## physics of arm-swing

### physics of arm-swing

I've been thinking about the physics of swinging my arms (or
torso-chest-shoulders) from side to side when skating -- how it can help my
forward-motion power.  Below is an over-simplified presentation of the
physics, with some implications for traveling farther in less time.

Ken

Implications:
(a) sudden quick acceleration of the arms is good. A critical measure of
upper-body effectiveness is the maximum sideways speed attained, relative to
the hips.  Serious racers might consider doing special training of the
muscles and joints doing the swinging: training focused on high acceleration
and velocity (? "plyometric" ?)

(b) longer range of sideways motion is good: the further out to one side I
can hold my arms before starting the sudden quick acceleration, the more
power I get from my arm-swing -- because it gives more distance to attain a
higher maximum velocity.

(c) swinging _both_ arms is better than swinging only one.  Adding the move
of the torso - chest - shoulders should help too.

(d) higher frequency turnover of the overall stroke-cycle with the legs

These implications are all subject to "other things being equal".  Of course
often they're not: like at high speeds lots of sideways arm motion might
also increase aerodynamic drag. Like higher-frequency turnover might
increase arm-power, but decrease the (more important) leg-power.  The

Obvious way to miss out on some extra power:  Synchronize arm-swing simply
and smoothly with leg-push.  Attaining higher acceleration and velocity (a)
requires that upper-body timing be "de-synchronized" from leg-push.
"smoothly" is another way of saying "lower-acceleration".
__________________
Physics over-simplified:

Moving portions of the mass of the body above (but not including) the hip
joints can add power to the push thru the skates into the pavement in the
form of "reactive" or "inertial" force, by Newton's Third Law "every action
has an equal and opposite reaction".  Even though this force is largely
sideways, the magic of the skate can convert it into forward motion by the
"inclined plane" principle.

The physical Work from swinging the arms (or torse) once, from one side to
the other is:

Work = h * m * a * s

where
h = efficiency factor (less than 100%) of transmitting this power into
effective forward motion.
m = mass of upper body part being moved.
a = rate of acceleration of this upper body part (assumed to be constant
magnitude, but positive during the first half and negative in the second
half of the motion)
s = total side-to-side distance

The justification for this formula can be seen as Work = Force * Distance,
where Force = m * a, and Distance = s / 2 for the acceleration part, plus
another s / 2 for the negative-acceleration.  Or it can be seen as the
Kinetic Energy at maximum Velocity = square root of 2 * a * s -- but with
the benefit received twice, first from acceleration, then from
de-celeration.  (But this doubling of the effective work comes only if the
de-celeration is timed when the skate-push is aimed in the opposite
direction from the acceleration.  If any de-celeration starts while the
skate-push is still aimed in the original direction, then the reactive force
from it _reduces_ the total effective work.)

Power = 2 * f * h * m * a * s

where
2 = two arm-swings in each total stroke-cycle.
f = frequency of total stroke-cycles (with both legs making their push).

Notes:
(1) Interesting that with reactive force sideways you can "win both ways",
and gain both in the acceleration toward one side and in the de-celeration
toward the other side.  If you get the timing right.

(2) The physics of the leg-push is different from this ("direct push" force
versus "reactive") -- with different constraints -- and with very different
Implications.
___________________

### physics of arm-swing

Quote:

> I've been thinking about the physics of swinging my arms (or
> torso-chest-shoulders) from side to side when skating -- how it can help my
> forward-motion power.  Below is an over-simplified presentation of the
> physics, with some implications for traveling farther in less time.

> Ken

AFAIK side-to-side armswing is poor technique.  I've always been
taught that it should be mostly forwards/backwards, like plucking an
imaginary apple off an apple tree in front of you, and throwing the
apple straight back behind you.

### physics of arm-swing

I think we have to ask:  good or poor technique _for_what_?  for what goal,
in what situation.

Mike van Erp wrote

Quote:
> AFAIK side-to-side armswing is poor technique.

