subsequent practice of this sequence of movement until it becomes habitual. In my experience, the sequence can be acquired with less than an hour of practice. Warm-up for each running session should begin with the swing drill and a period of relaxed running focussing on technique. Once the sequence of actions is habitual, execution of the procedure does not require conscious planning of each muscle action, but rather, the use of simple imagery to evoke the learned sequence.

 

General principles

Certain principles of physics and physiology can be invoked to determine the optimum sequence of actions. The guiding principle is that acceleration or deceleration of the body’s centre of gravity (COG) relative to the ground should be kept to a minimum, because acceleration and deceleration require energy and also have potential for injury. Furthermore, acceleration of one body part relative to another should also be used a sparingly. The following specific principles follow:

1) To avoid braking action, the foot should have near zero speed relative to the ground at foot-strike, so the foot should be moving backwards relative to the rest of the body at approximately the same speed as the COG is moving forwards.

2) Vertical motion of the COG should be minimized as downwards motion increases force on the ground and upwards motion requires energy. Nonetheless, during the airborne period, the body is unsupported and must fall. However, because acceleration under the influence of gravity causes a steady build up a speed, the body will fall less during a series of several short airborne periods than during a series of fewer longer airborne periods of the same total duration (See the article on calculations for the mathematical demonstration of this). Therefore, to minimize free fall under the influence of gravity, the airborne period should be relatively short.

3) Rotation of the body around a horizontal axis (i.e head moving forward and down relative to feet) should be minimized, as any rotation must be reversed if progressive lean and an eventual face-down crash is to be avoided. This principle must be set against the fact that a small degree of destabilization of the body from the stance will evoke automatic swinging forward of leg. The destabilization from stance is initiated by forward momentum, but when the COG is forward of the point of support, gravity will also contribute to the destabilization. Once the degree of destabilization is such that the torque exerted by gravity produces appreciable acceleration of the rotation, there is greater risk of wasting energy and of injury. Therefore, the body should lean only very slightly. Furthermore, because the body continues to move forwards over the grounded foot during stance, destabilization will increase the longer the foot remains on stance. Therefore, to minimize deleterious gravitational torque, the time on stance should be short.

4) If airborne time must be fairly short to minimize gravitational freefall, and time on stance must be short to minimize deleterious gravitational torque, then cadence must be high. Observation of elite runners indicates that it should be at least 180 steps per minutes (i.e. 90 full cycles of the gait cycle per minute)

5) According to Newton’s third law (action and reaction are equal and opposite) the vertical component of ground reaction force (GRF) must be equal and opposite to the downwards force exerted by the foot on the ground. The average value of the vertical component of GRF averaged over the full gait cycle must equal the body weight. As GRF is only exerted during stance, the average value during stance is the body weight multiplied by the ratio of total duration of the cycle to the time on stance. Thus if time on stance is half of the total gait cycle, the average GRF during stance will be twice the body weight. Peak GRF during stance might be considerably higher than this, unless the load is distributed as uniformly as possible over the stance period. This is probably best achieved by landing with the ankle almost neutral (or with a very slight degree of plantar flexion) so that weight is taken on the mid-foot; then rapidly transferred to the first metatarsal where the energy can be temporarily absorbed by some flattening of the longitudinal arch by a slight roll of the foot towards the inside edge (mild pronation). Some of the energy is stored in the stretched Achilles tendon, whose role includes sustaining the arch. This stretch can only be maintained if the calf muscle is contracted. Finally, the joints of the foot are stiffened by a slight roll laterally (supination) to promote recovery of energy by elastic recoil at lift off. The time on stance must be long enough to allow the transfer of energy between the structures of the foot, but in view of the fact that calf muscle contraction is required to maintain the stored energy, too long on stance will lead to exhaustion of the calf. Thus, consideration of foot dynamics also indicates the need for a relatively short time on stance. (But if airborne time is much greater than time on stance, GRF during stance will necessarily be high to ensure that average GRF over the entire cycle is equal to weight)

