caliber vs. recoil

[Flyboy_451]

This is a copy of a post I made on another forum detailing an informal study that I conducted comparing recoil of the .40S&W and . 45ACP. Just food for thought.

Go to any gun forum on the internet and you will see posts asking for opinions on this caliber vs. that caliber and which has less recoil or is easier to shoot. We have all seen and participated in these types of posts offering what insight we can to assist fellow shooters, but how good is this information really? Using myself as an example, I have been shooting for nearly thirty years. I own handguns in various configurations in calibers ranging from .22LR to .475 Linebaugh. I shoot a lot of big bore revolvers and have become accustomed to heavy recoil. For me to say that the recoil of a given caliber is not abusive or unpleasant may not be the most objective view. Not to mention such variables as hand size of the shooter, configuration of the gun, loads being shot and a multitude of others. This lead me to an idea for a long term experiment that began this summer and may continue well into my elderly years, but so far it has been fun and educational, so I thought I would share what results have been gathered so far.

This all began with the common question of "should I get a .40 or a .45?" I first asked myself how these two should be compared, as they really are very different critters. My opinion, though never tested objectively, was that I preferred the .45. My reasoning was that the larger caliber, loaded with bullets of the same or similar weights at similar velocity, was more pleasant to shoot due to lower pressure. Why bullets of similar weight and velocity? Simply because within these two calibers, factory ammo is readily available within these parameters, and I wanted this to be a comparison of caliber vs. recoil, not power (however you decide to determine it) vs. recoil.

To conduct the experiment, I needed two identical guns, but chambered in the two calibers. I already had a great shooting custom built STI in .45, so why not just build the same gun in .40? Problem solved! Now for ammo... I selected a 180grn bullet for use in the .40 and a 185 in the .45. These are readily available not only in component form as well as factory ammo, although the initial tests are being done with handloads. These two calibers are a wonderful set to compare because when using simlar weight bullets, max pressures in each cartridge achieve almost identical velocities, with a wide difference in pressure. In researching SAAMI specs for the two cartridges, I found that the max operating pressure for the .40 was listed as 35,000psi and the .45 as 19,900psi, a difference of 15,100psi. The .40 will drive a 180grn bullet at 1,000fps near the top of its pressure range. The .45 will do the same with a 185grn bullet near its max pressure.

Loads were assembled and shot across an Oehler 35P chronograph, then adjusted as needed to arrive at 1,000fps +/- 50fps. The load used for the .40 was 5.3grns of Unique and a 180grn cast bullet from Midstate Cast bullets for the .40, for an verage velocity of 1012fps with a standard deviation of 26fps. For the .45 was 6.4grns of Universal for 1008fps average and an SD of 16fps. Both of these loads generate about 425 foot pounds of energy for those who prefer that measure of power.


Now for the shooting…but who should do this shooting? If I do the shooting, as was stated earlier, it certainly would not be objective. I struck on the idea of going to the local range and asking random shooters there to shoot each gun and then fill out s short survey giving their impressions as preferences. The testing was conducted blind, so that the shooters did not know what caliber they were shooting (unless they cheated and observed the ejected brass), and every round was fired over the chronograph to verify consistent velocity. Each gun was loaded with ten rounds, and each shooter shot a total of twenty rounds through each gun, alternating between the two. After shooting both guns the shooters were asked to answer the following questions.

1. Could you feel a difference between the felt recoil of the two guns?
2. If a difference was felt, was it a matter of recoil force or recoil speed?
3. Did you prefer one gun over the other and if so, which one?

Keeping in mind that I am not a professional researcher, have no formal training in such matters and that there are certainly things that were not taken into account, I think the results are at least as valid, if not more so, than single opinions from various posters on any number of forums. My goal was to get general impressions from a wide variety of shooters, and I think that has been accomplished. A total of 210 shooters participated, all of them, strangers to me, and of various levels of experience. The results were as follows.

Of the 210 shooters, 178 (84%) shooters could feel a difference in recoil.

Of those 178 shooters, 143 (80%) of them felt it was a matter of speed rather than force.

Of the 178 shooters that were able to feel a difference, 156 (87%) of them preferred the .45 over the .40.

