Interesting finding on Blueprint

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Interesting finding on Blueprint

Post by kellytehuna »

I've been playing around with a trial version of Blueprint. It's been a VERY educational experience thus far. VERY good, complete piece of software.

However, there was one thing that stood out to me and I'm interested in hearing what might come of this discussion. The software allows you to simulate a shot on a given condition and lane surface. They give you a plot of the ball on the lane, as well as plots of change in tilt and rotation over time and change in revolutions and ball speed over time. Interestingly, the tilt/rotation plot show there is an intersection of the two plots after which, rotation decays to 0, while tilt declines at a much slower rate of decay, often ending at 8-10 for my stats (starting tilt of 17).

As far as I am aware, rotation can never be lower than tilt. That being the case, the results shown by the plots don't make sense. Thoughts? I realize everything is mathematically modeled, so perhaps this discussion might become a lesson in mathematical proofs, but I'm VERY interested in reconciling what I've been taught thus far (rotation <= tilt) and what is being shown by the mathematical model.
Last edited by kellytehuna on January 12th, 2012, 6:21 am, edited 1 time in total.
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Re: Interesting finding on Blueprint

Post by RevZiLLa »

At release, with rotation at 45* and tilt at 7*, rotation > tilt. IIRC, AR declines faster than AT and when the two are =, the ball stops hooking. Someone like PDW has a ton of AR and almost no tilt. Hypothetically, a ball with 90* AR and 0* AT will still hook.

I don't see the anomaly...maybe you need to state it more obviously for me to fathom it....
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Re: Interesting finding on Blueprint

Post by kellytehuna »

Axis rotation decays to 0, while Axis tilt degrades to a non-zero value (< 1), therefore axis tilt has a value GREATER than axis rotation. As far as I'm aware (and I'm open to being re-educated here), that's not PHYSICALLY possible.

<Begin discussion>
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Re: Interesting finding on Blueprint

Post by Bahshay »

kellytehuna wrote:I've been playing around with a trial version of Blueprint. It's been a VERY educational experience thus far. VERY good, complete piece of software.

However, there was one thing that stood out to me and I'm interested in hearing what might come of this discussion. The software allows you to simulate a shot on a given condition and lane surface. They give you a plot of the ball on the lane, as well as plots of change in tilt and rotation over time and change in revolutions and ball speed over time. Interestingly, the tilt/rotation plot show there is an intersection of the two plots after which, rotation decays to 0, while tilt declines at a much slower rate of decay, often ending at 8-10 for my stats (starting tilt of 17).

As far as I am aware, tilt can never be lower than rotation. That being the case, the results shown by the plots don't make sense. Thoughts? I realize everything is mathematically modeled, so perhaps this discussion might become a lesson in mathematical proofs, but I'm VERY interested in reconciling what I've been taught thus far (rotation <= tilt) and what is being shown by the mathematical model.
FWIW, I think this is the statement that caused the initial confusion. I think you have that backwards.
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Re: Interesting finding on Blueprint

Post by kellytehuna »

AH! You are correct, sir! This is what happens when you don't proof read! LOL! Thanks for pointing that out.
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Re: Interesting finding on Blueprint

Post by dukecrimson »

Wow... This is interesting...
Is the trial version of the Blueprint software open to public?
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Re: Interesting finding on Blueprint

Post by Ajvand0 »

I think there was a discussion about this awhile back. That doesn't seem to make sense that axis tilt can be greater then rotation. I was wondering is this based on the wrong assumption (i'e. incorrect mathimatical equation) by blueprint or if blue print defines tilt and rotation differently then what we define it.
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Re: Interesting finding on Blueprint

Post by kellytehuna »

Well, that's kind of why I opened the discussion. VERY interested in hearing from Mo and Blueprint in particular. I'm definitely more interested in the mathematics behind it. Not sure we'll get that in depth, but certainly interested.
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Re: Interesting finding on Blueprint

Post by elgavachon »

How far does Blue Print map a ball? Does a ball hit hook-out, then roll-out, then back up? depending on the factors?
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Re: Interesting finding on Blueprint

Post by Blueprint »

kellytehuna wrote:Well, that's kind of why I opened the discussion. VERY interested in hearing from Mo and Blueprint in particular. I'm definitely more interested in the mathematics behind it. Not sure we'll get that in depth, but certainly interested.
You are correct in noticing that, as far as Powerhouse Blueprint is concerned, axis tilt angle can exceed axis rotation angle. The reason for this being in conflict with the views of this forum is unknown, but it quite possibly does have something to do with a difference in definitions. I would recommend that we start this discussion by formally defining how Blueprint represents axis rotation angle and axis tilt angle and then we can take it from there. This will undoubtedly get a little technical (boring?), so I apologize in advance to those readers who have absolutely no interest in this!

