GRV: Lavillenie - From Stall Swing to World Record

This is a forum to discuss advanced pole vaulting techniques. If you are in high school you should probably not be posting or replying to topics here, but do read and learn.
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby Tim McMichael » Sat Jul 12, 2014 3:06 am

Thank you so much for this excellent work, PVstudent. It is very much appreciated.

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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby PVstudent » Wed Jul 23, 2014 1:06 pm

This post continues to establish the mechanical factors that will be used to underpin the comparative descriptive qualitative analysis of the Segei Bubka Technique versus that of Renaud Lavillenie that will eventually follow.
Vaulter weight force (-mg) induces varying magnitudes of torques about the Z axis to the XY plane of motion in the pole support phase of the vault from take-off to final pole release specifically is addressed in this post.

Guiseppe Gibilisco World Champion Statics Analysis Ist Phase Pole Support 1.jpg
Guiseppe Gibilisco World Champion Statics Analysis Ist Phase Pole Support 1.jpg (101.97 KiB) Viewed 9715 times


A vaulter must initially create counteracting torques to those produced by the vaulter’s varying weight force during the first phase of pole support.
During this time the vaulter must also apply, through muscular effort, sufficient force and torque magnitudes directed in such a manner that they impart impulses to assist bending and rotating the pole about the total system global axes located in the deepest part of the planting box.

The vaulter selects the specific body actions (precise coupled sequencing of both the upper and lower limbs momenta transfer exchanges via primarily wrist, shoulder and hip joint complexes) that develops, sustains and amplifies linear translation and rotational displacements of the total system, vaulter plus pole centre of mass (COMsys), simultaneously about Local and Global Principal Axes.

The amplitude and power of the vaulter’s total body pendular swing produce the tangential forces necessary to continue further pole bending and deflection laterally.

Tangential force and power of the pole recoil in the 2nd phase of pole support coupled with additional muscular work from the vaulter create the necessary net impulse to project the vaulter from the top grip into the 2nd takeoff and flight phases of the vault.

The vaulter has to generate and time momentum exchanges throughout the whole body pendular swing action sequence that propel the total system centre of mass (COMsys) along an upward and forward directed curvilinear pathway in the XY (Sagittal) plane of motion.

In the 1st phase of pole support the vaulter’s lower body and torso swing, pivoting about the hand grips, maintains the desired plane of travel by generating continuous propulsive forces and torques to partially raise the vaulter’s centre of mass (COMvaulter) to the hand grip locations on the pole.
Despite the ongoing “inversion process” the vaulter’s centre of mass (COMvaulter) is suspended at a height level slightly below both hands when maximum pole bend occurs.

Throughout the first phase of pole support the vaulter is considered to be a physical compound pendulum mass swinging about the grip pivots with a minimum shortening pendulum COMvaulter radial length as maximum pole bend occurs.

In relation to the Global Pivot point at the pole tip, the total system can be considered as an inverted physical compound pendulum mass (COMsys) with variable rate of shortening radial length from takeoff till maximum pole bend is reached.

The combined weight of the vaulter and the pole induces a variable torque resisting the rotational motion of the COMsys, about the(Transverse (Z) / Lateral (Z)) Global Axis. The varying resisting torque due to vaulter weight force acts throughout the pole support phases until the pole is straight (pole chord and pole longitudinal axis are coincident) and has rotated to a position perpendicular to the pole tip.

On pole movement in the direction beyond the vertical from the pole tip (angle greater than 90 degrees to the horizontal) and in the direction of the YZ (Lateral / Transverse) plane of the cross bar the COMsys induced torque assists the continuation of rotation in the Sagittal plane about the Global Z axis until final pole release.

Total system combined weight induced torque about the local axis increases in proportion to the horizontal displacement distance the COMsys is in advance of the the top grip pivot point during the 1st phase of pole support (takeoff to maximum pole bend).
How the bodyweight of the vaulter is used to generate assisting or resisting torques to rotate about the top grip hand (Local Axis) during the second phase of pole support is subject to more detailed analysis in a later post.

A Simplified Statics Analysis of the vaulter, as a single rigid mass suspended below the grips on the pole, will be used to clarify and elaborate some more detailed consideration of the role of weight force in 1st phase of pole support.What follows is my attempt to demonstrate the possible role of the arm tension forces due to gravitational effects acting on the vaulter in static suspension beneath both hand grips attached to an inclined pole.

The pole is considered as a long slender cylindrical tubular cantilever beam, clamped at the tip with an initial inclination angle to the horizontal represented by the black line AB in the following sketch .