At high speeds on flat terrain, swinging the arms increases air resistance
too much, so you can go faster by tucking them behind your back.

But for accelerating from a stop or slow speed, swinging arms is excellent
technique.  Just look at a video of the start of any inline race.  And for
climbing up a hill, the extra power from swinging the arms can help a lot.

Now look carefully at videos of elite racers at high speed with no
arm-swing, and notice that instead they are swinging their torso - chest -
shoulders from side-to-side.  Like Chad Hedrick:
or from the 1998 Northshore marathon:
http://nettracing.com/video/4c.wmv
Same physics principle of reactice side-force, but use different upper-body
parts to best handle the different aerodynamic situation.

Ken

### physics of arm-swing

Mike van Erp wrote

Quote:
> I've always been taught that it should be mostly
> forwards/backwards, like . . . throwing an
> apple straight back behind you.

Very interesting and helpful (and tricky) questions raised by that idea --
thanks for sharing what you had been taught.  I did some thinking and
experimenting, and here's what I've come up with:

(a) normal Two-sided Skating:  forward/backward arm-swing cannot add much
overall propulsive power to normal two-sided skating.  The positive effects
on one direction of swing pretty much get cancelled out by the negative
effects of the other direction.  With exact timing you could get some
benefit, but that might have to interfere with some other bigger sources of
power.  (In normal two-sided skating, it's mainly the side-to-side component
of arm-swing or torso-shoulder swing that delivers a net propulsive gain --
if timed right.)

(b) One-sided Skating:  forward/backward arm-swing can add propulsive power
in _one-sided_ skating:  like angle the right skate out to the side and push
with it, but keep the left skate aimed straight in the body's line of
overall motion and do not push with the left skate.

back).

Experiments:

All these experiments should be performed in a safe environment clear from
obstructions and other moving things, and using equipment that is safe for
possible falling or collisions.  The rolling surface must be smooth and
flat, and there should be no wind.  So an indoor floor would be ideal, but
smooth pavement outside is good enough.

(A-backward) on inline skates:  Stand on inline skates with both skates
aimed straight ahead.  Hold both arms out in front.  But move your hips back
so your total body weight is balanced centered over your ankles, not forward
on your toes.  Quickly and aggressively swing both arms straight back.  What
happens?  Do you move significantly? Which direction?

out behind you, and then swing them both straight forward.  What happens?

(A-sideways) normal Two-sided skating:  Stand with legs straight, knees
locked -- to try to prevent the leg muscles from providing any propulsion.
Angle both skates out to the side, but try to keep them close to underneath
you, to try to limit side-push with the legs.  Hold both arms out to the
right side.  Put most or all of your weight on your right skate.  Then swing
both arms aggressively all the way over out to the left side -- and at the
same time step onto the left skate (but without pushing off your right
skate).  When your arms stop on the left side, keep them both stopped out
there on the left for an instant.  Then swing both hands back to the right
sand, and at the same time step onto your right skate.  And repeat this
cycle one more time.  What happens?

Which produces more forward motion:  A-forward, A-backward, or A-sideways?

(B-backward) with One-sided skating:  On inline skates, aim the left skate
straight ahead, but aim that right skate at a right angle perpendicular out
to the right side.  Hold your arms out in front, but your hips back a little
so your total body weight is balanced centered beween the two skates.  Put
all your weight on the right skate.  Then swing both arms straight backward,
and at the same time step onto the left skate.  Do you glide anywhere?
which direction?

(B-forward) with One-sided skating:  Like B-backward, but reverse the
arm-swing.  Any glide forward this time?

(B-angled-forward) with One-sided:  Left skate pointed straight ahead at all
times.  Right skate angled somewhat out to the side, but not perpendicular.
Start with arms back behind, weight on right skate.  Swing arms forward
quickly while stepping onto left skate (without pushing off right skate).
Bring both arms back behind while weight is balanced on left skate.
Transfer weight to right skate, and swing arms forward quickly again, and
repeat two or three more times.

