How to measure your cube's Angle of cutting corners

[fanwuq]

People have been making ridiculous claims that their cubes can cut corners over 40 degrees. It is physically impossible. Here's how to calculate the true degrees.
I never understand it when people say their cubes can cut corners over ~30 degrees. Show me how that is possible.
45 degrees is when the middle of your corner hits the middle of the center. It would not move at all on any cube, it's physically impossible.
You measure degrees by looking at the black triangle that is perfectly hidden when the cube is aligned (0 degrees.)

0. make sure your cube is at even tension.
1. get the cube at a big angle, pull down 1 layer gently and only apply force on that layer.
2. do this until you get to the angle where you can just barely pull down that layer. (no cheating by applying even the slightest force directly on any other layers or allowing pops.) For example, I adjust U face for my reference of the angle and apply force by only dragging down the R face using an amount of force that is normal for speedcubing (not too much).
3. return cube to that exact position (taking a picture with camera can help.)
4. measure both legs of the triangle accurately! You should probably use mm and measure to at least 3 significant digits.
5. apply arctan.

For my cubes:
For my type A, I got arctan (12.2/20.2) = 31.1 degrees.
I think even this might be too high of a number. Perhaps I did not return to the perfect position and slightly exaggerated it or the ruler measurement was faulty. I suspect an error on my part. Do not make a mistake in your measurements!
For my type C, I got arctan (11.5/22.1) = 27.5 degrees.
For my type A core/store cubies, I got arctan (9.5/22.8) = 22.6 degrees.
For some odd reason, my store cubies are smaller than type A cubies and that cube is set to a looser tension. I don't know way it's worse at cutting corners.

I encourage everyone to apply this method and test their cubes. I expect most people to get results around 28 degrees on a loose DIY.

Edit: someone who already tried this method:

i
now it barely pops and still can cut corners (almost 45 degrees).

so i now i tried measuring my cube to which it can cut corners without trying to force it too much

and i got arctan (9.5/18.5) 27.18 degrees.

so thats how you measure it..some math stuff eh..haha

 

[Jgig1991]

nice way to calculate it, I got 24.4 degrees for my store cube

 

[IamWEB]

I'll test this out soon and edit this post with my results.

 

[vloc15]

haha..im honored to be the 2nd to try that method..lol
fanwuq does have a point u know

 

[toast]

I got 40mm and 35mm resulting in a 41.2 degree angle.

 

[Samlambert]

Because you can't do it with your cube doesn't mean some other people can't do it with their cube... As for my cube, It cuts corner from approximatively 42-43 degrees, I can almost cut from when the corner piece is in the middle of the edge piece, but a little less from that. I'm too lazy to actually calculate all the stuff and whatever.

 

[DavidWoner]

You should probably use mm and measure to at least 3 significant digits.

what are you measuring with? you cant get that kind of accuracy with a ruler, and not everyone has a dial caliper on hand.

 

[blade740]

The thing is, this has nothing to do with anything. While solving, you cut corners by doing a U and then an R', not by doing half a U, stopping, then doing R'. It's about how well your cube transfers between the two moves seamlessly, not about how you can turn it at rest.

Plus, if I pull hard enough, I can cut a >45 angle. For me, at least, it depends on the UBR corner (if trying to cut from U to R'). If it goes BEHIND the U center, it won't cut the corner. If it goes to the right, it'll slide around no matter how far the angle is.

 

[Faz]

type a third model - 28 degrees.

 

[ImNOTnoob]

Hey, when i pull a layer UP, it measures around 35+ degrees, but when i pull a layer DOWN, i get like 20+ degrees. Too lazy to calculate.

 

[wongxiao]

You should probably use mm and measure to at least 3 significant digits.

what are you measuring with? you cant get that kind of accuracy with a ruler, and not everyone has a dial caliper on hand.

As it happens, I have a digital caliper (don't worry its a good one, all steel construction, etc) which is accurate to one one hundredth of a millimeter.



Anyway, my results were:

tan^-1(22.09mm / 11.95mm) = 28.41 degrees.
DIYKit, C4Y Type D (Old).


On a final note, even with the tension "perfectly balanced," you probably wouldn't be able to say this sort of thing with such degrees of precision/accuracy unless you measured every possible face combination and did multiple trials each, averaging all of the results. And you'd still have tons of errors you could report...

Of course, I'm not suggesting that anyone do this sort of thing. I'm trying to point out that getting ultra precision is not only unnecessary (come on these are rubik's cubes we're talking about here!) but pretty impractical. As far as I'm concerned, getting it within +/- 0.5mm is fine.

EDIT: OH WOW, Never mind. Misread significant figures as decimal places.... wow... I feel dumb haha..

 

[fanwuq]

The thing is, this has nothing to do with anything. While solving, you cut corners by doing a U and then an R', not by doing half a U, stopping, then doing R'. It's about how well your cube transfers between the two moves seamlessly, not about how you can turn it at rest.

Plus, if I pull hard enough, I can cut a >45 angle. For me, at least, it depends on the UBR corner (if trying to cut from U to R'). If it goes BEHIND the U center, it won't cut the corner. If it goes to the right, it'll slide around no matter how far the angle is.

Your comment (2nd part) makes no sense. If you pull, it's just physically impossible, if it is over 45 degrees, it would POP our turn the other direction instead, in that case, you are measuring the wrong angle. Or, your are indeed putting pressure on another slice, in that case, I can argue that even the stiffest cube can cut over 180 degrees. It also sounds like your cube is not at even tension.

You should probably use mm and measure to at least 3 significant digits.

what are you measuring with? you cant get that kind of accuracy with a ruler, and not everyone has a dial caliper on hand.

Nevermind about that then, just try to get it accurate and precise.

I got 40mm and 35mm resulting in a 41.2 degree angle.

That's a BIG cube!!!

 

[toast]

Haha I measured the wrong triangles? ;p