Guiseppe Gibilisco World Champion Statics Analysis Ist Phase Pole Support 2.jpg
Guiseppe Gibilisco World Champion Statics Analysis Ist Phase Pole Support 2.jpg (105.65 KiB) Viewed 9715 times


A specific analysis of the instant in time depicted for Guiseppe Gibilisco as position 5 in the previous diagram and sketch above follows.
The role of the lower arm in counteracting the Moment of Force due to the vaulter’s weight (-mg) is first examined by analysis at instant 5 of the Guiseppe Gibilisco initial motion sequence following take-off.

Consider that the vaulter releases the lower grip (left hand grip release) whilst keeping his entire body as one fixed shaped rigid mass. The diagram above illustrates how the vaulter would rotate about the top grip wrist single pin pivot point until the net moments and forces acting become ZERO and equilibrium is achieved.The vaulter, when the equilibrium point is achieved, is assumed to be suspended motionless in the same rigid postural shape adopted at the instant the lower grip was released.

The Free Body Diagram clearly shows that at instant 5 the weight force of the vaulter causes a clockwise torque to rotate the vaulter in the direction of that torque on release of the lower arm grip.

The weight force (-mg) multiplied by the perpendicular distance (d1) induces a clockwise torque which rotates the vaulter’s rigid body about the pin axis of the top grip wrist joint when the lower grip on the pole is released.

The net sum of all torques is originally zero. When the grip is released the COMvaulter receives an angular impulse ( Average Torque multiplied by the Time during which the Average Torque acts) causing rotation about the top grip pivot point. Consequently the COMvaulter develops clockwise angular momentum about the pivot point. This angular momentum is in the same direction and proportion to the average magnitude of the torque until the instant the rigid body COMvaulter reaches a point located vertically below the pivot axis.

Due to the angular momentum (rotational inertia) developed in the clockwise downswing the COMvaulter continues in clockwise motion beyond this point into an upswing where the the vaulter’s bodyweight force creates an oppositely directly (anticlockwise) torque.

This counteracting torque acts until the angular momentum (rotational velocity (W) multiplied by moment of inertia (I)) is reduced to zero. At the instant the clockwise angular momentum reaches zero the COMvaulter clockwise motion upswing halts and the direction changes to anticlockwise due to gravitational torque.

The rigid body will continue to oscillate about the pivot point until some external forces such as friction, muscle activated increase of the wrist pin joint stiffness,air resistance or contact with an external object halts the oscillation.

When the weight force of the vaulter (-mg) in the negative direction (downward) is opposed in direction and magnitude, in the same straight line, by the pole reaction force in the positive (upward) direction the vaulter will have ceased to oscillate about the pivot and a state of equilibrium is reached.

Note: (Moment:the system is static or in a state of constant motion; Torque:the system is accelerating ie. Rotation speed is increasing /decreasing and or rotation direction changes).

Another simplified statics analysis of instant 5 in the Gibilisco vault sequence in phase 1 of the pole support gives an important insight as to the role the lower arm plays in relation to the vaulter’s weight induced torques (see following diagram).

Guiseppe Gibilisco World Champion Statics Analysis Ist Phase Pole Support 3.jpg
Guiseppe Gibilisco World Champion Statics Analysis Ist Phase Pole Support 3.jpg (100.06 KiB) Viewed 9715 times


Note: Only the effect of gravitational acceleration acting on the total body centre of mass of the vaulter is considered here.

The sketch and Free Body Diagram of the vaulter show the vaulter’s weight is supported by the tension forces acting via the arms due to the reaction forces of the pole.

The pole is assumed to be a long slender thin walled tubular cantilever beam with a fixed clamp at the tip in the planting box.

The vaulter is regarded as motionless (in equilibrium) and the COMvaulter is fixed in the position shown at time instant 5 in this part of the 1st phase of pole support.

The two primary assumptions being made are that (1) the vaulter is in equlibrium, and (2) the COMvaulter is that of a fixed shape rigid mass at this instant in time.

Using the data obtained from the video record and the specific mass / stature of Guiseppe Gibilisco the Free Body Diagram (FBD) for the vaulter the Tension Forces in the arms acting through a single pin joint axis at the right and left wrist and at the shoulder mid-point can be calculated.

