Exterior ballistics · G1 drag model
What actually happens after the muzzle.
Muzzle energy is one multiplication and it describes the first inch of flight. Past that, a light fast bullet and a heavy slow one stop behaving alike, and which one is ahead depends on how far away you are. Pick some loads and the curves will show you where they cross.
The arithmetic, in full
Nothing on this page is a lookup table. Every number comes out of these.
Muzzle energy
Kinetic energy in foot-pounds. The constant is 2 × 7000 × 32.174, converting grains to pounds and pounds to slugs, so weight can go in as grains and velocity as fps.
- m
- bullet weight, grains
- v
- velocity, fps
Momentum
Pound-seconds. Scales with velocity rather than its square, which is why heavy slow bullets rank differently here than they do on energy. Both are real quantities; neither settles an argument about terminal effect.
Sectional density
Weight against frontal area. A rough index of how well a bullet resists being stopped, independent of how fast it is going.
- d
- bullet diameter, inches
Drag deceleration
The one that matters. Derived from F = ½ρv2CdA with A = πd2/4; substituting BC = m/(i·d2) and Cd = i·Cd,G1 cancels the form factor and leaves the constant above.
- Cd(M)
- G1 drag, looked up by Mach
- BC
- ballistic coefficient, lb/in²
- ρ/ρ0
- air density vs sea level
Air density ratio
Standard atmosphere by altitude, corrected for actual temperature. Denver air is about 17% thinner than sea level, which is worth more downrange velocity than most load changes.
- h
- altitude, feet
- TR
- temperature, degrees Rankine (°F + 459.67)
Speed of sound
Sets the Mach number that selects the drag coefficient. It depends on temperature alone, not pressure, which is why a cold day moves the transonic crossing and altitude does not.
The trajectory itself is integrated, not solved. There is no closed form once Cd varies with Mach, so the equations of motion are stepped with fourth-order Runge-Kutta at 0.2 ms, and the launch angle is bisected until the bullet crosses the line of sight at your zero. Checked against published tables: a .308 168 gr match bullet at 2650 fps comes out 0.6% off at 100 yards, and the four handgun loads checked all land within 2%.
At the muzzle
Nothing selected
Downrange
Toggle any combination. With more than one, they share the yard axis and one crosshair reads them all.
Pick your loads
Up to five at once. Silhouettes are drawn to actual bullet diameter and length.
Down the range
Drag to orbit. Real drop is a few inches over 300 feet, so the vertical axis is stretched.
The stretch factor is not cosmetic dishonesty, it is the only way to see anything. A 9 mm zeroed at 25 yards sits about six inches low at 100. Six inches across three hundred feet is one part in six hundred, so at true scale every line here would be flat. The factor is printed on the view and the drop figures everywhere else on this page are real inches.
Distances this has actually happened at
Documented armed-citizen engagements, plotted on the chart above.
These are outliers, and that is the point of showing them. Selecting incidents for being high profile selects for being unusual, so this list is not a sample and no average should be taken from it. Civilian defensive shootings cluster at three to seven yards, where every load on this page shoots flat and arrives within a few percent of its muzzle velocity. The cartridge argument is close to irrelevant at conversational distance. It stops being irrelevant at forty yards, which is why Greenwood is on the list.
Every figure here is as reported, not as measured. Distances in these cases are estimates given after the fact, several were revised as investigations continued, and hit counts were not always released. Where a number is approximate or disputed the entry says so rather than picking whichever version reads better.
Penetration in gelatin
Published test results, not our measurements, and not calculated.
These are other people's numbers and they are ranges for a reason. Bare 10% ordnance gelatin under the FBI protocol, gathered across published test series. Lot, temperature and calibration all move the result, so a load averaging 15 inches will throw individual shots either side of it. The green corridor is the protocol's 12 to 18 inch window.
Loads marked "not published" are not being estimated. We tried modeling penetration instead: a retarding force with an inertial and a strength term gives a clean closed form, and it fits any single load you calibrate it to. It cannot fit two. Solved against 9 mm 147 gr HST and 9 mm 115 gr FMJ together it has no consistent answer, wanting the FMJ to run past fifty inches against a real twenty-six. Expansion is progressive, bullets yaw and jacketed hollow points shed mass, none of which a two-term model carries. Tuning it until the outputs looked sensible would have been a number generator in a physics costume.
Every load, side by side
Click a column heading to sort. Muzzle velocity is editable, so put your own chronograph numbers in.
| Cartridge | Load | Weight gr |
Firearm | Barrel in |
Muzzle vel fps |
Muzzle energy ft·lb |
Momentum lb·s |
Sectional density |
Energy @100 ft·lb |
Velocity kept @100 yd |
|---|
Export a comparison card
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Reading the numbers honestly
The velocities are estimates until you replace them. Manufacturers usually publish figures from test barrels longer than the pistol you own, so the numbers here are adjusted toward what the named gun really produces. They are still somebody's estimate. Every velocity in the table is editable; put your own chronograph readings in and everything on the page recomputes.
Ballistic coefficients are the softest number here. Handgun bullet makers mostly do not publish one, so these are taken from published figures where they exist and estimated from bullet shape and sectional density where they do not. BC affects the downrange curves only. Muzzle energy and momentum come from weight and velocity alone, so those carry no BC error at all.
This models flight, not what happens on arrival. Penetration depth, expansion and wound characteristics are measured in calibrated gelatin under a published protocol, not calculated from energy. Anyone converting a foot-pound figure into a stopping-power claim is guessing. Energy and momentum are on this page because they are real physical quantities worth comparing, not because either one settles that argument.
Two of the 5.7 loads cannot be bought. SS190 and SS198LF are restricted to law enforcement and military sale in the US. They are listed because the cartridge was designed around them and leaving them out would flatter the loads you can actually get, but the table marks them and so does the card.
Where every number came from
Each figure on this page is one of four things, and they are not equally solid.
Computed here
- Muzzle energy, momentum and sectional density, from the formulas above. No error beyond the weight and velocity you put in.
- Velocity, energy, momentum and drop downrange, integrated with the standard G1 drag function.
- Air density and speed of sound, from the standard atmosphere at your altitude and temperature.
Estimated, and labeled as such
- Muzzle velocities, adjusted from manufacturer figures toward the barrel length named on each row. Editable, so your chronograph beats our estimate.
- Ballistic coefficients, from published figures where they exist and from bullet form and sectional density where they do not. Affects downrange curves only.
- Bullet lengths, measured off published photographs, used only to draw the silhouettes to scale.
Other people's measurements
- Gelatin penetration and expanded diameter: published FBI-protocol results in bare 10% ordnance gelatin, recorded as ranges across multiple test series. Falcon Technix has not run these tests.
- Loads with no widely published figure are marked "not published" and are not estimated.
Incidents, with citations
Method references
- G1 drag function: the standard Gavre/G1 coefficient table, interpolated by Mach number.
- Standard atmosphere: pressure by altitude with a temperature correction, per the ICAO model.
- Solver check: a .308 168 gr match bullet, BC 0.475, at 2650 fps loses 199 fps over 100 yards here against roughly 200 in published tables. Four handgun loads checked within 2%.
Not on this page
- Terminal effect, stopping power or any conversion of energy into an outcome. Not modeled, not estimated, not implied.
- Recoil, muzzle blast, capacity, cost and concealability. All of them matter and none are exterior ballistics.
- Photographs of the projectiles or the people named above. The silhouettes are drawn from published dimensions; see the note in the footer.