Long Range Hunting Online Magazine Canting - the right answer
 Home LRH Store Forums Long Range Rifles Articles Reviews Group Hunts Shooting Classes G7 Ballistics Calculator Rules & FAQ Register Search Today's Posts Mark Forums Read

 Rifles, Bullets, Barrels & Ballistics

# Canting - the right answer

#57
05-23-2006, 08:24 AM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

[ QUOTE ]

Standby…

I’ve been having trouble with the idea being mooted here that at 500yds, the effect of a 10 deg cant for a rifle zeroed at 1000yds is roughly 10 times bigger than for a rifle zeroed at 100yds ………to use JBMs figures:

At 500yds
100yd zero 10 deg cant: x = 3.3” y = -0.2”
1000yd zero 10 deg cant: x = 31.25” y = -2.76”

This has been, for me, been entirely counter-intuitive [img]/ubbthreads/images/graemlins/smile.gif[/img] .
The effect should be the same in both examples……

[/ QUOTE ]

It's entirely intuitive to me and I think it would be to you (maybe not -- many people think of the same problem many different ways...) if you understand about what is happening when you cant. A certain part of the elevation angle is transformed under rotation to a new elevation angle and new azimuth angle. The more elevation angle you have, the more azimuth angle you end up with after rotation. That's why the zero range matters.

Look at what Gustavo posted:

[ QUOTE ]

100 yds ZERO

500(x) = 03.27"
500(y) = 47.30"

1000 yds zero

500(x) = 030.80"
500(y) = 108.84"

drop (500) = 65.8"

[/ QUOTE ]

For different zeroes he shows different cant -- by about a factor of 10. As I've said before, this agrees closely with my answers. So we have three methods (my derivation, the formulas Gustavo posted and my online calculator) saying almost the exact same thing.

[ QUOTE ]

..I’m embarrassed to say, it was only this morning whilst walking the dog, that the reason for the error in these calculations popped into my head:

Bottom Line Upfront: JBM et al; the erroneously low ‘100yd zero’ values you are producing are caused by the fact that you are basing your calculations on the fired QE (Quadrant Elevation)………..you should be basing them on the TE (Tangent Elevation) at the target range.

[/ QUOTE ]

They are not erroneous. The error caused by canting is entirely dependent on the angle between the bore and the line of sight (within the limits of the flat fire approximation which is very good for everything were talking about here). If it's zero you get no error due to canting. That was the whole point of showing the difference between the two zero ranges.

[ QUOTE ]

Here’s why cant effect calculations ‘factoring in zero distance’ are erroneous (and I hope you will see, counter intuitive):

[/ QUOTE ]

Zero distance only enters into it because that effects what I call the elevation angle -- the angle between the barrel bore and the line of sight.

[ QUOTE ]

Had the 500yd target been set up in a 47.5” dip in the ground (ie a small gully 4ft lower than the firing point) a rifle fired at the '100yd zero' QE of 3.98 MOA would have resulted in a target round.
ie the rifle would now be zeroed at 500yds

[/ QUOTE ]

No, the rifle is still zeroed at 100 yards, you just aimed 47.5" high at 500 yards.

[ QUOTE ]

So,
QE = 3.98 MOA produces a 100yd zero when AS (angle of sight) is zero
And
QE = 3.98 MOA produces a 500yd zero when the target is 4ft below horizontal

[/ QUOTE ]

That's not zeroed. All you're saying is that you'll shoot low when shooting past the zero range. I agree.

[ QUOTE ]

I hope you can now see that it is entirely counter-intuitive to assume that when we call QE 3.98 the ‘100yd zero’ it will produce a smaller cant error than the same QE when we call it ‘500yd zero (target 4ft below horizontal)’.

[/ QUOTE ]

Canting error is produced by a rotation about the line of sight, the bore of the scope. The angle that matters is the angle between the line of sight and the bore because it's the cause of the error.

Take a look at the formulas Gustavo posted:

[ QUOTE ]

The formulas Gustavo posted take this into account:

X(R)=H(R)*sin ß
Y(R)=H(R)*cos ß - Drop(R)

where H(R) is the height of bore line in relation to sight
line, as a function of range R:

H(R) = R/R0*(SH + Drop0)- SH

SH = sight height
R = range
R0 = zero range
Drop0 = drop at zero

[/ QUOTE ]

Notice the factor R/R0*(SH + Drop0) - SH. This can also be written R*Elev - SH, where Elev is the elevation (angle between the bore and the line of sight), because (SH + Drop0)/R0 is the amount you raise the barrel to zero at range R0 (again to within the flat fire approximation)

Now, X(R) = H(R)*sin(B) = R*Elev*sin(B) - SH*sin(B)
and, Y(R) = H(R)*cos(B) - Drop(R) = R*Elev*cos(B) - SH*cos(B) - Drop(R)

or if you substitute

e' = Elev*cos(b)
a' = Elev*sin(b)

You have

X(R) = R*e' - SH*sin(B)
Y(R) = R*a' - SH*cos(B) - Drop(R)

I think you could, with good agreement, use my formulas that I originally posted and find e' and a', then plug these into Gustavo's posted formulas and you should get about the same answers. Again, I don't know what Gustavo, et. al. are using for Drop(R) so there may be some difference there too.

