Tutorial: Explore Display -- Drag Function Conversion
The purpose of the Explore display is to allow special problems to be solved quickly by making it easy to back into solutions. That is, you change various inputs until you get the desired output. That may sound unsophisticated, but unless some programmer has thought of every conceivable problem and built it into the software you are using, it's likely you'll find yourself backing into solutions. The Explore display just makes it easy and quick.
Dr. Ken Oehler of Oehler Research (www.oehler-research.com) did a number of articles on ballistics for Shooting Times magazine. In the July, 2007 issue Ken explained his method of converting the ballistic coefficient referenced to one drag function to that of other drag functions. Ken used trial and error to find BC values in other drag functions that produced the same time of flight (TOF) at 1,000 yards as that of a given BC value in the G1 drag function. In other words he needed to back into the solution because no one thought of his method before, at least not to the point of publishing it. In this case backing into a solution was not unsophisticated, it was leading edge research.
In 1998 I programmed the equal drag at a given velocity method of converting BC's from one drag function to another into Ballistic Explorer. The equal drag at velocity method is now used throughout the industry, but Ken found that this method didn't produce good downrange matches between drag functions, if that's the goal. In his research he found that equal time of flight at a given range produced better downrange matches. In the rest of this tutorial these two methods are referred to as "equal drag" and "equal TOF", respectively.
Setting Up The Problem
For his "A Better Ballistic Coefficient" article Ken started with a G1 BC of 0.527, a muzzle velocity of 3,100 f/s, standard conditions and a range of 1,000 yards. He then found BC values for the G5 and G7 drag functions that produced the same TOF at 1,000 yards. Ken found these values be trial and error, but lets see how it can be done using the Explore display.
Prior to Version 6.2.0 when I opened three Trace windows and loaded the same load into all of them and then clicked the drag table button on Trace 2 (red box). This opens the following dialog.
This dialog lets you select from any of the available drag functions and gives a short description of each function. The drag functions are in the form of tables in external files. Ballistic Explorer makes it possible for advanced users to use their own drag functions with the program, be they for airgun pellets, black powder mini-balls, or shotgun slugs. Clicking OK opens the following dialog in versions prior to 6.2.0 (more about that at the end).
In this case we don't want to use the equal drag method so click NO, and repeat for Trace 3. Opening the Examine and Explore displays results as shown below. The Examine display is mostly hidden by the Trace windows, but the relevant time of flight data is shown in the red box.
All three traces have a BC of 0.527, but for three different drag functions. The Examine display shows the values of the time of flight at 1,000 yards and the Explore display shows a graph of time of flight. It's obvious that a G1 BC of 0.527 is much different then a G5 or G7 BC of 0.527.
Now lets use the Explore display to find the equivalent BC using the equal TOF method.
With the Trace 2 tab selected in the Explore display, I decreased the BC with the slider control to increase the time of flight until it matched that of Trace 1. The program updates all open displays as the slider control is moved, so it's quick and easy to back into the solution. I then did the same with the Trace 3 tab selected.
Note the time of flight values in the Examine display. No they are not exactly the same, but given that the BC values are just three significant digits, all you can expect is to match the time of flight values to three significant digits. You can also see how the BC values for Trace 2 and Trace 3 have changed.
Now lets see how well other parameters match.
The velocity at 1,000 yards is within 19 f/s of Trace 1, which is a very good match.
Bullet drop at 1,000 yards is within 1.4 inches of Trace 1, which is a another good match.
Wind Drift in a 10 MPH cross wind is within 0.15 inches at 1,000 yards of Trace 1, which is close to a perfect match.
The point of Ken's article, at least as I understand it, is that when BC's are measured over a distances of 1,000 yards it doesn't matter much which drag function is used. A G1 BC of 0.527 produces the same downrange results as a G5 BC of 0.335, or a G7 BC of 0.264.
With Version 6.2.0 I have programmed Ken's equal TOF method (Ken never called it that) into the program. After you select the drag function you want to use (first image in this tutorial) the following dialog opens.
Click the radio button for the method you want to use and accept the corresponding value or edit it. Then click OK to finish. Having repeated the process for Trace 3 you can see below that the results are the same as backing into the solution.
Some may think I just made the Explore display obsolete, but that's far from the truth. It's easy to program something, such as the equal TOF method, once someone figures it out, but until then the solution has to be backed into. It's likely you have problems that no one has ever programmed into a computer, but with the Explore display you have a powerful tool to make your own research easier and quicker.
Why are there so many drag functions?
The simple answer is that bullets of different shapes have different drag characteristics across the velocity range shooters are interested in. When plotted on a graph, these different drag characteristics produce a curve.
Note: The Drag Function Analyzer shown below was a precursor to the Drag Analyzer added to Ballistic Explorer for Version 6.6.0. The tool in Ballistic Explorer has greater capabilities and features.
Above shows the G1, G5, and G7 drag functions plotted as deceleration in G's (gravity) as a function of velocity in Mach. Mach 1 is about 1,119 f/s at standard conditions of 59° F and 78% RH. As you can see G5 and G7 are very similar. Lets take a closer look at just the velocity range covered in Ken's article.
Over this limited velocity range and using the BC values from Ken's article you can see all three drag functions are very similar. Contrary to conventional wisdom, it's apparent the G1 drag function can be used successfully with today's high performance bullets when the BC is accurately measured over a distance of 1,000 yards as Ken demonstrated in his article.
Bullet and ammunition manufacturers don't all use the same methods for determining the BC values they publish. At ranges out to 500 yards few shooters will detect even a 20% error in the published BC value. However, if your own observations indicate a consistent discrepancy between predicted values and actual values then it's likely the published muzzle velocity or BC values are not accurate enough.
You can check the muzzle velocity with a chronograph, and if that's OK, it's perfectly acceptable to adjust the BC or switch to another drag function using either of the two methods Ballistic Explorer provides. The Explore display makes it easy to fit the predicted values to your observations. With such fine tuning Ballistic Explorer's predictions should be more accurate at all ranges.