Preface

Background

Introduction to Terms:
Push, Pull, and Push-Pull

My dictionary defines push as a force moving an object away while a pull is a force which moves an object toward the source of the force. Already some confusion arises because the skater is both the source of the force and the object being moved. The medieval French had a clear idea of the concept as the medieval trombone (Sackbut) comes from the French words for "pull-push". This leads us into the concept of "push-pull" which in my dictionary refers only to the kind of power amplifier drawn at the top of this page. So I was astonished to find that the Encyclopedia Britannica refers to the term "push-pull" in 764 articles. These articles run from earthquake studies to Internet marketing strategies to economic models. So almost everyone will have some meaning for the term when he/she arrives here.

The figure above shows the push (excursion to one side of the baseline) and the pull (excursion to the other side of the baseline) which add up to the snake-like sinewave shown which is the output of the push-pull electronic amplifier.

This figure shows the concept of a different push-pull process as applied to the human body. Because of the lever-action a muscle can pull in one direction and result in a push in the opposite direction.

Complementary-Symmetry

Possibly because of the imprecision in the idea of pushing vs. pulling electrons through an electronic device the push-pull amplifier was renamed with the advent of modern solid-state devices. The push-pull amplifier now became known as an amplifier operating on the principle of complementary symmetry. This name follows from the fact that the "push" and "pull" phases shown earlier are both sequentially timed and the excursions are on opposite sides of the baseline. (A class of solid-state devices called "CMOS" was developed where the "C" stands for Complementary-Symmetry).

This concept has also found its way into art and an example of a picture using complementary symmetry is shown below. The images on left and right are symmetric and complementary colors are used on opposite sides.

If we visualize the ground track of the left skate and the right skate in the classic skating style it also forms a snake-like pattern. In addition the path of one skate doing the "snake" forms a similar oscillating pattern. So already we have a couple of examples of complementary symmetry in skating. But in the double-push both skates will be seen to leave a snake-like ground track. So the idea of complementary symmetry will come up twice and we will be concerned with the phasing of the two tracks.
 

Underpush, Heel Carve

Some of the following terms seem to have been introduced into the double-push literature by Eddy Matzger and Dan Berger (Eddy Matzger and Dan Berger, Dan's Double Push Stripped Bare, fasst, Early Summer 1999, pp10.-11). The first term is Underpush. The term "underpush" seems unique to Matzger and Berger. It refers to a push under the body (on the outside edge) and it seems to include what I call the "push", the turn, and the "pull" on the outside edge used on this page.

The next three terms are from the online snowboarding glossary.

 

1. Carve: A turn that uses the edge of the snowboard as opposed to the bottom. When you carve, your board moves straight ahead so that its tip and tail pass through the same point in the snow, leaving a razor-thin track in the snow. Technically, skipping or skidding while turning isn't a carve.
    
2. Heel Edge: The edge of snowboard under your heel.
    
3. Heelside: A turn made on the heel edge.

 

Carving and the Double-Push

Snowboards and skis have hard edges which cut a groove into the snow like a knife so the term carving seems quite appropriate. But when turning inline skates on edge the wheels become flatter and less like a knife so that if anything is being carved it would likely be the urethane the road removes from your wheels. Nevertheless, skates will ony turn while on edge and the body dynamics seem similar in inline and snow sports. The term Heelside appears more appropriate than Heel Carve in the inline context but the term carve was probably brought in because it has special meaning for snow racers. Namely, when the snowboard or skis are made with a curved edge there is found to be a particular radius of curvature of the edge where the skier moves fastest.

But the method of turning is quite different for a skateboard vs. inline skates(see turning) and it is not clear that there is a unique turning radius which gives an inline skater the highest speed. The figure on the right shows that for the 5-wheel skate there are three wheel-track radii in the absence of sliding. So there seem to be three distinct carving radii for a turn. Now the analog of a carve radius on the side of a snowboard or skis could be to move the inline wheels out of line so they all fall along only one of the three curves. But that would be helpful only when turning. So it might be better to put a carved surface on the inside and outside edges of the wheels while leaving their centers inline. In fact, the carve radius may be a self-fulfilling phenomenon. That is, if you skate with a particular radius of curvature the wheels may wear on the edges so that your turning radius eventually becomes the most efficient.

Because the inline wheels do no real carving into the ground there is no need to produce only one razor-thin carve track. In fact it would seem to take more energy to produce one wheel path (which all five wheels would follow) than three wheel paths since the wheels would have to be flexed sideways to make one track. It seems that the preferred radius of turn for an inline skate is infinite (straight ahead). But on edge it does not seem to require much effort to turn until the radius becomes rather small. Of course the skate will not turn when stopped unless you lift 4 wheels up. The skate needs some forward roll in order to rotate (One wheel rolls one circumference while rotating 360 degrees). The minimum turning radius without sliding seems to be a few times the distance between the 1st and 5th wheels. But the turning radius in the skater's frame of reference differs from that relative to the ground. Because of the skater's forward speed the turning radius relative to the ground (where the grip/slide occurs) appears much longer than in his own moving frame of reference. So already the minimum turn depends on speed. The point that there is a "best" or "carving" radius for the turn is a valid point but there is presently no framework to determine just what it is for an inline skate.