Of the 32 shooters that could not feel a difference, there was a pretty even split on preference of guns, with 15 (47%) preferring the .40 and 17(53%) preferring the .45. (Please do not ask me how people who could not feel a difference were able to select a preference. I can only speculate)

Please keep in mind that this was not intended to prove that one cartridge is better than another. No aspect of performance difference of the cartridges was considered. I will leave that up to others to debate. It was simply a comparison of recoil between two cartridges loaded to equal performance in terms of energy, with vastly different pressures. While this portion of the experiment only compared two cartridges, loaded with custom built loads to achieve the same ballistic performance with regard to bullet weight and velocity, some myths can be refuted.

A .45 does not necessarily have more recoil than a .40. The load makes the difference. A 230grn bullet is not the only option for a .45, just as a 180 is not the only choice out there in .40. Factory ammo is available in the weight and velocity range tested, in both range and self defense ammo. If you are a handloader, the options are even greater.

Higher pressure does not necessarily equal higher velocity, particularly if there is a significant bore diameter difference. This is for the same reason that a larger hydraulic cylinder will do more work than a smaller one operating at the same pressure. Having a larger area for pressure to work over creates significant improvements in work capacity.

The .40 has proven itself to be a very capable cartridge that has performed well for a significant span of years. The .45 has a 100 year history that shows similar effectiveness. I will let others argue about which is better, but here are some advantages of each:

.40S&W-
-More capacity in same size package
-Flatter trajectory due to higher velocity, and sectional density
-Slight advantage in cost when using handloads. Powder and bullets are bought by the pound, no matter how ya slice it and dice it.
-reasonable selection of bullets available.
-one of, if not the most popular semi auto cartridge on the market, making ammo and loading supplies readily available.

.45ACP-
-Larger bore diameter. I know that this is a hotly contested issue, but I think you would be hard pressed to show this as a disadvantage for most applications.
-wide selection of bullets available ranging from 155 to around 250 grn.
-Still one of the most popular cartridges currently in use, making ammo and components readily available.

I am glad I do not have to choose between owning one or the other, as they are both fine performers in their own right, although I give a slight edge to the .45 because it is so flexible in the roles that it can fill for a wide range of shooters. Through the use of handloading, it can be loaded to what I believe is a much braoder range of applications than the .40 can, even if handloading for it as well. Your mileage may vary.

As a side note, an idea came to me late in this experiment. I had several shooters compare the comfort of shooting the STI in .45 to my alloy framed, full size Kimber , also chambered in .45. While I did not keep records of this comparison, a noticeable majority preferred the STI. I can only speculate that this is a result of the shape of the grip, with the STI having a wider back strap, thus spreading the recoil over a wider area of the shooter’s hand.


This is not a completed project by any stretch of the imagination. Future plans include doing similar tests with a variety of factory ammo. This will obviously require a substantial financial investment, so is not on the slate for the near future. Other comparisons that I would like to make are .357mag vs. .44 special .44 special vs. standard .45 colt loadings heavy .45 Colt vs. .44mag . others may be done, but it is hard to say, largely because I feel that any comparison needs to be done in identical guns. This could get even more expensive than it has already! I encourage anyone to take on such projects as you are able to. Not only is it a lot of fun, I think that these types of comparisons can truly challenge our own beliefs and preferences.

[James K]

Recoil comes down the m x v = M x V. The mass (weight) of the projectile times its velocity is equal to the mass of the gun times its velocity. The right hand side of that equation is what we call recoil. With bullets of identical mass and identical velocity, and guns of identical mass, the recoil will be the same.

The problem is FELT recoil, which cannot be calculated. Even if the mathematical recoil is the same, the shooter's experience, grip, hand size, etc. will affect felt recoil. Further, an auto pistol will spread out the recoil over time, compared to a revolver, and the recoil will seem less.

But, given identical guns, of identical mass, and bullets of identical mass and velocity, there is no difference in recoil. Any difference in felt recoil is in the shooter, as indicated above.

Jim

[sigcurious]

James, that is a bit over simplified. The impulse can be measured which is the force over time. That would be major contributor to how a person feels the recoil. Granted what someone perceives is still subjective, but that does not exclude that there are more measurable factors at play than the magnitude of the recoil force alone.

