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Denton,

So how far off course would an SR71 doing 3500 fps for 5,280,000 feet in a fifty mph wind at 70 degrees wind up?

According to the formula, he should arrive directly on target as the lag time is zero.

Just kidding!

As I understand the meat of your post, the nose of the bullet turns with the wind and actually changes the direction of flight of the bullet. Rather than being similar to a yacht slipping sideways in an ocean currant.

Am I correct then in saying a cross wind close to the shooter can well have more effect on a 1000 yd bullet than a crosswind close to the target, even though the bullet is moving much slower when it is close to the target?


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Most people who study calculus start with, and most of those finish with, the Riemann integral. The Lebesgue integral is generally considered the heavy hitter though, mostly because of its powerful convergence theorems.

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Mathman,
I will have to look up that Lebesgue integral in my engineering mathematics handbooks(if they have it) sounds interesting!
BTW, I assume you hold an advanced degree in mathematics?


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Deer smeller; What is the difference between "velocity lost", and "extra flight time". Ballistic coefficient is itself a function of velocity loss.
Good Luck!

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Here are some "truisms" about 1000 yard prone shooting (and I acknowledge that 1000 yard benchrest groups are smaller, as one poster said).

1. In any cartridge, the bullet with the better BC is less deflected by wind, even if it starts out slower. For instance in 30-06 a 190 grain bullet at 2600 fps is a better choice than a 150 grain bullet at 3000 fps.

2. For any bullet, driving it faster will cause less wind deflection. Starting about the 1920s, someone won the 1000 yard Wimbledon Cup with a 300 H&H Magnum. The 30-06s almost never won it again, even though both rifles shot the same bullets.

3. Wind near the shooter causes more deflection than wind near the target.

Someone else can work out the math.


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3. Wind near the shooter causes more deflection than wind near the target.

Ya oughta hear the marines argue you to death on that one!! I totally agree and it can't really be any way though, IMHO

Jeff


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Am I correct then in saying a cross wind close to the shooter can well have more effect on a 1000 yd bullet than a crosswind close to the target, even though the bullet is moving much slower when it is close to the target?


It do. Don't confuse drift with deflection. Planes drift, bullets deflect. Deflection is about drag and the quantified offset of the drag vector. Rockets crab into the wind and do not drift, neither do airplanes properly navigated. It's all well and good to look at this matter up at the multi mach level, more educational to look at what happens in the transonic level....where a .22 RF Match bullet(slower) has less drift than a HV bullet(faster).............drag curves are what they are, drag in terms of retardation is higher in absolute values at higher velocities for any given bullet.....


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Riemann, Stieltjes, Henstock, Denjoy, Perron, Daniell, or Lebesgue?


I did not know there were so many! I do remember Riemann being able to handle piecewise continuous functions, but that was long ago in a galaxy far away.

In my circles, "lambda gamma tranform" is an inside joke.


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I do remember Riemann being able to handle piecewise continuous functions


You can enlarge that a bit. A bounded function defined on a bounded interval [a,b] is Riemann integrable if and only if it is a.e. continuous. The "a.e." is mathese for almost everywhere, which is everywhere but on a null set, a set of measure zero.

One reason that the Lebesgue integral is so important is that the monotone and dominated convergence theorems don't hold for the Riemann version. Also the normed linear space of Riemann integrable functions (usual integral norm) is incomplete, and for a variety of reasons complete spaces are where you want to operate.

Generally speaking the Lebesgue integral is an extension of the Riemann integral in that if something is Riemann integrable then it's Lebesgue integrable and the two integrals are identical. It's the convergence theorems and other mathematical goodies that make climbing the somewhat steep hill to technical facility with the Lebesgue integral worthwhile. For example, Lebesgue measure and integration are used to put probability theory on a rigorous footing.

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To get back to the barrels; Gain twist barrels are not commonly used for accuracy competition for a numberof reasons. At the top of the heap is the fact that the top barrel makers don't make gain twist barrels! Now, does this mean they have, as a result of extensive testing, found the uniform twist to be superior? No, it does not. It does mean they have found a properly built uniform twist barrel to perform perfectly well with no apparent shortcomings. If one builds a barrel using a uniform twist and has success with it, he is unlikely to experiment with a gain twist just to see if it will work as well. Those who do build gain twist barrels do so because they believe there is an advantage to the system; or because Harry Pope did it; or because not everyone makes them; or a combination of these. The people who buy them do so for the same reasons. I use a couple because I think they are kind of neat. They don't seem to provide significantly more velocity but I don't really care about an extra 50 or even 100fps even on my long range rifles. It's my belief that you can't outrun the wind but you can outsmart it if you practice enough! The point is, the gain twist barrels are just fine and appear to have no downside just like the uniform twist barrels. The only downside is to the maker who has to set up to make them.
If gain twist barrels do indded give better velocity, it may be due to the better gas seal afforded by the constantly changing pitch. GD

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Muzzle velocity is the integral of net force/mass * time. Net force is (the area of a cross-section of the bullet*pressure) - friction. Bullet mass is constant during acceleration. That's very well settled basic physics.