Result of calculations

Tension force required in the upper grip limb (Tug) = 440N @ 55deg to left horizontal.
Tension force required in the lower grip limb (TLg) = 477N @ 58deg to right horizontal.
Vertical Component of Tension in the upper grip limb (Tugy) = 361N
Vertical Component of Tension in the lower grip limb (TLgy) = 404N
Total Bodyweight Force of the Vaulter (Mass 78kg x -9.81m/s/s) = -765N

Note:
1. The lower arm tension force is larger than that of the upper grip limb.

2. The vertical component of the lower grip limb tension force required to hold its portion of vaulter bodyweight is also larger than the upper grip limb.

3. The more the COMvaulter is advanced horizontally in front of the top grip pivot joint the greater the clockwise torque becomes due to vaulter body weight acting about that point.

4. Correspondingly more tension force vertical component in the lower grip arm is required to counteract the clockwise gravitational acceleration induced torque the further the COMvaulter is advanced horizontally forward of the top grip pivot point.

5. The clockwise torque is acting in effect to swing (rotate) the COMvaulter in the horizontally rearward direction. The anticlockwise torque is acting in effect to swing (rotate) the COMvaulter in the horizontally forward direction.

It is clear from diagrams 1 and 3 that the COMvaulter is horizontally well forward of the top grip pivot point when the vaulter’s toe tip breaks ground contact at take-off. These two simple statics analysis have revealed that some magnitude in the vertical component of the lower grip arm tension force is required at takeoff and act continuously throughout the 1st phase of pole support.

The lower grip vertical component of the tension is required to counteract the clockwise (motion resisting) torque due to the actual portion of the vaulters bodyweight exerted downward at this instant in time.

(Since the takeoff net vertical impulse is sufficient to generate vaulter plus pole vertical velocity in the positive (upward) direction and the mass of the vaulter plus pole is constant, the COMsys must have been accelerated in the direction opposite to that of negatively directed (downward) gravitational acceleration.

Hence the COMsys weight force will have a reduced magnitude for some time post takeoff.

Nevertheless, even this reduced bodyweight force will create a torque that has to be conteracted. Even though both arms provide tension forces to suspend the vaulter during the 1st phase of pole support, it is the torque from the vertical component of the tension in the lower grip limb that must provide the counteracting torque effect to that produced by vaulter’s varying weight force).


In the 1st phase of pole support it is concluded that the limb with the lower grip on the pole must have sufficient tension to:

(a) exert a pull force against the pole to counteract the undesirable effect of the COMsys weight force torque.
(b) assist accelerating the COMsys tangential velocity arising from the centripetal force of the vaulter whole body swing about both grips by exerting additional pull force against the pole.

The next post will examine Bubka’s technique in both phases of pole support.
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby altius » Wed Jul 23, 2014 5:08 pm

JG you have simply GOT to put this all together into a book/booklet. It is just too good to let wander around in the ether. :idea: :yes:
Its what you learn after you know it all that counts. John Wooden

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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby altius » Wed Jul 23, 2014 5:09 pm

Gorms - you have simply GOT to put this all together into a book/booklet. It is just too good to let it wander around in the ether. :idea: :yes:
Its what you learn after you know it all that counts. John Wooden

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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby altius » Sat Aug 02, 2014 9:12 am

Indeed you should! Lets have some support for the idea. :yes:
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby Tim McMichael » Sun Aug 10, 2014 1:15 pm

Absolutely! I would buy it in a heartbeat.

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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby PVstudent » Thu Aug 21, 2014 12:20 am

Thank you for positive support and I am now ready to prepare the ground to the comparative analysis of Bubka's and Lavillenie"s technical similarities and differences from a biomechanical perspective.

What follows are what I believe to be well accepted basic understandings of facts underpinning techniques in flexible pole vaulting for maximizing legal bar clearance height.

Bubka pole support phase objectives in pole vaul.jpg
Bubka pole support phase objectives in pole vaul.jpg (108.24 KiB) Viewed 9287 times


The diagram above summarizes the functional objectives to be achieved by the pole support phases of the pole vault.

The pole itself is the tool (Simple Machine) in the pole support phases that enables the vaulter to achieve the pole support objectives because it has the capacity to:

1 Change length under loading by tensile and compression forces applied to it (possesses "elastic spring" like properties).

2 Undergo a pendulum like rotation about a relatively fixed “ball type” end axis at one end whilst at the other the distributed mass of a vaulter is in suspension or is being supported.

