Architect, born in 1971, now living and shooting in the UK
FT Hungarian Champion 2008-2009, World's 6th in 2010 / 9th in 2012
In spite of the ancient myth, the height of the rifle scope doesn't mean more sensitivity for canting errors. In most instances it's totally indifferent while with a particular aiming method it can be worse of even better than the low mounted scope. Detailed theoretical explanations and shooting test results.
I've heard many times from old shooters that 'The high scope isn't good because it's much more sensitive to canting...' – does it sound familiar? It seems to be logical at first glance – but not anymore when one investigates it a bit more thoroughly.
I started to deal with this topic back in 2007 when I was shooting with a 6 ft-lb rifle and used a rather high scope (we used to shoot up to 50 metres even with the low-powered rifles). I was told then that 'Oh boy, you're gonna suck with this high mount and miss even with the slightest cant, because high scopes are more sensitive to canting errors, all riflemen advise to set the scope as low as you can.'
PART I. – OF MYTHS AND FACTS
CHAPTER 1. – Misbeliefs
Well, I said to myself, let's see how much more sensitive is the high scope to canting. An old gunshmith explained it to me in the following way, this is the simplest mistake which says that the higher scope means more offset when canted with the same angle:
Of course this is right only if we shoot at a paper which is immediately in front of the muzzle. The bore line and LOS are not parallel, and the LOS' of different scope heights intersect on the target so the displacement is the same (see PART III. CH 1.) Then I found an article about it on the internet but it was rather confusing, in a few places I have corrected it with red:
The author used totally unnecessary parameters like apex of trajectory and the drop from this point and a so called error triangle, these things have nothing to do with canting. In exchange he left out the essence, the bore line and the error circles.
There are also other mistakes there, and the author had the conclusion that 'Use of large diameter objective scopes, mounted high off the barrel, exacerbates the cant error problem.' Sadly other websites e.g. like this took these pictures and explanations over without any critic. I saw already that there's something not quite right and I can't trust the internet stuffs.
Therefore I worked the ballistic model out on my own, starting from the very basics and I was surprised to find that the canting error should be calculated from distance, pellet data and canting angle only, but the scope height wasn't involved in the formulae. I double checked everything and it seemed to be right. It was the time to start experimenting to see who has the real truth...
CHAPTER 2. – My early experiments (2007)
So I drew a circle on a paper with the calculated radius, took my rifle (Walther LG-210, 6 ft-lb) and shot at the top of the circle with different canting angles. The hits landed roughly on the predicted circle only the wind blew the lot to the left but I could say that the POI's followed the circle.
I mounted a 9 cm high scope and then a 2 cm high diopter onto my rifle and shot indoors at 11 m. I had poor grouping with the diopter and with a strong drift to left. The shots with the scope landed on the calculated circle, though – My conclusions were that my theory worked (the hits landed on a circle with the previously calculated radius again) but shooting with diopter was not my style...
CHAPTER 3. – Authentic websites about canting
Of course I'm not the only one in the world who did not satisfy with regurgitating the old sagacity and thought it over.
I found a chap called Jeroen Hogema who made basically the same experiment in 1999. He also tried shooting with different LOS heights and found that the canting error doesn't depend on the scope height.
Another very correct and informative website is Perry Babin's where we can found a lot of ballistic explanations with interactive Flash animations. The page about canting is great.
PART II. – THE EXPERIMENT RELOADED (2012)
I didn't bother with this question anymore, mounted my scope to a comfortable height and didn't give a damn to the concerns. Recently, after talking with big-bore shooters about this question, I had to think it over again and found some exceptions to the rule: there are some special instances when the higher scope is more or less sensitive to canting, than the lower one. Therefore I thought it'd be worth making this question clear once and for all.
As a first step I repeated my first experiment. I took Aggie's rifle and calculated the canting error circle size for 21 metres. Then shot with different canting angles and saw my pellets landing around the circle again. It was already a proof since I didn't use scope height for the calculations therefore I would have got the same results with any other scope height.
I tried to shoot with a small and very low scope, a 4x mag 'butterfly-chaser' but had to realise that my grouping is about 3-4 cm with it and I would only repeat those shameful shotgun-style groups made with the diopter a long time ago. So I decided that I'll use Aggie's accurate big scope for both scope height tests and have to achieve the massive height difference in the other direction, with huge amount of risers instead of using this small scope. My other experience was that shooting from a shabby backyard bench is not too stable and I have to find something much better to have some really appreciable results. Let's see how I finally did it:
CHAPTER 1. – Preparation and conditions
I used Aggie's AirArms S-400 MPR-FT, this rifle is unmodified except for the free-floating barrel which ditched POI-shifts by temperature and air cylinder pressure changes. I used JSB Heavy pellets, the muzzle velocity was 205 m/s. The calculated pellet drop was 50.1 mm @ 20 m (I selected the range in a way that the canting circle is big enough but staying on the paper). I shot 3-shot groups in every 45°, the rifle rested on bean bags. The scope heights were 58 mm and 110 mm (centre-to-centre).