The Heel Carve emphasizes the fact that turning requires a strong sideways push at the heel and not at the toe. While turning the toe needs to move forward, not sideways. To use this sideways push the wheels need to grip if they are to avoid power loss to sliding. So there needs to be an adequate force component into the ground and not just across it. And to turn the heel will be "anchored" to the turning curve with the strongest downward force while a lighter toe downward push will alter the grip location at the front wheels so that they can turn. The front downward pressure cannot be so light that the front wheels slide however. But there is some value to a little slide -- studies of rubber friction show that the grip is actually strongest with 20% slippage so you may have a tradeoff on whether you accept the benefit of higher thrust from the extra grip at the expense of a little sliding (which occurs before a full slideout occurs at 100 % slippage!).

Inside Edge-Outside Edge

In the old skating style things are simpler: push right with your right skate (on the "inside edge" of your wheel or blade) then push left with your left skate (also on the "inside edge"). There is also a glide phase where the opposite skate coasts while the pushing leg thrusts. The new style has more elements as shown below:

The figure above shows the right leg and skate in three different positions (view from the skater's rear so that any forward-backward motions are not seen here.) which occur in the "CHAD"-Barry Publow version of the double push. The right skate pulls from the left-most position to center ( on the "outside edge" of the wheels) then pushes to the rightmost position (on the "inside edge" of the wheels). Then the right leg is lifted back to center and placed down to push to the left (on the "outside" edge of the wheels). The left leg pulls and pushes in the opposite direction. The classic iceskating stroke has only the push (on the "inside" edge) phase so we see that using a push and a pull lengthens the skater's stroke. Matzger and Berger refer to what I call the push and the pull phase on the outside edge as the underpush.

If you need some motivation for your double push workouts see the lyrics for Push Me, Pull Me and Olympic Platinum.

Show Me The Double Push

I am following Jonathon Seutter 's suggestion that the Double Push be divided into two categories: The "Chad" and the "Marathon Stroke". The distinction is based on where the foot is set down after its push on the inside edge.

1: The "Chad"

1a: The Barry Publow Version

According to Jonathon, the distinguishing feature of the "Chad" is that the skate which just pushed on the inside edge is lifted up and set down near the center line whereas in the Marathon Stroke it is set down across the center line. When Barry Publow described the "Chad" technique in faSST he said of the stroke on the outside edge: "Thus it isn't really a push, but a pull." Most skaters believe that the outside edge push is more important for producing thrust than the outside edge pull. And Matzger and Berger avoid the term pull altogether.
I adopted the term Double-Push-Pull and The figure below shows two complete cycles of the "CHAD" -Barry Publow version of the Double-Push-Pull. The skater's head and upper body moves from left to right along the black center line.

His left skate follows the blue curve while the right skate follows the red curve. Neither curve is drawn to scale and are illustrative only. Four icons of Barry are labelled 1-4 (click to see a large photo courtesy Barry Publow) and their approximate positions in a cycle are marked on the top set of curves. According to Barry Publow the double-push-pull involves sequentially a glide, a pull and a push. The glide or outside edge push crosses over the black center line is turned forward and "pulled" back to center on the outside edge to begin the inside edge push. The push is "gravity-assisted" as the skater starts to fall as his center of gravity crosses over the center line. The turn and pull stabilize him before he falls to the ground however. The Barry Publow version of the Chad technique involves a moderately long pull with the right foot crossing over the center line about halfway to the left-most position of the left foot. The skater can choose to maintain a shorter stroke by straightening his legs somewhat thereby increasing the blood circulation to the legs. By skating on the outside edge of the wheels I find the wheel grip improved for the push phase where the wheel turns over to the inside edge. Finally, the double-push-pull keeps your lower leg muscles active and also uses some upper leg muscles which are not used in the traditional technique.

Although this technique was named after Chad Hedrick it is not the only form of the double push that Chad uses nor does Chad do it exactly the same way that Barry does. Chad varies his stroke considerably and has been taped using continuous variations all the way from the "Chad" above to the marathon stroke shown later. The skate setdown angle seems different for Chad vs. Barry as Chad seems to do more turning. Also, as the video animations show (links at the top right of this page) the head and torso movement is not nearly as pronounced the way Chad does it.
 

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1b: The Andrew Love version

There are some helpful notes on the double push in the feedback section of the May-June 1997 issue of faSST by Andrew Love. Here I am presenting my interpretation of what he said. This is somewhat controversial since he did not draw any diagrams or present any photos.

