are the effects of cant worse on a pistol?

On the Lunatic Fringe of American Airgunning

Proud sponsor of team_subsonic

Charter member of the Western Heretic Alliance

What a great question.

By far the most relevant parameter in cant is the scope height (and the angle of cant, of course). The barrel length is secondary.

However, cant has the unique property that it reverses its effect on the POI, depending on distance. This distance, where the reversal happens, is a distance where the gun is relatively insensitive to cant. The higher the scope, the shorter this distance is. With a rifle, this distance where cant has a minimum effect is too short to be of practical interest (about 4 to 15 yards), but this may not be the case with a pistol.

If it is the case that you shoot your pistol at very short distances, you are likely to see much less of an impact of cant than a rifle shooter shooting at much larger distances.

Actually, cant error is not influenced by scope height. It's a common misconception.

The following thread covers the topic:

https://airgunwarriors.com/field-target/when-would-a-scope-riser-offer-an-advantage-on-an-ft-rifle/#post-4194

Cant is a rotation of the gun about the line of sight, not about an arbitrary axis. When you rotate the gun about the line of sight, the math gives you the precise amount by which the POI will change as you cant the gun. The lateral drift due to cant is given by a formula like this (this is an approximate formula, but is very good for most practical situations),

Lateral drift due to cant =

- scope height * sin (angle of cant ) + target distance * tan (elevation angle * sin( angle of cant))

As you see, the scope height is built into this formula, both directly and indirectly through the elevation angle.

No doubt it is a misconception that will die hard...if ever.

But please note the statement about scope height is not my assertion. It's thoroughly debunked in the article linked by mgkd:

http://www.szottesfold.co.uk/2012/03/high-scope-and-canting-end-of-ancient.html

And supported by the likes of Scotchmo, yrrah, Steve_NC, and Scot Heath.

Cant is a rotation of the gun about the line of sight, not about an arbitrary axis. When you rotate the gun about the line of sight, the math gives you the precise amount by which the POI will change as you cant the gun. The lateral drift due to cant is given by a formula like this (this is an approximate formula, but is very good for most practical situations),

Lateral drift due to cant =

- scope height * sin (angle of cant ) + target distance * tan (elevation angle * sin( angle of cant))

As you see, the scope height is built into this formula, both directly and indirectly through the elevation angle.

Actually, assuming that POI = POA at zero cant, the correct formulas predicting the effect of cant on POI are simpler and have absolutely nothing to do with sight height...

**Horizontal_Shift = sin(cant_angle) * drop_from_boreline**

**Vertical_Shift = (cos(cant_angle) - 1) * drop_from_boreline**

This interactive app by Perry Babin is accurate and fun to play with...

Cant is a rotation of the gun about the line of sight, not about an arbitrary axis. When you rotate the gun about the line of sight, the math gives you the precise amount by which the POI will change as you cant the gun. The lateral drift due to cant is given by a formula like this (this is an approximate formula, but is very good for most practical situations),

Lateral drift due to cant =

- scope height * sin (angle of cant ) + target distance * tan (elevation angle * sin( angle of cant))

As you see, the scope height is built into this formula, both directly and indirectly through the elevation angle.

Cant errors are determined by the amount of projectile drop at the given distance and the cant angle.

X = drop x sin(angle)

Y = drop x (1-cos(angle))

All canted impacts will lie on the circle of radius=DROP. With the 12 O’clock position of the circle at the aim point.

Cant errors at any specific angle is greatest in a gun with a slow projectile at long distance.

Changing the height will make no difference.

Changing the height will make no difference.

Absolutely true, ** provided** uncanted POI = POA (i.e., the rig is accurately zeroed for the range involved). If this criterion doesn't hold, then many other conclusions (e.g., the independence of cant error from sight height) likewise don't hold.

I suspect it was playing with (or thinking about) cases where the target wasn't placed at a zero that has led to many of the stubborn misconceptions about this subject.

As Steve says, it is correct that the drift due to cant is indifferent to scope height, but only at the zero distance.

The formula that I wrote above works for ALL distances, shorter and longer than the zero. It will work as long as the trajectory is not extremely loopy, like a mortar shell.

You can verify this with the JSB calculator, which is the only one on the internet (as far as I know) that computes trajectories with cant:

http://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi

For a 0.308, 220 grain bullet with BC 0.5, vel 900 ft/s, no wind and 10 deg cant, these are the drifts due to cant you get from JBM compared with my formula:

Sight at 2 in, elevation 22.790 MOA for zero at 100 y:

JSB my formula

100 y: 3.8 in 3.79 in

300 y: 12.1 in 12.08 in

600 y: 24.5 in 24.5 in

Sight at 3 in, elevation 24.223 MOA for zero at 100 y:

JSB my formula

100 y: 3.8 in 3.79 in

300 y: 12.6 in 12.60 in

600 y: 25.8 in 25.82

Conclusion: If you are uncertain about your zero, the height of the scope matters, otherwise not really :).

