Physics of shooting a rifle

[tangolima]

I didn't think tail or head wind a factor at all. It is certainly so for center fired calibers.

Where I shoot, it is mostly cross wind from 3 o'clock, with varying speed. I used to fire between gusts. Not anymore. I put myself on the clock to make myself read the wind. Constantly I adjust the reticle hold over from shot to shot. With time, hit rate improves steadily. First shot hit is still iffy. I allow myself one quick follow-up shot. 2-shot hits are getting more and more as a norm. Then I move up 25yd and start over.

-TL

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[stagpanther]

I didn't think tail or head wind a factor at all. It is certainly so for center fired calibers.

Where I shoot, it is mostly cross wind from 3 o'clock, with varying speed. I used to fire between gusts. Not anymore. I put myself on the clock to make myself read the wind. Constantly I adjust the reticle hold over from shot to shot. With time, hit rate improves steadily. First shot hit is still iffy. I allow myself one quick follow-up shot. 2-shot hits are getting more and more as a norm. Then I move up 25yd and start over.

I may have misunderstood unclenick's post (OK probably did) but in essence what I believe is that the drag factors are causing the most disruption on the projectile's trajectory as opposed to simply the velocity of the wind alone. That is what I observe in shooting 22lr at longer distances because the degree impact shifts I don't think are attributable to simply the wind alone. I could be wrong--just what I observe in my shooting. The nice thing (or bad, depending upon your point of view) about shooting 22lr at 200 yds is that the slightest shift in hold or the environmental conditions almost immediately shows impact drift.

 

[tangolima]

That's correct. It is difficult to explain in plain text as it involves vectors. The apparent wind experienced by the bullet produces the drag. It is the vector difference between the bullet velocity and wind velocity. The wind just steers this drag force so that it deflects the bullet.

When bullet speed is much higher than wind speed, the magnitude of the said drag force is not affected by the wind, only the small steering. However, when bullet speed becomes comparable to wind speed, both magnitude and steer will be strong functions of the wind. Once again the longer the TOF, the worse it becomes.

-TL

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[Dave P]

Just for fun, you can also calculate how fast the bullet is spinng, all the way to the target.

It is not unusual for bullets to disinegrate if they spin too fast. Just leaves a puff of grey a ways a way from muzzle.

 

[tangolima]

Found an interesting article that takes a good look at factors that influence drop/drift of 22lr. I like the emphasis on transonic zone and where/when it happens, and to what degree. The author also looks at scaling the ballistics of 22lr to that of bigger centerfire cartridges as an obvious boon to training. I'm not exactly sure that scaling can be done reliably in a linear way, I find very small variations in environmental conditions can have profound consequences on the bullet's drag/stability anywhere along its trajectory. Good food for thought.

Read the article. But I'm afraid I have different take on the subject.

The author proposed scale factor of 4x. But he kept target MOA size the same. Shooting center-fire at 8" plate at 500yd is equivalent to .22LR at 2" disc at 125yd.

My scaling factor of 2.5x is based on same TOF. Target sizes in inches are kept the same. Shooting center-fire at 8" plate at 500yd is equivalent to .22LR at the same 8" plate at 200yd. Same TOF, so similar bullet drop and similar wind deflection in inches with same cross wind.

I like mine better because it seems easier Actually 2" at 125yd is not much harder. Since it is based on TOF, my method doesn't have a constant scale factor. It depends on distance. 2.5x is for 200yd .22LR or TOF of 0.5s. It is therefore nonlinear, quadratic more or less.

-TL




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[tangolima]

Blowing on Bullets:

If only the wind pushing on a projectile explained its deflection to the side, same-weight, same area, higher BC bullets would have no less wind deflection for a given time of flight (TOF) than blunt shapes do, but they do have less deflection. When it comes to which otherwise-identical bullet will be least deflected by wind during a given TOF, it is always the one with the highest ballistic coefficient. That is because it has lower drag turned into the wind vector. It is the wind vector, in effect, steering the direction of drag that causes wind deflection. There is not enough direct force from a side wind to produce the amount of wind deflection that actually occurs.



