Physics of shooting a rifle

[davidsog]

This may help the discussion.

The pressure coefficient CP, lift coefficient CL, and drag coefficient CD from forces
were calculated from the equations given below.
CP =dP/(ρV2/2)

CL = FL/A*(ρV2/2)

CD = FD/A*(ρV2/2)


where FL is the lift force, FD is the drag force, V is the freestream velocity, ρ is the air density, and dP is the difference between ambient and static pressure. The details of the calculation of the bullet’s total surface area are provided in the Supplementary Materials S1, and the details are provided (equations a, b) in Figures S2 and S3

https://www.mdpi.com/2226-4310/9/12/...ion=1670847097

I did in post #155.

Yes you did and a very good concise explanation too.

[tangolima]

An other way to visualize the mechanism. In point mass model, wind deflection is proportional to lag time (Tlag), which is the difference between TOF and time (To) the projectile would have taken to travel the same distance in vacuum.

Tlag = TOF - To

With higher MV, both TOF and To reduce. However if decrease in TOF can't catch up with decrease in To, which can happen with high BC, Tlag increases, and so does wind deflection.

-TL

Sent from my SM-N960U using Tapatalk

[davidsog]

tangolima

The only thing I would change in your explanation is the term "drag". Drag is opposed by thrust and works only in that axis. What you are talking about is the sideforce created by the yaw of the bullet in the direction of airmass movement.

I know, it is nit-picky and yes that force is effected by velocity and mathematically is calculated is almost the exact same way as drag/lift.....as a function of dynamic pressure to static. The adherence to the reference axis is how we keep the forces straight when doing the vector resolution.

For example in a climb in an aircraft, Lift Force is decreased because a vector of thrust is now contributing to lift along the lift axis.

[tangolima]

Unclenick has comprehensive explanations on the wind deflection and drag in post #70. The way I see it, the cross wind changes the angle of the apparent wind on the projectile. That minute angle change can be visualized as yaw. If the drag force vector is decomposed into 2 orthogonal components, a small force is pointing sideways and causes the deflection.

-TL

Sent from my SM-N960U using Tapatalk

[davidsog]

Excellent synopsis.

[JohnKSa]

An other way to visualize the mechanism. In point mass model, wind deflection is proportional to lag time (Tlag), which is the difference between TOF and time (To) the projectile would have taken to travel the same distance in vacuum.

Tlag = TOF - To

Right--I know about the model and what it implies. The question asked was about how to gain an intuitive feel for what's going on, not for an explanation of how the mathematical model works.

In terms of intuitive insight, the TOF-To difference relationship to POI change is actually even more problematic because it sort of implies that the projectile somehow "knows" its flight time in a vacuum.

The point is that it's easy to see that if you have wind acting on a projectile, the longer it acts on the projectile, the more effect that will have on the POI. It's not at all easy to see why, in some cases that you can decrease the time the wind acts on the projectile without decreasing the effect on the POI.

Pointing out that it's a function of the difference between the actual TOF and the theoretical TOF in a vacuum may explain how the model works, but it still doesn't really give someone a good "feel" for why the shorter TOF doesn't result in less POI error.

Also, there's the issue of why this happens sometimes but not other times. Low BC is referenced, (airgun pellets, the referenced projectiles are not just low BC by bullet standards, they are off the charts low) but that implies that there's some sort of BC threshold. What is it? Pellets are usually shot at very low velocities, compared to rifle bullets, is there a limited velocity range where this occurs?

[stagpanther]

There is a fundamental misunderstanding in the term "Wind Shear". There seems to be some belief that turbulence is wind shear. It is not. Wind shear is a very isolated phenomenon that occurs between airmass in only four situations. Turbulence occurs in all airmasses. We feel turbulence because we are not physically a part of the aircraft. That is why they tell you to remain seated with your seat belt buckled when experiencing it.