(C-forward) on Quad-skates.  Same as A-backward and A-forward, but on
old-fashioned rollerskates.  The results are different between backward and
forward arm-swing.  Which arm-swing direction produces significant forward
motion?

I did all those experiments, except that instead of Quad-skates I used
"classic" non-skating "rollerskis" (two-wheel skates with a ratchet or
clutch on the wheels so they glide only forward, so I can push straight back
against them with my leg, like in walking or running).

The results were obviously and substantially different for the different
experiments.  The different results on real wheels and real pavement were
pretty convincing to me about which motions work and which do not.

Ken

### physics of arm-swing

Physics interpretation of arm swing:
How come forward-backward arm swing adds to propulsive power with
quad-skates (old-fashioned rollerskates) and with One-sided
inline-skating -- but adds little or nothing to normal two-sided skating?

Here's my attempt to figure out the physics.  It gets tricky, so I hope
someone can help by pointing out the flaws in the analysis -- or some clever

Principles of Physics:
(1a) acceleration or force or motion of the mass of body part relative to
the remainder of my body mass makes no overall difference to my forward
motion speed.  Because all my body parts have to stay connected with each
other.  Throwing a (big heavy) apple out behind me does actually make me go
faster overall, by Newton's Third Law -- it's the same principle used by
rockets in outer space.  Trying to throw my arm out behind me does make the
_remainder_ of my body mass go faster, but only for a very short time.  As
my arm reaches its limit and comes to a stop, it slows down the remainder of
my body just as much:  no net gain in speed or time.

(1b) the only thing that can make an overall difference in my forward motion
speed is applying force against something _outside_ all my body parts:
which means the air or the pavement (or maybe pushing against nearby trees).
There's no doubt that a sail or kite or big air-scoop paddles could make a
big difference, but let's leave those for another discussion.  So what
matters is wheels pushing against pavement.

(2) therefore reactive (or "inertial") forces can only help propulsion if
they are transmitted thru the skate wheels to the pavement.

(3a) an inline skate does a remarkably _good_ job of transmitting to the
pavement a large percentage of the component of force which is _not_
parallel to the line of the skate's wheel-frame, even if the wheel-frame is
not "edged" or tilted significantly to one side.

(3a) an inline skate cannot transmit to the pavement any component of force
which _is_ parallel to the line of the current weight-bearing skate's
wheel-frame on the pavement surface.  (3b) But an inline skate does a
remarkably _good_ job of transmitting to the pavement a large percentage of
the component of force which is _not_ parallel to the line of the skate's
wheel-frame, even if the wheel-frame is not "edged" or tilted significantly
to one side.

(4a) A quad-skate cannot transmit parallel force to the pavement while its
wheels are rolling forward on the pavement.  (4b) a quad-skate does transmit
to the pavement a force parallel to its wheel-alignment direction only while
its wheels are temporarily _stopped_ on the pavement.

Implications of those principles

If I start swinging my arm forward while my skate is stopped temporarily and
I'm pushing back with my leg, that motion generate a "reactive" force
backward.  To the extent that my central body structure (shoulders - chest -
abdomen - hips) "rigidly" _transmits_ that force into my legs and into the
skate (instead of absorbing the force by collapsing or shifting away) --
then this forward arm-swing is transmitted backward into the pavement (by
principle 4b) adds to useful propulsive work (1b).  (Note that if I instead
started swinging my arm _backward_ during my quad-skate leg-push, it would
_subtract_ useful propulsive work).

If I have timed my arm-swing to continue until after the leg-push is over
and the wheels start rolling again, then the stopping of the arm-swing does
generate a reactive force which is aimed forward, but this force is not
transmitted to the pavement (by principle 4a), so it has no negative impact
on my forward propulsion (1a).  Therefore there is a net gain in useful
propulsive work over the whole stroke-cycle.  (Note that if I finished my
arm-swing before the wheels started rolling again, the negative "reactive"
force from the de-celeration _subtracts_ from the useful force into the
pavement (by 4b), and the result for the overall stroke cycle is No Gain).

