Physics of shooting a rifle

[davidsog]

The headwind experienced by a bullet is always tangent to the trajectory arc,

Exactly

That headwind is termed the Relative Wind and it acts like any other Relative Wind upon an aerial object.



You can see from the definition of Lift and Drag that all forces are realized thru the Relative Wind.

[tangolima]

Originally Posted by Unclenick

Yes. It's messy and irregular. When the bullet clears the muzzle, the gas behind it in the barrel, being lighter than the bullet, accelerates and blows past the bullet. So, the bullet actually has a tailwind for a brief period between interior and exterior ballistic effects called transitional or intermediate ballistic period. That tailwind increases the bullet's forward velocity without increasing its spin (because it is no longer constrained by the bore and rifling). The effect on velocity is commonly on the order of three percent or so of the peak bullet velocity. During the transitional period, and especially in the first few calibers of travel out of the barrel (eleven calibers were measured by the military for artillery), if there was any flaw in the muzzle crown's axial symmetry or if the bullet was at all tilted in the bore, the muzzle blast will play unevenly off its base, and this contributes significantly to initial yaw and to lateral drift. But even if a bullet has no initial yaw coming out of the muzzle, as soon as it is clear of the bore, gravity starts pulling it down, and unless it is fired straight up, that starts to pull it into the trajectory arc. The headwind experienced by a bullet is always tangent to the trajectory arc, so as that arc turns down, that headwind starts to angle up, and that puts a vertical overturning drag on the bullet because its gyroscopic stiffness tries to keep it on the original bore line. As a result, the headwind itself becomes the source of an upward overturning force that initiates coning motion.



Note that there is also a lift on the bullet angled off the tangent line of the trajectory that moves the whole bullet and doesn't just act to overturn it. As precession causes coning to set in, the direction of that "lift" goes around the clock, causing the bullet's center of mass to travel in a spiral. Each time coning goes around the clock it pushes the bullet back where it came from, so this helix simply circles the trajectory path. I calculated it for a 30-caliber match bullet once long ago, assuming about one moa of yaw, and it worked out to be something like 0.02" in diameter, IIRC. I've forgotten the rate of twist and the bullet weight, but it's a small orbit that shrinks as a properly stabilized bullet goes down range because the coning radius spirals inward on such a bullet. In any event, you have a couple of cyclical motions here, such as the coning and the helical corkscrewing. The term epicyclic means to have multiple cycles at once, as when the moon orbits the earth, but the earth also drags it along an orbit around the sun at the same time, not to mention the whole galaxy turning, so the moon's motion is epicyclic, and so is a bullet's.



When I first started shooting Service Rifle matches back in the '80s, I noticed that when the sky was clear on Viale range, and you stood at the 600-yard line watching guns shooting at the slight upward angle that requires, you could see the mirage of the bullet wake when a rifle fired, and some were pretty straight, but some were a very pronounced helix, indicating bullets with less or more initial yaw, and the same gun might fire one and then the other or anything in between. This causes a small difference in ballistic coefficient from shot-to-shot, of course, but not nearly enough to spoil a good score.

The transitional ballistic period, the moment the bullet exits muzzle, is a critical moment. The stabilization mechanism hasn't been fully established. Slight perturbation during this period would have profound effect on the rest of the flight. Along this thought, do you think a muzzle device of enough length may do good by shielding the bullet from cross wind? 11 calibers for a 6mm bullet is 2.67". I will look for a 3" long flash can to try. I currently have a shorty on my .243 win.

-TL

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[stagpanther]

The reason I have a problem with some of the definitions is that they sometimes confuse what we on the ground observe as wind blowing through trees, flags etc. with relative wind to an object in flight--it is independent of this wind, it is what the flying object "sees"--hence it is relative to it only.

[Unclenick]

Originally Posted by tangolima

The transitional ballistic period, the moment the bullet exits the muzzle, is a critical moment. The stabilization mechanism hasn't been fully established.

