No link is needed just because you don't agree
My agreement has nothing to do with it. Facts don�t care who agrees with them. When an incorrect statement is attributed to somebody it�s always a good idea to go back to the original source and verify. It�s possible much was lost in the translation.
My statement is true and the numbers prove it within the stated limits of supersonic velocities.
Your statement is true, but you want to limit �supersonic velocities� to mean something other than �supersonic velocities?� That would be a different statement.
OK, even staying well within your Mach 1.2 limit (since you have the luxury of not worrying about where it really gets hard) your own data still shows error of 5.1� with one method and zero with the other at only 1300 yds. How exactly does five inches of error become �just as good as� zero inches of error? What does �just as good� mean to you, exactly?
By 1,500 yards 5.8 inches becomes insignificant.
Tell that to the target you just missed. Have you ever actually tried to shoot something at 1500 yds and hit it with your first shot? If you ever do, you may realize that you need
an additional six inches of error
on top of all the other potential errors inherent in making such a shot like you need a hole in the head. Especially when simply using more accurate data to which you have access can eliminate it. 5.1� at 1300 may even be worse as a percentage of �how far you miss with the first shot.�
All standard bullets have a form factor of 1.0, and thus, an actual bullet with a form factor of 1.0 is an exact match�. Simple math proves that a value of 1.0 represents a perfect match to a given standard bullet at a given velocity.
A given velocity is only a single point on a curve. It tells you nothing about how good a match the bullet is for the rest of the curve.
A value so close to 1.0 is a strong predictor of how well #24530 matches the G7 form factor at all velocities.
Wrong. It�s a
value. Not a predictor of other values. A curve is many values of one variable plotted against another, a single value is only a single point on the curve. Even an average tells you nothing beyond the average value�a vertical line and a horizontal line can have the same average value.
Without even getting out of the 6mm�s, Bryan�s data shows the Nosler 95 Partition, which has an average G7 I of 1.303 is actually a better match to the G7 curve than the bullet you chose, having only � the variation in form factor over the measured velocity range. And the Sierra 107 Matchking has an average I7 of 0.993�should be a �perfect match,� eh? Wrong. It has over seven times the variation the Nosler has. It�s actually a much better fit to the G1 curve than it is the G7 curve (even though its G1 I of 0.508 is quite a ways off from the �perfect� 1.0).
while the magnitude of drag depends a great deal on bullet shape at supersonic velocities, the profile (curve of the drag coefficient line on a graph) doesn't change significantly due to bullet shape at supersonic velocities.
Again, this relies upon your definition of �significant.� If the targets you shoot at 1300 yds are so large that 5� is not significant, you might learn more by shooting at smaller targets.
I'm basing Mach 1.2 on what others in this forum stated in my topic "Determining a load's maximum range". The consensus is that shooters are well aware of the inaccuracies induced at transonic velocities and consider a load's maximum range to be where its velocity drops below Mach 1.2, with some wanting to say above Mach 1.6.
Well OK then. You have a couple responses to one thread on this board. Obviously a new law of exterior ballistics has been created!
While some bullets don�t do so well below that and keeping above it means you never have to worry about it, it�s far from some all encompassing limit which means a ballistics method that ignores everything beyond it should be adopted as the industry standard. Many of us go below that all the time. My 6.5 Grendel would be pretty much worthless beyond 700 or 800 yds with typical loads if that was the limit. I have way too many sub-MOA groups at 1000 and even 1100 yds to know the right bullets can be fairly accurate well below that velocity.
The same applies to the techniques manufactures now use. Sierra has a 300 meter underground range, which I think is the longest in the industry.
Wrong. With a 300 yd range you can measure the drag of the bullet at different velocities by launching it at different velocities. With multiple data points, you can draw a curve. While far from ideal, you can get a boatload more information than a single TOF measurement from it.
For example, Doppler radar can't see wind in clear air, so you can only measure bullet velocity relative to the radar antenna and only along a straight line from the bullet to the antenna. Being a bullet's trajectory is parabolic�.
Wow, I�ll bet nobody using that thing had ever thought of any of this before! I�ll bet they had no idea what a waste of money it was�. Seriously, I think you�re insulting the intelligence of the people.
Of course, and that's why it only works for supersonic velocities. You know, the velocities anyone using a VLD bullet would care about.
