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Extended Range Truing, Why and How

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Extended Range Truing, Why and How Extended Range Truing, Why and How For a hundred and fifty years, ballisticians have table, there is a hidden drag function for each sought to improve their predictions of the path projectile. This hidden drag function was of the bullet after it leaves the gun. The bullet’s obtained from the radar data and was used in‐ behavior is primarily determined by the drag house by the ballistics group to compute the function of the bullet, or how does the firing table. deceleration of the bullet vary with the speed of the bullet. The influences of the atmosphere It has long been accepted that long‐range ballistic and the muzzle velocity are well known, and predictions are just about as accurate as is the both atmospheric characteristics and muzzle labeled nominal velocity for factory ammunition velocity can be readily measured. Modern or predicted by a handloader’s book. At best, predictions are refined by the inclusion spin velocity predictions represent average behavior drift, muzzle jump, Coriolis, and other variables. from several different guns firing several samples of “identical” ammo. More likely, velocity Until the advent of long‐range measurements predictions originate with one ammo lot fired in made with Doppler radar, the choice of drag one gun. Shooters recognize that they must functions was limited. Most widely recognized measure the actual muzzle velocity of their are the G1, G2 … G7, G8 family standardized by gun/ammo combo in order to make accurate the government proving grounds. In actual long‐range predictions for that combo. practice, only the G1 and G7 functions saw Determination of actual muzzle velocity is a significant use with small arms. By default, the significant part of the problem. Fortunately, G1 drag function has been accepted as the measuring muzzle velocity is relatively easy, and standard truth for sporting bullets. Recently G7 there are several solutions available. has been popularized and presented as a better alternative for modern low‐drag bullets. The bullet’s downrange behavior does not always fit the prediction. Predictions are based on drag Roughly fifty years ago, the government functions and ballistic coefficients. Recent tests abandoned the use of the Gx tables in favor of have verified that the commonly accepted G1 and collecting representative radar drag data from G7 do not accurately represent the bullet, and guns firing type standardized ammunition. The that the downrange behavior is significantly guns ranged from different battle tanks down to influenced by the individual gun used to launch different individual infantry rifles. Following the the bullet. The bullet only knows to follow the collection of firing data, the entire mass of data laws of physics as it travels downrange. While we was delivered to a ballistics research group for claim to understand the laws of physics and apply reduction to a “firing table” representing typical them to our prediction of the bullet’s flight, we performance from a typical gun. For each make small errors of approximation and ammo type, the firing table provided the application. The bullet’s behavior is absolutely estimated muzzle velocity along with governed by the laws of physics, and it is downrange characteristics such as sight influenced by subtle changes we didn’t recognize elevation for a particular range, remaining or measure accurately. As Todd Hodnett velocity at a range, wind deflection, et cetera. explains, “The bullet doesn’t lie.” The bullet does While it does not show up directly in the firing just what nature tells it to do. We must modify Extended Range Truing, Why and How ‐‐ Ken Oehler ‐‐ 12/15/2017 ‐‐ Page 1 of 6 PATENTS PENDING, PROVISIONAL APPLICATIONS FILED our prediction procedures so that our prediction as the bullet slows and thus give a reliable matches the measured behavior of our bullet indication of the drag. It is an excellent system fired from our gun. favored by the government proving grounds. The primary drawback of the Doppler system is its This all sounds easy in theory. We can glibly talk cost. Doppler radars capable of measuring about “downrange behavior” without defining it velocities near the muzzle are relatively and without describing how to measure it. Most inexpensive, but those systems capable of reliably often we are talking about a drag function tracking rifle bullets over thousands of yards are describing how fast a bullet slows down after it very expensive. While Doppler systems can has already slowed to a particular velocity. We provide very detailed data, such data comes at usually assume that either G1 or G7 exactly the expense of much post‐processing and is often describes our “family” of bullets and then we restricted to a few shots. measure bullet drag near the muzzle to determine a ballistic coefficient to indicate The down‐range