Recoil and Semi-Autos (and maybe Revolvers, too)...

[45_auto]

No way to explain it if you don't understand the concept of TORQUE, or a MOMENT.

Basically, a MOMENT (or TORQUE) = FORCE x DISTANCE.

https://en.wikipedia.org/wiki/Torque

Typically the FORCE applied to accelerate the bullet is applied above the pivot point of your wrist. Therefore your wrist has to resist the MOMENT created by that FORCE times the DISTANCE above your wrist.

Your reaction time is around .25 of a second. The bullet spends about .001 seconds in the barrel, during which time a FORCE of many thousands of pounds is acting at a given DISTANCE above your wrist to torque your wrist upwards. This means that the muzzle is going to flip upwards before you can do anything about it.

If you hold the gun upside down with the barrel below your wrist, the gun will torque DOWN. If you hold the gun sideways, the gun will torque SIDEWAYS. It all depends on where the barrel is in relation to your wrist. This is the reason that Olympic Free pistols are designed as nearly as possible to have the barrel in line with the shooter's wrist. They are trying to reduce muzzle flip by making the DISTANCE that the FORCE acts above the shooter's wrist as small as possible.

Some basic science in this article about halfway down page 8:

http://www.oglethorpe.edu/faculty/~j_cramer/documents/Chapter1_000.doc

Recoil has another effect worth mentioning: it makes the gun turn upward when fired. This effect is most problematic for an automatic weapon, like a machinegun, with a high firing rate. The muzzle rises and aiming is hard to maintain. It is also apparent when you shoot a pistol single-handed. The pistol jumps upward when fire.
The reason for this is that the recoil produces an upward torque on the gun. The recoil is applied along the barrel but the gun is held at a lower point by the hand or at the shoulder. The lower point is the natural pivot of the gun but the recoil is applied at a higher point and backward toward the shooter. Thus, the barrel moves back, turning up and around the pivot. The end of the barrel rises and the gun is now pointing high and off target.

Newton told us that FORCE = MASS x ACCELERATION 400 years or so ago.

Since a barrel is a constant length, for a given muzzle velocity ANY bullet no matter what the weight must experience the exact same ACCELERATION to reach a given VELOCITY at the muzzle. For example, a 230 grain bullet and 115 grain bullet must experience identical acceleration to reach identical velocities in an identical barrel length.

We know F=MA.

Since we know that the ACCELERATION is identical in both cases (given identical VELOCITY and barrel length) but the MASS is twice as much for the 230 grain bullet, it is hopefully obvious from F=MA that the FORCE to accelerate the 230 grain bullet must be twice as much as the FORCE to accelerate the 115 grain bullet. Given identical pistols with an equal DISTANCE above the shooters wrist, this means that the MOMENT causing the muzzle to flip upwards is twice as much for the heavier bullet. Therefore the muzzle flips up twice as far causing the heavier bullet to impact higher.

 

[mkiker2089]

If you want proof that the muzzle flip is after the bullet leaves you don't need slo-mo footage. Just find any video that uses a firing rig like Mythbusters. The rig usually isn't weighted so the gun fires, the bullet hits the target, THEN the gun lifts up and usually points towards the roof depending on the amount of give in the rig. If the bullet were affected by the recoil then the rigs would fire up instead of dead on.

I'd be willing to bet that heavier bullets hit higher due to a different parabolic trajectory. Sights are set based on certain given factors. Change any of those factors and the sights will be off. Low power ammo may be more affected by gravity and higher power less so. They would then hit lower and higher respectively.

The biggest thing I've taken from all this is that I really want a Chiappa Rhino. The lower the center of force the less muzzle flip you'll have. While I still say it has no effect on aim it is a bonus in other ways.

