Ballistic Coefficient

A ballistic coefficient is the single number that stands in for a projectile's entire drag curve. It says how much drag a bullet suffers compared to a standard reference projectile, and dividing a standard curve by it produces that bullet's curve:

Cd_bullet(M) = Cd_std(M) / BC(M)

A larger coefficient means a slipperier bullet and less drag. That one number carries a surprising amount of information, which is why ballistic coefficient is the primary unit that the long-range literature, the manufacturers, and shooters all exchange.

It works as a summary because the dominant influence on drag is the bullet's shape relative to its frontal area, and for bullets of similar shape that ratio varies only modestly with speed. lob expresses coefficients in pounds-mass per square inch, the customary American unit, and internally performs the division by folding it into the drag curve's own representation. The solver is therefore never aware that a ballistic coefficient exists: it evaluates one curve and that is all.

Standard curves

The coefficient only means something relative to a reference projectile, and lob ships the standard references that the literature uses: the G series, a set of reference projectiles spanning blunt and streamlined shapes, tabulated by the Ballistic Research Laboratory and published through JBM Ballistics. G1 is a flat-base projectile with a short ogival nose, and it is the default because it is the most widely assumed when nothing else is specified. G7 is a long boat-tail reference with a long ogive, and it is what long-range rifle shooters usually want, because a modern match bullet resembles it far more closely than it resembles G1. The others cover projectiles that sit between those two.

Choosing the reference is not the same as describing your bullet. The reference sets the shape of the curve; the coefficient sets the scale. A shooter who knows only a coefficient is implicitly saying "my bullet has this shape and is this slippery relative to it."

One coefficient, or several

Using a single coefficient for the whole flight assumes the bullet's shape relative to the reference is the same at every speed. For many bullets that assumption holds well enough, and a single coefficient is the whole interface: one number, one standard curve, done.

Real bullets are less obliging. The shock structure around the nose and the flow off the base both change as the bullet accelerates, so the ratio to the reference is not constant, and a single coefficient is a compromise that is wrong at both ends even when it is right somewhere in the middle. The mismatch is worst for the modern high-performance bullets that long-range shooting cares most about.

This is why manufacturers increasingly publish a coefficient at several velocities rather than one. It is also why lob accepts them directly. Given coefficients at a handful of speeds, it builds the smooth curve those measurements describe, rather than forcing the caller to pick one and live with the error.

The obvious way to use several coefficients would be to switch between them discretely as the bullet passes each measured speed. lob does not, because a discontinuity in the drag curve is a discontinuity in the trajectory and in its derivative, and a solver that never sees a kink is a solver that does not have to special-case one. Instead the measurements are interpolated into a smooth curve first, and that curve is what the bullet actually flies. The method is the subject of BC/Velocity-Band Transformation.

Ballistic Coefficient

Standard curves

One coefficient, or several

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