Yes. Boattails are sensitive to uneven or asymmetric wind deflecting of the slope of the boattail, tending to impart slow drift away from the intended trajectory in the direction opposite the gas deflection. The final stabilization mechanism in the relative wind that David defined can't begin until the bullet has exited the temporary blast sphere of accelerated gases, as we've all seen in Schlieren shadowgraphs of a firing rifle. Until that moment, the bullet has no slowing drag, and any hint of starting gyroscopic stabilization in that short time period would be a response to the tailwind. Since the twist direction for response to the tailwind is from the front of the bullet, that precession response will be backward from the precession off-axis drag on the nose will induce later. So if it made any significant attempt to stabilize in that short transitional period, it would have to be undone after it cleared the blast sphere.

Originally Posted by tangolima

Along this thought, do you think a muzzle device of enough length may do good by shielding the bullet from cross wind?

That muzzle blast sphere is already a shield for a foot or two. If you install a muzzle brake, though, it will reduce that sphere's size. The sphere is comprised of gasses that have exponential deceleration as they expand, which gives them more and more area of atmosphere to lose kinetic energy against. It's not quite a perfect sphere, but close enough that its force will be close to obeying the inverse square law that the strength gravity and light and magnetism from an isotropic source do. In other words, double in size and have four times the deceleration, so this stuff slows down quickly.

This suggests a gun with a muzzle brake will not only lose the last 3% of acceleration from muzzle blast, but the bullet will experience wind a foot or two sooner.

As far as seriously affecting wind, Harold Vaughn got his gun club to let him install 100 yards of sewer pipe to give them a zero wind firing point. Doing that for longer ranges is limited by the height of the trajectory, as the sewer pipe gets pretty costly when it's ten feet wide. But stopping the wind takes that sort of effort.

[tangolima]

Originally Posted by Unclenick

Yes. Boattails are sensitive to uneven or asymmetric wind deflecting of the slope of the boattail, tending to impart slow drift away from the intended trajectory in the direction opposite the gas deflection. The final stabilization mechanism in the relative wind that David defined can't begin until the bullet has exited the temporary blast sphere of accelerated gases, as we've all seen in Schlieren shadowgraphs of a firing rifle. Until that moment, the bullet has no slowing drag, and any hint of starting gyroscopic stabilization in that short time period would be a response to the tailwind. Since the twist direction for response to the tailwind is from the front of the bullet, that precession response will be backward from the precession off-axis drag on the nose will induce later. So if it made any significant attempt to stabilize in that short transitional period, it would have to be undone after it cleared the blast sphere.



That muzzle blast sphere is already a shield for a foot or two. If you install a muzzle brake, though, it will reduce that sphere's size. The sphere is comprised of gasses that have exponential deceleration as they expand, which gives them more and more area of atmosphere to lose kinetic energy against. It's not quite a perfect sphere, but close enough that its force will be close to obeying the inverse square law that the strength gravity and light and magnetism from an isotropic source do. In other words, double in size and have four times the deceleration, so this stuff slows down quickly.

This suggests a gun with a muzzle brake will not only lose the last 3% of acceleration from muzzle blast, but the bullet will experience wind a foot or two sooner.

As far as seriously affecting wind, Harold Vaughn got his gun club to let him install 100 yards of sewer pipe to give them a zero wind firing point. Doing that for longer ranges is limited by the height of the trajectory, as the sewer pipe gets pretty costly when it's ten feet wide. But stopping the wind takes that sort of effort.

Damn! I thought I was on to something that would work. Nothing new under the sun. I'm getting a plain thread protector then.

-TL

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[davidsog]

The reason I have a problem with some of the definitions is that they sometimes confuse what we on the ground observe as wind blowing through trees, flags etc. with relative wind to an object in flight--it is independent of this wind, it is what the flying object "sees"--hence it is relative to it only.

Exactly. Well put.

[davidsog]

The Army actually measured much of this behavior of a bullet as it exits the muzzle. You can see in the case of 5.56mm that the oscillations dampen quite rapidly as the bullet picks its angle of repose.



You can see that in the first few feet it loses 25% of it yaw, 75% by 50 meters, and the yaw is dampened by 130 meters. That is .137 seconds to dampened.

Due to the dynamic stability of the round, this yaw is known to damp out over the first 100–150 m of flight.

Some excellent photos of the bullet in flight. You can see the normal shock formation which leads to the rearward shift of the CP giving our bullet positive dynamic and static stability.