 

[Radny97]

When speaking of recoil I think it's important to differentiate between the physics of inertia and the kinetic force that a particular round imposes on the shooter v. the multi-faceted question of felt recoil. For practical purposes felt recoil matters a lot more than the kinetic push of a particular round in a particular firearm platform.
A discussion of felt recoil is nonscientific and subjective but more important IMO.
In my personal experience felt recoil has been affected by the following factors in descending order of importance:
1. Weight of the gun and bore axis of the gun. A sub-factor of this is length of the barrel. The heavier the gun and the longer the barrel the less felt recoil for me. Of all the factors this has been the most noticeable factor.
2. My grip of the gun. This includes both the way I hold the gun (i.e. The placement of my hands and fingers) the tightness with which I grip the gun, and the actual grips installed on the gun and the ergonomics of the gun. The higher to the bore axis I hold the gun, the harder I grip the gun, and the better the fit of the grips and ergonomics of the gun to my hand, the less felt recoil for me.
3. The pressure of the round. A sub-factor of this is muzzle velocity. A more slowly burning powder can achieve great velocity without a huge spike in pressure and the resulting snappiness. For example, a 38 special +p with a slow burning powder has less felt recoil for me than a 9mm at the same velocity (all other things being equal). I have noticed this pattern across several calibers and loadings.
4. The weight of the bullet. Compared to the other three above I have found this to be the least influential in felt recoil. However, that is not to say it is not a factor. I can definitely feel the difference between a 230 grain 45 acp bullet and a 125 grain 38 special out of a similarly weighted gun with similar pressure, etc.

I know there will be those who disagree with how I have grouped these factors and the order I have placed them in, but this is my subjective perception of how felt recoil works for me. Moreover I think that these factors are more important than a bare discussion of the inertia at issue when a round is fired.

 

[44 AMP]

But WHY is the barrel rising? That must still be explained -- and it must be explained as happening within the first fraction of an inch of the slide and barrel movement.

Barrel rise is from recoil, we all know that, right? Or we think we do, anyway.

Consider how small a difference in muzzle movement it would take to produce the rather small distance difference between the light and heavy bullet.

Consider that this small difference in movement might not be visible to the eye.

Consider the "heavy bullets strike higher" is a possibly misleading phrase being used to convey the observation that can also be stated as "faster bullets hit lower".

Physical mechanics says that the handgun, held by the grip MUST "rotate" around that point.

Get a Contender. Get barrels for the desired revolver and auto pistol rounds, so as many possible factors will be the same, and do some tests.

Consider a fixture so the barrel will not rise, and/or(?) some way to measure even tiny amount of rise. Then shoot some slugs, different weights and speeds and see where they go. I'm sure the results would be interesting.

 

[Limnophile]

44 AMP,

Consider how small a difference in muzzle movement it would take to produce the rather small distance difference between the light and heavy bullet.

Consider that this small difference in movement might not be visible to the eye.[/quite]

We have a winner!

Accuracy, precision, and differences in POIs is expressed in minutes of angle, moa, so as to allow comparisons among different shooting distances. A minute of angle is a very small unit:

- At 100 yd (beyond pragmatic pistol range), 1 moa equates to 1.047 in.
- At 50 yd (maximum effective pistol range), 1 moa equates to 0.5235 in.
- At 25 yd (the distance at which many pistols are sighted in), 1 moa equates to
0.2618 in.
- At 10 yd, 1 moa equates to 0.1047 in.
- At 7 yd, 1 moa equates to 0.07329 in.
- At 5 yd, 1 moa equates to 0.05235 in.
- At 0.194 yd (the length of a pistol), 1 moa equates to 0.002036 in.

I suggest that even with super slo-mo with an ultra hi-speed camera we are incapable of discerning a difference in muzzle rise of 0.002 in (0.05 mm) needed to result in a 1 moa difference in POI that might be apparent downrange.

I've never tried to discern differences in POI between rounds with different bullet weights, because my precision (which averages 30 moa with a 2-hand, unsupported grip) effectively gives all rounds the same POI.

If there is truth to the "heavier bullet impacts higher" meme, it must be attributable to greater muzzle rise due to either greater recoil momentum or longer residency time in the barrel because of slower speed. Without any muzzle rise at all, all bullets of any weight would be launched toward the target at the same angle due to identical sight alignment. The heavier, slower bullets would impact lower because they take longer to reach the target, thus giving more time for gravity to act upon them.

 

[micromontenegro]

The heavier, slower bullets would impact lower because they take longer to reach the target, thus giving more time for gravity to act upon them.

Not necessarily. For one, the heavier bullet will have more inertia, and beyond certain point, will shed velocity more slowly than the initially faster light bullet. Also, aerodynamics and barrel harmonics will come into play.

It is a complex issue.

 

[45_auto]

The rig usually isn't weighted so the gun fires, the bullet hits the target, THEN the gun lifts up and usually points towards the roof depending on the amount of give in the rig. If the bullet were affected by the recoil then the rigs would fire up instead of dead on.