Wind shear is a very different animal. In order for your bullet to experience Wind Shear effects it would have cross gust front of a Thunderstorm and the wind shift line between airmasses. They convergence of those two things MIGHT create a shear. Mostly it will just make turbulence.

The other conditions for Wind Shear are simply not something you would ever experience on a rifle range as they occur at altitude.

I assume this one is aimed at my drawing. Wind shear is most certainly a form of turbulence and I did not suggest the reverse. To say that it is a threat only at altitude I believe is incorrect; in fact it is statistically one of the biggest accident threats to aviation in take offs and landings, the regime that occurs closest to the surface. It is both a macro and micro phenomenon which is why pilots need to be especially aware of it. Shear does not necessarily need huge velocity differences or very sharp angles of intersection to occur; it can happen even with airmasses that might have just a few degrees of directional difference and fairly minor variations in velocity/temperature/density. In practical terms for us shooting at a range we're probably not going to have a computer with us that goes through all the technical computations with real-time doppler mapping of all air movement (and turbulence; whatever it's cause might be) between the muzzle and target--ALL I'm trying suggest is there is a another way of looking at near-surface air movement that MIGHT add to visualize/interpret what is happening other than sticking your finger up in the wind or taking a single point laminar air flow reading.

[tangolima]

Post #70 and #175 may help. If it still doesn't, please allow me some more time to work out an mathematical equation. After that, I'm afraid I will be quite out of witts.

High drag offsets the benefit of low TOF. That's what's going on. Low MV and super low BC for pellet. Probably super high MV and low BC of light varmint bullet would do the same.

-TL

Sent from my SM-N960U using Tapatalk

[stagpanther]

Post #70 and #175 may help. If it still doesn't, please allow me some more time to work out an mathematical equation. After that, I'm afraid I will be quite out of witts.

High drag offsets the benefit of low TOF. That's what's going on. Low MV and super low BC for pellet. Probably super high MV and low BC of light varmint bullet would do the same.

-TL

Sent from my SM-N960U using Tapatalk

And then there are the 22lr bullets--I fondly recall our equally Einsteinian discussion/argument of why subsonics (IMO) are more accurate than supersonics.

[tangolima]

Originally Posted by stagpanther

And then there are the 22lr bullets--I fondly recall our equally Einsteinian discussion/argument of why subsonics (IMO) are more accurate than supersonics.

Yup. That was before I read that airgun article. BTW, I still prefer supersonic 22lr to subsonic, all things considered. It is quite likely that with 22lr's MV and BC, higher MV is still favorable. I may have different take down the road more.

I'm freshly into airgun after buying my first PCP rifle due to some "bad influence". Airguners love to tune their guns for higher MV. That article pointed out that faster is not always better. There exists optimum MV for minimum wind deflection. For .177 cal pellets, 800fps ish is the optimum.

-TL

Sent from my SM-N960U using Tapatalk

[davidsog]

High drag offsets the benefit of low TOF.

That is easily illustrated in the relationship of all Drag Forces not due to lift (induced Drag). We separate drag into two main categories.

Parasitic Drag and Induced Drag. Induced Drag is a function of lift production.

Parasitic Drag is everything else.

Skin Friction Drag
Form Drag
Interference Drag
Leakage Drag
Profile Drag

Low Time of Flight = Higher Velocity

Velocity has a direct and squared relationship to Parasitic Drag.

Mathematically, the relations of Parasitic Drag to velocity it is expressed as:

Dp2/Dp1 = (V2/V1)^2

Dp1 = Parasitic Drag Force at beginning velocity
Dp2 = Parasitic Drag Force and ending velocity

V1 = Beginning velocity
V2 = Ending velocity

So doubling the speed is four times the Parasitic Drag forces.