 

The components of the gait cycle

As outlined above, during the full gait cycle, each foot is engaged in a stance phase and a swing phase. During the swing phase, the foot must be lifted, moved forwards and allowed to drop back to the ground, moving backwards relative to the COG at the point of foot fall. Thus, the foot follows a quadrilateral path, rounded at the corners as each stage of the cycle grades in to the next one. The four segments of the path are:

1) Base position
In the base position the foot is on stance: The COG moves forwards over the foot, and the body is destabilized, initiating a reflex swing of the leg forwards to prevent falling. According to principles 3) and 5), time on stance should be short. During this time the processes of foot pronation and supination absorb, store and redistribute some of the energy of impact. Also, in the latter part of stance the tensed quadriceps recoils releasing some of the energy that had been stored in that muscle on foot strike, reducing the flexion of the knee and imparting an upwards drive to the body which helps compensate for the loss of height during free fall in the airborne period.

2) Ankle lift
The ankle is lifted towards the hip. This action is initiated partly as a reflex response to the destabilization during late stance, and is assisted by the recoil of Achilles tendon and quadriceps, but it is also under conscious control. It requires contraction of the hamstrings. However, because the hamstrings cross both hip and knee joint, unopposed hamstring contraction would also produce hip extension which would move the leg backwards behind the line from lift-off point to hip. Observation of elite athletes like Haile Gebrselassie suggests that the ankle should in fact curve upwards in a path that arches behind the direct line towards the hip, as would be expected if the main action is hamstring contraction. What image should we use to guide the path of the ankle? Dr Romanov, who developed the Pose style of running suggests an image of a piston that moves in a direct up-down action, but I find that for me, this image results in too much engagement of the hip flexors. I am still experimenting to find the image that works best for me. Because lifting the ankle requires active work against gravity, this movement (and the associated backswing of the arm discussed below) are the only actions of the gait cycle that demand conscious application of effort. This action is the principle driver of the swing.

3) Leg swing
The leg swings forward, largely under the influence of gravity, as the knee extends. The knee should not extend fully but remain slightly flexed so that it can help absorb impact at foot fall.

4) Foot fall
The foot falls to the ground as the hip swings back towards the neutral position largely under the action of gravity, with the knee remaining slightly flexed. Although voluntary muscle action is not required, a strong automatic stabilizing contraction of the quadriceps must occur to prevent the knee collapsing on impact. Because the hip swings back almost to the neutral position during the fall, the point of impact is under the COG (or at most slightly in front of it), thereby minimizing any braking effect. The quadriceps absorbs a large amount of energy at impact, some of which will be recovered by elastic recoil to assist in raising the body to recover height lost during freefall, and in lifting the ankle towards the hip in the next swing phase.

The ‘swing drill’ (see separate article) entails practice of the three segments of the swing: ankle lift, leg swing and foot fall, while the body is stationary, supported by the opposite leg.

Torso
Upper body orientation and movement should be used to facilitate the leg movements. The torso should be held in an almost upright orientation, with the pelvis dropped down and forwards producing perceptible feeling of drag in the vicinity of the solar plexus, and the shoulders should be drawn slightly back and rest downwards in a relaxed state. This orientation of the body facilitates a relaxed foot fall to the correct position under the COG.

 

Arm swing
The arms swing in a minimal arc in a reciprocal action to the leg on the same side. As the ankle is lifted towards the hip the arm moves back moderately forcefully, reflecting the sharp, compact movement of the ankle towards the hip. Then the arm swings forward largely under the influence of gravity, but not in a floppy state, while the leg swings forwards and the foot falls to the ground. If a compact arm movement is practiced during the swing drill, the brain will readily associate the compact arm swing with a compact leg action. Because proprioceptive feedback from the upper limb is more strongly represented in the brain than that from the leg, good form can be monitored more easily if arm and leg are coordinated.