One-sided inline skating:
If my right skate is angled out to the side and my left skate is always
aimed straight ahead, then if I start swinging my arm _forward_ while
pushing out and back with my right leg, then the "reactive" force backward
is significantly transmitted to the pavement because the right skate is
angled in a different direction (3b).  So it adds to useful propulsive work
(by 1b), provided that my shoulders - chest - abdomen - hips "rigidly"
transmit that force instead of absorbing it by collapsing or shifting away.

The stopping of my forward arm-swing generates a negative "reactive" force.
But if I have timed my move so it doesn't stop until after I've transferred
my weight to the left skate, then forward/backward component of this
reactive force is _not_ transmitted to the pavement because the left skate
is pointed straight ahead (3a).  Therefore the there is an overall gain in
propulsive work.

normal Two-sided skating:
The gain in propulsive work from starting my my arm swinging forward while
pushing my skate out and back is the same as for One-side skating.

Then comes the big Problem: The forward arm-swing has to stop some time --
actually some time pretty soon.

In normal two-sided skating, whenever the move does stop, the weight of the
skater's body will be on one skate or the other, and that skate will be
angled out to the side, _not_ be pointed straight ahead.  And normally both
skates are aimed out to the side at about the same angle, so the
component-proportion of negative "reactive" force transmitted will be about
the same no matter which skate (by 3b) -- even if the skater is not yet
"edging" the skate wheels or actively pushing on that skate.  And it will be
about the same angle and so the same component-proportion transmitted as the
earlier positive "reactive" force.

So the net impact on useful propulsive work from forward/backward arm-swing
over the whole Two-sided stroke-cycle is No Gain.

Ken

P.S.
no gain . . . Unless
- - Jump up into the air as the arm-swing stops?
- - Find some useful reason to point the skate straight ahead for a moment
(like in double push?), and time the forward forward arm-swing so it stops
in that moment?
- - something else?
______________________________________________________

### physics of arm-swing

Up/down body movement is also bad technique, I'm afraid.

### physics of arm-swing

Thanks for another stimulating idea:  up and down motion.

johns wrote

Quote:
> What you are really after ... is the rise and fall of the body ...

I think this up-down move offers little or no overall propulsive gain for
normal two-sided skating (though I can see how rise+fall could deliver a
gain for One-sided inline-skating, and possibly for quad-skating).  My
reasoning is much like for my other post about the physics interpretation of
forward/backward motion.

Quote:
> the lift of the chest gives stronger push and greater speed.

Yes the upward lift of the chest does generate a "reactive" force downward
which can be transmitted to the pavement as added propulsive work.  The
magnitude of this added work is equal to the kinetic energy at the maximum
upward velocity attained by the mass of the chest.

But soon this upward motion must come to a stop.  Which then generates a
_negative_ "reactive" force.  And in normal two-sided skating, it's pretty
hard to avoid transmitting that force to the pavement to be _subtracted_
from propulsive work.  So the overall result for propulsive work is No Gain.

Unless
you time the up-move to stop while the skate is aimed straight forward --
like perhaps in between the inside-edge push and the outside-edge push of an
advanced racer's double-push stroke cycle.  But even then, the chest still
has to move back _down_ again to get into position for the next
stroke-cycle, and I'm not seeing how you'd time this down-move to avoid a
subtraction from propulsive work.

Quote:
> I can beat any inline skater who does
> an arm swing to get speed.

sure looks like in the first half-second he's finishing an arm-swing before
he tucks his hands behind his butt. And then in the next seconds look at all
those elite racers in the _background_:  Are they doing side-to-side
arm-swing or what?

Sure, at high speeds it's better to do a sideways swing of torso + shouders,
not arms (because of air resistance) -- so we see Chad switching to torso
swing:  But is it more up-and-down or more side-to-side? Check the video and
decide for yourself.