performance can be checked by which curve of the family fits our bullet. Using observing bullet drop for targets at long ranges. this ballistic coefficient that fits near the gun, Measurement of drop at long ranges is not easy; our muzzle velocity and atmospheric conditions, it is subject to the errors of visual scoring, wind we predict the bullet’s behavior over the entire conditions, range estimation and the ever‐present range. After all these years of trying, nobody aiming and holding uncertainties. The observed has found the perfect prediction. When the drop is compared to predicted drop and either prediction is tested by actual long range firing, the ballistic coefficient or muzzle velocity is the results usually don’t exactly match the adjusted so that predicted drop equals the prediction. observed drop. This procedure has been demonstrated to significantly improve the In order to make good predictions, we must predictions, and is referred to as truing. measure downrange behavior. Traditionally, ballisticians think in terms of drag or velocity The choice of truing the ballistic coefficient or loss. We know that the bullet’s drag plotted as truing muzzle velocity is left to the user. Most a function of velocity is an excellent measure of agree on two points: downrange behavior. Drag is extremely difficult 1. Truing MV or Truing BC provide similar to measure. To measure drag or deceleration results at the range tested. you must find velocity lost. To measure velocity lost, you must measure two velocities and 2. You should true the variable whose data subtract. Because both velocities are very large is most suspect. compared to the loss, a tiny percentage error in The Oehler System 88 takes a different tack; it either velocity measurement will result in a accurately measures the muzzle velocity and then large percentage error in the loss or drag. trues the BC. This provides a better prediction at all ranges, including the tested range. A Doppler radar inherently provides an output signal with a frequency proportional to the One downrange parameter can be measured velocity of the bullet. This is one step closer to accurately. We can now accurately and reliably the drag or velocity loss sought by the measure the time‐of‐flight (TOF) to a distant ballistician. The Doppler signal can be target. Muzzle velocity can be measured processed to indicate the change in frequency accurately. Given a muzzle velocity, distance to Extended Range Truing, Why and How ‐‐ Ken Oehler ‐‐ 12/15/2017 ‐‐ Page 2 of 6 PATENTS PENDING, PROVISIONAL APPLICATIONS FILED target and TOF you have effectively defined drag function, you will see a family of similar down‐range behavior. Given a drag function curves, all start with the same slope, but only one and the actual measurements, you can curve passes through the true downrange point determine a ballistic coefficient that forces a observed during the test. The ballistic coefficient match between measured and predicted TOF to of the one curve passing through the downrange a distant target. Prediction and results are trued distance/TOF point provides proper predictions. at the long range of the target. Using this You have found a ballistic coefficient based on the measured (or trued) ballistic coefficient, we can cumulative effect of the drag applied over the accurately interpolate ballistic behavior at long distance instead of the drag at one velocity. intermediate ranges. Repeat the process with a different drag function but with the same initial velocity and TOF. If you choose a test distance near the commonly Compare the curves passing through the accepted maximum range corresponding to a downrange point; they are almost identical and remaining velocity of approximately Mach 1.2, yield similar predictions for drop and windage. you have effectively trued for the most useful ranges. It matters little which of the Gx drag Truing over the common supersonic range is functions is chosen; an appropriate ballistic straightforward. This range includes practically all coefficient can be found that forces a fit ranges commonly used by most riflemen. What between measured and predicted TOF at the happens if we measure TOF at a range where the test distance. More important, you can use any bullet had dropped well subsonic? We now must of the drag functions to compute drop and wind account for significant differences in the drift at intermediate ranges and the predictions commonly accepted drag functions at velocities typically agree with each other within 0.1 mil. near the speed of sound. A prediction curve that Having started with the true muzzle velocity and passes through the first distance/time point will measured TOF over the long distance, we see pass through the subsonic point only if we are that the measured muzzle velocity and TOF extremely lucky. We are seldom so lucky that our (along with atmospheric data) define the chosen drag function exactly describes our bullet.
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