The last time I checked, 2000 fps was supersonic. Another new rule?
Not true for supersonic velocities from muzzle to the target, which is the distinction I made, it produces better trajectory predictions than current published BCs.
Another 5� off is �better� than �right on� sort of way?
But the equal TOF BC gives better results over the velocity range such VLD bullets are intended for, and that's the point.
Again, the only data you have provided shows
worse, not
�better� results.
OK, let�s try to explain this again:
Have you tired comparing Sierra's multiple BC results with a measured G7 BC and then compared it to a properly calculated equal TOF BC? If not then you have no bases for your claim. If you have, post your numbers.
It�s really very simple. While Sierra doesn�t make as many VLD-shaped bullets as Berger, one I�ve used a lot is the 30 cal 210 SMK with listed G1 BC�s of: .645 @ 1800 fps and above, .630 between 1600 and 1800 fps, .600 between 1400 and 1600 fps, .530 @ 1400 fps and below.
In my above comparison, if you shoot this bullet from a big magnum at 3500 fps, for a large portion of the flight from muzzle to subsonic the bullet will have a G1 BC of .645+ (actually higher if you look at Bryan's data). This will increase its average G1 BC from the muzzle to subsonic.
If you shoot it from a smaller round with a MV of 2000 fps, it will spend very little time at .645 (actually it'll stay lower according to Bryan's data) and thus will have a much lower average G1 BC for the entire flight from muzzle to subsonic.
Two markedly different G1 BC values. Which would you print on the box? Which would you declare as "accurate?"
When you look into the numbers you�ll see this is exactly what is happening with the bullet you chose for the comparison (using Bryan�s G1/velocity data in place of Sierra�s). See below:
I demonstrated with actual numbers that the G1 equal TOF BC better matches the trajectory than Berger's published G1 BC relative to the G7 BC for a bullet that's a near perfect G7 form factor match over the velocity range that bullet will be used for. In doing so I've demonstrated a limitation in technique Berger and others are using assuming that hitting the target is the goal of publishing BCs.
Like I stated, assuming the G7 BC trajectory is correct Beger's published G1 BC is less accurate than the one I calculated using Ken's technique. That suggests their technique for calculating BCs is not as accurate as Ken's technique, and thus, even their G7 value could be off.
It suggests that to you because you don�t understand what is going on. There is no relationship from which you can form this conclusion.
Assigning a single G1 BC to a bullet which does not follow the G1 curve well is an inherently inaccurate exercise. Your discovery of this is no discovery at all and is not evidence of similar inaccuracies in the G7 values because the bullets follow the G7 curves much more closely, which makes that a fundamentally different problem.
A single G1 value for such a bullet will only be correct for a single set of conditions. If you change those conditions it�s likely the value will be wrong. Berger is damned if they do, damned if they don�t. It�s a lost cause�which is why they�ve switched to G7 for their bullets.
Case in point: You came up with a �more accurate� G1 value for that bullet�.
under specific conditions you chose. Under different conditions, such as a lower muzzle velocity, the G1 value Berger advertises will be more accurate than the G1 number you came up with. Re-run and post the numbers you did in the very first post except change the muzzle velocity to 2500 fps. Which value is the �most accurate� now? As you can see, trying to put a single G1 BC on that bullet is inaccurate the way Berger does it,
and the way you did it.Hopefully that exercise will make you understand the folly of trying to use a single G1 value for a bullet that follows the G7 curve. When you look at the data, it�s obvious how that inherent inaccuracy of doing so in no way reflects upon the accuracy of using a single G7 value which will give accurate results for both velocities for a bullet which follows the G7 curve.
Some find that annoying, but that's how progress is made.
As you can see above, it may be annoying to study those numbers until you understand them, but after you do you will see no progress is made with your method at all. The real progress is made by using drag models which match the bullets� actual drag curves very closely. When that is done, a single BC can be pretty accurate for a bullet under any set of conditions. When the bullet�s actual drag curve is very different from a standard drag curve, any single BC of that drag curve will be a poor description of that bullet for all conditions no matter how you come up with it.
Naturally, there are some bullets that don't follow either curve very well. With multiple measurements such as are presented in Bryan's book, it is easy to identify such bullets so that you may come up with specific strategies to deal with them. With a single TOF measurement only, you'd never know.