DT

Aren't we saying exactly the same thing, DT?

I'm prettysure your formula only works if...

** target distance * tan (elevation angle) = drop from boreline + scope height**

...which is the same thing as saying the target is located at the zero distance: That is to say, at a distance where the elevation angle has been adjusted to cause POI to equal POA. Cant error is therefore * still *independent of scope height because height has already been incorporated into elevation angle.

If you're using a different definition for "elevation angle," please provide it.

Thanx Gang!

I'll give it extra care setting the pistol up, then it's on me while on the shooter's box..... One of those will be easier to get precise....... 🙂

On the Lunatic Fringe of American Airgunning

Proud sponsor of team_subsonic

Charter member of the Western Heretic Alliance

Steve, it is not exactly the same thing. My formula works everywhere along the trajectory, not just where the POI = POA. It describes the full trajectory line. In fact, that is how I derived it. I took the uncanted trajectory and perturbed it by rotating it about the line of sight. I did the same thing you do, but for the entire trajectory rather than the POI. The difference between the rotated trajectory (in 3 dimensions) and the uncanted one is the effect of cant "all along the trajectory". For each zero, you have a different perturbed trajectory, since, as you remark, the zero is incorporated into the elevation.

Because it was derived through a perturbation, the formula loses accuracy as the bullet drops more steeply, but I am really surprised how well it holds up when compared with a full solution (which the JBM calculator and my system do). Hope I am not missing something...

Thanx Gang!

I'll give it extra care setting the pistol up, then it's on me while on the shooter's box..... One of those will be easier to get precise....... 🙂

1.5" target at 35 yards, 12fpe pistol, 8.4gr pellet. An otherwise perfect shot will miss if you have 12+ degrees of gun cant.

1.5" target at 55 yards, 12fpe rifle, 8.4gr pellet. An otherwise perfect shot will miss if you have 4+ degrees of gun cant.

The potential for cant error to cause a miss is less for pistol FT only because the distances are less, and therefore total drop is less.

Steve, it is not exactly the same thing. My formula works everywhere along the trajectory, not just where the POI = POA. It describes the full trajectory line. In fact, that is how I derived it. I took the uncanted trajectory and perturbed it by rotating it about the line of sight. I did the same thing you do, but for the entire trajectory rather than the POI. The difference between the rotated trajectory (in 3 dimensions) and the uncanted one is the effect of cant "all along the trajectory". For each zero, you have a different perturbed trajectory, since, as you remark, the zero is incorporated into the elevation.

Because it was derived through a perturbation, the formula loses accuracy as the bullet drops more steeply, but I am really surprised how well it holds up when compared with a full solution (which the JBM calculator and my system do). Hope I am not missing something...

Thanks, DT, for your patient explanation. I initially misinterpreted your post as saying that movement of the POI with cant was independent of sight height elsewhere than at the zero(s), even though I now see your calculation clearly says otherwise. I think we're on the same page now. Actually this discussion reminds me of a similar one from years ago, which led to this diagram of mine (from 2004).

It demonstrates a number of minor curiosities that occur where range is different from a zero, like...

1. The "zero cant point" where line of departure intersects line of sight and POI is totally independent of cant, and...

2. Lower mounts have (somewhat) less POI movement vs cant everywhere except (roughly speaking) between the near and far zeros.

How does one find a thread once it is no longer visible on the right side of the screen?

I thought this is interesting.

Steve mentioned oddities that happen at short and long distances when you cant the rifle. An interesting oddity happens when you aim very close, with "high" mounts. The direction in which the POI moves with cant "reverses" at a distance approximately equal to scope height divided by the elevation angle. Your POI and POA would coincide at this distance "if" there were no gravity. In that case, the POI would not only be insensitive to the scope height; it would be (locally) insensitive to cant itself. Since there is gravity, the distance where the gun is cant-insensitive always lags behind the target, but for very short distances it doesn't lag by much. Paradoxically, this gives an advantage at very short distances to shooters with high scopes as far as cant goes - basically, the height of their scopes neutralizes cant. The higher the scope, the closer is this indifference point to the target.

Changing the height will make no difference.