Finally, the aerodynamic force axis for a bullet in flight:



https://apps.dtic.mil/sti/pdfs/ADA530895.pdf

There is quite a bit of very good info in the report. It represents actual measurement of bullets in flight. I will let you guys mill over it and we can discuss it as it comes up.

[stagpanther]

Stability of the bullet is generally viewed as a good thing. Some view the propensity of the bullet to yaw (or lack thereof)--in particular the M855--upon hitting the target in terms of lethality in incapacitating a combatant. It is a steel-tip penetrator design whose design aspects are for optimal combat efficiencies (or lack thereof depending upon firearm/range etc.).

[davidsog]

Stability of the bullet is generally viewed as a good thing.

Absolutely, without it we cannot hit the target.

Some view the propensity of the bullet to yaw (or lack thereof)--in particular the M855--upon hitting the target in terms of lethality in incapacitating a combatant.

Yep, we want the bullet to yaw in wound mechanics. Of course we are talking very different environments between the air and meat. The bad thing about the yaw at close quarters is the fact if the bullet strikes at specific yaw angles it has a tendency to cause penciling wounds instead of creating a wound cavity due to yaw.

I think that is where you are going. Correct me if it is not.

[stagpanther]

I think that is where you are going. Correct me if it is not.

Exactly what I meant and was trying to get across.

tendency to cause penciling wounds instead of creating a wound cavity due to yaw.

On that note, and obliquely referring back to our arrow discussion--I believe it has been proven by a researcher that the technology of primitive bows and arrows; even when using low lb draw (40 to 45 lbs lbs or so) and using fragile arrowheads the strength of glass that an arrow could achieve a complete pass-through through deer at close range of 20 yards--which is not all that much closer than the commonly accepted 30 yards used as a common hunting range in modern archery.

[Unclenick]

It's also very low kinetic energy. I looked at some modern bows and was getting on the order of 50 ft-lbs, IIRC, so kinetic energy at arrow velocities seems to give way to momentum as the more important characteristic. Of course, the principal nature of the damage is different. A stabbing weapon, especially something like an ice pick, doesn't usually have or need a lot of KE to do damage, either.

On yawing, take a look at Hatcher's Notebook. On pages 406 and 407, he's got a pair of sectioned oak block targets shot with M2 Ball ammunition. One fired at 50 feet has turned sideways and hooked off to the side. It made a big path but penetrated only 11¼". The other was hit at 200 yards and drilled a 32½" straight line despite its lower velocity. But all the initial yawing was damped out to about the last moa by then.

[tangolima]

That may put ballistic gel tests of rifle bullets in question. Most, if not all, are at rather short distances.

-TL

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[davidsog]

That may put ballistic gel tests of rifle bullets in question. Most, if not all, are at rather short distances.

Pretty much negates them. The is exactly what the Army concluded.
On the next Youtube Gel block test you can post down in the comments, "Did you record the yaw angle of the bullet as it picks the angle of repose?"

As half the internet blinks and cocks their head....

[stagpanther]

I recently started testing Eley's latest entry into the "super long range" 22lr market; Their "Ultra Extreme long range" ammo. Most people who spend their time shooting centerfire naturally think that the faster the better and out to greater ranges. 22lr, however, has yet to show that coorelation as being anything near enough to true to spur the success of a new supersonic that is more accurate or consistent than subsonics--though they keep trying (and I hope one day they succeed).

The almost universal drag model used by almost all new precision 22lr ammo is the RA4, not only for its superlative subsonic performance--but (conjecture on my part) almost all typical mass market 22lr chambers are cut with that particular model nose profile being "form-fitted" to the throat.

If you scroll down the the link to Eley's ammo--take a look at the terminal velocity figures for the bullet at the various ranges and you can see the remarkable low drag performance of the RA4 design enabling the bullet to soldier on to great distances with an "inferior" ballistic coefficient.

Past few days I've been shooting at 300 to 365 yards--I know it's hard to believe but sometimes I missed the target altogether and dinged the tubular steel holder instead.