All unnecessary muscle action should be avoided. However in addition to the actions described above there are several other important actions. Reflex contraction of the hip abductors minimizes pelvic tilt and dropping of the hip on the unsupported side. Footfall with slightly flexed knee and the impact absorbing foot action described above would be expected to minimise abrupt loading of the hip abductors while also protecting the knee joint and ankle joint and minimising sharp localized forces on the bones of the foot.

It should be emphasized that this description of efficient running is based in observation a few elite athletes and an attempt to apply the principles of physiology, anatomy and physics as described above, but has only been tested by the author himself. It has not been subjected to any form of controlled trial and hence must be regarded as a speculative proposal rather than a proven method of safe, efficient running.

 

 

Acknowledgments

Gordon Pirie, gritty and thoughtful elite athlete, former 5000m and 3000m world record holder and source of inspiration, whose thinking about running style has shaped my own;

Dr Nicholas Romanov, developer of the Pose technique of running, who has emphasised that running style can be improved by thoughtful application of principles;

Cable_Tow, sports medicine specialist and generous-spirited guru on the Fetcheveryone website;

nrg-b: Pose coach with a delightful sense of humour;

Jeremy Huffman, elite athlete and Pose coach;

Jack Becker, generous spirited Pose coach;

Jack Cady, developer of Stride Mechanics;

Haile Gebrselassie, elite athlete, marathon world record holder, and model for efficient running;

Fetch, founder of an amazing website for runners and pace-setter in one of the few races that I have ever won;

Danny Dreyer, developer of Chi running;

F. Matthias Alexander (1869-1955) who showed how changing one’s thinking can re-direct posture and movement, and honed the concept of listening to your body.

Changes from the original version posted 29th December 2007:

1 Jan 2008: The description of the path of the ankle following lift-off was modified to describe that curved upwards path exhibited by elite athlete, HaileGebrselassie

 

Long but very interesting post on a very important subject, both from academic perspective and for practical training. Body positioning and understanding gravity-assist form are really important .

Dynamic Stretching Exercises and Tips

Dynamic Stretching traditionally has been used in the athletic arena. But even everyday fitness, and weekend warriors need to use the this type of stretching. If you’re not an athlete you need to wake up muscles and stretch in a dynamic fashion too.

The Dynamic Stretching section will deliver content for many populations of people. Here you will learn the how to, why, when, where, for who of dynamic stretching.

Take your stretching and performance to new levels by incorporating this critical aspect of stretching in your day to day programs.

Check out the helpful resources and tips sections below to expand your knowledge.

Before starting your dynamic stretching routine read the

Dynamic Stretching Foundations

article.

 

Really all you need to start training. I mostly do 5mins of over/unders, jumping jacks and walking ground touches.

The Cerutty Legend “We can become what we believe we can become”

Excerpted from http://forums.glenhuntly-athletics.com and very close to what I prity much try to achieve in my current weight training workout. I mostly do single-leg excersises and low reps. Upper body bent-presses, push-presses, dumbbell snatches, chin-ups, pull-ups, some dips, all body-weight, lots of push-ups, mostly kuckle-style with one leg raised.  My heavy lift is only the deadlift and variations: farmer’s walk, single-hand barbell and sumo (wide-leg).

Two areas where Cerutty was particularly innovative were the use of weights and diet.

Percy saw strength training as essential to a runner’s development. He blew the myth that lifting heavy weights made and athlete bulky and slow. He advocated heavy weights with low repetitions.

The starting weight was what an athlete could move six times, but not ten (except for the dead lift). As soon as the athlete could move the weight ten times, the weight to be lifted was increased. Also, it was not uncommon for reps of two or three to be practiced.

The basic exercises were as follow: the snatch (to warm up, with a quarter to a third of the athlete’s weight), the rowing motion, military press, bench press, curls, the dead lift and one handed swings. The starting weight for the dead lift should be that the athlete can lift twenty times. This weight is lifted in three sets of ten.