I interpret the Andrew Love technique as involving a longer outside edge push and outside edge pull than the Chad-Barry Publow Version. Andrew describes his method:
a) The recovery skate is set down so early that "it seems unstable and unnatural". .
b) The pulling leg is set down very close " to the ankle of the pushing leg as it is finishing the push." I have labeled this on the figure above.
The reasons that compel me to the long push-pull conclusion are his statements that:
c) He describes the double push: "The extreme lateral movement of the skates underneath the body is disquieting at first, but becomes controllable..."
d) He describes the Chad-Barry Publow technique as an "overdrive" gear where you cruise at high speed in a relaxed fashion by using a standard classical length stroke but moving some of the stroke under the body so the legs can be straightened. In other words, he considers the Chad-Barry Publow technique to be a reduced stroke from the maximum stroke available (which seems to be the Andrew Love Technique ) so you can cruise with a lower power output.
The Andrew Love technique seems to be approaching the cyclists state of high duty cycle where the right and left legs push and pull the same (pedal-crank) distance. They are constantly "spinning" and the skater is generating maximum power for very high speed.

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1c: The Chris Hurschler Version

On the June 5, 1997 racing news forum Chris described his favored technique as having four steps:
 

1.(right-inside edge push), 2.(left-outside push), 3.(left-inside push), 4.(right-outside push).

It seems to me that there needs to be a glide phase even if there is no pull phase as shown in the figure below:

I think Chris has removed the pull and replaced it with a glide. One advantage of this method is that it looks like it might work on ice. Chris denies inventing this method but he has reported it. Although it is often claimed that the double push will not work on ice Chad Hedrick recently reported on a TV interview in the Netherlands that he developed the double push while playing ice hockey. So it appears that the problem is not ice, it is the curvature of the ice speedskate which may have a problem with the reverse turn.

2. The Marathon Stroke

Jonathon Seutter reports two distinct types of double push:

• 1. The push foot gets placed down on the same side of the body ( i.e. right foot goes down to right side of center balance, then comes in across the center balance point then out again. This is the "Chad".
• 2. The push foot goes down on the opposite side of center balance, then comes out. This is sometimes called the "marathon stroke" by the Dutch.

The "Chad" requires more power and a faster cadence. It is faster but takes more energy. The Marathon Stroke must be done with a slower cadence and is not as fast but can be used longer. It takes less energy and is good with a tailwind or downhill."
The Figure below shows a fairly extreme marathon stroke where the foot is set down rather far out over the center line. The push on the outside edge is then rather short or impulsive requiring less energy.

Analysis:
"Double" in Double Push and Phasing

Next we explore the meaning of the "double" in double-push and then consider phasing.

In the figure above the Classic Ice skating technique on the left involves two pushes on the inside edge, once with the left skate and once with the right skate. You can think of this as one meaning of double push. However, since the non-pushing foot glides, the duty-cycle is fairly low.
The kind of double-push I described on this page involves a push on the inside edge and a push on the outside edge by each skate. In the second drawing each leg does two pushes during a cycle and not just one as in the ice method. This kind of double push raises the duty cycle which is good. And the sequential thrusts produced by the two pushes in the snake add to the forward speed. But, these two pushes are not simultaneous-- in phase.
Finally, moving to the far right the double push method we are interested in here also involves a push on the inside edge by the left foot (in this example) and a push on the outside edge by the right foot. This is a third meaning of double push where both legs push in phase (simultaneously). Not only do the thrusts of both legs add (simultaneously), but the driving force produced by both legs (and gravity) also adds. Therefore, more force can be applied than could be done with one leg pushing. Furthermore, since the driving forces are in the same direction (outward), the reaction force must all come from the ground and none from the opposite leg. This ensures a further efficiency increase over the traditional skating technique. This third meaning of double-push is the one which I think is most significant.
Now I look at the phasing issue. The figures below show how two sinewaves add when in-phase (left) and when 10 degrees out of phase (right.)

When The left and right ground tracks are exactly in phase (zero degrees phase shift) the result of adding the two sines is to exactly double one sinewave. On the right the 10 degree phase shifted waves add up to not quite doubling a single wave. Now if we assume that the skater's power has a sinewave dependence:
 

where Angle = w*t, w=2*pi*f*t, and t is time, f is the frequency of the stroke wave, pi=3.14, w = angular frequency, we can estimate the power efficiency for various phase angles. I have no proof that this form for the power is "correct" but it provides a stroke where the power starts from zero (t=0 or w*t=N*pi, N=integer) and increases to a maximum of 1 at the maximum stroke extension where w*t=N*pi/2 or 90 degrees which is near the transition from push to turn. The power then drops and returns to zero at the end of the pull phase. This form for the power is like the ground tracks discussed above and we can add the left-right powers to find the phase effect which is plotted below.

Conclusions

Two double push methods were discussed and several variations were shown. The power which a skater can produce can be estimated from a product of the force applied, the stroke length, and the stroke frequency. The double push increases both the applied force and the stroke length. The frequency seems to be largely independent of these two -- chosen by the skater according to his ability and the minimum turning radius he can execute without significant power loss. It seems to me that the double push can produce considerably greater thrust than the classical technique, possibly doubling it.
Matzger and Berger raised the carving turn issue bringing the question of turning efficiency in the double push to the forefront. More work needs to be done to understand quantitatively what losses are involved with a given turning radius.
Moving from a classical stroke to the double push is rather like moving from a monophonic power amplifier to a stereo amplifier. Now the phasing between left and right channels can play a significant part in the total power output.

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