[georgehwbush]

tangolima: i have found that a break does tighten up my groups, and always expected that it was the fact that it removed the "passing" gas from the flight path. i have nothing to go on other than imperical observations. but i would think that venting to the sides rather than blowing up along side the bullet would be more stable.

i do get a few thousandths better 100yard groups with verses without the break on both my test guns.

and it is reproducible so what ever the physics behind it, it works. a suppressor also has the same affect.

[tangolima]

Originally Posted by georgehwbush

tangolima: i have found that a break does tighten up my groups, and always expected that it was the fact that it removed the "passing" gas from the flight path. i have nothing to go on other than imperical observations. but i would think that venting to the sides rather than blowing up along side the bullet would be more stable.

i do get a few thousandths better 100yard groups with verses without the break on both my test guns.

and it is reproducible so what ever the physics behind it, it works. a suppressor also has the same affect.

It is in other thread. I use muzzle.device as barrel tuner. When done right, I can cut down group size quite a bit. By muzzle device, I usually mean simple flash can or flash hider, instead of brake, unless it is a caliber or application that warrants it.

Also I shoot group at 150yd instead of anything shorter. Many a time, I can group better in moa at 150yd than 100yd. I suppose the bullet would more time to settle.

-TL

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[davidsog]

I would think a properly designed and installed muzzle brake accuracy improvement has more to do with barrel harmonics than gas flow at exit. The gas at exit can only travel at the speed of sound at the local flow level. The bullet is traveling much faster than that.

That is easily seen in the photographs by the formation of normal shock.

It is a physical property of gas to form that normal shock and the local velocity of a normal shock IS supersonic. The local velocity collapses to subsonic speeds on the backside of the shock.



In this photo, the bullet has not emerged from a bubble. That bubble represents air that is traveling at supersonic speeds and is moving slower than the bullet.

The bullet is traveling faster than the speed of sound and is ahead of that normal shock wave from the exiting propulsion gases. The bullet is outside of those expanding gases influence.



In a subsonic bullet muzzle blast would have an effect.

[Unclenick]

The bullet is outside of those expanding gases influence.

In the second photo, it is well past that point and outside the transitional velocity range. Initially, however, the expanding gases are propelled by the same muzzle pressure that the bullet is, so, being lighter, they accelerate past the bullet base, creating their own shockwave and inducing some transitional velocity effects. This fast gas is what causes the post-muzzle acceleration measured by Vaughn. The SAAMI standard recoil calculation (based on old British experimental work), uses, for high-power rifles, that the gas at the muzzle is accelerated to about 1.75 times the speed of the bullet initially. However, it does lose velocity quickly, which is why the influence on the bullet is so brief. While the military puts eleven calibers on the total range of influence, roughly the first three calibers of bullet base travel past the muzzle to see the most effect. You can see this in super slow-motion videos of the gases blowing over the bullet base and forward. Whether or not the leading edge of the muzzle blast succeeds in passing the bullet nose depends on bullet geometry, velocity, and muzzle pressure, of course.

22 Rimfire is a special case. Past powder burnout, which is usually given as about 16 inches down the barrel for 22 Long Rifle (though it is actually a range for the different loadings of from roughly 12 to 19 inches), the bullet gradually slows, and the pressure behind it is dropping. So you see some muzzle blast effect on 22 RF from a short barrel, like a handgun, but in a rifle, any barrel length from about 20 to 28 will generally get the same velocity within 50 fps or so.

Another issue with 22 RF is the high-speed ammunition exits the muzzle in the transonic range, so it leaps into a portion of the drag spectrum that is high enough to make it difficult to realize much advantage from the last 100 fps or so.

[davidsog]

The SAAMI standard recoil calculation (based on old British experimental work), uses, for high-power rifles,

I have no doubt those gases contribute to recoil.

The recoil formula is accounting for the force of recoil not disturbance of the bullet. It does not mean the bullet is encountering airflow that is 1.75 times the speed of the bullet.

It also does not mean that the gas expanding has enough force to influence the flight of the bullet. I was under the impression that it does not affect it.

If we look at these photos we can see the normal shock formation. Only so the readers can follow so please forgive me it is not my intention to lecture.

Keep in mind that each one of these lines represents air that is traveling at the speed of sound and no faster. It is speed limited in that it must form a shock.