3 Flex and rotate around the X,Y,Z axes of the relatively fixed pole tip load bearing point located in the planting box.

4 Store and release elastic potential energy that can rotate and translate the external load through large displacements when forced to rotate and "precess" due to the pole deflections and recoils. (Note: role of "pole precession" during pole recoil will be addressed later ... hitherto a not well understood aspect of the technique in the inversion and turn part of the 2nd phase of pole support!).

5 Transport the vaulter through a large horizontal distance forwards from the take-off whilst the pole chord shortens (penetration) to then project the vaulter load through an even larger vertical displacement and continue to maintain penetration but at a lesser rate.


The diagram below summarizes the 2D technical model of the Petrov-Bubka Pole Vault Pole support technique viewed in the XY plane.

Petrov - Bubka Technical Model Pole Support Phases 1 and 2.jpg
Petrov - Bubka Technical Model Pole Support Phases 1 and 2.jpg (84.43 KiB) Viewed 9287 times


Instants 1 to 4 define pole support Phase 1 defined as the instant of take-off until the instant of maximum pole bend.

Instant 4 is identified from subjectively assessed observation that recognizes the start of pole recoil and uses photographic images recording of the instant immediately prior to this as being Maximum Pole Bend which concludes Phase 1 and commences Phase 2.

Phase 2 of pole support is defined as start of pole recoil from maximum pole bend until final pole release.

The diagram is made from my drawings of the critical instants (video snapshots) that define the two phases of pole support.

Note the relatively larger 2nd phase vertical displacement achieved by the vaulter’s centre of mass (COMvaulter) compared to the horizontal displacement obtained in the 1st phase of pole support.

The total vertical displacement of the vaulter's COM is greater than the total horizontal displacement in pole support. This emphasizes the superiority of the flexible pole for pole vaulting with longer grip lengths and take-off point distance locations with respect to the planting box lowest point of the rear wall.

Without the “spring stiffness” flex capabilities, low mass to length and cross section ratios, long grip length with low pole carry torques of the poles currently used by both genders of elite pole vaulters to obtain the heights they achieve would not be practically feasible.

Radius of top hand to COM in the phases of the vault.jpg
Radius of top hand to COM in the phases of the vault.jpg (84.67 KiB) Viewed 9287 times


The pictures above illustrate the technique challenge the vaulter must meet in pulling and pushing the COM considered as a compound physical pendulum rotating about an axis located at the top grip hand in the pole support phases of vaulting.

Centripetal Force induced “Pull” swing rotation continues from take-off through maximum pole bend until the vaulter COM passes above the horizontal level of the top hand grip hand whereupon the vaulter-pole interaction "Pushes" the COM upwards until final pole release.

Whilst the COMvaulter is above the level of the top hand the vaulter weight force induced torque assists the pole rotation about its load bearing point in the box such that the pole chord attains the vertical position by the time the vaulter “Pushing” action is completed at final pole release.

The challenge considerations focussed on the vaulter doing work on the pole is just part of the demand requirement of flexible pole vaulting.

The total system has to be propelled (driven) and in the next posts this challenge will be introduced to establish a simplifying framework of understanding of the inverted and suspended double pendulum system "impulsive" forces and torques necessary to overcome non conservative forces in the pole support phases of a vault.
(continued…)
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby dbarrero » Thu Aug 21, 2014 5:44 am

What an amazing information we can find on pvp! Thanks PVstudent. Always search in forum new posts from you :yes:

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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby PVstudent » Sun Aug 31, 2014 7:57 am

Analyses based on energy considerations, because they involve mere scalar quantities, shed little light on the time, spatial location elements of the vaulter efforts during the pole support phases of the vault.

Energy only analyses are inadequate in informing coaches and vaulters as to the how, when, where and what actions in the vaulting sequence the vaulter should carry out to generate the muscular effort and momentum changing impulses that will achieve optimal propulsion and maintenance of the motion of the total system COM.

The vaulter’s primary challenge, in pole support, is to raise the total system COM and reach its “ideal” of 90 degree position perpendicular to the horizontal runway surface with the pole having returned to its original geometrical shape and length when the vaulter, fully inverted, faces towards the YZ plane of the cross bar at arm’s length above the final pole release point.

In 21st century pole vaulting, the pole makes a significant essential contribution to athlete performance enhancement. Improved pole design along with the materials used in their construction have increased pole capabilities to withstand larger bending, shear and torsion stresses whilst preserving and or increasing the ability of the pole to return rapidly to its original geometric shape as unloading takes place.

It is beyond the scope of this particular discussion to make an analysis of the differences in the way poles, of similar flexural stiffness at a particular vaulter’s weight force and chosen grip length actually performs in real life practice.