I knew already that shooting with a roughly canted rifle is quite difficoult, sometimes one has to aim with the left eye and fire with the right hand or vice versa, the rifle wobbles on the top of the parallax wheel and can't be shouldered normally, so shooting from a chair is somewhere between kneeling and standing shots if wee look at the grouping size...
Therefore I was looking for a professional shooting stand and found it in the form of my Renault Laguna. It may look awkward but I could shoot there from a very comfortable and stable position, the rifle rested on a cushion on the rear shelf. All the tools and air bottle were with me inside the car. The first motorised shooting stand with built-in stereo and air conditioning LOL.
These are not some alternative shooting positions for the Italian courses, just the canting test itself. I did shots from versatile shooting positions, I didn't use bubble level for the canted angles, aligned the rifle by using the 45° lines drawn on the target paper instead.
The weather was almost ideal, about 10 degrees with a negligible breeze, no rain and not too bright sunshine. First I zeroed the rifle on another paper and then shot 3-3 pellets in 45° steps to both sides, finally shooting even totally upside down. Then removed the 4-4 pieces of mount risers and repeated the above.
CHAPTER 2. – Test results
The results look quite similar, even without any further processing we can see that the almost doubled scope height didn't result in any significant difference.
Then I marked the shots with calibre size circles and drew the calculated canting error circle, too. Not too surprisingly, all groups were on the circle.
The following is the final result of the test, see the shots merged on one drawing. It speaks for itself.
My conclusion is that the scope height has NO effect on canting error so watch the bubble level my dear friends even with the lowest scope because it's equally important with any scope height.
PART III. – THE THEORY
CHAPTER 1. – How canting error works
Now a few words about my theory (CH 1-2.) and its extended version about the special instances (CH 3-4.) where scope height may count, though.
Shooting at 'R' range, the pellet drop value is 'D' which depends only on V0 and BC, not on the scope height. We can shoot with any canting: where the bore looks at the target plane the pellet hits with 'D' below.
This is how we aim and shoot: LOS looks at the target, bore line looks with 'D' above so the pellet (which drops 'D') hits the target.
Canting the rifle while aiming = rotating bore line around LOS as an axis. The axis is always the LOS because the aiming point stays on the target so the whole lot rotates around it when canting sets in. This means that the bore line draws a circle with radius 'D' and the hits are on a similar circle with 'D' below (this is my red circle on the shooting results).
Now imagine a rifle with two scopes on it, one above the other. Both LOS – high and low – looks at the same point so the bore line draws the same circle with the same radius 'D'. This is why canting error is independent from scope height, it depends only on pellet drop 'D' and canting angle 'A'.
Or the same thing with a different visual approach, if it's easier to accept it like this :-)
The horizontal/vertical canting error ('Ex' and 'Ey') and the absolute (radial) displacemenet ('Er') can be calculated with the formulas below. The drop value 'D' can be measured (see Part III. / CH 1. at the end), also Chairgun calculates it for you or simply use the following formula:
where BC is the real BC value, R is the range in yards, V0 is the muzzle velocity in fps, the error values and D come in inches.
Note that the scope height is not in the formula :-)
CHAPTER 2. – Different ranges, different lines of sight
All right, but what happens on another range? Let's examine a rifle which is zeroed at 'R0' range but we shoot with it at another 'R' range. The pellet drop value is 'D' at range 'R' so the bore line has to look with 'D' above the target in order to hit it.
Because of straight LOS and curved trajectory, the rifle which is zeroed at 'R0' shoots low/high (depending on ballistics) at 'R', the bore line looks with an 'X' above the target instead of 'D'. If we want to hit the target, we have to change the Bore-LOS angle so that the bore line looks exactly with 'D' above the target.
So we have to use different LOS for the different ranges, we adjust the LOS by clicking the turrets or using one of the mildots to aim instead of the crosshair. Whichever way, the thing is that we have changed the LOS and the actual LOS looks at the target again.
This is very important to understand: in fact the rifle is zeroed to each range where we shoot.
Now let's see that double scoped rifle again. Shooting at range 'R' aiming with the new LOS' the high or low mounted scopes look at the target again so the canted hits will be on a circle just with radius 'D'. The scope height hasn't got any influence on canting again, it depends only on the canting angle 'A' and pellet drop 'D' at range 'R'.
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But now comes the twist, dear fellow patients, please fasten your safety belts... We in Field Target always do zero our rifle to each and every distance. Once again, even shooting with mildots is a method of on-the-fly zeroing the rifle. So whichever way, our LOS looks at the target and if we cant, we rotate the bore line around the target itself, with the results shown above.