So wrong in so many ways. A little research on your part would greatly enlighten you.

 

[Walt Sherrill]

Accuracy, precision, and differences in POIs is expressed in minutes of angle, moa, so as to allow comparisons among different shooting distances. A minute of angle is a very small unit:

- At 100 yd (beyond pragmatic pistol range), 1 moa equates to 1.047 in.
- At 50 yd (maximum effective pistol range), 1 moa equates to 0.5235 in.
- At 25 yd (the distance at which many pistols are sighted in), 1 moa equates to 0.2618 in.
- At 10 yd, 1 moa equates to 0.1047 in.
- At 7 yd, 1 moa equates to 0.07329 in.
- At 5 yd, 1 moa equates to 0.05235 in.
- At 0.194 yd (the length of a pistol), 1 moa equates to 0.002036 in.

I suggest that even with super slo-mo with an ultra hi-speed camera we are incapable of discerning a difference in muzzle rise of 0.002 in (0.05 mm) needed to result in a 1 moa difference in POI that might be apparent downrange.

I've never tried to discern differences in POI between rounds with different bullet weights, because my precision (which averages 30 moa with a 2-hand, unsupported grip) effectively gives all rounds the same POI.

If there is truth to the "heavier bullet impacts higher" meme, it must be attributable to greater muzzle rise due to either greater recoil momentum or longer residency time in the barrel because of slower speed. Without any muzzle rise at all, all bullets of any weight would be launched toward the target at the same angle due to identical sight alignment. The heavier, slower bullets would impact lower because they take longer to reach the target, thus giving more time for gravity to act upon them.

Very nicely stated. All of that makes perfect sense. Especially the parts about being unable to discern much movement at even very high video speeds, and about many different loads/rounds hitting to the same point of aim due to the innate lack of precision of human physiology.

A serious question: if the muzzle rise is so tiny as to not be visible in high speed videography, will it be noticeable when the bullets hit the target? It all depends on 1) distance to the target, 2) velocity and 3) bullet weight, and those are variable that are typically compared, but not controlled (in the sense applied to tests using the scientific method -- a technique.) And, unless you're using a Ransom Rest (with the sights aligned for each shot -- not a typical part of Ransom Rest use), human error is still still a factor.

Some handguns are accurate/precise enough to let us hit what we're aiming at, but not as precise as we'd need to truly make many meaningful measurement when evaulating the things we're discussing here. Most folks don't notice or think about that lack of human precision.

(Please note, too, that I'm NOT in any way discounting your points above -- which I find valuable for this discussion.)

In theory, a heavier bullet fired at the same velocity as a lighter bullet will hit the target at the same time and place as the lighter bullet. The problem is that heavier bullets typically aren't loaded to the same velocity as lighter bullets.

It seems, too, that if there are forces causing the frame, slide, and barrel to rise, a very loose slide-to-frame fit might be a factor, too -- as the force that pushes a tight barrel and frame upward would travel upwards farther before being constrained by the frame rails.

The argument against barrel rise, which I didn't originally accept, was that most semi-autos, unlike revolvers, handle recoil differently than revolvers. There is some transfer of energy from the slide/barrel to the frame in that first 1/10th of a an inch of travel (which happens in .001 pf a second according to 45_auto comments, in his prior response.)

That force is, however, is not from something pushing directly upward, but is caused by TORQUE (again, from 45_auto) from forces that are primarily pushing forward and rearward: slide and barrel movement to the rear, recoil spring pressure against the frame UNDER the bore axis (but still above the wrist). The bullet going forward is trying to drag the barrel with it as it goes.

Given the RECOIL DELAY described by others in this discussion, is there sufficient immediate transfer of enough force to affect the wrist and raise the muzzle of the gun in that .001 of a second BEFORE the bullet leaves the barrel? And at what practical distance to the target must this motion be evaluated to know that it actually happens in a way that can be measured?

That vertical rise that affects bullet impact must happen during that brief .001 of a second after ignition. After that, the force retarding forward movement is greatly reduced -- as the bullet in the barrel, which is moving forward and trying to drag the barrel forward with it -- is gone. Any gas or un-ignited powder is no longer contained and loses its ability to have much effect on the mechanism in the shooter's hand. The slide and barrel are heavy and are continuing their journeys thanks to their momentum induced in that first .001 of a second. From that point in time onward, we REALLY see the effects of recoil on the shooter and the weapon. But the bullet is gone.

