Physics of shooting a rifle

[stagpanther]

Being able to dope out changes on the fly in variable conditions--that's when real skills come into play. That's why I try to avoid winds. : )

[tangolima]

Originally Posted by 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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Originally Posted by 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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Filling the hole I have dug.

When the rifle is canted to the right, the POI will land right and low. The amount of error depends on a few things, but as always long TOF doesn't help.

To counter bullet drop due to gravity, bullet leaves muzzle with certain launch angle. That angle puts small portion of the muzzle velocity in the vertical direction.

Without cant, that vertical velocity precisely aligns with gravity. The cant spills a small portion of that speed horizontally sideways. That makes the bullet drift sideways.

In the example of my marlin rifle, the launch angle for 25yd zero is approximately

1.5 / 25 * 100 = 6moa

Additional 22moa is dialed in for 200yd, so the total launch angle is

6 + 22 = 28moa or 0.47 degree

With muzzle velocity of 1250fps, the above said vertical velocity to counter gravity is

1250 * sin(0.47) = 10.2fps

With 1 degree cant to the right, a right-ward horizontal velocity is induced

10.2 * sin(1) = 0.18fps or 2.1 inch/s

It is a very low speed, so drag can be ignored. The bullet takes 0.5s to reach the target 200yd away. The sideways error is

2.1 * 0.5 = 1.05" or 0.5moa

Not a lot but observable, and more so at longer distance where TOF become unproportionally longer.

AR platform has much higher sight height. That significantly increases the launch angle for zeroing. That undoubtedly makes canting more critical. But I believe part of it is in the shooter's mind.

When we correct canting by twisting the rifle, we will see the POA goes off by an alarming amount. Erroneously some would think that's the error caused by the cant. It is even more alarming on AR platform because of the elevated sight axis.

I have found it a better practice to level the rifle before aligning the POA, instead of the other around. The other bad habit to correct is to adjust POA error by twisting the rifle, instead of moving the rear bag.

-TL

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[MarkCO]

Originally Posted by tangolima

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

All wind has an effect. A bullet fired in absolutely stagnant wind, at some point, based on the BC, twist and distance, will move off of the vertical and hit left or right of center. Aerodynamic jump is of course more pronounced in a crosswind, and it is different for left or right, enough to make misses over or under a target size that can be hit in the stagnant wind. Past 1000 yards, it becomes something that needs to be considered, based on the wind and target size.

But headwind and tailwind also do have an affect. Yes, it is minimal, and likely less than the confidence interval for groups. At 1000 yards, with 6.5mm bullets and a 10mph wind, head vs. tail is about a 2.5" difference in elevation.

In the transonic, a tail wind lengthens the time in the TS region and a head wind shortens it. If you have a well twisted (at the TS region) high BC bullet, the affect is going to be immeasurable and only can be seen with the best formulas in calculations. But a DEWC going through transonic in head vs. tailwind is absolutely measurable, which is only reasonably done to actually provide data for input into the formulas for verification.

[tangolima]

Absolutely. The question is whether it is significant factor to be considered. 200yd center-fire, probably not; 200yd .22LR, probably yes. I didn't think of that as I was still stuck with center-fire mind set, and where I shoot, the cross wind is always prevailing.

-TL

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[Unclenick]

You can just run this in a solver. I did it for the Lapua match bullet (an email from Lapua confirms all their match ammo uses the same bullet except their Polar Biathlon ammunition, which has its own design with a tapered shoulder that I want to try). Basically, a 10 mph headwind or tailwind, as compared to zero wind, makes no practical difference at 100 yards, about 0.25 moa at 200 yards, about 3/4 moa at 300 yards, and about 1.5 moa at 400 yards. These are all elevation adjustments up for a headwind and down for a tailwind. Note that I used the same 1070 fps MV I used in the previous post. Most Lapua match is rated at 1073 fps MV, except their Polar Biathlon, and the new Long Range and Super Long Range that you can't get yet are rated at 1106 fps MV. The faster MV Long Range cartridges increase the drop differences by about 10.5% because drag is higher at 1106 MV.

[stagpanther]

Wow! That does not match up with my shooting experience at long range in general--a headwind component always messes up my bullets at distance more than a tailwind. I guess I must be somehow inducing the aberrations myself.

[tangolima]

Unclenick. Is the solver 4D or point mass based? I'm going to try the same on Hornady's 4D solver. Didn't think of that. They may have 22LR bullets there.

Point mass model usually assumes flat-fire trajectory, where angle of attack is small. For long-range .22LR, the downward trajectory is very steep with low speed. Angle of attack to the wind may exceed the flat-fire limit. Just a thought.

-TL

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[tangolima]

Just did really quick and got slightly different results.

