SYSTEM AND METHOD FOR LONG-RANGE BALLISTIC CALCULATION

Abstract

A system for predicting exterior ballistics has first and second bullet detectors operable to detect the passage of a bullet, the first and second bullet detectors being spaced apart by a selected detector spacing distance, the first and second bullet detector each being connected to a common time signal facility that generates a time signal, the first bullet detector being operable to generate a first time of passage based on the time signal, the second bullet detector being operable to generate a second time of passage based on the time signal, the first bullet detector being operable to measure a first bullet velocity, a controller in communication with the first and second bullet detectors, and the controller operable based on the difference between the first time and the second time, and based on the first bullet velocity to calculate a ballistic characteristic for the bullet.

Claims

1. (canceled)

2. A method of ballistic measurement comprising: providing a velocity measuring instrument; positioning the velocity measuring instrument proximate a firearm operable to propel a projectile; providing a flight duration sensor system; providing a controller operably connected to the velocity measuring instrument and to the flight duration sensor system; propelling a projectile having an estimated ballistic characteristic value; operating the velocity measuring instrument to determine a measured velocity of the projectile; operating the flight duration sensor system to determine a measured time of flight between a first position and a second position; operating the controller based on the estimated ballistic characteristic value and the measured velocity to calculate an estimated time of flight; operating the controller to calculate an adjustment function of the measured the time of flight and the estimated time of flight; and operating the controller based on the function and the estimated ballistic characteristic value to determine a calculated ballistic characteristic value.

3. The method of claim 2 wherein the ballistic characteristic value is a ballistic coefficient.

4. The method of claim 2 wherein the flight duration sensor system generates a time signal that is a global positioning satellite signal.

5. The method of claim 2 further including the step of based on the calculated ballistic characteristic value, predicting the flight characteristics of a second projectile.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 shows the shows the elementary relationship between distance and time.

[0014] FIG. 2 shows the distance-versus-time curves for three bullets.

[0015] FIG. 3 shows similar curves using G7 predictions instead of G1 predictions.

[0016] FIG. 4 shows the G1 and G7 based predictions for drop and wind, which agree within 0.05 mils out to 1000 yards.

[0017] FIG. 5 shows the blue G1 curve is obscured by the red G7 curve out to approximately 1500 yards.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0018] For this discussion we assume that the initial velocity of the bullet can be accurately measured with a chronograph or other means and that the effects of the air density and the speed of sound in air are well known and accurately reflected in ballistic calculations.

[0019] The essential element of this invention requires an extension of the customary definition of ballistic coefficient. Ballistic coefficient is customarily defined as the drag of the theoretical projectile divided by the drag of the tested bullet at a specified velocity. When combined with the classical ballistic equations, this definition provides an accurate prediction of time-of-flight over the typical range (say 100 to 300 yards). We extend the definition to state that the extended ballistic coefficient is that value which yields a correct prediction of time-of-flight measured over a much longer range.

[0020] Extending the definition of ballistic coefficient in this way changes the function of legacy procedures from the extrapolation of short range data to the interpolation of long range data. The legacy procedure is forced to fit experimental data at long range to determine the extended ballistic coefficient. The legacy procedure is then used with the extended ballistic coefficient to interpolate the behavior at intermediate ranges. Customary use of the legacy procedure uses short-range measurements to extrapolate long range behavior. If the time-of-flight is measured over a short range, say 300 yards or less, then the extended ballistic coefficient converges back to the customary value. The Model 43 system was designed to operate in this region. At this time the universal applicability of the G1 drag function was accepted as “settled science”.

[0021] The extended procedure provides for prediction of behavior at a continuum of ranges from gun the maximum test range. The procedure requires increasing the test range for each step instead of simply testing over additional but separate shorter ranges. This assures forced fit of prediction to reality at multiple ranges.

[0022] Now consider the relationship between time and distance. FIG. 1 shows the elementary relationship between distance and time. If we start at 3000 feet per second and have no air drag, we reach 1000 yards in exactly 1 second. The relationship between time and distance is simple and constant. We have a straight line. Add air drag to the problem. At each instant in time the bullet slows an amount dictated by its velocity at the time and the assumed drag function. An extremely high ballistic coefficient coupled with thin air may get close to the straight-line plot, but we still must contend with the air drag.

[0023] Here are the distance-versus-time curves for three bullets. All have a muzzle velocity of 3000 feet per second. The thin black line at the top shows no air drag. The lower curves are those predicted using the common G1 drag function with ballistic coefficients of 0.750, 0.500 and 0.375. The green curve from the 0.750 BC is closest to the straight line, and the curves get progressively farther from the line as the BC diminishes. There is much discussion of G1 versus G7. G1 is customary and G7 is advocated as being a notch closer to perfection. You expect to see a difference. FIG. 3 shows similar curves using G7 predictions instead of G1 predictions.

[0024] The curves for G1 and G7 appear practically identical to 800 yards. We have shown only three curves of each drag function family, each corresponding to a unique ballistic coefficient. Within each family are thousands of curves corresponding to different initial velocities and ballistic coefficients.

[0025] How do we choose a curve that accurately predicts the behavior of our bullet fired from our gun? Time-of-flight is most important, but we must place our distant target at a specific place or range. Because we are confident shooting to maximum ranges where the bullet remains supersonic, we place our target to include that maximum range. It is often practical to set our target near the range where we expect the remaining velocity to be near Mach 1.2 or 1350 fps.