The use of the “wrapping” of the fibre glass sheets on the mandrel form used to manufacture fibre glass poles compared to the “alternating clock and anticlockwise helical coil carbon fibre weave“ of the material used for carbon poles can differentially affect pole performance when being used by any particular individual vaulter.

The subtleties of these differences are very important in practice and can lead initially to performance decrements and technical errors when making the “switch” from fibre glass to carbon pole type or vice versa. This is especially the case when the vaulter makes a pole type switch-over having already become an accomplished elite pole vaulter using the other type of pole.

The diagram below summarizes the essential features of load deflection and recoil of a vaulting pole due to flexural stiffness that the vaulter can exploit when using the pole as a vaulting tool.

Hooke's Law and Pole Spring Stiffness 1.jpg
Hooke's Law and Pole Spring Stiffness 1.jpg (81.89 KiB) Viewed 9072 times


The diagram represents the compression and tension conditions in the pole at about the instant of max pole bend.

The pole operates as a simple lever machine powered by the actions of the vaulter. Behaving as a “Hookean Type Elastic Spring” the pole assists the vaulter to achieve a “ballistic projection” of their COM located at a “desired optimal” position above the final grip release point achieved at the end of the recoil phase of the pole action. At this instant the vaulter's body orientation and configuration should enable the magnitude and direction of vaulter COM velocity to optimise the flight trajectory to successfully negotiate a legal bar clearance.

The speed with which the tensile forces return the pole to its uncompressed state is the key determinant contribution from the pole to the final release velocity achieved by the vaulter’s COM at pole release.

Inversion at Commencement of the 2nd pole vault take-off phase prior to ballistic flight on pole release.jpg
Inversion at Commencement of the 2nd pole vault take-off phase prior to ballistic flight on pole release.jpg (89.56 KiB) Viewed 9072 times


The diagram above shows some examples of the vaulter’s body to pole positioning at the start of the pole vaulter force and torque application interaction that produce the final “ballistic impulse” thrust from the pole to the vaulter. The final projection part of phase 2 of pole support requires that the pole recoil should initially pull the vaulter’s weight upwards and then as the vaulter’s COM passes the level of the top hand grip maintain the continuous upward motion of the vaulter’s weight by pushing it up from below the COM.

The continuity of force application is dependent upon the rate of pole recoil and the coordination and timing of the muscular effort impulse being applied downward by the vaulter to oppose the motion of pole recoil.

Considerable acquired technique mastery of the inversion “pull, turn and push action,” along with significant “power” development and physical conditioning of arm, shoulder joint and girdle muscle-skeletal functional adaptation is required to successfully accomplish the momentum transfer exchange involved in this critical 2nd take-off phase of a vault performance.

Unlike the pole the vaulter's muscular system is a highly non linear viscously damped force/torque generating system that allows the musculoskeletal system to be tuned to propel body segments, control body segment rigidity (stiffness) as well as being able to absorb and dissipate undesirable externally delivered forces or momentum impulses applied to the vaulter body. The vaulter is an adaptive learning biological organism controlled by purposefully directed intentional goal seeking behaviours that emerge from reflexive and learned interactions of intricate autonomous and voluntary substrates of sensory, nervous and muscular action subsystems.

In what follows I ask a series of questions in regard to pole function and invite the reader to consider what their own answers reveal in relation to what the vaulter needs to be able to do to exploit the pole and achieve the primary objective of the second take-off. I am leaving it to readers to form their own views as to the answers.

( Next Post...)
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby PVstudent » Sun Aug 31, 2014 9:27 am

Who better to illustrate the operation of Robert Hooke’s Law relating to the pole acting as a spring mechanism than Steve Hooker Australia’s former Olympic and World Champion Pole Vaulter!

Hooke's Law and Pole Spring Stiffness.jpg
Hooke's Law and Pole Spring Stiffness.jpg (122.52 KiB) Viewed 9067 times


In the photo and the diagram insert showing the pole attached to the total system COM note that:

1. The pole plus attached mass is an Inverted pendulum.

2. The pole-mass single lever system has 3 possible positions of equilibrium (a) lying on the ground to the right of the pole tip pivot point (b) at 90 degrees to the ground right horizontal (c) lying on the ground to the left of the pole tip pivot point.

3. Gravity will produce a torque on the pole-mass lever inverted pendulum system that will accelerate it clockwise about the pole tip axis as it is moved to the second position of equilibrium (Resists pendulum motion in the anticlockwise direction).