Or here's the leaders at the 1998 Northshore Marathon:
http://nettracing.com/video/4c.wmv
Which is it:  rise-and-fall or side-to-side?
And here's Barry Publow:
http://doublepush.com/video/publow.wmv
What do you see more of there?

Ken
____________________________________
johns wrote

Quote:
> Arm swing doesn't get it done. What you are really after
> in a good stroke is "drop in". That is the rise and fall
> of the body .. not the sideways swing of the body. It
> may look sideways, but that is only because the stroke
> travels on a slight curve moving out and back in to
> "carve" an arc for balance. If during the push, you
> lift your chest a bit, the lift of the chest gives stronger
> push and greater speed. The chest "drops in" just
> before the next stroke. I can beat any inline skater
> who does an arm swing to get speed.

### physics of arm-swing

Quote:

>Arm swing doesn't get it done. What you are really after
>in a good stroke is "drop in".

It's always good to have a guaranteed wrong answer to compare against.

### physics of arm-swing

Quote:

> Or here's the leaders at the 1998 Northshore Marathon:
> http://nettracing.com/video/4c.wmv
> Which is it:  rise-and-fall or side-to-side?

You are misinterpreting what you see. The head/torso is not moving
side to side, instead the head is on a straight line and the rest of
the body is moving side to side. The angle of the camera makes it look
like the head is moving - it isn't.

You have to pay attention to a few spots in the video to catch this.
Near the beginning when the race is focused on the leading pair, the
guy in second place glides for a short time. If you look at the first
place guy, his head does not move relative to the other guy's head.
Without a point of reference (ie, the guy in second place), it would
look like the torso was swinging. In reality, his upper torso is
barely moving. Another point happens about 3/4 of the way through when
the camera manages to get directly in front of the leader. Here it's
very obvious that the head is stationary while the lower body moves
sideways.

The arm swings you misinterpret are similar. The camera makes it look
like sideways motions due to the angle of the camera. In those few
instances where you catch background shots of racers when the camera
is directly in front of them, you will notice that the arms move
forward and backwards. The hands do not cross the centerline of the
spine. Again camera angle illusions.

If you don't believe me, you should attend a clinic held by Publow or
Hendrick or Matzger. Publow has held a clinic locally in Boston for
the past two years, while Matzger did it for the four years prior to
that. If Boston is too far away for you, speed skating clubs in large
cities will invite a nationally ranked skater to host an annual
clinic.

The real reason for the arm swing is NOT for momentum purposes. It is
due to physiology of the human body. Ie, the way the muscles interact
with each other, the way the body removes lactic acid, etc. Swinging
your arms in time with leg movement increases the power your leg
muscles can exert, but it also increases the amount of lactic acid in
the legs. Ie, short term gain, long term loss.
--
// T.Hsu

### physics of arm-swing

Quote:
> Russotto, go put on your ice skates and start swinging your arms. You'll
> break your freaking neck doing that. You 'll swap around before 50 feet.

You mean just like those OLYMPIC MEDAL WINNERS?
Guess what.  Figure skating may not be the same as someone actually trying
to go fast.

LMAO!

### physics of arm-swing

Quote:

>> Up/down body movement is also bad technique, I'm afraid.

>Bullshit. I can run past you so fast you wouldn't believe
>your eyes .. and do it backwards.

Does this mean you're finally going to answer one of the many
challenges issued here?

(didn't think so)

### physics of arm-swing

Quote:

>> It's always good to have a guaranteed wrong answer to compare against.

>Russotto, go put on your ice skates and start swinging your arms. You'll
>break your freaking neck doing that. You 'll swap around before 50 feet.

The subject is inline, but if you'd like to come out here I'd be glad
to race you on ice too.  I've never done speed ice but somehow I doubt
that would be much of a problem.  (ice speed skaters, of course, swing
their arms)