Canting - the right answer

[JBM]

[ 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?


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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

 

[Brown Dog]

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. (! /ubbthreads/images/graemlins/smile.gif!)

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 /ubbthreads/images/graemlins/smile.gif.

…..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. /ubbthreads/images/graemlins/smile.gif

 

[JBM]

[ QUOTE ]

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


[/ 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. /ubbthreads/images/graemlins/smile.gif

[/ QUOTE ]

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

JBM

 

[edge]

[ 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

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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 /ubbthreads/images/graemlins/smile.gif )

 

[JBM]

[ 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 /ubbthreads/images/graemlins/smile.gif )

[/ 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

 

[Brown Dog]

[ 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 ]

What?! /ubbthreads/images/graemlins/confused.gif /ubbthreads/images/graemlins/confused.gif

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?! /ubbthreads/images/graemlins/confused.gif

...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 /ubbthreads/images/graemlins/smile.gif I see this whole thing as a bunch of blokes debating stuff over a beer /ubbthreads/images/graemlins/smile.gif)

.......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 /ubbthreads/images/graemlins/smile.gif!

You'll all be pleased to know I'm not going to go 'around this buoy' again! /ubbthreads/images/graemlins/smile.gif /ubbthreads/images/graemlins/smile.gif

 

[JBM]

[ QUOTE ]

What?! /ubbthreads/images/graemlins/confused.gif /ubbthreads/images/graemlins/confused.gif

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?! /ubbthreads/images/graemlins/confused.gif


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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

 

[HoytemanPA]

Brown Dogs post looks as I understand what happens to a turret adjustable scope that is canted from bore centerline. To prevent this my rifles are 100 yard zeroed, flat forend level, then the scope line of sight is lowered 36 moa, rifle raised and another group is shot at 100 yards. If group is right or left from vertical the scope is turned in relation to the bore until the base zero group and the dialed group are exactly vertical from one another. A bubble level is mounted to the scope for reference and exact distance is measured between groups, divided by 36 and used as my "major mark" number for that scope.

When yall find the answer to this riddle it would perhaps be useful to someone trying to shoot off from his side under some pine boughs. A feature that would be desireable to a bow hunter for example. I designed an arrow rest that could be shot horizontal,along with preliminary work on a sight that matched. Could have used "the right answer" back then for sure.

Point being for a long range rifle application to estimate/calculate point of impact variations based on cant would require measurement equipment greater than needed to prevent it in the first place..... as in bubble level? Just an average joes observation.

I hope yall find "the right answer". And thanks much for a terrific Online Ballistics calculator!

 

[Bart B]

[ 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.

[/ QUOTE ]For what it's worth, a friend and I have done the following with .308 Win. match rifles after rebarreling.

First, shoot the same load we've always used for best accuracy to find out its muzzle velocity in that particular barrel.

Next, shoot the rifle prone with aperture sights; the front sight has a spirit level on it. Zero the rifle and ammo at 100 yards, then check a ballistics table/program for our atmoshperic conditions to find the bullet drop from level fire at 100 yards.

Calculate the actual bullet impact change for the rear sight movement per 0.002083-inch movement per click based on the sight radius used (varies from 32 to 38 inches depending primarily on barrel length), then adjust the rear sight down an amount equal to bullet drop plus front sight height above bore axis. Sight height's usually about 1.5 inches and bullet drop's about 1.9 inches, so move the bullet impact down 3.4 inches at 100 yards. Now the rifle's sights are set to mechanical zero; line of sight is parallel with the line of fire as the bullet leaves.

Then use a good ballistics software program to find the bullet drop at 300, 600, 800 and 1000 yards. Add sight height to those drop numbers then calculate how many clicks the rear sight needs to be raised to zero at these ranges.

How well does this work? Never been off more than two clicks (about 2/5ths MOA with a 38-inch sight radius) in elevation with several barrels. Sometimes more error in windage 'cause us humans can't dope wind that well all the time.

 

[Brown Dog]

Bart,

My sloppy language; my point should be amended to read as follows: [ QUOTE ]
I will be convinced when 1000yd competitors start using their (unchanged) 100yd zero at all ranges, simply applying 'perfectly vertical' holdover in order to reduce their cant errors by a factor of 10.


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