Originally Posted by ajhardle
But the drag coefficient is lower based on the drag curve. So if we shoot the same bullet at different velocities, [B]higher velocity has a lower coefficient of drag? Am i off beat on this one?
A "coefficient of drag", like a BC is number which is used to fit an equation describing someone's drag theory to observed reality. Just about all theories are simplifications of what's happening in reality. To describe an aerodynamics problem perfectly you'd need to know continuous vector velcity of every gas molecule that interacts with the bullet, either by direct collison or collision with neighboring molecules. No one could set up the model exacly and no supercomputer could handle the task for a single trajectory. So researches come up with models which give a decent fit to observed reality. Such equations input known data like time and velocity and tempearature and speed of sound and molecualar weight etc but they are not acturally calulating the moleules bouncing around, so if the models work (at least for some ranges of velocity) they are useful even if they aren't modeling what's physically happening. Observed or calculated coefficents need to be applied to make the equations work. I can't answer your questioin above. If the theory were perfect the drag model should give the correct answer for both velocities, as velocity would certainly be one of the variable coefficients in the model.
Wheneverr you reduce a comples funtion, such as the drag function of a sepecific bullet to a single number, such as a G1 or G7 BC, or "Coefficient of Drag" you are introducing errors unless the model is perfect for the range of all parameters what the equation is applied to. In my opinion BC should be thought of "Before Computers", not "Ballistic Coefficients." They were a handy tool in the days when rooms of mostly women were employed by the military to solve ballistic table (and other useful equations), but today even a high end eell phone has easily enough storage and computing power to handle complete numeric drag tables for each bullet model one shooter might use over the range of velocity they might shoot it and in small enough increments as not to introduce addtional error. That would less memory than a high resolution photo or video clip.
There are good reasons whey bullet manufacturers stick with G1 and G7 BCs. One is that all of the present ballistics calculators use BCs, and a single numner is easy to print in a catalog and it's a known fact that many shooters will buy one bullet over another it it has a 0.01 higher BC. Forget the fact that most bullet manufactures don't even state what velocity that number was correct for or how large the deviations are over the bullets useful range. I love Brian Litz's book. It provides two very useful things. One is giving precise details about many of the currently availabe long range bullets. The other is in pointing out clearly how well G1 or G7 coefficients do (or don't) match currently available bullets. My favorite example is the 240 Grain 30 Cal Sierra, wich in spite of being a a boattail the G1 model is the better fit, probably because of it's relatively short ogive, but for the 220 grain Sierra boattail the G7 coefficient is the better fit. It's not obvious why from looking at the shape of the two bullets. The magnitude of the error is similar but reversed in the two examples
Sierra is (or was) unique among bullet makers. Although they don't publish G7 numbers, they do publishe multiple G1 values vs velocity in typically 3 or four segments. That's generaly more accurate than one single valued coefficent, though it requires a ballistic program whcih can handle the multiple inputs. I believe Lapua is also offering multiple G1 values for some of their bullets. Having an actual correct drag table would also require modifiction of the available computer programs. No ballistic software I'm aware of on the market handles complete drag tables, though if they did they'd actually be simpler than the existing programs.
Likewise no bullet makers I'm aware of publish complete drag tables, though some either calculate the tables with programs like McDrag or measure drag tables using millimeter radar. Then they condense those curves down to one or a few values thowing away potentially useful information, particulary around transoinic velocities.
Are the existing methods good enough?. For most hunters, yes. For long range precision first shots, no. But then hunters don't have a method for measuring downrange wind vectors precisely so it doesn't really matter. Using spotter shots corrects for all meaurement errrors including air density , errrors in the difference of the G coefficients vs the actual drag curve, and the uncertanty of downrange wind measurements (actually estimates or guesses). Even using spotting shots doesn't correct for the fact that wind conditions are changing continuously. That's a problem with any instrument you might use to measure downrange wind unless it's built into the aiming device and does it's calculations in real time.
A Kestrel 4500 with it's built in weather sensors and ATRAG software may do what measurements it takes accurate to two decimal places and do the calculation are executed to better than six decimal palces. But the G() table have built in errors limiting their accuracy to two decimal palces, and the mini wind meter doesn't have a clue what the wind is doing more than a few feet from the meter. There is no place for the shooter to enter downrange wind information manually even if the shooter can guess what the wind is doing between his location and the target. Shooter wind estimates rarely better than 5% errror even with wind flags on flat terrain. In mountainous terrain with clear air and not foliage close to the trajectory guessing wind speed closer than 20% errror takes an excpetionally experienced shooter if it's possbible at all.
I'd suggest you simply believe the deflection estimates that your ballistic program gives you. They aren't perfect, but the available commercial ballistics programs don't have access to either the precise drag tables of each bullet or the downrange wind vectors to do a better job. Neither is the fault of the software. The people who wrote the software (most built on Robert McCoy's work) are aware of the limitations and don't bother to incude the calcualtions for the parts where data isn't likely to be availabe, particulary piecewise downrange wind vectors. They still do a far better job than anyone is likely to do by looking at two published BCs and their associated muzzle velocities and mentally calculate (or guess) which will have the lower lag time and thus the lower wind deflection.
Rober McCoy published McTrag which calculate trajectory, McDrag which calcullates bullet drag from bulllet dimensions & mass, which calculates bullet rotational stability from bullet dimensions and internal mass distribution based on years of research at the Aberdeen Ballistic Reesearch Labs (BRL). That was several years before he published the book Modern Exterior Ballistics.
In that book McCoy states that the US Army has mostly abandoned the used of G functions and works directly with measured drag tables for projectiles. BRL had not soved the problem of practical downrange wind vector measurements at the time of that publication.
There was a DARPA request for proposals arouund 2004 to the industy for an integrated rifle scope which could do multiple functions including rangefinding, weather, and and measuring downrnage wind vectors in two (or optionally three) dimensions. A web search of "scintillation anemometer" gives some idea of how the 2D type can work. A search on "particle image velocimetry" gives some info on 3D techniques. The hardware can be nearly as simple as a laser rangefinder and a cell-phone camera though the software is considerably more complex.
There was a writeup in VeryHighPower, the FCSA periodical of early experiments in Israel around 1994. At that time a simple version using one laser, two photodiodes, and a PC could give downrange horizontal crosswind estimation about as good as their skilled marksmen could estimate from mirage at ranges to over a kilometer. Measurement period was less for the instrument than it took the shooters to study and mentally estimate the bullet deflection. I've found no additional material from that source since. The technology has had 15 years to improve and be made more compact. While the DARPA request for proposal was not classified, resuts of the DARPA request are classified. I can only surmise what is currently available within the military.
It's anyones guess if or when Burris or Leica will offer such a unit commercally. I'm not sure I'd want one. It would make LongRangeHunting rather boring. Fortunately nothing on the market today comes close.