In a revolver, without any mechanism to delay recoil, and a very high bore axis, it seems logical that there would be more pronounced barrel rise. But with a semi-auto, the forces seem to be handled differently. Torque, as 45_auto mentioned earlier, would certainly be different: the bore axis is substantially different in those two types of handguns (unless you're look at something like the Mateba revolver with barrel at the bottom of the cylinder); that creates a different type of lever for each weapon type.

It only takes about .001 of a second, according to 45_Auto, for the bullet to leave the barrel. And Limnophile's calculations suggest that the barrel rise might might only be 0.002036 of an inch at the muzzle assuming a 1 minute of angle deviation from perfection. With some guns it could be less or much more! In the best case, it would certainly be difficult to see THAT small a movement in even the fastest slow-motion videos. But, I'm not sure it CAN'T be seen. And for guns with less tight fit between slide and frame?

Does anyone have a semi-auto with a slide that can be easily locked and access to a Ransom Rest? That person can shoot the same round without any slide-movement-induced delay. That semi-auto will be acting a bit like a revolver. There should then be a difference in the points of impact between locked slide and freed slide. Is there a measurable delay due to the locked breech/short recoil design that affects point of aim?

 

[Walt Sherrill]

The heavier, slower bullets would impact lower because they take longer to reach the target, thus giving more time for gravity to act upon them.

Not necessarily. For one, the heavier bullet will have more inertia, and beyond certain point, will shed velocity more slowly than the initially faster light bullet. Also, aerodynamics and barrel harmonics will come into play.

It is a complex issue.

It is a complex issue, but I think the assumptions for this part of the discussion was that we're shooting semi-autos, not long guns, and that the bullets being used would differ only in weight. Velocity would, of course change.

If the bullet types vary only in weight, I'm not sure that aerodynamics would be much of a factor in the handguns being shot a practical handgun distances; I'm also not sure that barrel harmonics would be a factor unless you're using a much longer barrel than is typically used in most semi-autos.

Inertia may be a factor -- as you've got to get that round going down the barrel -- but then all of Newton's three basic laws of motion seem to be at play.

 

[44 AMP]

The heavier bullet hits higher, or the faster bullet hits lower, depending on how you want to say it, RELATIVE to the same sight setting. (and we're talking the short ranges of regular handgun use.)

This is an observed fact. It happens no matter WHAT kind of handgun action the round is fired with. It happens with guns that have barrel movement in two axis during its cycle, the classic Browning tilt barrel locking system.

It happens in guns that have barrel movement in only ONE axis, in line with the bore, such as the Luger, or the Auto Mag.

It happens in guns that have NO barrel movement at all during firing and recoil, such as revolvers, single shots, and the Desert Eagle and Wildey auto, etc. Also include all the .22LR blowbacks, which all have fixed barrels.

Since it happens with all these different types of barrel movement, including none, logic would suggest that something OTHER than barrel movement relative to the frame is the cause.

IF muzzle rise is, as suggested, something on the order of 0.002" while the bullet is in the bore, it would take a well designed test rig to measure it accurately, a task the human eye (even via a high speed camera) alone is simply not up to.

 

[mkiker2089]

Let's not forget that inertia is speed * weight. A heavier bullet at a lower velocity may have more inertia.

 

[Limnophile]

micromontenegro,

For one, the heavier bullet will have more inertia, and beyond certain point, will shed velocity more slowly than the initially faster light bullet. Also, aerodynamics and barrel harmonics will come into play.

Not within pragmatic defensive pistol range. Take, as an example, the Federal American Eagle FMJs, 115-gr vs the flat nosed 147-gr -- http://www.federalpremium.com/products/compare/handgun_compare.aspx. The muzzle velocity of the former is listed as 1,180 ft/s, while that of the latter as 1,000 ft/s. Out of the muzzle the lighter bullet is 18% faster. At 100 yd, well beyond pragmatic pistol range, the 115-gr bullet is still faster -- 961 ft/s vs 914 ft/s. Only 5% faster, but still faster.

 

[Limnophile]

44 AMP,

IF muzzle rise is, as suggested, something on the order of 0.002" while the bullet is in the bore, it would take a well designed test rig to measure it accurately, a task the human eye (even via a high speed camera) alone is simply not up to.