[davidsog]

I assume this one is aimed at my drawing. Wind shear is most certainly a form of turbulence and I did not suggest the reverse. To say that it is a threat only at altitude I believe is incorrect; in fact it is statistically one of the biggest accident threats to aviation in take offs and landings, the regime that occurs closest to the surface. It is both a macro and micro phenomenon which is why pilots need to be especially aware of it. Shear does not necessarily need huge velocity differences or very sharp angles of intersection to occur; it can happen even with airmasses that might have just a few degrees of directional difference and fairly minor variations in velocity/temperature/density. In practical terms for us shooting at a range we're probably not going to have a computer with us that goes through all the technical computations with real-time doppler mapping of all air movement (and turbulence; whatever it's cause might be) between the muzzle and target--ALL I'm trying suggest is there is a another way of looking at near-surface air movement that MIGHT add to visualize/interpret what is happening other than sticking your finger up in the wind or taking a single point laminar air flow reading.

You are asking to argue established definitions and norms. Shear is a very specific thing that only occurs in four instances and at the boundaries of an air mass. I understand you are trying to envision what is going on but I think it would be more useful for you to gain clear insight without altering physics.

Air Mass has a very specific definition:

An air mass is a large volume of air in the atmosphere that is mostly uniform in temperature and moisture. Air masses can extend thousands of kilometers in any direction, and can reach from ground level to the stratosphere—16 kilometers (10 miles) into the atmosphere.

https://education.nationalgeographic...urce/air-mass/

Turbulence is characterized by changing Coefficients of Pressure resulting in torqueing moments about the CG. It is a Stability and Control problem NOT a Performance Problem. Different frame of reference and very different results.

Torque is a rotational movement ABOUT an axis. It is not a positional change in the axis itself. Density will remain constant so the axis position does not change. That is why we say, "An object in flight does not feel the wind".

Torque is the measure of the force that can cause an object to rotate about an axis.

https://byjus.com/physics/torque/

I don't pretend to know it all or understand everything about this particular problem. Nobody does and that is evidence by the report I posted earlier investigating the behavior of a bullet in flight.
Fluid dynamics, Aerodynamic, Advanced Aerodynamics, and Stability and Control were all classes in college for me. I think it is useful to explain the behaviors of a bullet using aircraft analogy. Much more useful than arbitrary Ballistic Coefficients and previous physics expressions.

[stagpanther]

So, cutting to the chase--because I can't understand a flippin thing about what you're saying here--you are refuting that 1) shear is a form of turbulence; and 2) it can occur at or near the surface (0 agl)?

That is why we say, "An object in flight does not feel the wind".

If you have been reading my posts on this subject over the years you would know that that is exactly the position I've always "advocated" (though I would modify that by including that the velocity of the object in flight exceeding the velocity of the wind)--but I made a promise I wasn't going to bring that up anymore.

[davidsog]

1) shear is a form of turbulence

No, Shear is not a form of turbulence. Turbulence is one EFFECT of a shear. The defining feature of shear is a large change in velocity and direction due to crossing the boundary or an air mass under specific conditions such as Thunderstorm formation.

it can occur at or near the surface?

There is a minor change in velocity and direction in an air mass due to ground friction but it occurs much higher than you are shooting a bullet unless you were shooting up a mountain or into the air.

Turbulence is created as an airmass moves across the ground due to trees, buildings, terrain, and other obstacles.

Turbulence is not shear. Turbulence is defined by creation of torque forces around the CG. Turbulence is a stability and control problem.
Shear is defined by large changes in density and velocity across an airmass. Shear is a performance problem as because of the magnitude of density and velocity changes.

Does that help?

[davidsog]

Stagpanther,

Maybe this will help.

You know what a Center of Gravity is right? NASA defines it as the "the average location of the weight of an object".

It is just a single point.

I can rotate that point any direction I want without changing the position in space of that point. That is the effect of turbulence.

If I move that point in space to a different location, that is the effect of Shear.

[davidsog]

If you have been reading my posts on this subject over the years you would know that that is exactly the position I've always "advocated"

Good. You are tracking then. Don't lose sight of the forest for the trees.

