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 Highspeed versus Lowspeed angles in poling
 Gearing of PolePush versus other motions
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 The pole delivers most power at low speeds when it most angled back.
 The pole delivers most power at high speeds when it is close to
vertical.
Why: When the pole is nearly vertical, the same angle of rotational
movement from the shoulder or elbow joint (or waist or hip joint) generates 40%
more horizontal forward motion than when the pole is angled back at 45
degrees. The same size muscleandjoint move matches a forward
speed 40% higher.
It's geometry. The horizontal position of the pole tip is
proportional to the cosine of the angle of the pole. You can see
how much change in forward position a 1degree move in angle
makes by getting the difference between cosine of 89 degrees and cosine of 90
degrees. Then compare that with the change between the cosines of
44 degrees and 45 degrees.
Or from calculus: The horizontal speed of the pole tip is proportional
to the sine of the angle of the pole (because in calculus the sine
function is the "derivative" of the cosine function).
The sine of 45 degrees is 0.7071 and the sine of 90 degrees is 1.0000 
which is 40% larger.
This gearing difference works the other way with forces. The
same muscle tension and joint stresses can generate higher forwardpush force
(at lower speed) when the pole is more angled back than when it is
closer to vertical.
Therefore:
 the more vertical angle is the "highgear" subrange of
the polepush motion: better for higher speeds where high force
is not critical.
 the more angledback pole is the "lowgear" subrange or
polepush motion: Better for high forces where high speed is not
possible.
Another reason why planting the pole further back is a
better match for climbing up a steep hill.
Note that each polepush motion always must start in a
"highergear" part of its range than where it
finishes.
This is a slight disadvantage, because in several motion techniques
there is a passiveglide "dead spot" immediately before the
start of the polepush  so the skier's speed is slowest just when the
polepush configuration is ready for a higher speed. This
disadvantage is greatest when climbing slowly up a steep hill.
This mismatch at the start of a push on a hillclimb is not shared
by the big leg muscles, another small reason why the focus moves to the
legs for climbing steep hills.
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Polepush compared with Classic Striding legpush
The polepush torques (or rotational forces) are applied from the
shoulder and elbow joints. Also from the waist and hip joints, but
the forces from these joints must still be transmitted through the
shoulder and elbow joints.
The shoulder and elbow joints are much farther away from the surface of
the snow than the knee and ankle joints, and somewhat farther than the hip
joint. Other things being the same, the length of forward motion
from a rotating joint tends to be proportional to its distance from
contact with the snow surface.
So the same angle of rotational movement in the poledriving joints
generates greater horizontal forward motion when it comes from the
shoulder than from the knee. The same muscleandjoint move from the
shoulder matches a higher forward speed.
Therefore the polepush is a better "highgear" motion  a
better match for higher speeds than the classic striding
legpush.
On flat terrain, the poletip also has a longer
effective distance of contact stopped in the snow than the ski  but this
longer effective range of motion is a separate advantage.
This gearing difference works the other way with forces. The
same muscle tension and joint stresses can generate higher forwardpush force
(at lower speed) it is applied through joints closer to contact with the
snow surface.
This is a very important reason why the knee and ankle joints (also
the hip) become the focus for climbing up a steep hill.
Polepush compared with Ski Skating legpush
The same arguments for why the Classic striding legpush is better
suited than the polepush for slower speeds and steep hills apply mostly
for the Skating legpush, since it also uses the knee and ankle joints.
But surprisingly, the Skating legpush is also better suited
than the polepush for very high speeds. The problem for the
polepush is that force can only be applied while the tip of the pole is
stopped in contact with the surface of the snow. So poletip must be
be moved at a speed relative to the rest of the skier's body which is the
roughly similar to the skier's forward speed over the snow.
Skating can apply force while the ski is moving on the snow, so
it is not subject to the "stopped on the snow" requirement,
therefore the relative speed of the ski does not have to be nearly as high
as for poling.
And controlling the angle of the skating ski out to the side enables a
wider range of "gearing" than is available in the polepush from
the vertical and angledback pole positions. The skating ski overall
has a wider range of speeds over which it can effectively match the
skier's desired speed without a falloff in power delivered. It
performs better than poling both above and below the optimal speed range
for high polepush power.
This analysis fits with how elite racers choose Skate motion
techniques:
 The polepush is usually in its "good" SpeedPower output
zone at "normal speeds" for gentle terrain  so the V2
skate motion (Canadian "1skate") is preferred by elite
racers, to use the maximum number of polepushes per stroke
cycle.
 At slower speeds up a steep hill, the lowgear inferiority of the
polepush shows itself, so the polepush is cut back to one per stroke
cycle, timed so that it does not interfere with the best timing for
the legpushes  V1 skate (Canadian "offset")
 At very high speeds on flats or gentle downhill, the veryhighgear
limitations of the polepush emerge  while the skate legpush can
still delive effective power. So skier keeps on skating, but
cuts the number of polepushes to none (SkateNoPoling) or to one
(Open Field Skate).
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