Ballistic figures

The figures printed beside a trajectory: the effective range, and the energy, momentum, knock-out factor, sectional density, relative stopping power and energy density at the muzzle. How each is worked out, and which inputs a record may not hold.

Effective range

The effective range is the furthest distance at which all three of these still hold. The solver steps the flight one metre at a time, out to 3,000 m, and stops at the first metre where any of them fails.

\frac{E_{x}}{A} \geq 80 J / {cm}^{2}

v_{x} \geq 1.2 a \approx 408 m / s

D_{bore} (x) \leq 200 cm

The second condition applies only to a load that leaves the muzzle faster than 1.2 times the speed of sound: a subsonic pistol load is never held to it. The air is the standard atmosphere the trajectory uses, and the drop is the fall from the bore line, not the path from a zeroed sight, so the range does not move with the zero chosen for the curve.

The three thresholds are conventions GunSpec sets, not figures quoted from a standard: an energy density below which a bullet is taken to have stopped doing useful work, a margin above the speed of sound where a bullet's flight is still stable, and a drop beyond which a shooter holding over is guessing. They are printed here so a reader can apply their own. The effective range a record states, where it states one, is the source's figure and is shown as such.

The figures at the muzzle

Five figures describe the bullet as it leaves the barrel, each from the load's bullet mass, its muzzle velocity from this gun's barrel, and its bullet diameter. They are comparisons between loads, not predictions of what a bullet does in a target.

E = \frac{1}{2} m v^{2}, p = m v

TKO = \frac{m_{gr} v_{fps} d_{in}}{7000}

SD = \frac{m_{lb}}{{d_{in}}^{2}}

RSP = E_{ft·lbf} \times π {(\frac{d_{in}}{2})}^{2} \times f

\frac{E}{A}, A = π {(\frac{d}{2})}^{2}

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$m, v, d$: The bullet's mass, its velocity and its diameter; a subscript names the unit a formula is defined in (grains, feet per second, inches, pounds, foot pounds).
$f$: Hatcher's form factor for the bullet's type, from the table below.

Form factor by bullet type. A type not listed takes 0.90.
Bullet type	Form factor
FMJ	0.90
JHP	1.00
AP	0.90
OTM	0.90
EPR	0.95
Tracer	0.85
SP	1.00
HP	1.00
FlexLock	1.05
SBT	0.90
Polymer Tip	0.95

The knock-out factor and the stopping power are long-standing comparisons from the hunting and handgun literature, kept because readers ask for them. Neither is a measure of wounding, and neither should be read as one.

What a record may not hold

Every figure on this page needs inputs a load record does not always state. Where one is missing the solver uses the fallback below, and a figure built on a fallback is rougher than one built on the record.

Bullet diameter: the cartridge record's bullet diameter. Where the cartridge states none, a short table of common cartridges, and where the cartridge is not in it, 7.62 mm. Every figure here that divides by an area rests on it.
Drag: the load's G7 ballistic coefficient, then its G1. A load with neither is flown with a flat drag coefficient of 0.3 rather than a drag table, which misses the rise in drag near the speed of sound, so its curve and its effective range are approximate.
Bullet type: the form factor for Hatcher's figure. An unlisted type takes 0.90.
Velocity: the load's reference velocity from its reference barrel, scaled to this gun's barrel by the power law on the Trajectory page. A load with no retention exponent of its own takes 0.30.

Worked example: a Glock 17 with M882

M882 ball, 8.04 g, from a Glock 17's 114 mm barrel: 359 m/s and 517 J at the muzzle, a 9.01 mm bullet from the 9x19mm record, full metal jacket.

Figure	Value
Effective range	185 m
Momentum	2.88 kg·m/s
Taylor knock-out factor	7.4
Sectional density	0.141 lb/in²
Relative stopping power	34
Energy density at the muzzle	811.1 J/cm²

Every value in the table is the API's own function run on the record's figures as the page loads, so it is the value the ballistics answer returns for this load and this barrel. M882 leaves the muzzle below 1.2 times the speed of sound, so its effective range is set by energy density and drop alone.