[Flyboy_451]

As you have said, the math can be used only to calculate the force of recoil, not how the shooter perceives it. Felt recoil is subjective, but I also think that there are some generalities that apply to a large segment, if not the majority shooters. One of those being that lower pressure loads delivering equal performance to a high pressure load, are generally speaking more pleasant to shoot for most people, given identical platforms.

This is why I enlisted the number of shooters that I did for this project. Seeing this theory demonstrated across a fairly large number of people lends credence to the theory.
while this non-scientific study does not prove anything beyond refute, it does shed light on some questions and offer alternatives to the standard answers we have all seen and repeated for years. This was the purpose of the study.

JW

[L_Killkenny]

Basicaly what you proved is people are falable. You didn't state bullet weight in the .45 but with speed being equal and energy being equal than you must have been using 180gr bullets in the .45 too? Were they lead or jacketed? I'm gonna assume lead for the time being. Now for what I mean by people being falable has nothing to do with you. But in identical platforms with identical weight bullets moving identical muzzle velocity guess what recoil, felt or real, will be? The same, Who'd a thunk it? In other words those who thought there was a difference were dreaming. Of coarse the smaller hole in the barrel could have made weight slightly more with the .40 but enough to notice? Maybe to a computer.

LK

[Flyboy_451]

You guys are overlooking pressure in you calculations. The velocity of the bullet is not what creates the rearward thrust that contributes to recoil. The pressure driving the bullet does this. the velocity achieved is not material to recoil, pressure is! This is called thrust. This is calculated by multiplying the pressure in pounds per square inch by the area that it is acting on. For a .40 cal bullet, the area of the base is .502 square inches. For a .45, it is .63 square inches. The total thrust for a .40 S&W operating at or near max pressure is a total of 17,500 pounds (35,000psi X .502). The thrust generated by a .45 operating at or near its max pressure is 12,537 pounds (19,900psi X .63). There is a thrust difference of roughly 5,000 pounds.

If there is an engineer or a physisist in the house, perhaps they can correct me if I am wrong, but I am pretty sure that would cause a difference in recoild that could indeed be felt.

Now, as has been stated in my previous posts, I was not out to prove anything! I simply sought to gain impressions from a fairly wide range of shooters and present that information for others to draw their own conclusions from. If you don't like the information, by all means, disregard it. Or better yet, go conduct similar research and present your methodology and results here for other to view. I never said this was a perfect study, as a matter of fact, I stated upfront that I had no formal training in such research. Feel free to conduct research and/or present evidence that refutes what I have posted.

Jw

[Discern]

I agree that chamber pressure is one factor in how much recoil a firearm appears to have. I also agree the .45 ACP is more pleasant to shoot than the .40 S&W. The recoil is different with the .40 S&W being snappier than a .45 ACP, and the higher chamber pressure of the .40 S&W is a major factor if not the factor for the snappier recoil of the .40 S&W.

If have found that people with smaller hands prefer single stack mag semi-autos, and people with large and very large hands prefer the double stack mag semi-autos. What fits better is more comfortable and provides more control. Some will prefer a flat backstrap while others will prefer a more curved backstrap. The grip angle is also a contributing factor on how a shooter likes a particular handgun. Every hand is different. This one reason why if we don't like a particular model of a quality, reliable handgun we should not be knocking that model down or those who own them. It may not be the model for us but be a great model for someone else.

[michael t]

All I know is I bought a 40 Shot 1 mag . Took back to dealer and bought another 45. . You can keep the 40 I will take 45 acp any day.

[Mello2u]

Flyboy_451

[From 1st post]
Loads were assembled and shot across an Oehler 35P chronograph, then adjusted as needed to arrive at 1,000fps +/- 50fps. The load used for the .40 was 5.3grns of Unique and a 180grn cast bullet from Midstate Cast bullets for the .40, for an verage velocity of 1012fps with a standard deviation of 26fps. For the .45 was 6.4grns of Universal for 1008fps average and an SD of 16fps. Both of these loads generate about 425 foot pounds of energy for those who prefer that measure of power.

[From second post]
You guys are overlooking pressure in you calculations. The velocity of the bullet is not what creates the rearward thrust that contributes to recoil. The pressure driving the bullet does this. the velocity achieved is not material to recoil, pressure is! This is called thrust. This is calculated by multiplying the pressure in pounds per square inch by the area that it is acting on. For a .40 cal bullet, the area of the base is .502 square inches. For a .45, it is .63 square inches. The total thrust for a .40 S&W operating at or near max pressure is a total of 17,500 pounds (35,000psi X .502). The thrust generated by a .45 operating at or near its max pressure is 12,537 pounds (19,900psi X .63). There is a thrust difference of roughly 5,000 pounds.