10mph head wind adds 3.4" bullet drop at 300yd, or 1.1moa. 8.7" at 400yd, or 2.2moa.

-TL

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[stagpanther]

I can easily think of one aspect that might not be accounted for in this model (don't know if it is). Because of the effects of turbulence on terrain, winds are almost always faster as you gain height from the surface; in other words advective drag on the wind slows it down at or near surface levels. Elevation adjustments are "massive" in 22lr starting around 200 yds--it's sort of like lobbing an artillery shell compared to a faster centerfire cartridge. Thus, I think it's quite likely the bullet's trajectory will pass through a "layered cake" of different headwind velocities when shooting at longer distances. Food for thought 2.2 MOA might not sound like much--but you're talking around 10" at 400 yds; and that's assuming the trajectory is otherwise identical shot to shot. If any other factor induces let's say another MOA or 2 of variation that can mean missing the target altogether.

[tangolima]

With terrains, straight head/tail winds can produce up/down drafts, which can more effects on poi than the head/tail winds. The model doesn't account for that.

You were shooting better than 2moa groups. Even 0.5moa variation is significant.

-TL

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[MarkCO]

Originally Posted by tangolima

With terrains, straight head/tail winds can produce up/down drafts, which can more effects on poi than the head/tail winds. The model doesn't account for that.

You were shooting better than 2moa groups. Even 0.5moa variation is significant.

I have a Bergara Terrain in 6.5CM. It accounts for terrain automatically.

I've had a few solutions where I had to account for shooting over a light colored dirt field and then very thick dark vegetation with the target sitting on a rock face. When the sun went behind the clouds for 20 minutes, it changed the hold by almost 0.5Mil. Another case, the bullet flew about 300 yards over water in the first 400 yards, then over a cliff making it about 100 feet AGL to the target in a hayfield. No-one in the match got a first round hit.

[tangolima]

Digging another hole.

I have been wanting to discuss preloading bipod. It is believed that it will improve accuracy. I tried that and I'm quite convinced.

How does it work?

Not every rifle is equipped with bipod, or circumstances may not allow deployment of bipod. Are there ways to have benefits of bipod with having bipod on a rifle.

-TL

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[MarkCO]

Originally Posted by tangolima

Digging another hole.

I have been wanting to discuss preloading bipod. It is believed that it will improve accuracy. I tried that and I'm quite convinced.

How does it work?

Not every rifle is equipped with bipod, or circumstances may not allow deployment of bipod. Are there ways to have benefits of bipod with having bipod on a rifle.

It serves to minimize the rifle moving around, especially inconsistently, during and after the trigger press. Same thing as weight in benchrest rifles.

Yes. A sling, properly used, is one way. A good NPOA and the hand on top of the bell of the optic is another. Enough bags can get the job done too.

Just don't use a lead sled. Hard on the gun and not repeatable in the field.

[tangolima]

Preloading bipod by pushing forward. Would pulling back work? Why so?

-TL

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[MarkCO]

Originally Posted by tangolima

Preloading bipod by pushing forward. Would pulling back work? Why so?

-TL

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If you can maintain fundamentals, yes. It reduces movement of the rifle.

[Unclenick]

TL,

Pushing forward is for bipods like the Harris, whose legs normally fold by swinging up and forward but have a hard stop against pressure from the rear when folded down. A bipod that folds rearward and has a hard stop swinging forward would get the opposite treatment. This is an interesting article if you haven't run into it before.

The software I used is 3 DOF, so it does figure spin drift (the windage corrections you see in that table), but it can't figure vertical aerodynamic jump the way the Hornady software does, so I expect that's the source of the result difference. The free Lapua cellphone app has a 6 DOF solver for their bullet catalog. Harold Vaughn published a description of 6 DOF code in Appendix D of his book, Rifle Accuracy Facts.

[Picher]

That would be acceleration over 24"...not 24'.

[tangolima]

Originally Posted by Picher

That would be acceleration over 24"...not 24'.

Right. Correcting it. Embarrassed.

Oops I can't. Time has run.

-TL

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[Unclenick]

I used my moderator superpowers to fix it for you. I didn't notice it the first time through, either.

Originally Posted by stagpanther

Wow! That does not match up with my shooting experience at long range in general--a headwind component always messes up my bullets at distance more than a tailwind. I guess I must be somehow inducing the aberrations myself.

Well sure. A headwind is blowing into your face and up your nose. Top competitors everywhere agree that sneezing during shot release almost always affects POI.

I always wish for something akin to the Houston Warehouse to be available for testing this stuff indoors. It could even have a big, reversible fan at one end and a vent at the other to create headwinds and tailwinds. But I don’t see the sort of funding power that would require anywhere in my near future.

