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The Physics of ChiRunning, Lean … Analysis

This is the first of a few posts on the subject of physics in the running gait cycle. This post is a little long with some more technical content but my intent was to keep a potentially complex subject simple. A previous post (The Physics of ChiRunning, Lean) provided a way to feel the pull of gravity on an aligned column. If you can feel this effect and it works for you, leave it at that and keep practicing. If you want to dig a little deeper to see what might be causing this effect, then this and other posts here may be helpful to you.

Recently a number of opinions have surfaced online that oppose this body sense of falling forward and state gravity does not contribute to forward motion in running or walking. Who is making these statements is not really important. In general their message is that a force only moves an object in the direction of “that” force; and since gravity is a vertical force, it cannot contribute to horizontal motion.

This is a rather simplistic view of physics. Specifically, Newton’s First and Second Laws refer to a NET force on an object not a single force on an object. And so what if there are other forces also acting on the runner in addition to gravity? Newton suggests that would change the overall NET force on the object and therefore the effect on motion.

Physics problems such as this are usually analyzed based on Newton’s laws while stating any assumptions. The physics analysis is a simple “free body diagram” which shows all the forces on the object so that the resulting NET force can be determined. But the opinions presented include no such physics analysis. Without the analysis, they are simply passing off their opinion as fact.

[Note: There is one case of a physics analysis available (ref *) for a fee. In My opinion, the free body diagram included there is hardly complete nor are the stated assumptions proven to be true for all runners. More on this below.]

Here are just a few of these opinions being stated as fact:

  • “All three said that gravity can do nothing to improve your running efficiency on a flat surface. That’s because gravity provides no horizontal force; it simply pulls you back down to the earth.”
  • “… the net effect of gravity must be zero in the horizontal direction.”
  • “Gravity does not give forward momentum.”
  • “There can be no net gain from gravity in running and it can’t make you go forward.”
  • “We are not propelled forward by something that pulls us down.”

Here is an analogy to put the opinion “a force only moves an object in the direction of that force” into perspective. They are saying:

  • Only waterfalls exist in nature, but not streams or rivers … and we know that is not true.
  • But in some cases the experts suggest you can run downhill aided by gravity.

OK, so let’s take another analogy to put “a force only moves an object in the direction of that force” in perspective. They are also suggesting:

  • Sailboats only sail in the same direction as the wind.
  • And if the wind is from the north, the sailboat will only move directly to the south.

But we know this is also not true, and that a sailboat can sail at many angles to the force (wind). Sailing downwind might be similar in concept to running downhill. But sailboats can also sail perpendicular to the wind, and they can even sail upwind.

Now they will probably say those analogies are not the same as a falling person. I agree these are analogies; and that water is different from solid material and the forces on a sailboat are considerably more complex. I am suggesting that they are the same in concept. Apply gravity to the water or wind to the sailboat and it can move in a different direction. Remove “that” force and it stops moving in that different direction. So it is possible for a force to result in motion in another direction.

A Physics Analysis for Your Consideration

So here is an analysis for you to consider which includes some basic physics with assumptions stated. The analysis is presented knowing that although the body is a complex machine, simplifying usually provides some insight into what might be possible. As above, the physics analysis is a simple “free body diagram” which shows all the forces on the object so that the resulting NET force can be determined. The NET force on the object determines the resulting effect on motion.

Basic Column

First let’s look at a basic column moving from vertical to slightly tilted forward in the following diagram (click to enlarge).

Assumptions: The force of the air on the column as it moves is non-zero but considered negligible for this analysis. The contact point with the ground is stationary with friction and the base acts like a fluid hinge with no resistance.

Vertical Column:

  • The vertical force of gravity G pulls down on the column, represented at its center of mass (COM).
  • The ground pushes up on the column, called the normal force N.
  • The two forces oppose each other and there is no NET force on the column.

Leaning Column:

  • In a slightly leaned position, the vertical force of gravity still pulls down on the column at its center of mass (COM). This force can be represented as two force vectors, one force C acting down the column to the ground and one force P acting perpendicular to the column.
  • The ground pushes up on the column, again called the normal force N.
  • A force of friction F acts against the component of force C to the left to keep the base stationary.
  • The combination of N + F oppose the force down the column C keeping the base stationary (see inset diagram detail).
  • The force P perpendicular to the column becomes the NET force pulling the column down AND forward about the stationary fulcrum at the base of the column. The column loses COM height as it moves to the right.

The application question becomes: Did the column, or tree, or broomstick move horizontally to the right under the force of gravity? My answer is yes; the column’s center of mass moved to the right under the force of gravity. If the force of gravity did not exist then the column would not move to the right.

What if this same scenario could exist within a runner’s gait cycle? Meaning what if a runner’s “position” resulted in gravity pulling the runner forward? And what if this position and subtle effect could be repeated over and over with each step?

Now some opinions state this is true but the runner’s only choice is to fall on their face. This I agree is true if the runner does not:

  • Turn over their feet fast enough to keep up with their forward fall.
  • Regain the minimal center of mass height lost as the column falls forward with each step.