If you used hand loads in your test you do not know the pressures. It is possible that the .40 S&W load developed much less pressure than maximum. It is possible that both the .40 and the .45 developed nearly the same pressure.

1) I am curious whether you prevented the shooters from observing the muzzle of the guns.
2) I'm also curious about what sort of targets the subjects shot.
3) Further, if they shot paper could they see the difference in the size of the holes made by the bullets?

The above three factors could effect the responses to the question of whether they could tell a difference.

Your study was a nice effort. I thank you for posting your findings.

[Flyboy_451]

The loads were selected because, according to multiple manuals, the powder and charge weights used were shown as near max pressure loads and near the target velocity. Without pressure test equipment, this is the best I can do. Some adjustment was needed to arrive at velocities that were very close, but the difference in pressure would not likely have been large as the adjustments were about .1 grain from charges listed. The .40 would have likely seen the largest difference due to case capacity, but even then, I doubt it was a significant enough difference to close the 15,000psi gap between the two cartridges.

No targets were used. The shooters fired through the chronograph and into a grass covered berm 50 yards away. That was something I actually considered.

The muzzle was not blocked from view. I thought about it but deecided against it for two main reasons. This was a test of simple preference not measured muzzle rise or recoil. I did not want to hide any of the effects of shooting the guns. This includes muzzle rise, blast, noise and recoil all combined. I actually thought about including questions about felt blast and noise but elected not to in the end in an effort to keep the survey simple by only asking for general preference.

Future projects may include a more detailed survey. I am undecided at this point.

JW

[jephthai]

The velocity of the bullet is not what creates the rearward thrust that contributes to recoil. The pressure driving the bullet does this. the velocity achieved is not material to recoil, pressure is!

I believe you are incorrect here. As Discern said, pressure is a factor, but it turns out it's a small factor. It's not like the "jet" of compressed air/gas/etc. is the most significant component of recoil, by a long shot. What is potentially significant is the acceleration of the gases produced during the combustion of the powder, as this results in additional kinetic energy (and with moving masses, you have momentum).

The fact that mass leaves the system is what makes recoil, as a consequence of Newton's law -- the whole equal and opposite reaction thing. If all you had was a jet leaving the gun, the only "recoil" you would experience would be related to the mass of the particles ejected. Since the bullet is the largest mass, by a humongous margin, its movement is, in fact, the source of the recoil.

Since momentum is conserved, it is the most useful measure of recoil. As stated, ρ = mv, or mass times velocity. The momentum of the bullet leaving the firearm is equal to the momentum of the firearm towards the shooter's hand.

If you have a 180gr bullet at 1000fps (say), we're talking about a momentum of the bullet of 25 foot-pounds per second. This is the recoil component of the bullet.

If you have 5.3 grains of powder, exiting the muzzle at, say 1,500 fps (a reasonable figure -- my ballistics textbook says to use a general rule-o-thumb that the gas expands at 1.5x the velocity of the bullet for "small arms"), then you have 1.13 foot-pounds per second of momentum.

In this back-of-napkin thought experiment, this powder expansion / acceleration makes up only 4% of the total momentum of the system. Humans, in most domains, cannot perceive more than a 10% "change", so this is practically an un-noticeable contribution to recoil.

More significant to the current discussion is the comparative difference between your 5.3gr powder load and the 6.4gr load -- this results in a difference in momentum of only 0.24 foot-pounds per second. This is a very minor issue.

The "real world" is blurrier than this, since there are complicating factors. E.g., the exact velocity of the expanding gas is hard to know, powder conversion to gas is not 100%, etc. Nevertheless, according to resources at my disposal, "pressure" or "muzzle blast" contributes very little to felt recoil in handguns.

As I said, momentum is a popular metric for recoil, but it's not the only means, and not necessarily the "best". That said, I have several equations in my book here for rigorously calculating recoil, and none of them use pressure as a term. They are all consumed with breaking down the component masses and velocities in various combinations to calculate recoil energies. This is very complex, because energy is hard to track in a real-world system (though energy is conserved, there are many ways this happens -- heat, noise, bullet deformation, barrel deformation, etc.), which is why the easily calculable conservation of momentum remains useful.