[stagpanther]

There is a minor change in velocity and direction in an air mass due to ground friction but it occurs much higher than you are shooting a bullet unless you were shooting up a mountain or into the air.

Turbulence is created as an airmass moves across the ground due to trees, buildings, terrain, and other obstacles.

Turbulence is not shear. Turbulence is defined by creation of torque forces around the CG. Turbulence is a stability and control problem.
Shear is defined by large changes in density and velocity across an airmass. Shear is a performance problem as because of the magnitude of density and velocity changes.

Does that help?

A bit, though I still think you're being slippery with definitions. The hang-up on specifics of whether or not shear is a type of turbulence is sort of a chicken before egg kind of argument--what I think you're saying is the action of shear is like drawing two rasp files at an angle across each other--but that action in and of itself is not turbulence. I don't know of any kind of atmospheric shear phenomenon that does not produce/induce turbulence. It is not strictly a horizontal phenomenon either, nor is it exclusively reserved to "massive" air masses intersecting each other. In any event, in my little drawing above I tried to include boundary layer shear as only one instance of "induced" turbulence. I have thousands of hours in slow flying gliders near the surface (which I would define as 0 to 10,000 ft agl although I have been higher with supplemental O2 out west) and staying airborne--and frankly alive--meant understanding intimately the dynamics of air movement and turbulence. Lacking power there was no second chance go around, either.

[davidsog]

nor is it exclusively reserved to "massive" air masses

Only on the internet. Shear requires an airmass change otherwise the rotational moments will simply compensate without the large changes in density and velocity between air masses.

[davidsog]

Wind shear
Wind shear is one of the causes of turbulence and is described as "the change in wind direction and/or wind speed over a specific horizontal or vertical distance." It occurs in certain atmospheric conditions, including along weather troughs and low-pressure areas, around a jet stream, and in areas of temperature inversion.

https://simpleflying.com/wind-shear-vs-turbulence/

weather troughs and low-pressure areas, around a jet stream, and in areas of temperature inversion.

Are all airmass boundaries.....


All wind shear will create turbulence but all turbulence is not wind shear. In fact, turbulence created by wind shear is a rare occurrence.

There are four primary causes of turbulence:

Mechanical turbulence is caused by friction between the air and the ground, particularly over irregular terrain.

Thermal or convective turbulence is related to currents of warm air rising and cool air descending. A plane will experience bumpy conditions as it flies through the different currents.

Frontal turbulence is the rising of warm air over the sloping surface of a cold front, causing friction between the opposing air masses.

Wind shear, which is described below.

https://simpleflying.com/wind-shear-vs-turbulence/

Nobody ever said anything about this being strictly horizontal or vertical. I don't know where you got that from.

[stagpanther]

I agree with your definitions for the most part, I think the differences between your interpretations and mine are due mostly due to nit-picking interpretations. For example, an upper air inversion--the bane of thermal soaring pilots--I would describe as more of a stabilizing body of air than one associated with turbulence since it's warmer than the previous layers of air underneath it it tends to repress or stop altogether adiabatic lapse activity from rising convectively heated air. You can easily observe this when flying and see a clearly-defined boundary between "clean air" and murky, polluted air trapped below it. Inversions also can aid as a "bounce barrier" in setting up wave amplitude propagation to great heights and distances; enabling soaring unpowered aircraft to reach altitudes that are attained by airliners and fly well over a thousand miles.

What does that have to do with us shooting on the ground? Not much, except that any time the sun is out we're likely going to be experiencing convective heating and there are periods during the day when greater equilibrium between ground and near above surface air temperature will be reached.

By the way, when I clicked on the link for your linked article, this is what popped up on my browser; I just love those people who cherish our privacy.

[44 AMP]

I guess this is one of those physics problems I just don't get. Like the one where a guy gets into the pool, swims to the far end, swims back and climbs out where he went in.

