Drag Model

Drag dominates an exterior ballistics trajectory. Everything else in the model, gravity, wind, Coriolis, spin corrections, bends the path; drag sets how fast the bullet bleeds energy and where it stops. So the question that matters most is not which forces lob models but how it represents the one that matters most.

lob's answer: a projectile's drag is a curve of drag coefficient against Mach number, resampled once onto a small set of smooth spline knots and evaluated as arithmetic. Every path that supplies a drag curve, whether it is a published standard or your own measurements, ends up in that same representation, and the solver only ever sees the spline.

What a drag curve means

The curve answers: at this speed, how much does the bullet slow down? Speed is expressed as Mach number rather than raw velocity, because what resists the bullet is the difference between its speed and the speed of sound in the surrounding air, and that dividing line moves with altitude and temperature. A curve is therefore a statement about a projectile flying through air, independent of the conditions that air happens to be in.

The published standard curves lob ships, G1 through G8, come from Ballistic Research Laboratory drag studies. They are broadly similar bullet shapes, measured and published through JBM Ballistics. The distinction between them is mostly nose shape and boat tail, and the practical difference shows up in how much each one loses energy through the transonic region.

Four ways to describe a bullet's drag

A standard curve, scaled by ballistic coefficient. The common case: pick G1 or G7, then say how much of it applies to your bullet with a ballistic coefficient. The curve's shape does the work and the coefficient scales it, which is why a single number can stand in for a whole measured table. A coefficient only makes sense relative to an atmosphere convention, so lob converts it between the Army Standard Metro and ICAO references internally, so the same number always means the same thing to the solver.

Your own Mach versus drag table. If you have measured data, or a manufacturer published one, you can supply the curve directly. lob fits it onto the same spline knots the standard curves use, so a custom table costs nothing at solve time beyond the fact that it was fitted at build time. The table must be ordered by increasing Mach and cannot report negative drag. If it does not span the full Mach range, the spline extrapolates smoothly past the ends rather than clamping, on the understanding that you told us the shape of your data; extrapolation that would imply a negative drag coefficient is rejected instead of quietly believed. Pad the table with explicit entries at the ends if you want to define the edge behavior yourself.

Ballistic coefficients measured at several velocities. Real bullets are not G1-shaped at every speed. Manufacturers publish drag coefficients measured at a handful of velocities, and the true curve is narrower than any standard curve, which is exactly the regime where long-range accuracy is won or lost. lob transforms those bands into a form-factor curve and blends it with the standard curve you selected, giving a projectile-specific drag function instead of a scaled standard one. The transformation is worth understanding on its own, and it is covered in the ballistic coefficient chapter.

Raw spline coefficients. An escape hatch for the cases the others do not fit: round-tripping a context between lob instances, or importing coefficients computed elsewhere. It sets the curve directly and skips both table fitting and coefficient scaling, which means the ballistic coefficient and atmosphere settings stop mattering to anything. Reach for it when you already hold the answer.

How the solver uses the curve

At every step of the trajectory integration, the solver evaluates the curve at the projectile's current Mach number and scales it by the local air density. Two things follow from how that works.

Mach is recomputed each step from the projectile's speed and the local speed of sound, so a bullet climbing through changing air is corrected as it goes rather than being evaluated once against fixed conditions. Relatedly, there are two variants of the step: one holds the density and speed of sound at the firing site, and the other recomputes both per step for shots that climb far enough to care. Which one the inverse solver picks is a speed-versus-fidelity tradeoff; they are not guaranteed to agree when altitude-dependent drag or speed-of-sound corrections are nonzero, and any agreement claim is limited to conditions where those corrections do not affect the result.

Evaluation happens outside the curve's defined Mach domain by holding the edge value. The standard curves are defined across a range that covers everything from subsonic through supersonic flight, and a trajectory that never leaves that range never hits the clamp.

Drag tables are resampled onto their spline knots once, at build time, and the standard curves are projected at compile time, so the solver pays only for evaluating a short polynomial. Evaluating a drag curve is one of the most frequent operations in the whole solver, which is why that evaluation is a handful of arithmetic operations rather than a table search.