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# Canting - the right answer

#71
05-24-2006, 03:06 PM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

[ QUOTE ]

Well, I am...
A question, though. On that page, your unit vectors v (=no cant) and v'(=with cant) both start in the origin of your X,Y,Z coordinate system, right?
But when canting, i.e. rotating the bore around the sight line, the muzzle of the rifle (=the origin of your XYZ coordinate system) moves as well.

[/ QUOTE ]

Absolutely the muzzle moves. It's not shown here, because I'm only interested in the direction, not offset (in this case). You're right in that you still have to find the offset and add that to any change.

[ QUOTE ]

Going to extremes to show what I mean: if you have 2" between the bore and the scope, and rotate 180 degr, the bullet starts 2" ABOVE the sight line, not below.
So, yes, the Az and El angles change, but so does the location of the muzzle.
Or do you take this into account in another way?

[/ QUOTE ]

In my ballistics programs it is taken into account by using the starting point of the bullet as a vector r0 = [-sight offset, 0.0, -sight height]. The initial velocity is taken as a rotated velocity vector and in doing that you only worry about direction since the integration routines start from the point r0. The formulas I derived were meant to provide a new elevation and azimuth angle that could be used to adjust a trajectory. You are absolutely right that you have to worry about the change in r0, but it is small. For small cant angles it would negligible. Even for a 10 degree cant the error in the X direction (cross wind) is only 0.3".

JBM
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm
#72
05-25-2006, 04:56 AM
 Gold Member Join Date: Sep 2003 Location: Blighty Posts: 637
Re: Canting - the right answer

JBM,

Don’t know if you spotted this in one of my posts preceding your most recent:

[ QUOTE ]
Aha!! I have the cause of our differing views:

Your calculations assume that, despite the cant, the holdover has been applied perfectly vertically.

Mine assume that the holdover has been applied with the same error as the cant angle.

[/ QUOTE ]

Diagrammatically the 2 ‘schools of thought’ are shown below.

Yours on the left ……….despite the cant, the holdover has been applied perfectly vertically. ….if this were the case then I agree that the Az and El errors would relate only to the canting of the zero range TE. (! [img]/ubbthreads/images/graemlins/smile.gif[/img]!)

Mine (or should I say, the conventional !) on the right. In this instance, I hope you would agree that the Az and El errors would relate to the canting of the target range TE

When considering the ‘conventional view’ it may be worth considering how the canted scope looks to the firer (it provides a false vertical reference against which to apply holdover):

Which is more likely in the real-world? …..we could argue it until the cows come home [img]/ubbthreads/images/graemlins/smile.gif[/img].

…..but in terms of a ‘common sense’ check:

I will be convinced when 1000yd competitors start zeroing at 100yds and then applying 'perfectly vertical' holdover in order to reduce their cant errors by a factor of 10. [img]/ubbthreads/images/graemlins/smile.gif[/img]
#73
05-25-2006, 10:59 AM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

[ QUOTE ]

Which is more likely in the real-world? …..we could argue it until the cows come home [img]/ubbthreads/images/graemlins/smile.gif[/img].

[/ QUOTE ]

or at least 60 or 70 posts.

If I were going to simulate what you have shown, it would be with a canted angle to get the cant error and extra windage to get the offset due to raising the muzzle at the canted angle. I would guess (I haven't done the derivation) that the extra windage would be holderover*sin(cant). I agree that it will introduce an additional error, but I wouldn't call it cant error because the launch angle is the same.

[ QUOTE ]

I will be convinced when 1000yd competitors start zeroing at 100yds and then applying 'perfectly vertical' holdover in order to reduce their cant errors by a factor of 10. [img]/ubbthreads/images/graemlins/smile.gif[/img]

[/ QUOTE ]

There are many other reasons not to do that either...

JBM
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm
#74
05-25-2006, 11:41 AM
 Platinum Member Join Date: Nov 2005 Posts: 1,088
Re: Canting - the right answer

[ QUOTE ]
SNIP
I agree that it will introduce an additional error, but I wouldn't call it cant error because the launch angle is the same.