I have a hard time imagining where in that equation gain twist would make a difference in velocity. Where does the extra energy come from?


I haven't read all of the thread, so maybe this has been discussed already, but if the gain twist barrels are faster, as some have said, could the extra velocity be due to less friction, at least in the in the early stages of bullet travel?

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OK, I see I'm way behind the curve. My thought was that the coefficient of friction might might be less as the angle of the rifling approaches zero degrees relative to the bullet's axis, but you make a good point about 10" vs. 12" rifling. How much velocity difference is there, on average, between the two?

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They don't seem to provide significantly more velocity but I don't really care about an extra 50 or even 100fps even on my long range rifles. It's my belief that you can't outrun the wind but you can outsmart it if you practice enough!


It depends on how far you are shooting, how windy it is, and how predictable the wind is. Out here we constantly have a gusty, quartering tailwind. Very few guys--if any--in my 1K BR club can pick conditions well enough to be competitve. I do know I haven't seen that approach win matches or set records. The shooters who win the most consistently and set the most records are the ones who "run" their shots together as fast as the can. Regardless, an extra 100 fps would indeed be a big enough deal in 1K BR to pursue it. Reading the wind does seem to work a lot better in Highpower than 1K BR, at least for me.

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The point is, the gain twist barrels are just fine and appear to have no downside just like the uniform twist barrels.


The down side is radical gaint twist (starts with straight rifling) can damage certain bullets as they travel through the bore.

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Talk about wind blowing something off course...................


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Blaine,
Reading the wind pays dividends regardless of the type of shooting. Having said that I will admit that 1000yd BR is a bit different for a couple of reasons. First, many of the 1000yd BR ranges seem to be set up so you are shooting over a valley so there is a shortage of usable wind flags. In addition, at the 1000yd matches I have attended, the competitors shoot blind. That is, shots are fired with no knowledge of where the previous shot landed so it's hard to determine just what the effect of the wind on a shot might have been.
Now, and again, back to the barrels. While it is true that a radical gain can distort the bullet jacket, it's not an insurmountable problem. I avoid this problem by specifying a gain of not more than 50% usually around a third (ie. 12 in to 8 in.). Looking at recovered bullets, I can see no evidence of significant distortion although it is possible to see the effect of the changing pitch.
I'm quite sure, if Krieger decided he wanted to make gain twist barrels, these barrels would be just as good and would perform just as well as his uniform twist barrels but no better. Since he can sell all the uniform twist barrels he makes he has no reason to make a gain twist. The same is true of the other top makers. The quality of the barrel is the important thing and the established top makers produce proven quality barrels of a given type. The makers of gain twist barrels are lesser known and this is the reason you don't see a bunch of gain twist barrels at various competitions. When a competitor is buying a new barrel and spending 260.00 to 350.00 for it, he's not too inclined to experiment.
I believe two barrels of equal quality will perform much the same from an accuracy standpoint whether uniform or gain twist. Just as a 4 groove barrel will perform the same as a 6 groove. I've not seen any solid evidence of velocity increase although there is plenty of anecdotal evidence to support it. If such exists, I believe it could be due to the better gas seal rather than a change in the pressure curve. GD

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I talked to Jack Krieger about this very subject 6 or 8 years back. His take was that he found no appreciable or inherant improvement of gain twist barrels over standard twist barrels. Since good standard twist barrels are easier to make than good gain twist barrels, he makes standard twist barrels.

Jack modified a lot of the original barrel making machines he uses, so if a gain twist was beneficial, I have no doubt that he could set up his machines up to do it. None of the other good Wisconsin barrel makers do it either. Obermeyer, Broughton, Bartlein, all are standard twist.

Fast Ed


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So far as I know the only person to ever rise above the fray with gain twist barrels was Harry Pope. I think it significant that he was shooting cast bullets in those guns. Were it possible to make perfectly identical barrels of gain and conventional twist I doubt there would be a measurable difference in performance between the two.

Pope did a few other things in the process of making his barrels that no doubt contributed to his legend but I'm doubtful that his use of gain twist was his advantage.


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From what I've read Pope was concerned with distortion of his lead bullets. He believed that an easier start and the gas seal of the tightening twist were beneficial. At least he proved it to himself.
Good luck!

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Some tanks and artillery use gain twist. The rub there, of course, is that you're dealing with projectiles of considerable mass and typically with narrow driving bands.

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