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words + phrases

normal-push stroking:  the normal way that most people skate, with alternating pushes by the two legs, each one aimed diagonally forward toward its own side, each one pushing toward the outside on its own side.

double-push stroking:  a special motion sequence where each leg makes two pushes in a row without the other leg making any push in between those. The first push (here called the in-push) is directed inward across toward the other leg's side, then the second push (here called the main-push) with the same leg is directed outward toward its own side. Or the other way of looking at it is that there are two pushes in succession toward the same side (but by different legs), then two pushes in succession toward the other side (by different legs).

So the sequence of pushes is like: (L2) left leg push outward toward the left side, (R1) right leg push inward across toward the left side, (R2) right leg push outward toward the right side, (L1) left leg push inward across toward the right side, (L2) left leg push outward toward the left side, and keep repeating . . .

As of 2005, this motion is used mainly by expert speedskaters on inline skates, though it is straightforward to perform it on ice using skates with a rockered blade. It is usually rather difficult to perform effectively with skating skis.

"big" style of double-pushdouble-push stroking which is characterized by: (a) landing the skate or ski with a significant non-zero aim-angle toward the inside; (b) followed by significant travel of the foot toward the inside during the Under-push; (c) push-force directed partly backward during the in-push.

"lite" style of double-push double-push stroking which is characterized by: (a) landing the skate or ski with aim-angle nearly straight in the forward-motion direction; (b) push-force directed nearly all sideways during the in-push.

main-push:  a push by the leg directed diagonally back and outward toward its own side. This is the only kind of leg push used in normal-push stroking, and it's also used in double-push stroking (where it's the second push made by each leg without interruption by a push by the other leg).

in-push:  a push by the leg directed inward across toward the other side (and often also directed partly backward). This kind of push is used in double-push stroking, where it is the first push made by each leg without interruption by a push by the other leg.

Speedskaters doing cross-over stroking around a curve make a push inward across toward the other leg's side, often called the "under-push" -- but that might (or might not) be somewhat different than the in-push used for double-push stroking.

forward-motion direction: the overall average direction of the skater's center-of-mass while skating on the quickest path from one place to another on uniform terrain. At any instant the skater's mass is moving diagonally toward one side or the other, so in order to get a consistent stable direction-vector, we use the overall average. (symbol = x )

center-of-mass ("CoM"):  the overall average position of all the mass of all the body parts of the skater (including attached equipment and clothing). (symbol = rcom)

Note that the center-of-mass (CoM) is not any fixed point on or in the skater's body, such as the navel or the pelvis-center. The CoM is a "virtual" position determined by a difficult triple-integral calculation. Its relationship to any particular body part changes as the skater's overall body configuration changes. In some bent-over body configurations, the CoM is in the air somewhere out in front of the skater -- not anywhere inside or on the surface of the skater's body.

foot-ground-connection (or "fgc", or just "foot position"): the position which is the effective center of the transmission of forces between the skater's foot and the ground surface. (symbol = rfgc or nothing -- since its position is normally implicit as the Origin of the positional cooordinate framework. )

aim-angle: the angle between (a) the aiming direction of the skate or ski, and (b) forward-motion direction of the skater. So if the aim-angle is zero, then the ski or skate is pointed straight forward, while if the aim-angle is 60-degrees, then skate or ski is pointed way out toward the side. (symbol = α )

out-of-balance slant angle (or CoM-fgc slant angle or just "slant angle"):  the angle away from vertical of the line from the center-of-mass to the foot-ground-connection (but excluding any component along the aiming-direction of the skate or ski). Slant angle of zero means that the skater's foot is directly under the skater's center-of-mass. Slant angle of 45 degrees means that the skater's foot is way out to the side.

symbols in formulas

positions + directions

origin of positional coordinate frame is normally the foot-ground-connection ("fgc" or , unless otherwise stated.

rfgc  = position of foot-ground-connection ("fgc"), or just "foot position". Usually this symbol is not shown, the foot-ground-connection is normally used implicitly as the origin of the positional coordinate frame.

x  =  forward direction unit-vector, in the skater's overall forward-motion direction (parallel to the ground surface plane).

y  =  sideways direction unit-vector, in the direction of the cross-product z x, which is normally toward the left of the the forward-motion direction and parallel to the ground surface plane).

z  =  upward direction unit-vector; perpendicular to the ground surface plane. So if the ground surface plane is tilted to represent climbing up a hill, then z is not straight vertical. (or more formally, if γ 0, then z g 0).

a  =  aiming-direction unit-vector, the line along which the skate or ski is currently gliding or rolling.

n  =  pushing-direction unit-vector, the intended direction of the propulsive push, which is in the ground surface plane, perpendicular to the aiming-direction of the skate or ski, generally in the sense of pointing backward rather than forward.

rcom  =  center-of-mass ("CoM") of the skater's body (sometimes just r).

scalar quantities

α  =  aim-angle of the ski or skate, away from straight forward. [ α = cos (x a) ]

β  =  out-of-balance slant angle (or CoM-foot-slant angle, or just "slant angle").

γ  =  slope angle of hill being climbed. If γ = 0, then the ground surface is flat.

m  = mass of a part of the skater's body, which might include attached equipment or clothing.

M  =  total mass of skater's body including attached equipment and clothing.

g  =  constant acceleration of gravity at the surface of the Earth. (g = |g|)

forces

ffgc  = net total of all forces applied between the skater's foot and the ground, at the "virtual" position rfgc of the foot-ground-conection ("fgc"). [ ffgc = fn + fa + fz ]

fn  = pushing component of force through fgc; component in the intended pushing-direction, which is the "currently propulsive" force. [ fn = (ffgc n) n ]

fa  = aiming-direction component of force through fgc; component in the aiming-direction a of the skate or ski.

fz  = upward component of force through fgc; component in the upward direction z.

g  =  gravity vector. The acceleration of gravity, vertically downward (from the surface of the Earth). So the force of the skater's body weight = M g.

more . . .

other kinds of definitions:

see also