4. Gravity will produce a torque on the pole-mass lever system pendulum system that accelerate it anticlockwise about the pole tip axis from the vertical equilibrium point towards the third position of equilibrium (Assists pendulum motion in the anticlockwise direction).

5. Since the vaulter is attached to the pole by the hands (Contact points axis of rotation is external to the vaulter’s whole body COM) and undergoes various distributions of body mass during the vault with respect to the external axis at the hands the vaulter’s moment of inertia (I) about this axis is determined by the vaulter’s mass (m) and “radius of gyration” (K) ( I = m(K x K ) vaulter moment of inertia (I) is mass x radius of gyration (K) squared) and not the radius length to the COM as is often assumed.

6. It is the “radius of gyration length (K)” that should be used in any determination of the pendulum length (L vaulter) from the hand grip axis to the centre of the distributed segmental masses (COM vaulter) that comprise the vaulter’s entire body. This is because the vaulter can be considered as a “real” physical compound pendulum moving about an axis that is not directed through a Cardinal / Principal axis passing through the total body mass centre.

Hooke's Law and Pole Spring Stiffness 2.jpg
Hooke's Law and Pole Spring Stiffness 2.jpg (112.03 KiB) Viewed 9067 times


The next post will consider some of the mechanisms available to enable the vaulter to exploit longer grip lengths on the pole and yet achieve effective transfer of momentum from the vaulter to the pole on completion of the 1st take-off.
I will also introduce the double-pendulum propulsion challenges in the first phase of pole support which will conclude the setting up of an agreed framework upon which subsequent discussions will rely.

Having set up the framework I then hope to be able to proceed to build a qualitative technical comparative analysis of similarities and differences in pole vault techniques used by Sergei Bubka and Renaud Lavillenie.

Caveats to future discussion

It is unfortunately not possible, for me, to use verified quantitative comparative data for both vaulters (Bubka v Lavillenie: I don’t possess the necessary facts) and therefore I consider it not possible to make objective evidence based comparison in this particular “vaulter relative efficiency” issue.

I am therefore forced by lack of objective evidence to delimit future discussion as being purely qualitative.

Bearing this in mind I will be attempting to inform the Bubka v Lavillenie comparisons by applying established principles of mechanics and biomechanics to some selected visual evidence source records published in the public domain.
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby PVstudent » Thu Sep 04, 2014 2:18 am

The next two diagrams illustrate how to achieve preparation effectiveness to minimize Momentum Exchange Transmission Losses from vaulter to the pole (and vice versa) at the instant the toes of the take-off foot break ground contact.

In the first two diagrams below please note that what is being schematically represented is that the total system COM is being accelerated primarily by linear momentum (P) which is simply the total system centre of mass (COM total system) multiplied by its linear velocity (v) and that this COM is experiencing predominantly horizontally directed translation and at the same time receives a lesser amount of vertical translation.

The initiating source of this acceleration is the net impulse (average ground reaction force multiplied by the total time the ground reaction force acts) which as a vector quantity must be a major determinant of the impulse magnitude and direction of the resultant COM total system acceleration when added vectorially to the net effects of other external average forces multiplied by the time they act (for example net combined vaulter + pole weight impulse) at the instant depicted in the diagram.

Consequently the action line of the momentum (linear inertia) of the COM total system is directed in a linear path at an angle phi to the horizontal at the instant just before completion of the take-off ground contact.

The resultant impulse acting on the total system combined COM (Vaulter + Pole) is observed to change with reference to an inertial three dimensional (3-D) coordinate reference frame located at the pole tip contact point in the deepest level of the pole planting box.

The outcome of the COM total system collision with the earth at this contact reference point allows the post impact motion of the vaulter-pole COM to be determined with respect to the post impact inertial reference of the earth because the post impact inertial motion of the earth is infinitesimally small compared to that of the Vaulter + Pole total system’s COM.

The motion of the earth post impact is considered in this case to be Zero at the origin of the 3-D reference fame. Any linear or angular displacement observed to take place with respect to this 3-D origin point in the reference frame can thus allow the changes in the path followed by the total system COM (vaulter + pole) to be determined.

The first (velocity) and second (acceleration) derivatives of change in COM path displacements in the time taken for the observed changes to take place enables the forces and torques causing these changes to be calculated.

Although the impact between the Vaulter + Pole COM and the mass of the earth via the pole tip in the planting box must conserve energy and momentum it is not an “ideal” elastic collision in that some of the energy and momentum before impact is dissipated in the collision as noise, heat due to friction losses and imperfect elastic restitution characteristic of the material properties of the pole, the vaulter’s body and the contact interface of the planting box with the mass of the earth.