[jephthai]

By the way, I in no way feel that your research is not valuable (just your physics model for understanding recoil ). In fact, I find this experiment absolutely fascinating. Regardless of the physics, the fact that you had such a skew in your figures indicates that there's something going on.

You could do some hypothesis testing to estimate the odds that you'd have an 87% slide, but it's not even worth doing so -- there is no way in heck that this size data-set is an "aberration". Even looking at your survey questions, I don't see anything that would bias the testing by "leading" the test subjects to answer one way rather than the other.

I will be thinking about your results quite a bit, now! Thanks!!

[Flyboy_451]

Jep,

I still think that you are missing something with regard to pressure, or maybe I am. Perhaps you can explain it if I am. Imagine if we could drive a bullet down the bore without increasing the pressure behind it. In other words, the velocity would be self contained and caused by magic. If this were the case, there would be no rearward thrust generated, as a matter of fact, there would be a forward pulling effect due to the friction in the bore. It would be the same as if you had a stationary object and drug a moving object against the side of it (imagine a car striking a glancing blow to the side of another). The momentum of the moving object would "drag" the stationary object in the same direction, would it not? The only rearward thrust that my pea brain can see in the operation of a gun comes from the pressure exerted on the breech face. Without this, where else could rearward force come from?

One example of this force can be seen when firing a handgun with a much heavier bullet than it is sighted in for. This is a common problem in big bore revolvers (particularly Rugers). Dramatically heavier bullets, such as shooting a 335grn bullet in a .45 Colt will shoot much higher in relation to sight alignment than a lighter bullet such as a 250 in the same gun. This is why those of us that have Rugers and shoot heavy bullets in them, often replace the front sight with a taller one. This indicates that recoil is beginning before the bullet leaves the barrel. Otherwise, no sight correction would be required. The muzzle is rising before the bullet leaves it. Because the center line of the bore, and thus the breech face, sits above the axis of your your, the rearward thrust of pressure causes the gun to rotate upwards. I don't see how this action could be caused by velocity.

I think the idea of viewing velocity as a cause is the fallacy in your argument. Velocity is result of the pressure exerted on the base of the bullet. I think it is more of a reaction than an action. Of course, I could easily be wrong. I do not claim to be schooled in physics. All I can do is apply rational thought to observations. Any ideas?

JW

[jephthai]

The issue I have with your example is that you invoke magic. Now physics don't apply and we're not talking about the real world. Another of Newton's laws states that an object in motion will remain in motion unless a force acts upon it. This applies to a stationary object as well (zero motion). To move the bullet, a force must act upon it. In other words, the bullet cannot magically move down the barrel on its own.

Physics is physics, and if anything acts on another thing to move it, it will itself, in turn move in the oppositee direction. The pressure presses against the chamber and bore just as it does the bullet. When the gun and bullet separate, how do we measure this equal and opposite force (forward on bullet, rearward on gun)? The magic of physics, or the genius of Newton, we find that these forces can be discussed in terms od energy and momentum.

As I stated, the jet effect of the gas counts, but its effect is equal to the gas's mass times its velocity -- it's small. The mass of the bullet doesn't CAUSE the recoil -- it happens that the forces involved result in recoil that can be calculated using the m x v of the bullet, because physics works.

Sent from my Ally using Tapatalk

[Flyboy_451]

Jep,
I am not arguing that physics should be ignored by invoking a magic bullet that requires no pressure. It was exactly my pont that a force must act on the base of the bullet. This is the only force present (that I can see, anyway) that produces a rearward thrust on the gun itself. My point was simply that the forward velocity of the bullet does not generate a rearward thrust or force.

As to what you are referring to as the "jet effect", I can only offer this opinion at this point. I have shown that the force pushing on the bullet is roughly 15,000 pounds in the .40. This force is produced by pressure. for that pressure to act on the base of the bullet, it must have something to push against. IT pushes against the chamber and barrel of the gun as the bullet passes down the bore. According to newtons law, this force will cause an equal reaction in all directions. But, since the bullet moves forward, and the sealed nature of a firearm prevents escape or movement to the sides, there are only forward and rearward pressure.