It takes a lot of energy to cross that shock boundary. In fact, it takes so much energy that is why fighter aircraft had to have afterburners to break the sound barrier until the recent advent of supercruise. That is because our understanding of all this has changed and grown.

There are multiple normal shock waves in these photos. You can see the normal shock formation caused by the object moving faster than the speed of sound is behind the object and the normal shock formation at the front. The angle of those waves tell us our Mach number. You can also see the local shock formation along the length of the bullet as well as what is termed an expansion wave. Those are shock waves, just not normal and have different properties. However, all shock is defined by fact each of the little striations is a point the local velocity of the air is the speed of sound. Normal Shock is high energy to the point all flow is subsonic behind the wave.

You can see this in super slow-motion videos of the gases blowing over the bullet base and forward. Whether or not the leading edge of the muzzle blast succeeds in passing the bullet nose depends on bullet geometry, velocity, and muzzle pressure, of course.

Two things:

1. This very much explains the absolute importance of good crown on your barrel and the effect of the crown on accuracy. At the interface of the barrel, I have no doubt the expanding gases forced thru a defect would cause disruption in the flight of the bullet.

2. I can see in some cases were bullet geometry (boat tail with a defect on the tail) might make a difference. I would also think a large diameter, flat nosed bullet would create what's termed a detached Bow Wave might be a candidate too.


I will certainly look into it further.

[tangolima]

Originally Posted by Unclenick

In the second photo, it is well past that point and outside the transitional velocity range. Initially, however, the expanding gases are propelled by the same muzzle pressure that the bullet is, so, being lighter, they accelerate past the bullet base, creating their own shockwave and inducing some transitional velocity effects. This fast gas is what causes the post-muzzle acceleration measured by Vaughn. The SAAMI standard recoil calculation (based on old British experimental work), uses, for high-power rifles, that the gas at the muzzle is accelerated to about 1.75 times the speed of the bullet initially. However, it does lose velocity quickly, which is why the influence on the bullet is so brief. While the military puts eleven calibers on the total range of influence, roughly the first three calibers of bullet base travel past the muzzle to see the most effect. You can see this in super slow-motion videos of the gases blowing over the bullet base and forward. Whether or not the leading edge of the muzzle blast succeeds in passing the bullet nose depends on bullet geometry, velocity, and muzzle pressure, of course.



22 Rimfire is a special case. Past powder burnout, which is usually given as about 16 inches down the barrel for 22 Long Rifle (though it is actually a range for the different loadings of from roughly 12 to 19 inches), the bullet gradually slows, and the pressure behind it is dropping. So you see some muzzle blast effect on 22 RF from a short barrel, like a handgun, but in a rifle, any barrel length from about 20 to 28 will generally get the same velocity within 50 fps or so.



Another issue with 22 RF is the high-speed ammunition exits the muzzle in the transonic range, so it leaps into a portion of the drag spectrum that is high enough to make it difficult to realize much advantage from the last 100 fps or so.

The bullet experiences tail wind within no more than 11x calibers, right? Any cross wind during this short distance is bad news. Yaw is increasing. I still want to give it a try. A cheap 3" aluminum flash can be had for not much money. As soon as there is head wind, however weak, the yaw is decreasing.

About bullet acceleration after powder burn out, it doesn't necessary mean bullet starts decelerating. There is still pressure behind it, although decreasing. As long as the forward force overcomes the friction, the bullet still accelerates. The friction is not much (remember slugging a barrel?).

-TL

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[stagpanther]

I've dinged the crown accidentally on more than one barrel--the degradation in performance was immediately apparent. Other than the barrel's freebore and throat--the muzzle crown is what I obsess the most about in my OBD (Obsessive Borescope Disorder). I was always under the impression that most of the deflection that resulted was more likely because of the bullet being mechanically deflected by being compressed out through the damaged crown (?).

I'm also wondering if the exiting gas analysis takes into account the effect of a brake/device's baffling--they take a beating and can turbulate the gas exiting with bullet's firing.

[tangolima]

Originally Posted by stagpanther

I've dinged the crown accidentally on more than one barrel--the degradation in performance was immediately apparent. Other than the barrel's freebore and throat--the muzzle crown is what I obsess the most about in my OBD (Obsessive Borescope Disorder). I was always under the impression that most of the deflection that resulted was more likely because of the bullet being mechanically deflected by being compressed out through the damaged crown (?).