The instructions for that one said to use physics to prove he went nowhere.

I don't think he went nowhere.

Aircraft terminology isn't very helpful to me, when looking at bullets in flight all I know is that a cross wind moves the point of impact of my bullet, proportional to the force and direction of the wind.

[mehavey]

He (the swimmer) in fact "went" nowhere.
Vector A + vector B = 0
No physics involved.


Looking backwards though... the bullet does feel the full force of the crosswind upon muzzle exit.

But as it gradually succumbs to the force over time, and increasingly drifts in the direction of that cross force, it "feels it less and less

[44 AMP]

He (the swimmer) in fact "went" nowhere.
Vector A + vector B = 0
No physics involved.

So, why does leaving home, going to the store then going home again add milage to my car? Pretty sure it thinks I went somewhere.

I KNOW the gas tank thinks so,

[stagpanther]

So, why does leaving home, going to the store then going home again add milage to my car? Pretty sure it thinks I went somewhere.

I KNOW the gas tank thinks so,

The Matrix has you.

[davidsog]

I just love those people who cherish our privacy.

Yikes! My computer security just blocks all that and I never saw anything otherwise I would put a warning out.

Looking backwards though... the bullet does feel the full force of the crosswind upon muzzle exit.

Yes it does and that is stated in the aerodynamic investigation into bullet shape I posted.

Numerical and Experimental Analysis of Drag and Lift Forces
on a Bullet Head

https://www.mdpi.com/2226-4310/9/12/...ion=1670847097

What happens is the bullet rotates about its CG until those torque moments equalize the force and the bullet achieves equilibrium just like an airplane.

Yes, it is decelerating from the moment it is fired as a finite amount of thrust force has been applied by the powder charge but does not negate the principle of it achieving equilibrium in the side force yaw axis.

That is an almost instantaneous process as the force is applied. While it is interesting to examine what is going on in that tiny moment in time, it is a Tree and not the Forest. The POSITION of the CG remains the same despite it rotating about its axis.

Once equilibrium is achieved, the bullet no longer feels the wind but moves as any other object suspended in fluid. The whole mass of fluid is moving so the bullet moves just like a passenger on a train.

From Stick and Rudder: An Explanation of the Art of Flying

And then, there is the wind.
Much of the art of flying has turned out much simpler than you
had expected: the airplane stable, the air without pockets, the height
not at all terrifying. But then, there is the wind: the air, the medium in
which you move, is itself in motion. And that now brings on a whole
string of quite unexpected complications. You discover that,
whatever wind there is, even the slightest breeze, has its effect on
you every single minute of flight: it distorts your curves, it falsifies
your climbs and glides, it pulls your figure eights out of shape, it
makes your ship go one way while its nose points another way. If the
wind is across your direction of flight, it makes the airplane sidle over
the scenery in a crablike gait: sometimes so much so that, if you
want to look where you are going, you must look out the side window
of the cabin!
If the wind is on your tail, it makes the airplane hurry amazingly
and keeps messing you up by getting you there too soon, before you
have had time to plan your next maneuver. If the wind is from ahead,
you lose speed; and with a slow ship in a strong wind it may happen
that you stand still in the air or even go backward.
It is dismaying to find that mere wind - so flimsy, so intangible a
thing - can blow a heavy powerful machine about at will; but it is
even more dismaying to discover, by and by, that the effects of wind
are almost exactly what your common sense would not expect them
to be.

From Stick and Rudder: An Explanation of the Art of Flying

THE FIRST KEY IDEA: AIR IS A SOUP

The first key idea is the idea of air: that air is real stuff, a thick
and heavy fluid, quite similar to water.

Air is a fluid and the physics of fluid dynamics are useful in explaining an objects behavior in the air.