SNIP

[/ QUOTE ]

IMO, what else could it possibly be??

If you take a rifle that is perfectly zeroed, and you fire it canted, the bullet does not hit its mark! Canting is the Sole reason for this error.

edge.

( IMO [img]/ubbthreads/images/graemlins/smile.gif[/img] )
#75
05-25-2006, 12:24 PM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

[ QUOTE ]
[ QUOTE ]
SNIP
I agree that it will introduce an additional error, but I wouldn't call it cant error because the launch angle is the same.

SNIP

[/ QUOTE ]

IMO, what else could it possibly be??

If you take a rifle that is perfectly zeroed, and you fire it canted, the bullet does not hit its mark! Canting is the Sole reason for this error.

edge.

( IMO [img]/ubbthreads/images/graemlins/smile.gif[/img] )

[/ QUOTE ]

If I cant the rifle and aim to the right, 1 moa, what is the source of the error -- it's both. My point was that I would model that shot as two different errors because that is, mathematically, what is happening. I'm going to argue semantics, I don't really care about that. You can call it anything you want. I tend to call the cant error that due to rotation of the bore around the axis of the line of sight and that's only part of the problem introduced in the drawings above.

Think of it this way. If Brown Dog moves his firearm/scope to the left to match the drawing through my scope, he has done a windage correction. He still has the cant error which I've been describing. That's why I say it's really two different errors.

JBM
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm
#76
05-25-2006, 01:29 PM
 Gold Member Join Date: Sep 2003 Location: Blighty Posts: 637
Re: Canting - the right answer

[ QUOTE ]
I agree that it will introduce an additional error, but I wouldn't call it cant error because the launch angle is the same.

[/ QUOTE ]

The boreline has been further elevated in the Plane of the Cant...the fired QE has changed in direct relation to that; so has the azimuth....but this isn't cant error?! [img]/ubbthreads/images/graemlins/confused.gif[/img]

...I think your thinking would be helped if you were to visualise the rifle being elevated about trunnions fixed horizontally through the chamber area.

....your initial scope cant causes the trunnion to be tilted at the cant error. Further elevation (holdover) takes place at that same trunnion tilt.

That's me done.....JBM et al, you'll either accept that or you won't (which, of course, you are free to do [img]/ubbthreads/images/graemlins/smile.gif[/img] I see this whole thing as a bunch of blokes debating stuff over a beer [img]/ubbthreads/images/graemlins/smile.gif[/img])

.......this has been an interesting thread, it's made me think in detail about elements of theory I haven't considered in detail for over 10 years.....thank you all for that [img]/ubbthreads/images/graemlins/smile.gif[/img]!

You'll all be pleased to know I'm not going to go 'around this buoy' again! [img]/ubbthreads/images/graemlins/smile.gif[/img] [img]/ubbthreads/images/graemlins/smile.gif[/img]
#77
05-25-2006, 01:49 PM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

[ QUOTE ]

The boreline has been further elevated in the Plane of the Cant...the fired QE has changed in direct relation to that; so has the azimuth....but this isn't cant error?! [img]/ubbthreads/images/graemlins/confused.gif[/img]

[/ QUOTE ]

Once again, I'm not going to argue semantics. What I said was that I would model it as two different errors and that's how I think about it. I don't really care what you call it. I don't really care what you do about it. I think of it as two different rotations and therefore two different errors. I think of the cant error as the rotation around the line of sight (what you see through the scope). As you increase the elevation, you're aren't increasing that rotation since you are by your own definition increasing the elevation along that angle of cant.

If you look at your pictures, you are really rotating around a line that intersects the impact point. Not the line of sight. I cannot find that definition of cant in any of my texts. That's why I don't think of cant that way.

[ QUOTE ]

...I think your thinking would be helped if you were to visualise the rifle being elevated about trunnions fixed horizontally through the chamber area.

....your initial scope cant causes the trunnion to be tilted at the cant error. Further elevation (holdover) takes place at that same trunnion tilt.

[/ QUOTE ]

I understand the problem and I understand what you're saying, I just don't think of it that way.

JBM
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm

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