down-kick in striding + an alternative

Lots of people have been recommending to add an extra _downward_ push to the
leg-push kick in classic diagonal stride. I've done a lot of striding
without it, but I wondered if I might be missing out on something. So I
looked at some elite racer videos and thought about the physics, and here's
what I came up with:
-- the double-benefit of down-kick.
-- the special situation where elite racers use it.
-- the big hidden cost from down-kick.
-- alternative move elite racers use instead

Double benefit: In addition to the obvious and important improvement to
grip, extra push _down_ during the kick also adds to _forward_ power and
speed. This seems contrary to our experience with quasi-static forces, but
in the physics of speed situations, power in one direction is easily
"transmuted" into the direction of forward speed.

Steep hills: Elite racers use _big_ down-kick for bounding up steep hills.
To the point where the reactive up-force sometimes launches them into the
air.

Hidden cost: In order to kick _down_, you have to extend the knee joint
(using the big quadriceps muscles). So some things have to go _up_, and one
of those things is the _hip_ joint. But in order to keep on pushing with
your leg out _behind_ you the hip must stay low, otherwise the ski must come
off the snow -- it's the geometry of the triangle.

Therefore the extra downward push by the leg must result in a _shorter_
horizontal range of motion for the leg-push. But the shortness of the
leg-push is already a critical performance bottleneck for classic striding
(that's why racers spend so much time double-poling), and this down-kick
move just makes it worse. That would explain why I don't see any elite
racers using down-kick in any video clips I've checked.

Upper-Body alternative: Yet extra down-force _is_ a good thing (the
double-benefit), so elite racers have found another way to add extra
down-force to their leg-push. They use their _back_ muscles to lift their
chest and shoulders and head _up_ during the leg-push -- which generates a
"reactive" force _down_ through the leg into the kick zone of the ski.
Since this lifting is all in their upper body, they can do it without moving
their hip joint up.

Third benefit: This lifting of the weight of the chest+shoulders+head
builds "potential" energy -- which can then be released into the "forward
fall" onto the pole-push. Provided that the skier is using "offset" pole
timing, where most of pole-push is made before the start of the kick.

So this back-extension lift move both protects the range-of-motion of the
leg-push _and_ adds power to the arm push.

Ken