[ QUOTE ]
...to see the effect on the method on harmonics, I guess you need to take a more serious approach...and of course, get some sophisticated instrumentation and LOTS of experimentation, and of course, all of that is beyond the scope of recreational reloading, at least to me
Unfortunately, nobody came up with a statistically correct method, than what, we simple reloaders, could grab without getting ourselves into the realms of college labs.
[/ QUOTE ]Gustavo, here's some simple things to consider when thinking about ladder tests. I doubt few people have considered them.
First, a rifle barrel has one resonant frequency. It's low and typically between 30 and 90 cycles per second, or Hertz (Hz). Chamber it, then screw it into an action and the barreled action's resonant frequency will change a small amount. Bolt that barreled action in a stock and it'll change a bit more. Mount a scope and base on it and there'll be another change. But once the rifle's assembled, the frequency the barrel vibrates at is the same. Doesn't matter if it's chambered for a tiny cartridge or a huge one; the frequency it vibrates at doesn't change. Only the magnitude. Most interesting is folks come up with different resonant frequencies for the same barrel; but just the barrel, never a barrel in a complete rifle. The only way to find what the ready-to-aim-and-shoot barrel's resonant frequency is, one has to measure it. Whatever it is, it's the same all the time. A friend measured several with magnetic induction accelerometers that don't touch the barrel and learned the frequency at the greatest amplitude of the vibrating barrel was vertical and well under 100 Hz. Shooting different velocity ammo didn't change it.
Second, most barrels folks use for long range accuracy are medium to heavy weight. The rifle's barrel's resonant frequency is about 50 Hz for several tapers and calibers. Which means it takes .020-seconds (20 milliseconds) to go through one cycle. As the barrel droops straight down from gravity a few MOA when held horizontally, upon firing the rearward movement in recoil while the bullet's going down the barrel causes the muzzle to rise because the recoil axis is higher than where the rifle's butt rests against someone. That high frequency ring barrels make when struck is a multiple harmonic of its fundamental frequency and has a magnitude of insignificant size. That ring changes most as the barrel length is changed because it's based on the speed of sound through steel going back and forth at 15,000 Hz. Even a round musical chime tube rings the same frequency whether it's lightly tapped with a cotton ball or smartly smacked with a ball peen hammer; only the volume changes not its tone or frequency.
Third, when a bullet leaves a 30 inch rifled section of a 32.5 inch barrel at 3000 fps, it takes longer than 2.5 times what it takes to move the first foot out the barrel due to acceleration in the barrelfrom 0 to 3000 fps; .000333 seconds per foot. Powder type and charge weight differences will change how long the bullet's in the barrel because pressure curves aren't all the same for them and a given bullet. Most folks feel 1.25 times muzzle velocity's time for the bullet to go one foot. So, barrel time will be more than multiplying time per foot of exterior bullet speed times barrel length in feet on in this case, 0.8325 milliseconds. In this example, barrel time will be around 1.040625 millisecond. This is the reason why I think .22 rimfire bullets taking about three times as long to leave the barrel really exit near the peak of the muzzle's whip and different muzzle velocity lots have different barrel times. Folks usually get best accuracy with another lot when its factory test muzzle velocity is the same as what was used before.
Fourth, with the bullet taking a bit more than 1 millisecond to leave the barrel and the barrel taking over 5 milliseconds to whip down a few degrees then up to the top of its whip cycle where it's slowed down and virtually motionless, the bullet's out the barrel long before the barrel's to this "node" point as so many people call it. The bullet leaves when the barrel's moving upward pretty fast but it's hard to tell where.
Fifth, the only bullet that'll exit at the upper peak of this barrel's upward whip is one with much longer barrel time and much lower muzzle velocity.
Sixth, many folks feel the barrel's whip characteristics will change with different loads. As the rifle's component parts remain the same, everything will still vibrate or whip at the same frequency; time remains the same. The only thing that changes is how much.
Seventh, I've never had anyone explain why they think their different bullet weights fired with different muzzle velocties and each load's tuned for the barrel's "node" when the time in the firing cycle, that node is always at the peak at the same time. Maybe they do and/or use special stuff to attain the same barrel time but different muzzle velocities to make that happen.
Note: The Brits made some spark photograph tests many years ago comparing their SMLE rifles to the Mauser 98 ones. The rear-locking SMLE receiver allowed too much barrel whip which allowed faster bullets to leave sooner but shoot to the same long-range point of impact as slower bullets leaving later in the barrel's upware whip; short range accuracy wasn't nearly as good as it had a lot of vertical stringing. Front-locking Mauser actions didn't have this problem with the same ammo; all the bullets left about the same place which made long range groups larger and virtually directly proportional to muzzle velocity.
All of which is why I've always used the same load (OCW)others get great accuracy with in my barrels of all sorts of lengths and diameters in all sorts of stocks using different sights. The all shot great in spite of bullets leaving at different points in the whip cycle. All the bullets left long before the barrels whipped up to where their muzzle axis was at the top of its arc. I know the barrel time's not the same for a 168, 180, 190, 200 and 220 grain 30 caliber bullets leaving at 2800 down through 2350 fps. But they've all shot very accurate in any one of several 1:11 twist 308 caliber magnum barrels. Their 15-shot test groups are all about the same size at 600 yards but needed different elevation to zero.
Ne'r the less, use whatever method to develop any load you like and have confidence in. There is, much to some folks disbelief, some "magic" in handloading. Too bad even the best of us cannot learn and understand what it really is. However, there are some things that just don't add up to the results we get. Observed barrel whip to its high point and claiming loads are adjusted to push the bullet out at that point is just one of those processes that don't. The above explains this one as I understand it.