Absolutely true,

uncanted POI = POA (i.e., the rig is accurately zeroed for the range involved). If this criterion doesn't hold, then many other conclusions (e.g., the independence of cant error from sight height) likewise don't hold.providedI suspect it was playing with (or thinking about) cases where the target wasn't placed at a zero that has led to many of the stubborn misconceptions about this subject.

Then we are not talking about "gun cant". That would be an "aiming error".

If you cant an otherwise properly aimed gun, scope height has no bearing on the amount of error.

Regardless of whether my gun is canted, when I "zero" for the shot, the POA and intended POI both lie on the vertical crosshair. If they don't, then the gun is either not setup correctly, or I am aiming incorrectly

If the gun is not zeroed correctly, than I would fix that rather than attribute the error to gun can't.

Through improper aiming, it is possible to cant a POA-POI vector, relative to the target, without actually canting the gun. For instance, when using target holdover, rather than retical holdover, and the target is canted. If that is the case, than scope height will matter. But that is not gun cant.

...An interesting oddity happens when you aim very close, with "high" mounts. The direction in which the POI moves with cant "reverses" at a distance approximately equal to scope height divided by the elevation angle. Your POI and POA would coincide at this distance "if" there were no gravity. In that case, the POI would not only be insensitive to the scope height; it would be (locally) insensitive to cant itself. Since there is gravity, the distance where the gun is cant-insensitive always lags behind the target, but for very short distances it doesn't lag by much. Paradoxically, this gives an advantage at very short distances to shooters with high scopes as far as cant goes - basically, the height of their scopes neutralizes cant. The higher the scope, the closer is this indifference point to the target.

Please note this "oddity" is mentioned as #1 in my post above -- the "zero cant point" -- which I defined as the point where line of sight and line of departure (a.k.a. boreline) intersect.

Then we are not get talking about "gun cant". That would be an "aiming error".

If you cant an otherwise properly aimed gun, scope height has no bearing on the amount of error.

Regardless of whether my gun is canted, when I "zero" for the shot, the POA and intended POI both lie on the vertical crosshair. If they don't, then the gun is either not setup correctly, or I am aiming incorrectly

If the gun is not zeroed correctly, than I would fix that rather than attribute the error to gun can't.

Through improper aiming, it is possible to cant a POA-POI vector, relative to the target, without actually canting the gun. For instance, when using target holdover, rather than retical holdover, and the target is canted. If that is the case, than scope height will matter. But that is not gun cant.

True.

Still sadly, in this imperfect world, imperfect marksmen (who? me?) sometimes (however rarely) imperfectly aim our guns -- sometimes even simultaneously combining multiple imperfections! Therefore the subject of interactions between various factors (e.g. sight height) with said imperfections of aim is potentially interesting -- even potentially useful!

After all, isn't cant itself an example of imperfect aiming in the first place?

Sorry, Steve, I didn't mean to steel your "oddity". I actually lost track of the thread and couldn't find your comment by the time I wrote mine and didn't remember you had marked it on your plot. 🙂

By the way, detecting this oddity is a test that any system that claims to account for cant must pass. The JMB system and mine passed the test.

Sorry, Steve, I didn't mean to steel your "oddity". I actually lost track of the thread and couldn't find your comment by the time I wrote mine and didn't remember you had marked it on your plot. 🙂

By the way, detecting this oddity is a test that any system that claims to account for cant must pass. The JMB system and mine passed the test.

No problem, DT 😎 . By the way, it's JBM. Not JMB or JSB.

Yes - Interesting and very useful if we take the time to understand it.

I guess we now have three types of cant. "aiming error" is when the gun is setup correctly and is held correctly, but you are simply pointed in the wrong direction.

1) Scope cant

Scope cant is dealt with 1st by insuring that the vertical reticle intersects the bore-line. This is done by having the scope correctly rotated in the rings before finally cinching it down.

2) Gun cant

This is when gravity throws you a curve. Gun cant is dealt with by installing a bubble level on the scope that indicates when the vertical crosshair is perpendicular to earth. And then insure that the bubble is level when you take the shot.

3) POA-POI cant (aiming error)

If you keep POA coincident with the intended POI, there will be no POA-POI cant. If you choose to use a non-coincident aim point, verify that the gun is level AND that the intended POI lies along the vertical reticle. If you are attempting to use target holdover with a plain bullseye or dot sight, the target orientation needs to be perfectly vertical.

Cant is a deviation from a vertical or horizontal plane or a surface. I make it a point to specify which one I'm talking about, scope cant or gun cant.

Often they are lumped together under the general term "cant". It is common to have both present, but mixing them up makes the subject confusing.