(Note: everything that follows assumes a right-handed bowler)

Axis rotation angle and axis tilt angle are the two parameters that allow us to represent the ball's angular velocity as a 3D vector (with X, Y, and Z components) that is relative to the ball's direction of travel. So, for use as an aid in this discussion, we should first define this coordinate system...this is done in the image below:
Axis_Rotation_Tilt_Coordinate_System_Definition.jpg
Using this notation, here are some examples of how certain balls' angular velocity vectors are oriented: a ball with no side roll and no tilt has its angular velocity vector oriented in the +Y direction; a ball with pure side roll and no tilt has its angular velocity vector oriented in the -X direction; a ball that is spinning like a top has its angular velocity vector oriented in the +Z direction. This coordinate system discussion really doesn't become too important until much later (if/when we discuss why axis rotation angle decays to zero, but axis tilt angle does not), but I thought it would be best to mention it early so we're all on the same page.

Blueprint treats axis rotation angle and axis tilt angle as the two angles of a spherical coordinate system. An example of a spherical coordinate system is the one used to describe points on the surface of the Earth, where each point is uniquely described by its longitude and latitude. The situation of describing a ball's angular velocity vector (which is oriented along its axis of rotation) is quite similar, except we use the terms "axis rotation angle" and "axis tilt angle" instead of "longitude" and "latitude". The convention used by Blueprint for these two angles is shown below:
Powerhouse_Blueprint_Axis_Rotation_Axis_Tilt_Definitions.jpg
In the above attachment, I've included images of the traditional back view, along with a top view for improved clarity. When you look only at the single 2D image of the back view, it can be easy to forget that we're talking about a 3D object. Hopefully, providing two views makes it more clear.

Is any of this making sense so far? Hopefully, this at least partially clears up how Blueprint represents the two angles. The next step is probably to better understand the definitions used on this forum. Can anyone provide a description of the axis rotation angle and axis tilt angle definitions that are used here and how they might differ from what Blueprint uses?
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Last edited by Blueprint on January 13th, 2012, 3:27 am, edited 1 time in total.
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Re: Interesting finding on Blueprint

Post by Blueprint »

dukecrimson wrote:Wow... This is interesting...
Is the trial version of the Blueprint software open to public?
The trial version (as well as the full version) is available to the general public. It can be downloaded from our website at http://www.blueprintbowling.com.
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Re: Interesting finding on Blueprint

Post by kellytehuna »

As I understand it, Axis rotation is the angle at which the ball's rotation is moving relative to the initial translational vector of the ball. If the axis of rotation is parallel to the initial trajectory, the ball has 90* axis rotation. If the axis of rotation is perpendicular to the initial trajectory, it has 0* axis rotation.

Axis tilt is the vertical offset of the axis of rotation, relative to the lane's surface, again, relative to the initial translational vector of the ball. 90* would put the axis of rotation at the very top of the ball, while 0* would have the axis of rotation parallel to the lane bed.

I'm sure someone will correct me, if this is incorrect.
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Re: Interesting finding on Blueprint

Post by The Kid »

That sounds right, Kelly. But, I think that's simply initial axis rotation and tilt. I believe both are measured at any moment relative to the direction of motion at that moment. For instance, when the ball is in a roll, axis rotation and tilt are measured (near 0°, and equal) from the direction the ball is then traveling.

Or, another way to put it is to say that the "origin" (0° tilt and rotation) is on the line (vector) through the geometric center of the ball in the direction of motion. So, while the ball is still skidding, there is a constant origin. While it is hooking, the origin is constantly changing because the direction of motion is constantly changing. It becomes constant again during the roll phase.