I'm also wondering if the exiting gas analysis takes into account the effect of a brake/device's baffling--they take a beating and can turbulate the gas exiting with bullet's firing.

Damaged crown definitely screws things up immediately. Funny is that its effects look pretty random, although the damage must be deterministic. I think somehow it magnifies the random variations of the bullet. However, here in our discussions let's assume no damage to the crown.

The baffles and holes in muzzle device must change the pattern of the muzzle gas. I generally avoid brakes (baffle) to make myself less an a-hole to the other range goers. Linear comp (end cap with small holes around the exit) or flash can is my main route. I sort of favor the latter for its simplicity and slightly lower price. I'm ordering an 3" long for my .243 win. <$30.

-TL

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[davidsog]

When a bullet exits the muzzle of a gun, it immediately begins some angular pitching and yawing motions which have several possible causes including the crosswind.
These angular motions are small, cyclical, and transient

This is what the Sierra Engineers say...
Notice the term Possible is used. In other words, there is debate as to what is exactly causing all of the angular motions on a bullet the moment it exits the muzzle. I would not make a statement that they never interfere except as a generalization of general behavior. Like most things, if you get into the weeds, there are exceptions.

Knowing what I know of Aerodynamics as a someone formally educated in Aeronautical Sciences my first instinct is that the gases escaping from the barrel do not influence the flight significantly in MOST cases provided everything is in proper working order for the rifle and ammunition.

That is not because it does not impart some degree of movement. I just know it takes a lot of energy to cross that shock wave. The other thing leading me to that conclusion is the measured data leading to a conclusion from the Sierra Engineers that these movements are:

These angular motions are small, cyclical, and transient

That literally means they do not affect the overall outcome.

I can think of situations where the gas exiting the muzzle would have more of an opportunity to interact and therefore more of an opportunity to influence the behavior of the bullet.

Here is an article on "Full-scale high-speed schlieren imaging of explosions and gunshots" from the ResearchGate website. The article is exploring ways in which high speed imaging can help researchers. The article adds value to the conversation in that one can see in the photos of a revolver being shot, the gas expansion from the cylinder actually reaches the muzzle before the bullet exits.

In my own speculation and not concluded in the article, this would be a case where it is very possible to see some effects of the expanding gases from the cylinder influencing the motion of the bullet exiting the muzzle.

https://www.researchgate.net/publica...s_and_gunshots

The article is there if you scroll down the page you will see the portion about the revolver.

Here is a clickable link to the photo:

https://www.researchgate.net/figure/...fig4_253222217

The article was uploaded to the Public Text Section of research gate by one of the Authors.

All credit for the information goes to the authors:

Gary S. Settles*a, Torben P. Grumstrupa, Lori J. Dodsona, J. D. Millera, Joseph A. Gattob
a Gas Dynamics Lab, Mechanical and Nuclear Engineering Department, Penn State University, University Park PA 16802 USA
b Transportation Security Lab, US Transportation Security Administration, W. J. Hughes Technical Center, Atlantic City, NJ 08405 USA

[tangolima]

Originally Posted by tangolima

Lest we jump back to the same heated debate we went through not long ago, let's jump into another more productive rabbit hole, shall we?

It is actually an discussion I was involved on other forum. It is about spring poundage. Say my AR has a 16 lb recoil spring. What exactly does 16lb mean? In physics a spring's Hook's constant specifies its stiffness. How are poundage and Hook's constant related?

-TL

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No interest?

-TL

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[JohnKSa]

That literally means they do not affect the overall outcome.

It literally means that they are small, cyclical and transient. It does not guarantee they don't affect the overall outcome. There's no guarantee that when the small, cyclical transient motion dies out, the bullet will still be exactly aligned with the bore. It does indicate that if there is a misalignment after the transient motion stops, it should not be a large misalignment.

I have no doubt those gases contribute to recoil.

Correct. The normal way to take them into account is to take the weight of the powder charge and multipy it by 5000fps (the nominal velocity of the escaping gases) and then to include that with the bullet momentum when calculating recoil.