Air position with a straight rotation axis.

Angles as perceived by an observer are not what they appear.

This detail of the jump landing is taken from the last image at bottom right.  It gives the appearance of a jump perilously close to being under-rotated.

The red line has been added perpendicular to the line of flight.  A landing with the foot on the red line, or farther clockwise, would appear to meet the definition of under-rotated; i.e., perpendicular to the line of flight or past that, and thus missing one-quarter rotation or more.

Angles, however, are distorted by projection effects from the viewing angle of the observer.  In reality, any foot position up to the short yellow line would be less than one-quarter rotation short of the line of flight for this jump.

Downgrade calls with the blade along the line of sight are unambiguous for all viewing angles, but under-rotation calls cannot be accurately made without taking into account the line of sight of the viewer.

Projection effects are worse the closer the viewer is to ice level and also depends on the orientation of the line of flight relative to the line of sight of the observer.  Thus, the correction for projection effects is specific to the geometry of each jump and the location of the observer.

Current replay systems do not take into account projection effects when used to determine under-rotation calls in competition.  An additional complication is that the viewing angle of the Technical panel in real-time is significantly different from the viewing angle of the replay camera.

(24 February 2020)  The ISU is currently willing to give full credit to quad attempts no matter how little rotation they really have, as long as they give the illusion of a quad and are not under-rotated on the landing.  So much so, you might come to think fully rotated quads just can't be done.

But that isn't the case.

We present here as an example, a quad Salchow executed by Yuzuru Hanyu in the Short Program of the 2019 Grand Prix Final that illustrates the geometry of a fully rotated quad.  It doesn't get much better than this when it comes to complete rotations.  This jump was 0.76 sec in the air, and ever so slightly under 3 3/4 rotations in the air. (1)

	The skater is on a clean back inside edge at the takeoff.  The green arrow shows the line of flight the jump would have had if the skater had jumped exactly vertically at the takeoff - tangent to the takeoff edge at the moment of leaving the ice.  The yellow arrow shows the actual line of flight of the jump in the air. Notice how open the arms and free leg are at takeoff.  Skaters who pre-rotate this jump (and other quads) are already significantly pulled in at this point, often turning forward on the skating leg before they are about to leave the ice.
	There is no turn, scrape or pivot off the skating foot, as seen in the close-up of the entry edge.   The green arc is drawn just below the entry edge of the jump.  The green arrow shows the line of flight the jump would have had if the skater had jumped exactly vertically at the takeoff.  (The broad scrape from center of the image to upper right corner is not part of this jump.) The yellow arrow shows the actual line of flight in the air.  The short yellow extension to the right of the yellow arrow is the perpendicular to the line of flight on the ice as projected by the viewing angle of the camera.  The angle between the green and yellow arrows is a bit more than one-eighth rotation.
	The skater is well into the air in the first quarter rotation. The skater is still not fully pulled in.
	Note the position of the hands when pulled in used by the skater, with the right hand in a fist pushed into the open palm of the left hand.  This position very slightly increases the moment of inertia compared to both hands with flat palms against the torso.  This technique is used by a small number of skaters.
The air position of the skater departs from ideal in several respects:  the body of the skater is somewhat bent along the long axis at the waist and knees; the legs are not straight and in contact with each other; the arms are not tight at the side, the hands are not flat against the torso.  And yet the skater had no problem fully rotating the jump. Compare the bent rotation axis of this position to the straight rotation axis for Nathan Chen at top left.
Bent rotation axis slows the rotation.	Other factors that slow the rotation.
	The skater remains pulled in until nearly the instant of contact with the ice (no more than the last 80 msec in the air).  This jump was landed with a higher rotation rate than most skaters are capable of controlling, about four rotations per second. The average rotation rate was 4.9 rotations per second with a peak of about 6.1 rotations per second, making the air rotation efficiency about 80%. (2, 3) The relatively narrow shoulders and hips of the skater, compared to other competitors,  gives this skater an advantage by allowing a potentially lower moment of inertia and higher rotation rate than typical.
	The skater lands cleanly on the toe picks and exits the jump fairly smoothly.  The landing blade makes an angle of nearly one-eighth rotation with respect to the line of flight at the landing. The yellow arrow shows the actual line of flight in the air, extended past the point of landing.  The short yellow extension to the right of the yellow arrow is the perpendicular to the line of flight on the ice as projected by the viewing angle of the camera.  The green arrow is the landing orientation of the blade.  The angle between the green and yellow arrows is a bit more than one-eighth rotation.

Fully rotated quads, where we define fully rotated to be near one-quarter rotation short of integer rotation,  are not only achievable in theory, they are actually being executed by some of the best jumpers.

Due to the difficulty of a true quad compared to a triple, the high point values for quads in the Scale of Values compared to triples is warranted for jumps that are complete. Skaters who take shortcuts through pre-rotation, however, should not be rewarded with the same base points for doing a less difficult attempt, nonetheless called as a complete quad, that might only have 3 1/4 rotations in the air - though unfairly they currently are.

Notes:

(1)  Fully rotated Sachows do not have an integer number of rotations in the air.  Due to the motion of throwing the free leg to the side across the skating leg during the takeoff, as the skater remains on a back inside edge, the jump takes off somewhat to the side instead of directly backwards.  Fully rotated Salchows are near one-quarter rotation short of integer rotations, generally about one-eighth short each on the takeoff and landing, as was the case in this example.

(2)  We define the air rotation efficiency to be the average rotation rate from takeoff to landing divided by the maximum rotation rate.  Values of 0.8 to 0.9 are typical for skaters.

(3)  If the skater were to refine the air position, a peak rotation rate of 6.5 rotations per second is within grasp.  Food for thought: 6.5 rotations per second + 85% air rotation efficiency + 0.78 seconds air time + an acceptable one-quarter pre-rotation = quad Axel.

 Text and all photos Copyright 2020 by George S. Rossano