There seems to be a lot of discussion how the rocker size affects skating. I just drew two arcs of 9 inches long , one was of a 7ft radius, the other of 8 ft. Guess what? The lines are parallel! Try it by anchoring a measuring tape and a piece of paper and draw the arcs.
It seems that the most difference will be only in the spin rocker, in the front of the blade....
Thoughts???
Of course the lines are parallel, ANY circle that you draw with the same center will be concentric, so lines of an arc will be parallel, but the curvature of these is not the same. The curve of the circle w/ an 8 ft diameter over any amount of length is less than the curvature of a 7 ft diameter circle over the same amount of space.
You can find a degree of curvature by determining how much of the circumference the 9 inches takes up.
If the diameter is 8 feet, the circumference is 25.12, so 9 inches is 128.98 degrees of the circle.
If the diameter is 7 feet, the circumference is 21.98, so 9 inches is 147.41 degrees of the circle.
Fairly significant difference I think.
Try this- make the entire circle for each, then mark off where 9 inches (I'm assuming that is your blade length) is on the arc (make sure to measure the arc, not a straight line). Then, set them on top of each other, aligning two of the marks- you'll be able to see that 8 ft one is shallower, because the second mark on the 7 foot circle will be lower than the circumference of the 8 ft circle- it has a deeper curve.
My thoughts though: In skating, the littlest change makes a difference. I bet most people have a preference for what they started with. One isn't necessarily better than the other.
If the two rockers are tangent to the same line at one end, they should be 0.012 inches apart at the other end along the direction perpendicular to the line.
A simple way to evaluate the effect of rocker size r on spins is to assume that the blade is pressed into the ice by a fixed depth d. Then the length of the blade in contact with the ice would be
r*arccos((r-d)/r)
which is approximately proportional to
sqrt(r)
A complete analysis of spinning would require understanding the mechanical properties of ice, which are complicated. However, this simple model tells us that you should expect about a 7% difference between an 8 ft rocker and a 7 ft rocker.
I just wanted to add that by definition, arcs cannot be parallel, even if they have the same radius and orientation. But lines can be.
ooh, skating math. ;D
The spins are not performed on the primary rocker, though. Therefore, you would expect that it should not make a difference.
Quote from: nicklaszlo on July 27, 2011, 10:57:55 PM
I just wanted to add that by definition, arcs cannot be parallel, even if they have the same radius and orientation. But lines can be.
I disagree- curves can be parallel, and arcs are finite curves.
Wolfram is a respected math site: http://mathworld.wolfram.com/ParallelCurves.html
Mathworld includes definitions which apply only in specialized contexts.
On reflection, my analysis does not assume one is spinning. Perhaps it best describes stroking and stops.
I'd also like to add that most skating blades aren't made up of just one radius. They're generally a combination of 2 or 3.
Therefore what one manufacturer calls an 8ft won't be the same as another manufacturer's 8ft before of the different radii they use.
Ignoring all the maths, the spin radius is the bit which affects most of the spinning and jumping (I've switched from one 8ft to another 8ft so can attest to this). The rest of the rocker affects the footwork.
A better comparison would be to trace different manufacturers blades to see what the differences in profiles actually is.
(And while I'm professionally an engineer, when it comes to skating, it's the feel that's important).
In my experience the placebo effect also plays a role.
Quote from: nicklaszlo on July 28, 2011, 11:26:48 AM
In my experience the placebo effect also plays a role.
Meaning that all new blades change things because they've not be ground flat?
The placebo effect is what I am leaning towards as well. Is 7% really a big enough difference to notice? Although, that being said, I have read that Brian Boitano equated jumping a quad jump to balancing on a dime sized spot vs on a basketball sized one for a double.
Since I am not jumping quads anytime soon, perhaps a change from a 7 ft rocker to an 8 would not be such a big deal... I am thinking of switching from a Coronation Ace to an Ultima Matrix Legacy.
For what it's worth, I've heard it's easier to spin on a 7 ft rocker, but jump on an 8 (more surface to land on, since it is flatter...) Not sure if there is truth in this, but if you don't have great jumps, that may make it easier.
I think based on how different a rocker if from old blades to new blades, 7% is probably a big enough difference.