An Example:

A CCI 22 LR Standard Velocity round is fired from a rifle at the factory-claimed 1070 fps. Its flat fire TOF to 100 yards in an ICAO standard atmosphere is 0.3024 seconds. If it is fired in a 10-mph crosswind, it will deflect 3.877 inches at the target. If we calculate how far the wind could blow that bullet in that circumstance, we get a much smaller number. About 0.068 inches. Even if we pretend the bullet doesn’t yaw to point into the wind and instead pretend the wind moves with the bullet and blows on the side of it, in 0.3024 seconds, it works out that a 10 mph wind will blow the bullet, not quite 0.55 inches. So there is no way to account for the observed amount of deflection by having the wind blow on the bullet.



I have attached a file with the calculations for anyone interested in them.



Estimating TOF from Bullet Drop:

In the air, everything has a terminal velocity. Assuming point-forward bullets, those with higher ballistic coefficients will have higher terminal velocities. This means that when fired at the same velocity as otherwise-identical bullets with lower BCs, their total drop will be greater. If I fire the old Hornady .308" 150-grain RN at 2800 fps, after 1 second, it has traveled 525 yards and has a total drop of 141.5 inches. If I fire the Hornady .308" 150-grain FMJ BT at the same velocity, after 1 second, it has traveled 674 yards and has a total drop is 157.4 inches. A bullet dropped in a vacuum, using the 32.17405 ft/s² gravitational constants, will fall 193.04 inches in 1 second so that you can see almost a quarter of the gravity drop is being shaved off by drag.



Estimating TOF from bullet drop is most easily done using a point mass solver. If you know your muzzle velocity and zero, plug those in, then tweak the BC until you see the same drop on paper that you actually measured. At that point, the program’s TOF should be a good match.

Unclenick. Read through your calculation and the derivation in McCoy's book. You are right about wind deflection being caused by drag. I was stuck by the orthongonality of the wind vectors. By the drag force is proportional to the square of the apparent wind vector's magnitude. Orthogonality is hence lost. The derivation is assuming flat-fire condition in which angle of attack is so very small that lift force to the bullet can be ignored. This assumption is valid in most situations in which bullet velocity is several order of magnitude of wind speed. Not quite so for slow projectile in strong cross wind, I'm afraid, such as subsonic .22LR after traveling 200yd.

Thanks for your inputs. It is enlightening as always.

-TL

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[tangolima]

Rifle canting.

Is it that critical? What would happen to POI if I cant my rifle to the right? Some say it is more critical on AR platform. Why so?

Say my silly Marlin 81 .22LR shooting 1250fps HV bullet. The scope is 1.5" above bore. Zeroed at 25yd (first crossing). I have to dial in elevation of 22MOA to hit 200yd. If I cant the rifle 1 degree to the right (that's quite a bit), how much will the POI be off?

-TL

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[stagpanther]

I was shooting yesterday at 255yds with R100 and tenex, I could typically get 4 out of 5 shots sub MOA but then one of each 5 shot group would land further away. Was it due to [lack of] consistency of hold or slight variation in winds down range? For me, impossible to tell. What I have noticed is that past 200/225 yds it gets even harder for the bullet (and me as the shooter) to "keep it together." Cant (or lack thereof) is certainly one of the factors that has to be repeatedly consistently. That in turn can lead to a whole discussion about the different types of cant indicators, how accurate they are, and even how well the eye and brain can process the differences.

 

[tangolima]

Between the rifle muzzle and the target lies the varying air mass and the mostly constant gravitational pull. A lot of things can happen during the bullet's journey down range. The bottom line is sooner the bullet reaches the destination, less can happen to affect its landing. That's why I keep going back to TOF (t). The shorter TOF the better.

Variation in ammo gives rise to muzzle velocity variation, which shows up as variation in TOF (dt). Bullet drop (h) corresponding to TOF (t)

h = 1/2 * g * t^2

The variation in bullet drop caused by variation in t

dh = g * t * dt

dh can be visualized as vertical size of a group. It grows with t. It is like TOF magnifies the ammo's non-idealities.

The wind deflection in real situation is even more complication as the wind is never constant. Longer TOF definitely can only make things worse.

The shooter's skill is part of the equation, canting is one of the factors. But compared to the wind, it is still minor, I think.

-TL



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[stagpanther]

The shooter's skill is part of the equation, canting is one of the factors. But compared to the wind, it is still minor, I think.