You have shown with mathematics that a 180grn bullet traveling at 1000fps carries 25 pounds of recoil energy, can you you explain how that energy would cause a rearward push or thrust on the gun? This is what is not explained by your model. Where does this come from? It is rather obvious that large amounts of pressure are required to drive the bullet down the bore, due to everything from the initial mass of the bullet, to friction of bore contact. Friction, I think, being the largest part of resistance. If you have ever slugged a bore, you definitely know what I mean.

You mentioned various formulas for calculating recoil in your first post and that none of them mentioned pressure. I can not answer why this may be, but I can offer a possibility. Perhaps they are simplified formulas that consider pressure a constant or they account for it in some way through the use of a constant. Perhaps, because pressure it is difficult or impossible for most of us to measure, these formulas assume a linear pressure/velocity relationship. I don't know. As you stated, there is evidence of something happening that 87% of people were able to perceive. The only sizable differences in the experiment were bore size and pressure. Because these to variables are linked and there is a mathematical way of calculating the effects of pressure over area, I can only conclude (with the information I have available) that this must be the cause of the difference felt.

Please do not take any of my comments as being argumentative. I am only trying to parse out information and gain understanding, and your comments have been thought provoking and are very welcome. Thanks for participating in the discussion.

JW

[Ralgha]

Recoil is impulse, not force. The flaw in your reasoning is that the force applied in the .40 is, in fact, greater than the force applied in the .45.

The reason you all come up with the two having identical force is that you're discounting time. They would only have identical force if the bullet was accelerated instantly, which is what is assumed in the equations you are using.

Both calibers go at the same velocity (virtually), the .45 is accelerated by a lesser force over longer time (lower impulse) and the .40 is accelerated by higher force over shorter time (higher impulse). The equation for force that you need to use is F = (change in momentum) / (change in time). Then find the impulse by taking the integral of that force over time.

[Noreaster]

Now please do a similar test with the 357 sig and 40 S&W. I have carried the 357 Sig for many years now and I've come to the conclusion that the muzzle blast and shock wave aren't worth it. I have trained new officers that came from PDs carrying the 40S&W and they initial had trouble with the 357 sig. I'm not saying the 357 sig has a significant recoil, but the blast and other effects are substantial. Extended indoor shooting has become painful with headaches after the session. Any indoor shooting requires double ear protection. This is not a comparison of recoil per say, but all the other effects added in.

[brickeyee]

The thrust generated by a .45 operating at or near its max pressure is 12,537 pounds (19,900psi X .63). There is a thrust difference of roughly 5,000 pounds.

And these forces are solely within the barrel and do not actually have any real effect.

What you are probably looking for is called 'jerk.'

It is the rate of change in acceleration and is not a very common engineering unit but has its place.

For recoil it measures how quickly the bullet is accelerated and this is perceived as the 'sharpness' of the recoil.

A gentle push or a hard blow.

It is related to impulse, but accounts for the duration of the impulse, again the difference between a gentle shove and a punch.

[Seaman]

As a handloader all I can say is that the more powder I put in the case, the louder the boom and the heavier the recoil. And the greater a manufacturer's published rating for ME, the heavier the recoil. All my tests were involved with accuracy and penetration, so I don't have an answer to your theortetical opinion re recoil.

What amazes me is that, that old dog of a cartridge, the 45 ACP, is so accurate, compared to the 40 S&W and the 9mm para.

It seems that the 45 ACP is very accurate in a variety of handguns: i.e. large 1911s, polymers like the SW99, or tiny pistols like the AMT BACK UP.

I don't know why.... if its me (a subjective measuring tool) or the cartridge.

Thank you for your research, it is valuable and informative.

PS: Just asked my kid (a college freshman) whether it is velocity or energy, he said: "That's simple, its energy." Out of the mouths of babes....

[Flyboy_451]

Ralgha,

I am not sure who you are addressing. Time does indeed have an effect on recoil, particularly how it is felt. I am not discounting this, but it is not something I have a way of measuring or calculating. Not only do I lack the equipment to measure acceleration, but also the mathematics expertise to make use of such information. Recoil is often expressed in pounds per second, if I am not mistaken (foot pounds per second maybe? I don't have resources in front of me right now).