I had to consider that all of these 'high scope is bad' opinions come from firearm shooters. Is there a chance they do anything differently which can change things? Yes, they do. I had to revise my stand. Still standing by everything I have written above, I examined the third aiming method when one shoots to another aim point holding over/under with the appropriate distance which is measured on the target.
CHAPTER 3. – When a higher scope is worse
This time the rifle has two theoretical scopes on it, a low and a high one. Both scopes are zeroed at range 'R0' but we want to shoot at distance 'R' which is GREATER than 'R0'.
The rifle which is zeroed at 'R0' doesn't hit at range 'R' because the bore looks above the target with 'L' (low scope) and with 'H' (high scope) instead of 'D'. It can happen under certain conditons that 'L' or 'H' is equal to 'D' but this is a rare exception (it happens only if 'R0' and 'R' are the two zero points of the actual Trajectory-LOS combination). The relation of the red, blue and green points can vary with ballistics but 'L' is always LESS than 'H'.
So we aim with the crosshair at a point which is above/below the target with the appropriate amount 'LA' and 'HA'. In this case, the bore line hits the target plane with 'L' and 'H' above the aiming point and in both cases with 'D' above the target, and when the pellet drops with 'D' then it hits the target.
If we cant the rifle, the bore line is rotated around the LOS again – but they are different with this aiming method! This means that the radius of the canting error circle is 'L' with the low scope and 'H' with the high scope instead of 'D'. Because 'H' is greater than 'L', the higher scope gives MORE canting error.
CHAPTER 4. – When a higher scope is better
And now let's see the opposite instance. The rifle still has two theoretical scopes on it, a low and a high one. Both scopes are zeroed at range 'R0' but this time we shoot at distance 'R' which is SHORTER than 'R0'.
The rifle which is zeroed at 'R0' doesn't hit at range 'R' because the bore looks above the target with 'L' (low scope) and with 'H' (high scope) instead of 'D'. The relation of the red, blue and green points can vary with ballistics but 'L' is always MORE than 'H'.
So we aim with the crosshair at a point which is above or below the target with the appropriate amount 'LA' and 'HA'. In this case, when the bore line hits the target plane with 'L' and 'H' above the aiming point and in both cases with 'D' above the target, and when the pellet drops with 'D' then it hits the target.
If we cant the rifle, the bore line is rotated around the LOS – but they are different with this aiming method. This means that the radius of the canting error circle is 'L' with the low scope and 'H' with the high scope and 'H' is smaller than 'L'. This means that in this case the higher scope gives LESS canting error.
CHAPTER 5. – How to get rid of canting errors
1. Keep canting on 0. This is the easiest way, simply use a well-aligned bubble level and all canting errors are sorted! Does it sound too easy? There are other ways, too:
2. Reduce the drop value. Using lighter pellets with higher velocity reduces 'D' and this reduces the effect of the canting error by reducing the error circle radius.
3. If you hate bubble levels and don't want to change pellets but are a ballistics freak, you still have got a (rather theoretical) way to avoid canting errors: reduce the radius of the canting error circle to 0 so the canting angle doesn't count anymore. How to do this? Simply zero your rifle in a way that the LOS and bore line intersect at the target plane. Aim of course with 'D' above the target. You can shoot then with whichever canting angle, the radius of the circle is 0 now so there will be no canting error at all... :-)
Just another use of our new knowledge: if you would like to know your pellet drop at a given distance, just zero the rifle at the range and shoot with the rifle canted in 90° to the left. The POI will be exactly with 'D' to the left and also with 'D' below the aiming point.
PART IV. – CONCLUSIONS
1. In general, especially in FT shooting, where we do the required correction of LOS within our scope (i.e. adjusting turrets or holding over with certain mildots), the canting error is totally independent from the scope height, higher scopes are NOT more sensitive to canting angle than low ones.
2. If we do the correction outside the scope (i.e. we have zeroed the rifle at a given distance and then shoot at another target with a holdover which is measured at the target), the canting error can be different – more or less – with the higher scopes. It will be more if the new range is greater than the zero range and less if it's shorter.
Considering that we are allowed to use bubble levels on our rifles so canting is not a real aspect for us, I say that we can rise the scope as high as we want to, it will mean no disadvantages with canting. The more important point is that even those who have lower scopes have to pay the same attention to levelling the rifle because their canting error is the same as the others' with high scopes.
Although canting is indifferent for us, the higher scopes have other advantages and disadvantages, too:
– flatter trajectory at greater ranges allows more misranging
– more comfortable upright head position
– more space for loading the rifle
– may run out of click on the very close ranges
– greater danger of shooting in the ground on inappropriately built courses
We have to consider all these aspects before deciding the mount height, but canting is not among them – I hope this ancient myth is over now.
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