Headwind adds directly to the atmospheric velocity of the bullet, and faster makes for more drag, so the difference in TOF as compared to still air and to total drop in that air is a little bit higher for a headwind than for a tailwind, but it looks like only about 10% difference in the change they make as compared to still air flight, at least in the 3 DOF model. If I fire right at the speed of sound, the difference is bigger because the drag increase with velocity goes up faster at that part of the transonic velocity range.

I posted the Cd plot for the RA4 drag function before. I'll add one below for the actual drag that Cd variation in the first graph produces as compared to what Newton expected would happen. Working in the late 1600s, he never anticipated the “sound barrier” or shock waves.



As a historical side note, when Benjamin Robbins published a description of his ballistic pendulum in 1742, the fact his measurements showed supersonic musket balls slowing down faster than Newton anticipated was considered proof that his pendulum didn't work, and he suffered some ridicule over it.

[tangolima]

Filling the hole on bipod preloading.

For what I can gather, what special about preloading bipod is to eliminate "bipod hop".

The recoil force acted on shooter's shoulder (see earlier posts) gives rise muzzle-up torque. The weight of the rifle keeps a muzzle-down static torque in the meantime. If the former exceeds the latter, the muzzle starts to rise. If such movement takes place while the bullet is still in the bore, the poi will change. Pushing the rifle forward against the stop of the bipod adds on to the static downward torque. When the preloading is adequate, the bipod feets contact the bench top at all time, and hence no bipod hop, indicating no muzzle rise at all.

Here are some figures to illustrate the point.

Rifle weight 10lb
Center of gravity from butt stock 24"
Peak recoil force on shooter's shoulder 75lb
Bore height above center of butt stock 4"
Bipod height 8"

Without preloading, the static downward torque

Td=10 * 24 = 240 lb-inch

Upward torque caused by peak recoil force

Tu=75 * 4 = 300 lb-inch

Tu > Td, muzzle will rise.

If the bipod is forward preloaded by, say, 20lb.

Tu = (75 + 20) * 4 = 380 lb-inch
Td = 240 + 20 * 8 = 400 lb-inch

Tu < Td. Rifle recoils straight back with no muzzle rise.

Similar results may be achieved by adding weight to rifle, preferably at the tip of the handguard. Pressing down handguard with hand, slinging up to strap down the the handguard work too.

Pulling back rifle against bipod stop? I don't know. Unless the bipod feet hook on to the bench top, it looks counterproductive, as it adds torque in the wrong direction. At least it feels awkward.

Now all this is assuming the rifle is resting on bench top or something solid, with or without the bipod extended. Shooting offhand is quite a different story. It leads to the next rabbit hole;

Sling or not to sling, das ist hier die Frage.

-TL



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[tangolima]

Digging another hole.

I zeroed a rifle at 100yd. Still had several rounds left, I decided to shoot the soda can on the berm at 150yd. Expecting poi lower than POA, I held 1" above the can. To my surprise, it hit where I aimed, about 1" above the can or even a little higher.

Huh! How does it work? I haven't seen anything like that.

The rifle was an AR-15 in 5.56 NATO.

-TL

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[stagpanther]

Wild guess--projectile is still on uphill portion of its trajectory before arcing downhill.

[tangolima]

Originally Posted by stagpanther

Wild guess--projectile is still on uphill portion of its trajectory before arcing downhill.

Right on.

The follow-up question. Why doesn't it happen on other rifle designs? I have seen it only on AR platform.

-TL

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[stagpanther]

Can't say; though it's possible that some user error is introduced by using inherently higher mounted optic on AR's; the difference between line of bore and line of sight will tend to magnify errors. The two points at which the line of sight and trajectory intersect may also change somewhat (try shooting 9mm AR zeroed at 50 yds at longer distances with high scope mount to really boggle your mind )

[tangolima]

It is actually result of sight height and MV. The projectile needs flight distance before its trajectory apex reaches the line of sight.

Assuming ideal case in vacuum.

h is the sight height;
L is the distance;
V is MV;
Vv is the vertical upward component of MV;
t is TOF for the projectile reaches the apex;
g is the gravitational acceleration.

Vv^2 = 2*g*h
t = Vv/g = sqrt(2*h/g)
L=V*t=V*sqrt(2*h/g)

High MV and sight height require longer distance for zero to be on descending slope of the parabolic trajectory. Before that zero must be on ascending slope.

For AR, V=3000fps, h=2.5"

L= 340'=114yd,

so 100yd zero must be on ascending slope (funky).

For other my rem 700 in 30-06, V=2500fps, h=1.5"

L=220'=73yd

so 100yd zero has to be on descending slope (normal).

One may have noticed that AR zeroing carries way more confusion than other designs. That's related to this.

-TL

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