...to see the effect on the method on harmonics, I guess you need to take a more serious approach...and of course, get some sophisticated instrumentation and LOTS of experimentation, and of course, all of that is beyond the scope of recreational reloading, at least to me
Unfortunately, nobody came up with a statistically correct method, than what, we simple reloaders, could grab without getting ourselves into the realms of college labs.
[/ QUOTE ]Gustavo, here's some simple things to consider when thinking about ladder tests. I doubt few people have considered them.
First, a rifle barrel has one resonant frequency. It's low and typically between 30 and 90 cycles per second, or Hertz (Hz). Chamber it, then screw it into an action and the barreled action's resonant frequency will change a small amount. Bolt that barreled action in a stock and it'll change a bit more. Mount a scope and base on it and there'll be another change. But once the rifle's assembled, the frequency the barrel vibrates at is the same. Doesn't matter if it's chambered for a tiny cartridge or a huge one; the frequency it vibrates at doesn't change. Only the magnitude. Most interesting is folks come up with different resonant frequencies for the same barrel; but just the barrel, never a barrel in a complete rifle. The only way to find what the ready-to-aim-and-shoot barrel's resonant frequency is, one has to measure it. Whatever it is, it's the same all the time. A friend measured several with magnetic induction accelerometers that don't touch the barrel and learned the frequency at the greatest amplitude of the vibrating barrel was vertical and well under 100 Hz. Shooting different velocity ammo didn't change it.
Second, most barrels folks use for long range accuracy are medium to heavy weight. The rifle's barrel's resonant frequency is about 50 Hz for several tapers and calibers. Which means it takes .020-seconds (20 milliseconds) to go through one cycle. As the barrel droops straight down from gravity a few MOA when held horizontally, upon firing the rearward movement in recoil while the bullet's going down the barrel causes the muzzle to rise because the recoil axis is higher than where the rifle's butt rests against someone. That high frequency ring barrels make when struck is a multiple harmonic of its fundamental frequency and has a magnitude of insignificant size. That ring changes most as the barrel length is changed because it's based on the speed of sound through steel going back and forth at 15,000 Hz. Even a round musical chime tube rings the same frequency whether it's lightly tapped with a cotton ball or smartly smacked with a ball peen hammer; only the volume changes not its tone or frequency.
Third, when a bullet leaves a 30 inch rifled section of a 32.5 inch barrel at 3000 fps, it takes longer than 2.5 times what it takes to move the first foot out the barrel due to acceleration in the barrelfrom 0 to 3000 fps; .000333 seconds per foot. Powder type and charge weight differences will change how long the bullet's in the barrel because pressure curves aren't all the same for them and a given bullet. Most folks feel 1.25 times muzzle velocity's time for the bullet to go one foot. So, barrel time will be more than multiplying time per foot of exterior bullet speed times barrel length in feet on in this case, 0.8325 milliseconds. In this example, barrel time will be around 1.040625 millisecond. This is the reason why I think .22 rimfire bullets taking about three times as long to leave the barrel really exit near the peak of the muzzle's whip and different muzzle velocity lots have different barrel times. Folks usually get best accuracy with another lot when its factory test muzzle velocity is the same as what was used before.
Fourth, with the bullet taking a bit more than 1 millisecond to leave the barrel and the barrel taking over 5 milliseconds to whip down a few degrees then up to the top of its whip cycle where it's slowed down and virtually motionless, the bullet's out the barrel long before the barrel's to this "node" point as so many people call it. The bullet leaves when the barrel's moving upward pretty fast but it's hard to tell where.
Fifth, the only bullet that'll exit at the upper peak of this barrel's upward whip is one with much longer barrel time and much lower muzzle velocity.
Sixth, many folks feel the barrel's whip characteristics will change with different loads. As the rifle's component parts remain the same, everything will still vibrate or whip at the same frequency; time remains the same. The only thing that changes is how much.
Seventh, I've never had anyone explain why they think their different bullet weights fired with different muzzle velocties and each load's tuned for the barrel's "node" when the time in the firing cycle, that node is always at the peak at the same time. Maybe they do and/or use special stuff to attain the same barrel time but different muzzle velocities to make that happen.
Note: The Brits made some spark photograph tests many years ago comparing their SMLE rifles to the Mauser 98 ones. The rear-locking SMLE receiver allowed too much barrel whip which allowed faster bullets to leave sooner but shoot to the same long-range point of impact as slower bullets leaving later in the barrel's upware whip; short range accuracy wasn't nearly as good as it had a lot of vertical stringing. Front-locking Mauser actions didn't have this problem with the same ammo; all the bullets left about the same place which made long range groups larger and virtually directly proportional to muzzle velocity.
All of which is why I've always used the same load (OCW)others get great accuracy with in my barrels of all sorts of lengths and diameters in all sorts of stocks using different sights. The all shot great in spite of bullets leaving at different points in the whip cycle. All the bullets left long before the barrels whipped up to where their muzzle axis was at the top of its arc. I know the barrel time's not the same for a 168, 180, 190, 200 and 220 grain 30 caliber bullets leaving at 2800 down through 2350 fps. But they've all shot very accurate in any one of several 1:11 twist 308 caliber magnum barrels. Their 15-shot test groups are all about the same size at 600 yards but needed different elevation to zero.
Ne'r the less, use whatever method to develop any load you like and have confidence in. There is, much to some folks disbelief, some "magic" in handloading. Too bad even the best of us cannot learn and understand what it really is. However, there are some things that just don't add up to the results we get. Observed barrel whip to its high point and claiming loads are adjusted to push the bullet out at that point is just one of those processes that don't. The above explains this one as I understand it.