The challenge to the vaulter during the collision is to minimize any unnecessary dissipation of the energy and momentum during energy and momentum exchanges between the bodies (masses) involved in the impact.

Forces Sketch instant before pole tip rear wall impact and completion of take - off Vaulter A .jpg
Forces Sketch instant before pole tip rear wall impact and completion of take - off Vaulter A .jpg (90.6 KiB) Viewed 8973 times


Forces Sketch instant before pole tip rear wall impact and completion of take - off Vaulter B.jpg
Forces Sketch instant before pole tip rear wall impact and completion of take - off Vaulter B.jpg (91.38 KiB) Viewed 8973 times


Error correction diagram directly above: "COM dB" should read "COM dA in front of the Top Hand"

As you examine the two diagrams readers should bear in mind:

1 It is the same vaulter who has position A and Position B an instant just prior to take - off which is defined to occur the instant the toes of the take-off foot breaks ground contact.

2 All the external force magnitudes remain the same for the vaulter in assuming body orientation and positions A and B.

3 In position B due to the higher height (YB) location of the total system centre of mass above the ground the angle of the average ground contact force at this instant must be slightly higher which in turn increases the angle phi of the resultant final momentum at the instant shown.

4 The angle psy, the angle coloured green in the diagrams, determines the magnitude of the torque due to vaulter + pole combined mass acted upon by gravitational acceleration (system weight) by increasing or decreasing its moment arm (dA) to axis A. In position B there is less gravitational (weight) induced torque to be overcome at take-off due to the slight increase in vertical height of the total system COM.

5 The perpendicular distance from the line of action of the resultant inertia (length from OB to pole tip axis B) is longer when the vaulter obtains the higher location of the COM total system achieved in Position B.

6 Because of the interacting effects of the preceding points above (2-5), by achieving position B before the pole tip contacts the rear wall of the planting box the vaulter creates greater potential to be able propel and rotate the total system COM from a higher pole ground angle (ie., less angle for the pole chord to be displaced through (angle Beta) and reach the vertical). Also the applied torque, for the same magnitudes of resultant applied force acting on the total system centre of mass becomes greater due to the increased moment arm to Axis A (length OB to Axis A, perpendicular to the action line of resultant momentum of the COM total system, is longer in position B).

By achieving a higher total system COM simultaneously with vaulter (B) making their entire body behave with high flexural stiffness (high rigidity) an instant before the pole tip collides with the rear wall of the planting box the hands are enabled to transfer more of the final inertia (momentum) at the vaulter’s COM to the total system COM as it becomes suspended below the pole at take-off.

This is provided that the grips of both hands on the pole are sufficiently strong and both wrist joints held firmly enough to efficiently transfer the vaulter + pole COM momentum to the pole. The momentum transferred to the pole becomes the Effective Resultant Inertial Force due to the total system COM momentum when the pole tip collides with the box.

Another not well understood advantage of the more upright, firmly “braced” (total body flexural rigidity) body configuration at the instant pole impact occurs is that the higher pole ground angle increases “eccentricity” of the forces being applied to the pole via the hands.

This external force applied to the COM total system through the hands, because they are acting “eccentrically” with respect to the pole tip on impact with the rear wall of the box (meaning not in the same action line and orientation to the pole central longitudinal axis), will automatically induce bending of the pole provided that the vaulter maintains a high rigidity (flexural stiffness the index that indicates the force required to bend or flex the material of which a particular object is made) throughout the duration of the collision between the pole tip and the rear wall of the planting box.

Eccentricity to the pole tip of the applied forces at the hands also causes an increase in the effective torque magnitude in initially turning the inverted pendulum total system COM about the pole tip axis during the pole planting box rear wall collision at the instant the take-off toe tip losses ground contact.

If the pole has undergone rotation (about a transverse axis through the pole tip) as its tip slides on the inclined bottom surface of the box at the end of the pole plant and continues this rotation as the pole tip impacts with the rear wall the subsequent elastic collision cannot be directed along the same straight line as the central longitudinal axis of the pole.

Not only is the pole impacting the box non centrally (“off centre ie., eccentric”) but directed at an oblique angle (180 degrees minus theta degrees) to the horizontal displacement component of the total system centre of mass motion. The larger the angle Theta the less oblique the angle of the pole at impact and thus the greater the turning effect applied to the total system COM will be.

