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Long Range Accuracy Starts With Measured Time of Flight

Why the key to long range prediction is measuring time of flight, not picking a drag function.

Source: Long Range or Long Time?
Dr. Ken Oehler
About 5 min
Advanced

Time of flight measurement setup — Measuring how long the bullet takes to reach the far target is where the whole chain of reasoning starts.

In short

Dr. Ken Oehler, founder of Oehler Research, argues that long range ballistic prediction turns on measuring time of flight rather than on choosing the right drag function. Parameters such as drop and wind drift are governed mainly by muzzle velocity and time of flight. Take three values, the muzzle velocity, a distance close to the practical maximum range, and the measured time of flight over that distance, and the average ballistic coefficient derived from them will give correct drop and wind drift at that range, while the choice of drag curve matters very little. The difficulty is that the timing interval starts at the muzzle and ends at a distant target, so it can only be captured with a hard wire or a dedicated radio link. The Oehler System 88 was built for exactly that. It delivers information that used to require precision Doppler radar, at a fraction of the initial cost, and it is operated by one person, carried on foot, and independent of mains power.

Drop and wind drift depend mainly on muzzle velocity and time of flight
Force the fit to a far measured point and the drag function matters little
Velocity and distance are easy to measure; time of flight is the hard one
Ballistic coefficient depends on the barrel as well as the bullet
System 88 takes over the Doppler radar role at a fraction of the cost

What is missing is input, not math

For first round hits at long range, the bottleneck is rarely the solver. The industry has discussed ballistic computation, and which drag function to adopt, at great length. What has been missing is a simple way to describe how one particular round actually behaves at a distance close to its practical maximum range.

Oehler dates his position on long range measuring equipment to a 2011 meeting with Pete Gould. He wrote the idea up for that discussion, and what followed is the measurement approach described here.

Drop and wind drift are mostly functions of velocity and time

McCoy and others established long ago that ballistic parameters such as drop and wind drift are mainly functions of muzzle velocity and time of flight. Over the part of the flight where the bullet still retains a significant fraction of its muzzle velocity, those parameters are relatively insensitive to which drag function was used.

The practical consequence is large. Rather than argue about which drag curve to pick, measure the time of flight.

Distance against time plot: a drag free constant velocity line reaches 1000 yards at 1.00 second, the real trajectory needs 1.50 seconds, the 0.50 second difference is marked as lag time and converted to wind drift below — **Figure 1** Wind drift follows how late the bullet is, not how far it has flown: a 10 mph crosswind times 0.50 seconds of lag time is about 88 inches of drift at 1000 yards.

Three measurements pin down one round

Oehler describes the flight of a round with three measured values: muzzle velocity, a distance close to the practical maximum range, and the time the bullet takes to cover that distance. The average ballistic coefficient (BC) derived from those three values gives correct drop and wind drift at that stated range.

The key is the forced fit. Because the fit is constrained to agree exactly at the stated distance, the predictions at intermediate distances come out very close as well, so the choice of drag function has little effect.

That guarantee has a boundary. Extrapolate past the measured distance and the result depends on the drag function again. At that point the function that best matches the real drag behavior of that bullet gives the better extrapolation.

Why time of flight is so hard to measure

Muzzle velocity is easy: a chronograph does it. Distance is easy: a laser rangefinder does it. The hard measurement is time of flight, because the timing interval starts at the muzzle and ends far downrange at the target. Tying the two ends to one time base means running a hard wire or using a dedicated radio link.

That is why this measurement stayed theoretical for so long. Nobody doubted it mattered; it simply could not be done on the range.

Range layout: a skyscreen at the muzzle provides the start signal and an acoustic target 1000 yards away provides the stop signal, with the two ends tied into one time base by hard wire or a dedicated radio link — **Figure 2** Muzzle velocity and distance can both be measured beside the shooter, but time of flight requires the stop signal from 1000 yards away to reach the timer at the muzzle. That is the real reason it stayed theoretical for so long.

Where it sits next to Doppler radar

Equivalent information used to require a precision Doppler radar system. The position of System 88 is clear: the initial purchase cost is a fraction of a Doppler system, one operator is enough, the shooting cadence is faster so statistically meaningful sample sizes are easier to accumulate, and the system can be carried by one person and does not depend on a power supply.

After 2011 System 88 was developed and put into service, and field testing has confirmed the principles set out at the time.

What long range time of flight buys you

Measuring time of flight at long range gives you three things. First, accurate drop prediction without relying on a particular drag function or on the ballistic coefficient a manufacturer publishes. Second, a view of how consistent the ballistic coefficient is at long range. Third, confirmation that the ballistic coefficient depends on both the bullet and the barrel.

Oehler does not claim to have discovered that time of flight matters. Newton saw it three centuries ago. What his team did was make the measurement practical. His analogy: shooting without a long range time measurement is like bore sighting a rifle and never actually zeroing it on a target.

Glossary

Ballistic coefficient (BC): The coefficient that relates a real bullet to the chosen drag function. A BC is only meaningful when quoted together with the drag function it was derived against.
Drag function: A curve describing the drag behavior of a standard projectile. A ballistic solver uses it as the reference from which the flight of a real bullet is computed.
Time of flight (ToF): The time a bullet takes to travel from the muzzle to a target at a stated distance. It starts at the muzzle and ends far downrange, which makes it the hardest of the three parameters to measure.
Average ballistic coefficient: The ballistic coefficient derived from muzzle velocity, a stated distance and the measured time of flight over that distance. It gives correct drop and wind drift at that distance.

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

Read Original Oehler Research PDF