[0026] With no air drag, our sample bullet starting at 3000 fps takes exactly 1 second to travel 1000 yards. Assume that the air drag slows the bullet so that it actually takes 1.500 seconds to travel 1000 yards. That gives a data point on our picture of distance-versus-time. If we look at curves from the G1 drag function including a muzzle velocity of 3000 fps, we find that one curve with an extended ballistic coefficient C1=0.471 passes through the downrange data point where the time is 1.500 seconds at the range of 1000 yards. Eureka! We've found a predicted curve that exactly fits the bullets behavior at the long range.

[0027] Using the same muzzle velocity and time-of-flight, we find a curve from the G7 family with ballistic coefficient C7=0.238 also passes through the downrange point. We anticipate trouble because we have two solutions for the same problem. Which solution should is correct? Plot both curves.

[0028] The blue BC1 line remains perfectly hidden behind the red BC7 line out well past 1000 yards or 1.5 seconds. It makes no practical difference if you choose to use G1 or G7 out to 1000 yards if you have accurately trued at 1000 yards. If you first measure both muzzle velocity and the time-of-flight, then your prediction is trued when you determine the ballistic coefficient that causes the curve to pass through the long-range true point. Comparing the G1 and G7 based predictions for drop and wind, you will find that they agree within 0.05 mils out to 1000 yards.

[0029] There are slight differences beyond 1000 yards. For many years, Sierra and others have provided ballistic coefficient values “stepped” as a function of velocity. At some velocities the measured drag of the bullet differs from the drag predicted by the G1 function and the ballistic coefficient is adjusted in steps to reflect this misfit. This procedure is well proven. Sierra's stepped ballistic coefficients are typically provided only for supersonic velocities where variations in ballistic coefficient are relatively small. Tests indicate that the stepped procedure remains applicable over longer distances when the steps are properly chosen.

[0030] We have shown how to determine an extended ballistic coefficient for accurate predictions down to Mach 1.2 using the legacy ballistic procedures but substituting an extended ballistic coefficient. To include ranges where the bullet becomes subsonic, fire a second test at a range where the bullet has dropped well subsonic. Using a ballistics program allowing for stepped ballistic coefficients, enter the extended ballistic coefficient for the first range. Enter the observed target velocity (computed from muzzle velocity, distance and time-of-flight from your first test) as the lower limit of the range. Adjust the extended ballistic coefficient of the next step until the total predicted time-of-flight matches the observed time-of-flight. This gives a set of two extended ballistic coefficients meeting the requirement of passing through both the experimental points of the distance versus time curve. These stepped ballistic coefficients may look rough, but they yield accurate (typically within 0.1 mil) predictions of drop and windage at ranges from muzzle to the subsonic target point.

[0031] Let's continue looking at our curves. If we assume that the bullet fired actually behaved like a G7 bullet, then it would have a time-of-flight of 2.57823 seconds at 1400 yards and its extended C7 ballistic coefficient would remain BC7=0.238. If we choose to work using G1, we must adjust the extended G1 ballistic coefficient to BC1=0.331 at velocities below 1350 fps.

[0032] After adding the stepped change in the extended G1 ballistic coefficient, the blue G1 curve is obscured by the red G7 curve out to approximately 1500 yards. If you want your predictions to reliably extend to even longer ranges, then you must test at longer ranges and add the additional trued steps to your ballistic coefficients.

[0033] This procedure is automated in the Extended Range Truing program included with the Oehler System 88. The Extended Range Truing program requires inputs of initial velocity, distance to target, time-of-flight, and atmospheric conditions. The Oehler System 88 measures the initial velocities and times-of-flight, and includes provision to record the other parameters. The program output suggests extended ballistic coefficients for up to five velocity ranges and includes the values of the step points. The user can select the drag function to be used. (Remaining velocities must have been estimated prior to tests and targets placed as convenient to fit the estimates. Estimates need only be reasonable, but the actual test range must be recorded precisely.) As inputs to the Extended Range Truing program, we suggest using the mean values for muzzle velocity and time-of-flight obtained during tests of a bullet. For indication of stability in the transonic region, we suggest examination of the extended ballistic coefficients indicated for each bullet at the transonic step. Large variations may indicate instabilities.

[0034] What has been demonstrated is a greatly improved version of “truing” where the prediction procedure is forced to match actual long-range results. You cannot predict drag functions or ballistic coefficients from published data any more than you can predict muzzle velocity from factory specs or reloading books. They will all vary from rifle to rifle, and you must true with your gun and your ammo. Application of this procedure forces your predictions to match your results at long range and at all instrumented intermediate points. This procedure eliminates uncertainties due to visual drop estimations, wind induced errors, hold errors, and the use of too-few shots.

[0035] This procedure can use any reasonable drag function. If you are comfortable with G1, and your computer handles stepped G1 ballistic coefficients, then you can use G1 with no significant loss in accuracy. If your computer handles custom drag functions or radar drag functions, use the procedure with your favored drag function. Adjust or “true” your extended ballistic coefficient so that your predictions match measured long-range times-of-flight. (In the case of Hornady's 4DOF program, adjust the axial form factor to provide a match between observed and predicted time-of-flight at the maximum range.)

[0036] The output parameters are not unique. They form an excellent approximation on which to base predictions. You may obtain different ballistic coefficients and velocity ranges depending on exact range to test target and desired drag function.

[0037] Things get difficult in ballistics when you must relate time to distance. By shooting and actually measuring time-of-flight to a distant range, you have measured “truth” at one or more points. By adjusting your prediction method until your prediction matches reality, you have trued the relationship and found the extended ballistic coefficient. It is important to note that there may be multiple points of truth along the distance versus time curve. The method outlined forces the predictions to match reality at all of the measured points. The number of test points can be increased to provide the required accuracy.