This “eccentricity” with respect to vaulter B’s COM more rapidly negates the smaller gravitational torque acting on the vaulter resulting in greater angular acceleration of the vaulter’s COM about both hands.

Because all the magnitudes of the applied external forces are the same for the vaulter in Position B as those in Position A, the oblique angle at impact is less, due to the higher height of the total system COM. Hence a greater turning effect (Torque) on pole rotation due to the impact can be obtained from the same magnitudes in the external forces applied to the vaulter + pole COM total system.

Understanding how the vaulter-pole interaction affects the pole tip impacting the box at take-off paves a way to resolve the controversy about the role of the bottom arm in the first phase of pole support. It is my hope that this will become clear as the analysis framework for the double pendulum (Vaulter and Pole) system is completed.

Pole vault suspended and inverted pendulums as constrained reciprocal physical pendulums by the pole spring linkage.jpg
Pole vault suspended and inverted pendulums as constrained reciprocal physical pendulums by the pole spring linkage.jpg (102.99 KiB) Viewed 8973 times


Note in the diagram above that the pole chord (shortest distance between Axis A and B) must be the constraining link to the pendulum length changes of the Vaulter (Pendulum A: suspended pendulum) and the Pole (Pendulum B: inverted pendulum) throughout all of phase 1 and most of phase 2 of the pole support part of the vaulting process.

The instant the take-off foot toes break contact with the ground the dynamics of what happens to the total system COM changes from pure linear translatory motion considerations to those of the combined effects of both linear and rotatory translatory motion. This will result in a curvilinear path being followed by the total system COM once the take-off has occurred.

Vaulter B’s COM suspended pendulum acceleration actually assists the vaulter in B to generate and maintain more effective momentum transmission from the take-off into Higher Tangential Velocity of the Total System COM about the pole tip at the start of phase 1 of pole support.

The radial distances from Axis A and Axis B to the spatial X, Y, Z, 3-D coordinate reference frame origin in the deepest point in the planting box of the total system COM can be determined. These radial lengths can then be used to enable the motion of the COM total system to be treated as that of a physical “Double Pendulum joined at a multiaxial “Gimbal” like pin joint Total System COM Bob”.

The motion of the “Bob” (COM total system pendulum weight) of the total system COM double pendulum is constrained because the vaulter acts as a “suspended pendulum” on the COM total system through fixed Axis A on one end of the pole and the pole acts on the COM total system “inverted pendulum” through fixed Axis B at the pole tip.

At any instant during the pole support phase it is the pole chord length that determines the vaulter pendulum length from axis A to the COM total system. The same constraint applies to the pole pendulum length from axis B to the COM total system.

By focusing the pole support analysis to the double pendulums acting on the Total System COM , recognizing that both these pendulum lengths change in proportion and synchrony in time due to the binding constraint of the flexing pole chord length coupled with the fact that the system is powered by an adaptive and intelligent human operator, simplifies the inherent complexity in understanding the double pendulum action challenge confronting pole vaulters.

The system viewed from this framework perspective is not as "Chaotic or as Complex" as it may initially appear to be.

Also, recognizing that the Tangential Velocity of the Total System COM is the primary determining control variable in the pole support phase of the vault also simplifies both cognitively and motorically the technique requirement in this phase of the vault.

The next post will continue to flesh out the framework established so far with further consideration being given to the action of the double pendulum effects and the mechanisms of momentum exchanges.

The magnitudes and directional changes in the COM total system Tangential Velocity of the Total System COM will be shown to be the critical components determining the outcome in the raising of the vaulter’s COM to maximum effective height and the pole to the vertical equilibrium point so they coincide at the instant of final pole release.
Every new opinion at its starting, is precisely a minority of one!

PVstudent
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Re: GRV: Lavillenie - From Stall Swing to World Record

Unread postby PVstudent » Fri Sep 05, 2014 2:42 am

My apologies to readers for some inadvertent omissions and a minor error on one of the diagrams in my previous post.

I have edited / amended it slightly in the hope it will be easier to read and corrected the error.

I believe the approach I am presenting will ultimately provide a way of observing and understanding the pole support phases that reduces the complexity that occurs if the actions of the vaulter and the pole are viewed as separate pendulum motions.

RPVA03 could you pm me and let me know if you have received my reply to your message. My reply is not showing up in my sent list! If your answer is No, could you include your e-mail address and I will respond by that means. Thank you.
Every new opinion at its starting, is precisely a minority of one!


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