Just to clarify, I'm not suggesting any degree of difference in POI height between bullets of different weights, as I have no experience measuring such. I merely selected 1 moa as a reference distance to show how small of a muzzle rise is needed to create such a difference. If anyone has data on POI differences showing that heavier bullets impact higher I'd be interested in seeing them.

Going back to the American Eagle FMJ pair I mentioned above, Federal's external ballistics tables don't shed light on the issue, because I'm sure their trajectory values are generated by formula not empirical observation. That formula sets the POI at the POA at 25 yd, regardless of the round. What we desire to know here is what happens when you fire 147-gr rounds out of a pistol sighted in at 25 yd with 115-gr rounds. My guess is their formula ignores the effect of recoil so would have the 147-gr rounds impacting lower.

Walt,

Some handguns are accurate/precise enough to let us hit what we're aiming at, but not as precise as we'd need to truly make many meaningful measurement when evaulating the things we're discussing here. Most folks don't notice or think about that lack of human precision.

Being something of a statistician, I found myself fretting over how poorly I seemed to be shooting my carry sidearms. I had never concerned myself about the accuracy and precision of my Browning Challenger III, because its primary function was a plinker. My quantitative assessments on shooting were confined to bench-rested rifles, where my goal was 1 moa. Because that benchmark was ingrained in my head, I was routinely dismayed with my performance with my carry pistols.

One day I decided to conduct an analysis of variance to determine which of my four steel-framed compact CZs was most precise with me firing slowly with an unsupported 2-hand grip. I shot four 5-shot groups from each gun in alternating sequence and measured precision as the maximum group dimension. I was surprised to find no statistically significant difference in group size between guns, which included an 83 in .32 Auto, an 83 in .380 Auto, an 82 in 9 Makarov, and a 75 Compact in 9 Luger.

The pooled mean precision was 34 moa (my best group of the 16 was 15 moa), the pooled standard deviation was 11 moa, and the pooled standard error was 2.7 moa. (The design had 12 degrees of freedom.) Given my precision a change in POI would have to be on the order of (off the top of my head) 5.4 moa to have a chance of detecting the difference. Given a muzzle rise of 0.002 in/moa, the incremental muzzle rise needed to produce a detectable change in POI would 0.01 in -- a movement I doubt can be discerned with the super slo-mo cameras used in the videos presented in this thread.

While I'm sure many can better my handgun precision, I assuaged myself by digging up the following benchmarks:

- stock pistol in a Ransom rest -- 7.6 to 11 moa
- stock pistol rested on a sandbag -- 11 to 15 moa
- slow-fire bullseye 8-ring (in the black) -- 15 moa
- NRA Marksman rating (slow fire, unsupported 2-hand grip) -- 115 moa.

Clearly, handguns can't hold a candle to benchrested rifles, and while there is room for me to improve, I'm not so bad for an old cripple.

 

[44 AMP]

Clearly, handguns can't hold a candle to benchrested rifles

There actually are a few handguns that can. However they don't fall into the duty or service call, and no sane individual would carry one on the street for a personal defense weapon.

It is rather interesting to note that for generations, the benchmark for an "accurate" rifle was 1 MOA, while the standard for a pistol or revolver was a 2-2.5" group at 25yds.

Not only are handguns more difficult to shoot with equal accuracy, MOST of them aren't as accurate mechanically. Some are.

 

[Limnophile]

I should have said that defensive handguns held unsupported can't match a benchrested rifle.

A 2.5-in group at 25 yd is darn good -- 9.6 moa. I assume that's bench rested. I realize bullseye shooters are using a 1-hand grip, but I'd be more than happy if I could keep all my slow-fire, 2-hand grip shots in the black (9-ring or better) on a rapid-fire bulleye target -- 22 moa.

 

[Limnophile]

Walt,

In theory, a heavier bullet fired at the same velocity as a lighter bullet will hit the target at the same time and place as the lighter bullet.

Only in a vacuum. Recoil considerations aside, the bullet with the higher ballistics coefficient -- almost certainly the heavier one -- will decelerate less quickly due to improved aerodynamics.

Another comparison of American Eagle FMJs -- this time the 9 Makarov 95-gr vs the 9 Luger 147-gr flat nose: http://www.federalpremium.com/products/compare/handgun_compare.aspx.