Be very hard to quantify that without some tightly controlled testing I would think. I think everything effects the 22lr bullet in magnified ways compared to other cartridges--even how the trigger breaks and the firing pin hits the rim. It is what makes the 22lr so fascinating and addictive for me to shoot--on paper it shouldn't do very well at distance--but if I can try to get everything just right--and repeat it (that's the hard part for me) then I can get amazing (to me) results with it.

A slight cant in my hold at distances 200 yards and beyond will definitely throw the bullet's impact significantly. As far as by how much compared to the wind, I can't say--but it will probably be on the order of MOA+--enough to ruin the shot and group.

 

[tangolima]

Controlled experiments are indeed impossible with the resources I have. But I made the following observations when I was shooting groups 150 to 175yd.

With little or no wind (twinight hours), the groups are mostly vertical ovals.

With noticeable cross wind, the groups become horizontal bands, with width horizontal spread several times over vertical spread.

After I installed level and started paying good attention to canting, the horizon spread improved in no-wind environment. Such improvements however are mostly unnoticeable with wind.

With active wind call and corrections, groups tend to improve. However the results vary. Sometimes it could even seem worse.

-TL

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[stagpanther]

After I installed level and started paying good attention to canting, the horizon spread improved in no-wind environment. Such improvements however are mostly unnoticeable with wind.

If it was noticeable in no wind but not when there was wind--I would guess it's probably because it's simply being masked by the wind's effect--or maybe by some chance one might have negated the other a bit by random serendipity. One "trick" I've learned--it's not one I would recommend as improving one's shooting--is that if I mess a shot up--if I consistently mess up in the same way that's a "second best" recovery for not doing it right in the first place.

 

[tangolima]

The error introduced by the wind is several times over the canting error, so masking is probable. Also I could be too busy reading the wind to do a good job leveling the rifle.

At least so in my case, cross wind my biggest problem, so much so that hitting a soda can beyond 175yd is pretty much issue in doubt.

-TL

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[stagpanther]

so much so that hitting a soda can beyond 175yd is pretty much issue in doubt.

That's a narrow target if you can't reliably spot the fall of the initial shots. I see guys do it on youtube like it's nothing--but I wonder how many shots in the same conditions preceded that. Anyone who can walk up sight-unseen to a target at that distance in cross gusty conditions--anything over 5 mph that intersects the bullet's trajectory-- and nails it with a 22lr fist try is a Jedi Knight in my book. I think I might be able do it after maybe 2 or 3 shots that I could spot the fall of. Anything over 10 mph--unless it was a tailwind (or I didn't mind wasting cheap ammo)--I'd go home and save my money.

 

[tangolima]

I didn't make it easy for myself. I only allow 1 quick follow-up shot. Then I have to wait a couple of minutes. That's the way I force myself to re-read the wind.

-TL

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[stagpanther]

I didn't make it easy for myself. I only allow 1 quick follow-up shot. Then I have to wait a couple of minutes. That's the way I force myself to re-read the wind.

That's why I spend money on top-tier 22lr ammo--makes it easier for me to figure out what deviations are due to me/environment and not the ammo. My biggest issue with the expensive stuff is having the discipline to call it a day and not blow through a whole box--balanced against pushing the learning envelope.

 

[tangolima]

I do allow a 3rd exception follow-up shot, if I think the previous round(s) totally out of wack abnormal, mostly way high or low.

With my $90 marlin 81, premium ammo is probably a waste. Aguilar fits the bill and identity. Balancing between transonic effects and shorter TOF, HV is chosen as default.

-TL

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[stagpanther]

You're doing better than I could with my $3K set-up if you're getting hits fairly consistently using HV at that distance!

 

[tangolima]

Currently the hit rate is 1:2 at 150yd, 1:5 at 175yd, 1:10 to 1:20 at 200yd if I am in shape. It has been improving slowly. I:2 at 200yd is the goal.

The groups you have shot at 200yd, I could do it only in my dream.

-TL

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[stagpanther]

The groups you have shot at 200yd, I could do it only in my dream.

As much as I'd like to take credit for being a skilled shooter--the simple truth is with the right gear and right ammo--and the right conditions (the best times being dawn and dusk calm IMO)--it's much easier than most people think--the biggest barrier is just believing it's possible (and worthwhile) to make the investment and effort.