Formula
The bullet is a point. Drag opposes the velocity relative to the air. Gravity is the only other acceleration. The bore is angled so the bullet crosses the line of sight at the zero range. Sight height is above the bore, so the drop at the muzzle is minus the sight height.
|a| = ρ · π · g · Cd · v² / (1152 · BC)
energy = grains × fps² / 450,437
MOA = drop inches / (1.047 × yards)
MIL = drop inches / (3.6 × yards)
Cd comes from the BRL G1 or G7 table at the Mach number. BC is the shooter coefficient in pounds per square inch, and it has to be the G1 or G7 number that matches the table. g is 32.174 ft/s². Density uses a moist-air equation from the temperature, station pressure, and relative humidity you enter, so a density altitude is implicit in those three. The integrator is fixed-step RK4 at 0.0004 s. Through 500 yards this stays within 0.5 in and 20 fps of the Shooter’s Calculator chart in the sources. At 1,000 yards, within 2% in drop and 3% in velocity. Drift will not match a solver that adds spin drift. The bullet energy calculator is the same 450,437 identity with no trajectory. This page does not produce a reloading recipe.
Worked examples
G7 0.240, 175 gr, 2,600 fps, sight 2.5 in, zero 100 yd, 10 mph at 90°, 59°F, 29.92 inHg, 50% humidity. The 100 yard row is the zero: drop about 0, velocity about 2,415 fps. The published comparison line is 2,419 fps. At 500 yards the drop is about −60.6 in against a published −60.17, and the velocity is about 1,752 fps against 1,766.
The same bullet at the muzzle. Drop reads −2.5 in, which is the sight sitting 2.5 in above the bore. Energy at the muzzle is 175 × 2,600² / 450,437.
A headwind. Set the angle to 0. Drift goes to about zero, and the velocity falls a little faster. A 180° angle is a tailwind.
Reference
The check load, every 100 yards. Drop is inches from the line of sight. MOA and MIL are that drop divided by the range factor, not a turret click.
| Yards | Drop | Drift | Velocity | Energy | MOA | MIL |
|---|---|---|---|---|---|---|
| 0 | -2.5 in | 0 in | 2,600 | 2,626 | 0 | 0 |
| 100 | 0 in | 0.76 in | 2,415 | 2,266 | 0 | 0 |
| 200 | -3.5 in | 3.17 in | 2,238 | 1,946 | -0.02 | -0 |
| 300 | -13.9 in | 7.4 in | 2,069 | 1,663 | -0.04 | -0.01 |
| 500 | -60.6 in | 22.26 in | 1,751 | 1,192 | -0.12 | -0.03 |
| 1,000 | -426.5 in | 113.72 in | 1,081 | 454 | -0.41 | -0.12 |
Questions
How close is this to a published chart?
Against the Shooter’s Calculator point-mass table for a G7 BC of 0.240, 175 gr, 2,600 fps, 2.5 in sight height, 100 yard zero, and a 10 mph full-value wind at sea-level standard air: through 500 yards the drop stays within 0.5 inch and the velocity within 20 fps. At 1,000 yards the drop stays within 2% and the velocity within 3%. Their 100-yard line is 0.00 in and 2,419 fps.
Does this include spin drift or a powder charge?
No. The bullet is a point mass with G1 or G7 drag and a steady wind. There is no spin drift, no Coriolis term, and no reloading data. Energy is grains × velocity² / 450,437, the same identity as the bullet energy calculator.
What is the drag model?
BRL Cd against Mach for the G1 and G7 standard projectiles, integrated with a fixed-step Runge-Kutta step. The deceleration is ρ · π · g · Cd · v² / (1152 · BC), with BC in lb/in². That is the JBM Cd form written in shooter units. Air density uses the temperature, pressure, and humidity you enter.
Sources
- Drag: BRL standard-projectile Cd(Mach) for G1 and G7, the tabulation used by JBM and McCoy. G1 Cd at Mach 3 is 0.5133. G7 Cd at Mach 3 is 0.2424.
- Deceleration follows JBM’s Cd form, a = −ρ · π/8 · Cd · |v| · v / C, rewritten for a BC in lb/in². The factor is 1152.
- Check chart: Shooter’s Calculator, G7 BC 0.240, 175 gr, 2,600 fps, 2.5 in sight, 100 yd zero, 10 mph at 90°, ISA-like 59°F / 29.92 inHg / 50% RH. Tolerance stated in the formula section. JBM’s own calculator was not fetched successfully for this check.
- Energy: grains × fps² / 450,437. No reloading, pressure, or powder-charge data.