Both have a muzzle velocity of 1,000 ft/s, but the 147-gr bullet is faster downrange because its ballistics coefficient is almost double that of the 95-gr bullet. When fired from a gun sighted in at 25 yd, the less streamlined 95-gr Makarov impacts lower, ranging from 0.1-in lower at 50 yd to 0.8 in at 100 yd.

 

[45_auto]

Let's not forget that inertia is speed * weight.

Really?

Aircraft carrier:

Speed of zero times weight of a 103,600 tons = inertia of 0

Golf ball:

Speed of zero times weight of 1.62 ounces = inertia of 0

Definition of inertia:

Inertia: the resistance an object has to a change in its state of motion.

http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Inertia-and-Mass

You really believe that an aircraft carrier and a golf ball have the same resistance to a change in their state of motion?

I would suggest that to test your belief that you strike a stationary aircraft carrier with a golf club and a stationary golf ball with a golf club and see which one goes further.

You may want to study up on the definitions of INERTIA and MOMENTUM.

 

[JohnKSa]

Recoil begins the instant that the bullet begins to move.

The key to understanding this issue is realizing that MUZZLE RISE is NOT the same as recoil. It is one possible effect of recoil if the conditions are right to cause muzzle rise.

It is entirely possible for a gun to recoil without the muzzle rising. For example, if the resistance to recoil is directly behind the bore then the gun will recoil straight backwards without any muzzle rise.

In a revolver, the bore is significantly above the resistance to recoil (the shooter's hand). Since the revolver barrel and frame of the revolver are, for practical purposes, all one piece, when the barrel of the revolver begins to recoil the whole revolver begins to move. That motion is resisted by the shooter's hand which is below the bore. That means that muzzle rise will happen and since the revolver recoils as a single unit, the muzzle rise will begin the instant that recoil begins.

The locked breech autopistol is NOT all one piece and therefore some pieces can move (for at least small distances) without the whole unit moving. In particular, the slide and barrel can move directly backwards without the frame moving--at least for a little while.

So the bullet starts moving and the slide and barrel start recoiling at exactly the same time as the bullet begins to move. Because there is no significant resistance to their movement they recoil nearly straight backwards** until the barrel begins to unlock. HOWEVER, at the point that the barrel starts to unlock, the bullet, by design, is already out of the barrel. Once the barrel starts to unlock, the force of the barrel impacting the frame (or some component attached to the frame) begins to cause muzzle rise because that force is resisted at a point below where the force is applied.

**There is some resistance to the initial movement of the slide & barrel provided by the recoil spring but it's not significant enough to cause noticeable muzzle rise.

A couple of years ago, I started looking at revolver bore lines vs sight lines and found that a revolver muzzle is pointed downward significantly in comparison to the sights. That is to compensate for the muzzle rise while the bullet is still in the barrel. Recoil, in a revolver, immediately forces the muzzle upwards and that upward motion means that the barrel at the moment of bullet exit is pointed quite a bit higher than it is at the moment that the trigger is pulled. The sights are set to compensate for that motion.

I wondered if the same were true of autopistols and found it was not so.

Here's a diagram comparing the boreline vs. sightline for a number of handguns. One revolver and three autopistols.

I made the diagram by putting a long, straight, tightly fitting dowel down the bore and placing a yardstick across the top of the sights. Then I traced the lines created by both on a sheet of paper to see the difference between the two lines.

It's pretty easy to see that there's a difference between the revolver and the autopistols. In the revolver, the muzzle points downward in relation to the sights. In the autopistols it actually seems to point slightly upwards in relation to the sights.

It took me awhile to figure out why the difference existed. But the diagrams gave me a great starting point to work from. They made it clear that in a revolver, there's a significant amount of muzzle rise while the bullet is still in the bore but in an autopistol, there's little or no significant muzzle rise until the bullet exits the barrel.

 

[45_auto]

JohnKSa, I've noticed the same thing.

I used the drawings here:

http://brlcad.org/design/drafting/M1911-A1_REDUX.pdf

I believe that I calculated that the nominal sight line of a 1911 DROPS 1.4 degrees in relation to the frame rails (in other words, rear sight is taller than front sight), while the bore axis drops 0.9 degrees. That was a while back, I may have slightly mis-remembered the numbers.

It's pretty obvious in the cross section on Sheet 1 (section A-A) of the drawing.

Calcs are at work, I'll try to post them Monday.

 

[JohnKSa]

I'll be interested to see them!