Runners’s Column

Now let’s look at a runner’s “column” moving from vertical to slightly forward from a relaxed hinge at the ankle in the following diagram (click to enlarge).

Assumptions: The force of the air on the runner as it moves forward is non-zero but considered negligible for this analysis. The contact point with the ground is stationary with friction and the ankle acts like a fluid hinge with limited resistance.

From a vertical to slight forward position:

  • The left foot lands as close to under the body’s center of mass (COM) as possible, as shown with the dotted outline.
  • A moment later the body’s position and weight has moved over the foot and is “loaded” on structure.
  • The body’s aligned column subtly falls forward losing a minimal center of mass height as it moves forward.

A Subtle Fall Gait Cycle Option?

Putting this scenario into a gait cycle might look like the following diagrams (click to enlarge). The images are not equally sequenced nor is it suggesting an absolute representation of what an individual person’s gait cycle might look like. The images depict a landing/loading position, a falling position, an end of fall position, a foot peel off position and a flight position.

  • From Landing through the End of Fall, there is a slight decrease in center of mass height.
  • From End of Fall position to/through Peel Off and into Flight, there is a recovery of center of mass height.

The Question: Is it possible for this (half) gait cycle to happen? Or more importantly, is it absolutely IMPOSSIBLE for this gait cycle to happen? You get to decide of course … but what if this is possible for you? That would mean that your running could be a series of micro-falls and micro-catches made possible by a SUBTLE forward position, relaxation in the lower leg/ankle and a SUBTLE recovery of your COM height lost on each micro-fall. But how can you regain COM height?

There are at least six OPTIONS the body might use to regain its height. Here are just four of them:

  • Actively pushing off late in the gait cycle with toes/lower legs. This is potentially difficult to time after the fall, plus any lower leg effort tends to create resistance (tension) to a forward fall. This option is not suggested. But some experts suggest this is absolutely required to prevent falling on your face …
  • Passive arch and Achilles recoil
  • Straightening the knee with the big muscles of the upper leg, hip and core before peel off.
  • Swinging the return leg forward. With practice this can occur passively via a full body recoil after pelvic rotation.
  • [The remaining two are more advanced and may be the subject of a future post.]

I don’t know about you but I would much rather regain a little COM height passively or by using big muscles than propel myself forward and upward (like a pogo stick) with the small muscles of the lower leg.

Secondary Opposing Opinion

Secondary to the opinions stated above, some experts specifically say this subtle fall gait cycle is not possible, including here (ref *). These positions assume that “our lowest point in our stride is at mid stance when the knee is bent the most” and “from mid stance to terminal stance [lift off] in running, the height of the athlete’s COM is increasing.” This, they say, prevents us from falling forward since we have to fall down and forward. If we are already at our lowest point before we fall or our height is increasing, then we can’t be falling. True, but when does the subtle fall occur … before or after mid stance? I guess this depends on your definition of “mid” stance and the whole gait cycle.

What If? As in the diagram above:

  • It were possible to maintain a slightly bent (“soft”) knee limiting additional knee “bend” from landing through subtle fall?
  • And, the subtle fall occurs before “mid” stance? Then the lowest point in our stride would be at mid stance, but not because our knee is bent the most. It is the lowest point in our stride because it is at the end of our subtle fall.

ChiRunning® suggests just this scenario maintaining a tall posture, maintaining a “soft” knee and a quick cadence. A quick cadence reduces the opportunity to bend or “sag” the knee. But for the subtle fall to work you have to allow it to happen. Forcing it or controlling it negates much of the opportunity to fall and its effect. In general, it is much less lean than you think and much more about relaxing. Specifically, relaxing the lower legs and peeling the feet from the ground.

So I repeat, is it possible for the above subtle fall gait cycle to happen? Or again more importantly, is it absolutely IMPOSSIBLE for this subtle fall gait cycle to happen? This gait cycle is what it feels like to me. It feels like a series of subtle micro-falls and micro-catches to create and maintain momentum. But as I said here (The Physics of ChiRunning, Lean), if you don’t think gravity can help you, it can’t. If you do think gravity can help you, it probably can. Your choice.

Next on this blog we will consider this subtle fall gait cycle related specifically to a main goal … creating and maintaining momentum, and what simple physics might have to say about that.

[Please comment if you want to share your thoughts. If you have an alternate view on the physics analysis, please either a) identify a specific physics law that is being broken here or b) provide a reference to YOUR complete free body diagram analysis with assumptions if you want your comment to be posted.]

Ref: (* http://www.tandfonline.com/doi/abs/10.1080/14763140802255804)

[See the Physics Resource Page for more information.]

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David Stretanski is a holistic health, fitness and wellness coach – and Certified ChiRunning®/ChiWalking® Instructor.  For more information on David, please see his About MeContact page or his website at http://www.eChiFitness.com.

ChiRunning® and ChiWalking® are registered trademarks of ChiLiving, Inc.

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Posted on Thursday, May. 10th 2012 11:17 AM | by echifitness | in All, ChiRunning, Gravity | No Comments »

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