As far as force is concerned, I have demonstrated the difference in force applied to the bullets as being on the order of 5,000 pounds. If there is an error in my calculations, please feel free to offer any corrections. This experiment been a fun and educational project thus far, and will become even more educational as information is shared by more comments.

If anyone is aware of a way of calculating the expansion of gasses as the bullet exits the barrel and how this might effect recoil forces, I would love to hear it! Any other information is also welcome. I think this has been one of the more interesting threads I have participated in for quite some time.



Noreaster,

.357 vs. .40 is probably not one that I will pursue. This is largely due to the fact that I strongly feel that any comparison made should be conducted with identical guns. I am not aware of a currently produced gun in both calibers. This becomes a financial barrier, as a custom gun in a caliber and configuration that I have no desire to own would be required. Sorry...


JW

[Ralgha]

I was addressing those who argue that the force is the same in each caliber and that it shows that the recoil is the same, which is incorrect. There is, of course, some subjectivity in the observation of the recoil differences, but the recoils themselves are also very different, proven by the difference in impulses.

[Mello2u]

I am not a physics major, and my college physics was a few decades ago. I would assert that impulse is force.

I found this:


Consider that the energy generated by firing a cartridge in a semi-auto handgun is confined to the barrel, chamber, the frame by connection to the barrel via the barrel link, and the slide.
The time that it takes for both the .40S&W and the .45ACP bullets to travel the length of the barrel should be almost identical and their muzzle velocities are similar.

I think what is needed is an objective measure of the energy exerted on the grip of the two guns as they are fired and the time it takes for that energy to be exerted. Is there an instrument which can do this. Maybe an accelerometer?

[Lost Sheep]

You could also consider that the pressure against the breechface is not felt by the shooter at all. The breechface is part of the slide. It is the recoil spring that transfers the force to the frame, then to the shooter, then, later, the force of the slide hitting the stop.

If you went to heavier and heavier recoil springs until the slide no longer went to it's full travel against the stop, but still traveled enough to cycle (meaning the spring absorbed ALL the recoil as it compressed - over what length of travel?), this might be informative.
.
At that point, observing the difference in the spring weight of the recoil springs would give a quantitative measure. Of what, I don't quite know, but it would be a measure of something.

Yeah, we got a mystery here. The only thing actually measured by Flyboy_451 (by his intent and successfully, I would say) was perception of the sample population of shooters where simple physics tells us there should be none. That PROVED that more than simple (or simplistic) physics is involved. But I think that you guys are on the right track and I look forward to the investigation. From what I have read so far, if you combine forces, you will make real progress and I thank you both for it, as well as the other contributors here.

Now, I want to know why the felt recoil of 480 Ruger vs 454 Casull (loaded down, even) both fired in Super Redhawks is said to be so much less.

Lost Sheep

[Ralgha]

Force = PSI * area

.40 Force = 35,000 * pi * .2^2 = 4398
.45 Force = 19,000 * pi * .225^2 = 3021

Velocity in both cases = 1000 fps

F = m*a -> a = F/m
180 grains = 0.000799224433 slugs
185 grains = 0.000821425112 slugs (to keep some semblance of real units)

.40 accel = 4398 / .000799224433 = 5502834 fps/s
.45 accel = 3021 / .000821425112 = 3677754 fps/s

a = ΔV / Δt -> Δt = ΔV / a

.40 Δt = 1000 / 5502834 = 1.817E-4 s
.45 Δt = 1000 / 3677754 = 2.719E-4 s

The .40 takes only 66% of the time to reach 1000 fps as the .45 does, that's not insignificant.

With the .40 you see a higher force with a shorter time, hence the recoil is, as most people describe, a sharper kick. With the .45 you get a lower force with a longer time, so you get a recoil described by most as a longer or smoother push.

[Flyboy_451]

Ralgha,

Thanks for the input! The formulas for acceleration are above my head, so I can only assume that you are correct. It would seem that the pressure and the time in which it acts is where the difference exists. This was my theory to begin with, thus the questions posed to those that participated in the shooting. Thanks to all who have participated in this discussion! We may not have solved the mysteries of felt recoil, but I think a lot of good information was brought to light! This is what discussion forums are all about. Once again, a hearty thank you to all who participated!
JW