The only problem I have with these equations -- the only problem I've EVER had with these equations -- is what is essentially a new elevation and azimuth of Elev*cos(B) and Elev*sin(B). It's not entirely correct. The actual angles under a rotation are what I've shown in my first post. These are very close, but they aren't entirely correct. I ONLY brought it up because I have ballistics book(s) saying that it's an approximation and that it may not work at longer ranges and this is after all LongRangeHunting.Com. If this were ShortRangeHunting.Com I wouldn't have ever posted.

JBM
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm
#58
05-23-2006, 12:08 PM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

I've put a derivation of my equations on my website at cant if anybody is interested.

JBM
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm
#59
05-24-2006, 02:54 AM
 Gold Member Join Date: Sep 2003 Location: Blighty Posts: 637
Re: Canting - the right answer

JBM,

..I would have thought that my earlier powerpoint slides show that I’m singing off the same song sheet regarding cant producing Az and El changes [img]/ubbthreads/images/graemlins/smile.gif[/img].

….I think where my thinking has diverged (quite possibly due to an assumption on my part [img]/ubbthreads/images/graemlins/blush.gif[/img]!) is in the practical application of this.

………clearly, if you set your sight at a 100yd zero, adopt the prone position and attempt to hit a target that is horizontally 500yds away from you all you’ll do is carve mud furrows somewhere between you and the target.

………As such quantifying Az and El changes relating to canting the set 100yd QE, when used at 500yds, is not of much practical use.

……my point, (or my dissonance [img]/ubbthreads/images/graemlins/confused.gif[/img], or my reasoning problem [img]/ubbthreads/images/graemlins/confused.gif[/img] [img]/ubbthreads/images/graemlins/smile.gif[/img]) comes when (or if!) you are proposing to use the 100yd zero cant data whilst hitting a 500yd target (using your 100yd zero scope; either because the target is in a 4ft dip, or because you have aimed ‘up’ by 4ft)

….in that instance, the fact that the rifle/scope has a 100yd zero becomes irrelevant. The cant effect will relate to the 500yd TE and be the same as if the rifle were zeroed at 500 yds……the 'boreline' to'100yd zero scope angle' is no longer relevant, ( if you're hitting the target and not ploughing furrows ) the cant effect has to be calculated in relation to the fired TE at that target range.

….I think my reasoning was drawn this way because at some point someone mentioned using this data to aim off using dots on their reticle.

….apologies, the rabbit-hole was mine [img]/ubbthreads/images/graemlins/smile.gif[/img]….
#60
05-24-2006, 03:21 AM
 Platinum Member Join Date: Dec 2001 Location: Mukilteo, WA Posts: 1,092
Re: Canting - the right answer

While all of this is fascinating, have any of you done any sort of useful test--like measuring your maximum cant error when "keeping the crosshairs square to the world" is on your mental checklist before taking a shot? Like I said before,
[ QUOTE ]
I don't think I could shoot a rifle canted at 10 degrees unless somebody had just hit me in the head with a hammer. [img]/ubbthreads/images/graemlins/laugh.gif[/img]

[/ QUOTE ]

In short, what are the realistic errors one could expect vs. the nice round 10 degree figure?
#61
05-24-2006, 05:30 AM
 Platinum Member Join Date: Dec 2005 Posts: 2,483
Re: Canting - the right answer

JonA, I've been watching this thread for quite a while. It's got more than interesting; closer to amazing.

My bottom line is, just multiply the bullet drop at the target range by the sine of the cant angle. The error in the answer from "exactamundo" (means to 43,210 decimal places) from all the math, sight height, et al, in this thread is much smaller than your holding errors and rifle/ammo accuracy.
#62
05-24-2006, 07:33 AM
 Gold Member Join Date: Sep 2003 Location: Blighty Posts: 637
Re: Canting - the right answer

Bart,
I agree.

JBM, Tiro et al,

My previous post was addressing this issue (as posted by Tirofijo):
[ QUOTE ]
But when you have a hunting rifle you don't normally change the scope's settings, so you may take a shot at 400 m even if your zero is 200 m using holdovers. In this case the angle between LOS and bore line corresponds to the 200 m zero and the effect of canting would be smaller than if the rifle was zeroed at 500.