Other weight lifting exercises were included, as were sit ups, chin ups and press ups. Sand hills, hills and stair climbing were preferred over weights to make the legs stronger.

His view on diet, as it was on most things, was strict and uncompromising. Raw, unrefined and unprocessed was how Cerutty liked his food. Rolled oats, dried fruits, fruit, vegetables, fish, water (litres each day), milk, nuts and a little meat were the basis of the diet. “Tasty” dishes and processed white bread were avoided. The food was predominantly uncooked.

Much of what is common knowledge and accepted these days was advocated fifty years ago by Cerutty.

 

Ode to Inverse Problems

Deep into the night and before calling it a day for today (disgusting rhyme but “lasciamo stare“) this is one of my geek-break-musing from actual work. The topic is a fascinating family of mathematical problems called “inverse problems”.  Wikipedia is a good place to get some more formal information but to make it really short here is a definition by example: 2+4=6, no doubt about it and this constitutes our “forward problem”, i.e. given a defined input we calculate a unique result; but what if some one asked to find out what you had to add up to get 6 but had no way to ask you or otherwise determine the exact combination? There are 4 different combinations to get 6 by adding two numbers and even more if you can add more than that, so how can you say? Well you can’t really and this is what makes an “inverse problem”, i.e. when you are trying to deduce the right answer from a pool of equally plausible alternatives. Welcome to the mathematical equivalent of delusion.  Now for the necessary soundtrack I will go for something very mathematical and at the same time delusional: enter sandman in the form of Gould.

 

In the very essence this is an area of applied mathematics but us lowly engineers sneak in, as always, to muddle elegant theory into crude and practical results. The later, the muddle bit, is in a broader sense the topic of my doctoral dissertation.  In my thesis I look into the problems arising in the stochastic reconstruction of random heterogeneous materials, like porous rocks for instance.  In simple terms I ma trying to come up with ways to get from a statistical description of 2D images to a fully 3D representation of the material that is true to the very nature of the original. Now, how can you describe statistically a 2D image? This is hard if you think in terms of a complex full colour image but if you picture  a simple black & white checkerboard this might become easier to grasp. Such a

El Tunel
El Tunel

 pattern can easily be translated to some rule (read statistic) that simply says “every 1 step of 10cm paint a black square, immediately followed by the same in white and then repeat  until you have reached so-and-so dimensions”. This is the recipe to make a black-and-white Rubik-type of cube were each sub-cube is of alternate colour. This is the idea that is applied to complex heterogeneous materials, a nasty term that means “something like a (natural) sponge, all irregular and weird but also the same way weird no matter which way you look at it”.  Now that we have established our toolbox of statistical descriptors we can venture to the real world. This methodology suffers from a serious practical limitation: it is not computationally feasible and to an extend even theoretically possible to have a complete statistical description of the intricate morphology of a complex material just by examining 2D sections of it. As always the mathematicians did their brilliant part and then we engineers started cutting corners and trying to fit our need to the delusional nature of this endeavour. My contribution, more like a mashup really, was to pick-and-choose ways to improve getting to a realistic representation of the real material by (in effect) cheating.  The “cheat”  consist of some educated guesses that use previously know information on how nature or industry generates/constructs a material and use this information to guide our solution algorithm through the maze of multiple plausible solutions to the one like the actual material we are trying to recreate. I’ve written about 180 pages of instructions manual to practising (dis)illusionists, called it a thesis and hope to get a PhD out of it the 17-Feb-09.

To end this musing I want to draw the attention to an intriguing and very personal experience of  inverse problems, that is learning from experience. Now at this point a disclaimer is of order; I am going to misuse and abuse scientific terms a little to make this artsy-fartsy, literary ending sound pompous. Don’t buy it, it is just fluff with no substance but I can’t resist making analogies out of analogies.  Think about it every time you are trying make a rational choice based on previous experience. What you  (we)  are really trying to solve is a horribly inverse problem. We are trying to estimate a new state of future affairs based on the (arguably) incomplete evaluation of past events, a classic in parameter estimation for those versed in reaction engineering. Now how much this helps when getting into an argument with your concubitus is another story and I wish you my best of luck!