From Stick and Rudder: An Explanation of the Art of Flying

THE SECOND KEY IDEA: MOTION IS RELATIVE

The second key idea has nothing to do exclusively with the air
but is a general one that might be called the relativity of motion ; you
have to limber up your ideas of what motion really is. Skipping all
fancy business, it will be useful to observe a man who is walking
about inside a moving railroad train. This is because he is just like an
airplane flying in a wind, as will be shown; but while the airplane in a
wind is puzzling, you know or can easily try out just exactly what
happens to a man who walks about in a moving train.

A bullet is nothing more than an unmanned, unguided, aerial vehicle. Once the bullet leaves the barrel its frame of reference changes from being an object on the ground to an unmanned aerial vehicle in flight. It obeys the same physics as an airplane.

From Stick and Rudder: An Explanation of the Art of Flying

THE THIRD KEY IDEA: YOU’RE in THE AIR

For here is the third key idea - an airplane that flies in moving air
is like a man who walks within a moving train. This, mark well, is not
a simile, not a figure of speech, but a precise statement of fact.

From Stick and Rudder: An Explanation of the Art of Flying

This motion of the airplane through the air is in no way affected
by the fact that the air itself is in motion - any more than the
passenger’s walking within the train is affected by travel of the train.
The train passenger finds that it is just as easy to walk forward in the
train as it is to walk toward the rear or from one side of the train to
the other: it requires no different balancing, produces no different
sensations. In the same way, the airplane cannot ’‘feel” any
difference between down-wind flight and up-wind flight and crosswind
flight. It feels the same; the engine has to pull no harder; the
airspeed indicator indicates the same; the lift is the same.

Stick and Rudder: An Explanation of the Art of Flying

THE AIRPLANE DOES NOT FEEL THE WIND

If the train passenger does not look at the moving scenery
outside, he cannot tell which way the train is moving; if the pilot does
not look down at the ground, he cannot tell which way the wind is
blowing.

From Stick and Rudder: An Explanation of the Art of Flying

MOTION with THE AIR

Look next at the airplane’s moving with the air. This is exactly the
kind of motion that a train passenger performs by just simply sitting
still - or rather the kind of motion that he performs, because of being
in a moving train, regardless of what antics he may cut within the
train. Regardless of what maneuvers the airplane executes within
the mass of air that surrounds it, it helplessly participates in the
motion of that air mass; it “drifts” with the wind.
Beware of thinking that the airplane drifts because the wind is
blowing against it. It would be like saying that the passenger gets to
Chicago because his coach pushes, shoves, kicks, and pummels
him to Chicago.

Once the bullet leaves the barrel it is now a part of the air mass movement we feel on the ground as wind. It will move in that air mass just like the passenger on a train moves with train or a fish moves with the current. It does not feel the wind.

From Stick and Rudder: An Explanation of the Art of Flying

COMPOUND MOTION

Altogether, then, the path that the airplane takes over the ground
is always compounded of those two separate types of motion: its
motion through the air and its motion with the air. The two are
entirely dissimilar. Motion through the air produces lift, drag, stability
and control. Motion with the air is the free-balloon sort of motion - it
has no further effects on the airplane other than to move it. The two
are dissimilar; yet to the eye they are indistinguishable. The eye,
which cannot see the air but can judge only by reference to the
ground, simply records the compound of the two - the resulting
motion of the airplane relative to the ground.
This causes some confusion for the pilot - especially for the
beginner. Even though he may understand it in theory, he is still only
a ground animal, not an air animal. He still can see only the ground,
not the air. His sense of balance, his sense of motion, his nervous
system, tend to react simply and naively to his observed motion over
the ground, whether he wills it so or not. But, since his motion over
the ground includes both motion with the air and motion through the
air, his resulting control actions are bound to be wrong.

Stick and Rudder: An Explanation of the Art of Flying (ISBN 978-0-07-036240-6) is a book written in 1944 by Wolfgang Langewiesche, describing how airplanes fly and how they should be flown by pilots. It has become a standard reference text for aviators.