[/ QUOTE ]

To which the short answer is 'No!!!!!' [img]/ubbthreads/images/graemlins/shocked.gif[/img] [img]/ubbthreads/images/graemlins/smile.gif[/img] for all the reasons given in my previous post.

As soon as you apply holdover you are, in effect, re-zeroing to the new target range.

The error of reasoning here is based in the fact that people have fixated on the angle between the boreline and the ‘zeroed at X yds scope’.

When you are hitting a target at a given range; the critical angle for the purposes of cant effect calculations is:

[boreline’s elevation relative to a horizontal datum (ie its Quadrant Elevation)] MINUS [True Angle of Sight to the Target (ie AS)] = Tangent Elevation [The tangent Elevation being that part of the QE that has been applied to account for the bullet’s drop at that distance.]

(Sorry, but it’s dawned on me that people are not understanding the terms ‘QE’, ‘TE’ and ‘AS’ …….perhaps they don’t translate well across the pond! [img]/ubbthreads/images/graemlins/smile.gif[/img]]

....which Bart neatly summarises as: [ QUOTE ]
just multiply the bullet drop at the target range by the sine of the cant angle

[/ QUOTE ] (bullet drop at a given range being another way of quantifying the TE)

You all (not Bart!) need 'Red Leg' [a US term that I know won't require transatlantic translation! [img]/ubbthreads/images/graemlins/smile.gif[/img]] advice; not more formulae [img]/ubbthreads/images/graemlins/smile.gif[/img] [img]/ubbthreads/images/graemlins/smile.gif[/img]

#63
05-24-2006, 07:50 AM
 Silver Member Join Date: Jan 2004 Location: New Mexico Posts: 113
Re: Canting - the right answer

[ QUOTE ]

My previous post was addressing this issue (as posted by Tirofijo):
[ QUOTE ]
But when you have a hunting rifle you don't normally change the scope's settings, so you may take a shot at 400 m even if your zero is 200 m using holdovers. In this case the angle between LOS and bore line corresponds to the 200 m zero and the effect of canting would be smaller than if the rifle was zeroed at 500.

[/ QUOTE ]

To which the short answer is 'No!!!!!' [img]/ubbthreads/images/graemlins/shocked.gif[/img] [img]/ubbthreads/images/graemlins/smile.gif[/img] for all the reasons given in my previous post.

As soon as you apply holdover you are, in effect, re-zeroing to the new target range.

[/ QUOTE ]

Maybe we're agreeing here, but I don't think so. Zeroing is defined as where the bullet crosses the line of sight. If you hold over this doesn't change so holding over doesn't change the zero. It also doesn't change the angle between the bore and the line of sight -- the cause of the canting error.

[ QUOTE ]

The error of reasoning here is based in the fact that people have fixated on the angle between the boreline and the ‘zeroed at X yds scope’.

[/ QUOTE ]

Because that is what causes the cant error. You're rotating the firearm around the line of sight. It's the angle relative to the line of sight that causes the error.

[ QUOTE ]

When you are hitting a target at a given range; the critical angle for the purposes of cant effect calculations is:

[boreline’s elevation relative to a horizontal datum (ie its Quadrant Elevation)] MINUS [True Angle of Sight to the Target (ie AS)] = Tangent Elevation [The tangent Elevation being that part of the QE that has been applied to account for the bullet’s drop at that distance.]

[/ QUOTE ]

Are you defining the Tangent Elevation as the angle between the bore and the line of sight? If so I agree. If not, please derive this and post it somewhere so we can see it.

[ QUOTE ]

You all (not Bart!) need 'Red Leg' [a US term that I know won't require transatlantic translation! [img]/ubbthreads/images/graemlins/smile.gif[/img]] advice; not more formulae [img]/ubbthreads/images/graemlins/smile.gif[/img] [img]/ubbthreads/images/graemlins/smile.gif[/img]

[/ QUOTE ]

Yeah. Heaven forbid we should understand what is going on.
__________________
JBM Small Arms Ballistics -- http://www.eskimo.com/~jbm

 Bookmarks

 Thread Tools Display Modes Linear Mode

 Similar Threads for: Canting - the right answer Thread Thread Starter Forum Replies Last Post mo Long Range Scopes and Other Optics 13 09-27-2009 10:51 PM Dangerous_dave308 Rifles, Bullets, Barrels & Ballistics 6 08-05-2009 12:04 AM flims Equipment Discussions 5 11-01-2006 01:21 PM Gustavo Rifles, Bullets, Barrels & Ballistics 0 05-09-2006 09:33 AM Gustavo Rifles, Bullets, Barrels & Ballistics 11 05-05-2006 09:00 AM

All times are GMT -5. The time now is 07:37 PM.