Blueprint, I think the working definitions are identical. I'm excited for the math and illustrations.
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Re: Interesting finding on Blueprint

Post by M4R10 »

Hi

I think it's really just matter of definition regarding axis rotation with tilt being less of a factor.

The main difference is that Blueprint is rotating the coordinate system along with the ball so that its X-axis always faces the direction the ball is moving.

If the ball has ended the hooking phase then axis rotation simply, mathematically and physically has to be zero by Blueprint's definition of the coordinate system. Otherwise the surface of the ball would still be crossing the surface of the lane at an angle to the ball's path. This would result in further hook...

The ball can still have tilt, though, while rolling straight. Think of a stunt car going on two wheels (LH or RH wheels, not a wheely). The tires go forward but are tilted. Pretty much the same.


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Re: Interesting finding on Blueprint

Post by MegaMav »

Its not possible to have tilt without rotation.
Tilt is a vertical component of rotation, they are dependent.
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Re: Interesting finding on Blueprint

Post by Blueprint »

Thank you to all for the replies. As many readers are likely aware, this website has already had several very heated debates on this topic (axis rotation angle / axis tilt angle relationship)...people obviously have strong feelings about this and I don't intend for my comments below to contradict anyone or refute anyone's long-held beliefs, as I don't think we've heard from all sides or properly understood everyone's assumptions. As long as this discussion can stay rational and civilized and people can keep an open mind, I think it should continue. Even if the end result is that we all agree to disagree, my opinion is that this discussion is still worth having.

I must admit that I continue to struggle to understand some of the statements that are being made on this topic, both in this thread and in some of the prior ones. This makes me feel like there is perhaps still a subtle definition difference causing the discrepancy. For this reason, I’ll limit my discussion below to the topic that I do understand, which is how Blueprint works. Getting back to the topic of kellytehuna’s original question, which involved him wanting to better understand the math behind all of this…

It can be shown mathematically by deriving the bowling ball’s rigid-body equations of motion that, when using the definitions for axis tilt angle and axis rotation angle that were shown by me previously, axis tilt angle can exceed axis rotation angle. It can also be shown mathematically that the surface of the ball slips/slides past the lane surface beneath it until axis rotation angle equals zero. As a consequence of this, it can additionally be shown mathematically that frictional forces will contribute to making the ball hook until axis rotation angle equals zero. Equations of motion supporting these statements have been published four separate times by four separate groups of Ph.D.-level physicists and engineers in several peer-reviewed academic journals over the course of the last 30+ years. Our own derivation of the ball’s equations of motion and subsequent on-lane testing program further support these statements.

If anyone is still extremely interested in this topic, please let me know. I’m willing to volunteer to contribute derivations, equations, and diagrams for a simplified case that support the statements made above. This will take considerable effort on my part and there are only so many hours in the day, so this is only worth doing if there is genuine interest and if people are willing to approach this with open minds.
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Re: Interesting finding on Blueprint

Post by JohnP »

Sounds like Blueprint and Math is Truth need to get together. -- JohnP
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Re: Interesting finding on Blueprint

Post by kellytehuna »

I am most definitely open to discussion. I would be happy to look at the articles you mention from the PHD level physicists and any other supporting documentation. I'm not saying anyone is wrong, or anything like that, I just want to understand the topic better.

I'm unaware of how Mo and Steve Fresh came to their conclusions, but I'm sure it wasn't without thorough collection of empirical data. However, if there is some mathematical derivation showing that it's possible, then I for one would be happy to see that. From there it becomes a matter of whether or not it's possible within the physical constraints of the bowling environment.

I look forward to continuing this discussion.
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Re: Interesting finding on Blueprint

Post by JohnP »

I understand the need for understanding the theory, but does it really have any practical influence on lane play or ball layouts? If axis tilt CAN be greater than rotation, what changes? -- JohnP
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Re: Interesting finding on Blueprint

Post by kellytehuna »

JohnP wrote:I understand the need for understanding the theory, but does it really have any practical influence on lane play or ball layouts? If axis tilt CAN be greater than rotation, what changes? -- JohnP
The more completely you can understand the way the ball transitions, which includes the way rotation and tilt are "burned off", the more complete the picture of ball motion becomes, which has to be good for the greater community, right?
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