Re: sub 1 MOA at 100, 4+ MOA at 350???
<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Bryan Litz</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: timelinex</div><div class="ubbcode-body">
The following explanation was given:
<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">A bullet's dispersion is usually initiated at the muzzle, as a small velocity component that's perpendicular to the intended flight path (up, down, left, or right). If that velocity component results in a miss distance of .25" at 100 yards, you can calculate how much miss distance there will be at 1000 yards by looking at the ratio of flight times.
For example, if the bullet strays .25" at 100 yards, where the flight time is .111 seconds, at 1000 yards, it will have strayed by .25*1.632/.111 = 3.7". 1.632 seconds is the flight time to 1000 yards. Note the bullet does not stray by the 2.5" you would expect by multiplying .25" by 10.
This same logic goes for group sizes as well. If you can shoot a .5" group at 100 yards with your rifle, the best you can expect to do at 1000 is 7.4" under ideal conditions and zero MV variation.</div></div>
While I respect his knowledge of the field, unless he's leaving something out OR I'm missing something, this is just simply incorrect.
...
He's mapping the group size idea to be based on flight time instead of distance, but it depends on distance and not time. </div></div>
t,
Thank you for taking the time to provide a well thought out reply. Like you, I'm not looking for a fight, just wanting to discuss the 'why'.
The above quote of mine was (I think) taken from a post on this forum. In my book, you'll find a more complete development of my ideas on dispersion. I'll try to sum up here.
One can describe two basic types of dispersion: those from aiming error, and those that occur from disturbances at the muzzle (static imbalance for example).
Dispersion from aiming error is totally linear, as you describe, for the reason you describe. The bullet is simply flying a straight path. If the miss distance is 1/4" at 100 yards, it will be 2.5" at 1000 yards, etc.
However, the other kind of dispersion which comes from disturbances at the muzzle does not behave this way. Imagine a bullet that has a static imbalance, spinning at 200,000 RPM. The instant the bullet exits the muzzle, it will be 'dispersed' in the direction the CG was moving as it exited the muzzle. In other words, the bullet has a component of lateral velocity (different than simply being imperfectly aimed). For example, let's say this bullet has 2 inches per second of lateral velocity. <span style="font-style: italic">That lateral velocity will result in the bullet being displaced further at long range than at short range.</span> It's true that the velocity magnitude of the bullet slows as it flies downrange. However, it's the main (forward) component of bullet velocity that's being resisted and decreasing the most. In other words, the forward velocity may decrease from 3000 fps to 1200 fps, but the lateral velocity wouldn't slow much from 2 inches per second (.1666 fps).
If my explanation is not adequate, you can refer to these references for other, more mathematically based derivations of bullet dispersion being related to tof and not range:
Modern Exterior Ballistics by Robert McCoy: Chapter 12
Rifle Accuracy Facts by Harold Vaughn: page 170
Harold Vaughn's equation for bullet deflection due to static imbalance is:
sigma = 24*pi*(V/t)*(TOF)*delta
where:
sigma is dispersion in inches
V is muzzle velocity
t is twist rate in inches per revolution
TOF is time of flight in seconds
delta is the CG offset of a bullet in inches.
*typically delta is less than 0.0001" for good bullets.
Other examples of dispersion that would be a function of time of flight are those related to barrel whip or moving platforms (like jerking the trigger).
So you're not wrong in your explanation, but I believe you were only considering one type of dispersion, and not other types.
Looking forward to your thoughts on the subject.
-Bryan </div></div>
Thanks for chiming in and taking the time to explain it further.
As I said in my post, I'm probably just missing something, and you showed a side to the overall picture that I was missing. I didn't account for the different dispersions as you said.
I did do further digging though, and couldn't find how static imbalances would cause the shift. I don't have the books quoted, but I have found similar texts. It seems that equation is correct, but from the form's that I find it in, it is based on cylindrical cordinates. What I'm getting at there is that imbalances do cause shifts in flight, but they are cylindrical and rotate around an axis, and so they do deviate from the path, but back and forth(because its spinning). So essentially it looks like it's describing the 'yaw' that was talked about earlier and concluded to not cause significant changes.
Here is a source I found on this, click
here . You can read through the everything in there, and for those that would rather get to the meat and potatoes, go to page 294 and you will see the illustrations of trajectories caused by static and dynamic imbalances. Both cause the bullet to deviate from its straight path, but only around a center point. The equation's are meant to find where it is in space in relation to that center path at any given time. Thats why time is the factor and not distance, because the phenomenon is internally based only on the object moving and has no relation to the distance it flies or the environment.
LASTLY, assuming the thoughts on dispersion that were mentioned in your post were true, this wouldn't explain most questions anyways. It would explain why someone has exaggerated grouping's at 1000 yards compared to 100 but many of the questions are differences between 100 yards and 200 or 400. Thats when most the 'gurus' step in and say bad form is exaggerated. If you look at flight times between 100 and 200, they are almost identical, at 300 it is .02 seconds off and even by 400 it is only .05 off. This means that a .5 MOA group could possibly open up to a .55 group. Noone complains about this, but rather much bigger differences like .5 going to 1.5.
Someone is definitely missing something, and it could very well be me, since there's no argument that groups consistently open up with new shooters as targets get farther. I'm still jsut trying to get to the bottom of what the actual cause is. So Bryan, maybe you clear up what I'm missing.
Also I appreciate your post Lowlight, and completely agree with you that we can theorize all we want but it won't change the pattern you see with real life expereience.