Re: Ballistic coefficient G1 and G7
There are several things I'd like to respond to over the last several posts.
1) The algorithm, vs the model, vs the drag curve.
Ballistic solvers are comprised of two basic parts:
A) The '<span style="font-weight: bold">algorithm</span>', aka the simulation. This is the basic framework for solving the equations of motion. These equations of motion are not debatable, arguable or questioned since Newton established them. In particular, it's newton's second law (F=ma) which equates force to an objects mass and acceleration. In ballistics, the force is aerodynamic drag, the mass is the bullet, and the acceleration (or de-celeration) is the bullet slowing down. The acceleration is integrated to get velocity, which is integrated to get position, and the trajectory is solved. This is just how it's done. It's the same equations of motion that every modern fire control is based on. Needless to say, some amateur programs fail to properly code the equations of motion, or use approximations that compromise the calculations in some way. The Pejsa approach is an example of an approximation. It was much more handy to use approximations before modern computers were able to solve the equations directly (numerically)
B) the <span style="font-weight: bold">model</span>. There is an atmosphere model that has to calculate the correct air density based on temp, pres, hum. This is one task that several amateur programs fail to do correctly, or will mix elements of the ASM and ICAO atmospheres, or not match the atmosphere model to the atmosphere used to calculate a BC. Anyway, the atmosphere is one model in the ballistic 'simulation'.
Another model, the one which is the topic of this thread, is the bullet model. The diameter and mass of the bullet are two important but easy elements to model. The drag coefficient of the bullet as a function of speed is the difficult one to model. For several reasons it's convenient to reference a bullets drag to a fitting standard. G1 and G7 are two of the many options for standard drag models.
The standard most representative of long range bullets is the G7.
When G7 BC's are measured and corrected for a standard atmosphere model, and that same atmosphere model is used in a properly written ballistic solver (algorithm), there will be very little error in the predicted trajectories.
The large caveat here is that all the inputs have to be accurate. It doesn't matter if you're using all the right tools, BC's, atmosphere model, etc, if you're MV is 50 fps faster or slower than you think and input, the predictions will likewise be off. If you enter the same set of inputs into a poorly written, uncoordinated program, it may actually appear to be closer to the observed drop because the errors in the program can offset the 50 fps error in MV (this speaks to what Cory and KY agreed to).
The point is that there is a 'right' way to model the equations of motion (algorithm). The algorithm itself doesn't require alteration. There are no crazy genius out there who can improve on the equations of aeroballistic motion (Newton was the crazy genius). Likewise the atmosphere is well understood and if written properly, a program can assign the appropriate air density to a given set of temp/pres/hum. There is room for improvement in modeling bullets, as even the G7 model isn't perfect for every bullet. Although it is 'good enough' to get you within 1 click thru the supersonic range of the trajectory (2 experimental examples of this in chapter 8). 'Custom drag curves' for bullets that don't rely on referencing a standard offer improvement over G7 referenced BC's. However getting them is a challenge and the improvement is trivial for supersonic ranges.
The benefits of the standard way of doing things as described above is that BC's can be measured and stated for all to use. If the BC's are plugged into properly written solvers, they will produce the same results, for everyone, all the time, everywhere. Then why, you may ask, don't all programs give the same results? The answer to that question is that not all solvers are properly written! Is is really a suprise that that $2.99 app you bought or that 30 yr old software package may not be perfect? JBM, and anything running my solvers produce the same results BECAUSE they're both properly written. Anything that doesn't match them is in error by the amount they differ. If you 'hit closer' with something else, it's because there are other errors in the system which offset the error of the solver.
LB. As I stated in a previous post, LB is a one off. The fact that it produces the same solutions with G7 and G1 is direct evidence that it's not modeling G1 and G7 the way they actually are. The two trajectories SHOULD be different because they're different drag models. I hate to be against LB because I know Gus and consider him a friend. But the fact is that his system is simply not compatible with modern ballistics. Example. I've published a book with hundreds of BC's for modern bullets that will work well for any standard solver. Where's the book of 'LB' BCs that work just with that program? Until there is such a source of matched data for that solver, users have to find their own BC's that work with that unique program. Some users don't mind that and it's fine. However my objective is to provide predictive capabilities to the masses. Having 'one off' programs out there and people advocating them confuses the issue for shooters who are trying to learn the conventional approach.
Enough on solvers for now.
2) LL. "I didn't hear about G7 in sniper school in the '80s, so why do we need it now?" C'mon man, really? At some point fuel injection was new too. You're basically advocating a mindset that isn't open to change. When there's a better way of doing things, if you don't want to advance, that's fine. But there's no reason to hold everyone back with you.
You say you talk to 'many experts' about ballistics. The only material you've referenced in this thread; LB and those quotes come from the same guy (Gus). And that's a guy who's selling his own special brand of software. Critical thinking.
3) LL (again). You said you don't use my .243 G7 for the 175 SMK in your new gun the same as all the rest, but that you use .239 instead. To put that in perspective, that's an error of 1.6%. 5" at 1000 yards. And that's assuming everything else is right. What your saying is that you can pick up a new rifle as if you've never shot 175 SMK's before. Used my .243 G7, and been within 5" at 1000 yards (of course after getting all the other inputs right). I find that an acceptable result. You've also described in another thread (a while ago) how all the programs gave different results and that some needed a G7 quite different than .243 to match your data. But in a program that used a standard solver (I forget if it was JBM or one of mine) .243 was right on. That's what I'm talking about regarding the value of standardized methods. That's how they should work. Throw other variations into the mix and it's easy to be confused, but if you stick with the conventional solvers and matched standard data, the results are very good (caveat once again; assuming everything else is right).
It's an important caveat because if you don't get everything else right, then you can't attribute a hit or a miss to G1 vs G7 at all.
Some other facts that make the G1 paradigm difficult to deal with.
<span style="font-weight: bold">Stepped BC's.</span> You can improve the effectiveness of G1 BC's by stepping them. But why go thru this complication if it's not necessary?
<span style="font-weight: bold">Velocity dependence.</span> Bullet company 'X' might test and advertise a perfectly accurate G1 BC over 100 or 300 yards. But that BC, despite being technically 'accurate' will not be effectively accurate for a 1000 yard trajectory. Furthermore, the BC that's right for 1000 won't be right for 1500, etc. G7's have this same problem, but it's much much less, and for practical purposes you can ignore it's effects because it's less than a click.
<span style="font-weight: bold">Methods for determining G1 BC.</span> If you measure a G1 BC based on tof vs one based on velocity decay, you'll get <span style="font-style: italic">two different numbers!</span>. The reason again goes back to the mismatched drag curve.
Considering all of the above, the only reason I can every see why someone would choose G1 over G7 for a modern long range bullet is if there simply isn't a G7 BC available. Even then, if you're going to have to 'tweak in' a G1 because the one supplied is probably not accurate to begin with, then why not 'tweak in' a G7 BC? It will be more extensible in other situations and velocities than the G1.
I hope I don't offend LL enough that he takes his pixels and goes home. I suspect there are many who are learning from this thread.
-Bryan