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Introduction In the first page on turning I gave a qualitative explanation of how an inline skate turns. Here I will extend the turning analysis becoming somewhat quantitative and showing how the torsional grip properties of the wheel leaned "on edge" lead to new phenomena. In fact, it will turn out that there are two kinds of turn which I call the "Stealth Turn" and the "Normal Turn". The normal turn is what everyone recognizes as a turn but the stealth turn is so subtle that it seems to have gone unnoticed until now although everyone has looked directly at it. The image on the right shows five inline wheels (on edge) which were rolling in the direction of the light gray arrow. In the first turning article I showed how the torsional grip in the contact patch led to motion in the direction of the blue arrow. This off-axis motion is the result of a pull-force generated while rolling on edge. Now if all five wheels generate the same pull force the result would be a sideways motion across the original direction of motion. I had noticed this possibility but did not mention it because I was not ready to accept it then. This page shows that the cross-axis motion is very real.

The Edge Force

The Stealth Turn

Above I discussed what happens for a constant wheel lean angle on edge. But as you skate the lean angle is 90 degrees at the center line and decreases as you push the skate outward. So as you start to stroke the edge force causes the skate to roll in the frame direction at the center line and then its trajectory will curve up to 5 degrees away from the frame direction as the leg is extended. The trajectory of the center of mass of the skate will be curved but the frame direction remains fixed so long as you are not sliding. I call this a stealth turn because if you look at the frame it never changes direction but it's location traces out a curve which can change direction by 5 degrees for these wheels.

The Cornering Force And The Normal Turn

Below I have drawn a figure expressing the fact that when you add a heel push to the sideways edge force the result is a cornering force which pulls the front of the skate toward the skater and propels the rear of the skate forward. While this is qualitatively correct it is not quantitativly accurate as the edge force and heel push interact as they occur.
The heel push here has been chosen as strong enough to cancel the sideways motion due to the edge force at the heel. Now the sideways motion of the heel is halted as the torsional edge effect is suppressed. If the heel push becomes much larger the heel will slide. If the heel push is too weak the turn will not be very sharp.
The reason I say this figure is not accurate is that it would lead you to believe that by halting the sideways motion at the heel the edge force at the front would provide up to 5 degrees of turn. Actually tke skate achieves an edge motion of 5 degrees in about a skate length or about a foot for a five wheel skate. So you might expect the skate to be able to turn "chasing its tail" as a rate of about 5 degrees per foot travelled. Fortunately, this is not so as you can easily demonstrate on the table-top. If you roll the skate forward a foot (on edge) while suppressing the sideways motion at the heel the cornering motion at the front wheel is twice as large as when you leave the rear wheel alone (no heel push). So you turn at the rate of 5 degrees per foot from the front edge force and another 5 degrees per foot from the heel push. Cansequently my five wheel skate can turn at about 10 degrees per foot without sliding.

Below I have drawn the two types of turn. The straight blue line is the skate direction of roll when the skate is upright (not on edge). As you lean it further on edge as you roll the skate can curve up to 5 degrees (red curve) but the skate maintains its original direction as it performs the "Stealth Turn". The green semicircle is the path a skate can travel when the heel push is added to perform the "Normal Turn". Now my skate turns at the rate of 10 degrees per foot travelled so it will turn 90 degrees in about 9 feet. And if the path length (quarter of the circumference) along the semicirle is 9 feet its radius is 5.7 feet for a diameter of 11.4 feet. In fact this seems to be about the minimum size circle I have seen experienced speedskaters accomplish without sliding on a tight maple floor. They start from a 20 foot diameter circle building up speed and spiral down to a small circle resting one hand on the floor at the center of the smaller circle to keep from falling over.

It seems a lot of skaters can't get no satisfaction in turning without the rolling cones. So I will try to see how they fit into my observations on turning. Now when they talk of a "cone" they mean a thin section of a cone or a conic section. So the surface of an inline skate wheel could be approximated by a conic section. One end of the "cone" has a smaller radius and the other end of the "cone" has a larger radius. So as you roll the "cone" the end with the larger circumference moves faster than the smaller end and the "cone" turns. This idea works pretty well for a single wheel but if the wheel is fairly rigid the turning radius is rather limited as it is fixed geometrically by the wheel profile. The "cone" idea doesn't work too badly for 2-wheel vehicles like bikes because the front wheel can be turned by the handlebars so the turning center and turning radius of the front wheel does not fight the rear wheel. The "cone" model gets pretty tricky for an inline skate however.
The inline skate has two (or 3 or 4 or 5..) wheels fixed in-line by the frame. So now when the frame is leaned on edge the front wheel wants to turn about the center of the first wheel and the last wheel wants to turn about the center of the last wheel. But the frame prevents this turning -- all the wheels have to turn together about a single center or none will turn. So if you had two or more "cones" in your frame and tried to roll the frame forward either the frame would not budge (if the grip were very strong) or parts of the cones would slide or something else would happen. As the following demonstration shows, the third alternative is correct -- something else happens.
For this test I have Two Gripper wheels in a frame. I laid two parallel threads on a glass tabletop and fastened them to it at the ends with tape. Another thread was attached perpendicular to the other threads. Now the rear wheel is laid on the threads (and the glass) and the frame is pushed forward along the pair of threads. It is seen in the sequence of photos below that the wheel is attempting to wind up the threads. This shows that the contact patch of the "cone" (wheel) has a torsion developed as it rolls. In other words, if the frame prevents the wheel from turning the wheel responds by turning only the surface layer of wheel at the contact patch where the "cone" meets the road.
Unfortunately the contact patch was too faint to photograph under these conditions but it was observed by eye. The vertical thread is rather sensitive to the motion of the contact patch as it rolls over it. The third photograph down shows the torsion in the vertical thread. As I watched the wheel roll over the vertical thread I saw the torsion begin to develop at the start of the contact patch but its torsion relaxed about one millimeter before the end of the contact patch. I take this as confirmation that the grip has failed at the tail end of the contact patch. The effective (gripping) part of the contact patch is now centered about a half millimeter in front of the axle. This motion of the grip patch is what leads to the sideways walk of the frame or the "edge force". In terms of the cone model the grip failed at the back of the cone so effectively the cones have rotated forward allowing the off-axis roll.