Marketing advice to Twitter

Now don’t get me serious on this. I am an engineer by training and only worked in R&D so marketing is something I only read about and never actually practised. So, again this is just a musing on my beloved new social web tool or micro-blogging or whatever-makes-the-poets-happy you wanna  call it.  Please you people on Twitter inc. don’t fail! Make sure that in these difficult times you end up with a viable revenue stream to keep the service alive.  Now to my naif suggestions that could also be read as genuine questions to satisfy my curiosity.

1. Set up a “pro” or if you don’t like the connotations a “plus” type of account were you get a tick next to your name (say @mgpolitis +plus) and charge a pettiness for it, say 5 USD per year via paypal or similar.  For some icing in the cake through non-cost options in the deal like extra templates only for “+plus” users, more space for the short bio field in the user profile or any silly perk you can come up to that in reality costs zilch.

2. Set up a more professional offering with one-click backup and restore account options, added features like transparent user switch off (a.k.a. “muting”: removing the updates of  selected followers without un-following them), click and pick thematic group creation and charge even more for this.

Now this is just what I came up with in some milliscoble worth of my time. I am pretty sure you have brilliant people working for you. Can you please explain to me why on earth you are not doing even the most obvious to raise some money? Please, I am really interested because it is impossible for me (I said I’m an R&D Chemical Engineer) to understand why you are not doing it.

thank you!

taking a break to talk to myself

“In the internet no one knows you are a dog”, this was the defining moment of the proto-internet, the one before web 2.0 shenanigans that really transformed  the way we interact with the medium. This post is an almost surrealistic automated-writing type of musing that is not fact-checked and pretends to be my idea of having a break from actual work to do something relaxing.  Yes, for me this is actually relaxing, I’m a geek you see… Since every self-respecting brake needs a song, I am starting with a taste of Mina in a monumental live cover of Lucio Battisti’s “Io vivro”.  

I’ve been around since the beginning of the web as we know it, seen the ‘dogs’ chatting, the ‘personal web page’ era and the return of the blogs (they were relational databases of html archives, hand-coded by super-geeks, at their conception).  But what really changed everything was facebook, the teenage, hormonal and in-your-face uber-popular eponymous-by-explicit-choice web experience. By all means FB was not there first but as always the winner takes all the credit but the concept applies equally to friendster, orkut and other ‘social media’.  The implications are profound and moving to a virtual world with all the “stone age” social constructs is a profound shift in human evolution of co-operative interactions. As it is expected, this also makes Orwellian scenarios a scary prospect and marketing based on data-mining user habits and real-life choices a very appealing tool for all sorts of products, not always tangible but also political or ideological. If we sprinkle some twitter on this and look at this time-shifted, cached, instant peer-to-peer communication network the effect can be transformative in many ways.  I think of politics and participatory democracy but this is drab and Cornelious Castoriadis already preached about technology enabling the return of direct citizen democracy back in the ’80.

As a more fun closing to this musing and as my 30min brake comes to an end, I was thinking of the way eponymous web transforms people networks, how it can complement, extend and enhance the way you share a moment with your kid that studies abroad, with your wife while you are away and sneak a tweet of two or even how you actually create or add-to your network of friends, those of the real-life-variety, those that you have a drink with.  The parting song of this musing I feel like it must be  King Crimson’s Epitaph cause “Knowledge is a deadly friend | When no one sets the rules”; but sod the lyrics, the guitar part is just mind-blowing.

Addentum: on a second thought Billy Bragg’s “Greetings to the New Brunette” from Talking with the taxman about poetry, is what this piece of verbal diarrhea needs for a soundtrack