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The Missing Link: Where Does Your Ballistic Coefficient Come From?

Every ballistics program asks you for muzzle velocity and a ballistic coefficient. None of them tells you where to get either one.

Source: System 88, The Missing Link
Dr. Ken Oehler
About 6 min
Advanced

Muzzle velocity and time of flight measurement setup — Velocity is measured at the muzzle and time of flight at the target. The ballistic coefficient is solved backwards from those two measurements.

In short

Given the same inputs, every reputable exterior ballistics program returns the same answer. All of them ask the user for a muzzle velocity and a ballistic coefficient (BC), and none of them says where those two numbers should come from. Dr. Ken Oehler calls this the missing link. A BC quoted to three decimal places does not carry three digits of accuracy: BC itself is hard to measure better than a few percent, lot to lot variation can run several percent, it is affected by rifle characteristics such as barrel twist and crown, and most published values are measured within a few hundred yards of the muzzle. The Oehler System 88 works the other way round. It measures muzzle velocity and long range time of flight, then solves for the ballistic coefficient that makes the predicted time of flight equal the measured time of flight. Because the fit is forced to agree at both the muzzle and the distant target, the distance against time curves for G1 and G7 nearly coincide. What matters is the far measured point.

Every ballistics program needs a BC and none tells you where to get one
A BC printed to three decimals is not accurate to three digits
BC varies with lot, barrel twist and muzzle crown
System 88 solves for BC from measured time of flight
The far measured point matters more than the choice of drag function

Three things you learn from long use

Anyone who has used exterior ballistics programs for long enough tends to arrive at three conclusions. First, given the same inputs, every reputable program produces the same answer. Second, all of them ask you for a muzzle velocity and a ballistic coefficient (BC). Third, not one of them tells you where those two numbers are supposed to come from.

Oehler calls the third point the missing link. Over the past century the methods ballisticians use for downrange prediction have not changed much. The computer replaced the hand work of looking up Siacci tables, which made the computation faster and easier, but it did nothing about where the input data comes from.

The three required inputs

A downrange ballistic prediction needs three inputs: a known muzzle velocity as the starting point, a drag function that suits the bullet, and a ballistic coefficient relating that bullet to that drag function. The program itself handles the differences in air density and speed of sound caused by pressure, temperature and humidity.

Of the three, muzzle velocity is the simple one. A chronograph measures the actual velocity of this lot of ammunition from this rifle.

Flow chart of the three inputs to a ballistic solution: muzzle velocity can be measured and a drag function can be chosen, while the ballistic coefficient alone is drawn with a dashed line as having no source, with the reasons published ballistic coefficients are unreliable listed below — **Figure 1** Muzzle velocity and drag function both have a stated source. The ballistic coefficient does not. That three decimal number on the box carries neither three digits of accuracy nor any note of which rifle and which distance produced it.

G1 or G7 is not the real question

Choosing a drag function is less difficult than it is made out to be. G1 is in general use and most manufacturers publish their ballistic coefficients against it, and G1 works perfectly well at intermediate range, say 400 to 800 yards. In recent years it has become clearer that G7 fits streamlined bullets designed for long range better, and usually predicts better through the transonic region.

Both share one condition. Paired with the correct ballistic coefficient, G1 and G7 both give reasonable predictions until velocity falls into the transonic region, typically taken as Mach 1.2, about 1350 feet per second. There is no one drag function that fits everything; G7 is simply closer to modern bullets.

The ballistic coefficient is the unreliable input

Shooters are used to seeing a BC printed to three decimal places, and naturally assume it is good to three significant digits. In reality the ballistic coefficient is hard to measure better than a few percent, different lots of the same product can differ by several percent, and BC is affected by barrel twist, muzzle crown and other rifle characteristics.

The measuring distance matters even more. Most ballistic coefficients in circulation are measured within a few hundred yards of the muzzle and then extrapolated downrange using the chosen drag function. Oehler puts it bluntly: a coach cannot predict marathon performance from a sprint time, and using a short range test to predict long range behavior is no more reliable.

The irony is that many shooters who would never enter a catalog or reloading manual velocity as their muzzle velocity will treat a published three decimal ballistic coefficient as a sacred constant.

Solve backwards: force theory and measurement to agree at both ends

System 88 runs the process in reverse. Normally you give the program a muzzle velocity and a ballistic coefficient and it computes a time of flight. System 88 measures long range time of flight and muzzle velocity, and its built in program solves backwards for the one ballistic coefficient that makes the predicted time of flight exactly equal the measured time of flight.

The user can pick any of the common drag functions, or define one. For any drag function, System 88 finds the ballistic coefficient that fits both the long range measurement and the muzzle velocity. Change the drag function and it again forces theory and measurement to agree at the muzzle and at the distant target.

Plot it as distance against time and this becomes obvious. The curve starts at zero time and zero distance, its initial slope is the muzzle velocity, and its end point is the measured time of flight. Overlay the curves produced by different drag functions and they nearly coincide. In other words the fit to that one far measured point matters far more than the choice of drag function. G1 and G7 serve equally well short of the transonic region, provided you have actually measured the long range time of flight.

Distance against time curves whose initial slope equals the measured muzzle velocity and whose end point passes through the measured time of flight at 1000 yards, with the G1 and G7 curves almost perfectly coincident — **Figure 2** Once the origin is locked by measured muzzle velocity and the end point by measured time of flight, switching between G1 and G7 makes almost no visible difference. Accuracy is decided by that far measured point.

A measurement system built for field work

System 88 is set up for professional field use. It runs on batteries, so it works at remote ranges with no power supply. Setup is quick and simple. The wireless link is verified to one mile. One person can operate it, and results are available within seconds of the shot.

At the muzzle it uses the proven Oehler skyscreen. Downrange it uses a ruggedized microphone, with square, fly-by and fly-over acoustic targets available. A single shot can yield several targets and several ballistic coefficients, and an impact target can be added to measure subsonic time of flight. Data exports to Excel and PDF, and Oehler provides technical support.

Glossary

Drag function: A curve describing the drag behavior of a standard projectile. G1 and G7 are the common ones: G1 is the most widely applied, while G7 is closer to the streamlined bullets used at long range.
Ballistic coefficient (BC): The coefficient that relates a real bullet to the chosen drag function. It is hard to measure better than a few percent and is affected by lot variation and by the characteristics of the rifle.
Transonic: The region where bullet velocity approaches the speed of sound, with the boundary typically taken as Mach 1.2, about 1350 feet per second. Past this region the differences between drag functions start to show.
Skyscreen: An optical sensor that detects the bullet passing against the sky as its background, used to obtain an accurate muzzle velocity at the firing point.
Time of flight (ToF): The time a bullet takes to travel from the muzzle to a target at a stated distance. It is the measured basis from which System 88 solves for the ballistic coefficient.

This article is Evencat's write-up of the technical paper "System 88, The Missing Link" by Dr. Ken Oehler. The argument belongs to the original author; where figures or conclusions differ, the original governs.

Read Original Oehler Research PDF