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Quick Start
Enter bullet specifications, environmental conditions, and target parameters. Click "Calculate Trajectory" to generate ballistic data.
Bullet Parameters
Weight (grains): Bullet weight in grains. Typical: .223 (55-77 gr), .308 (150-180 gr), .30-06 (150-220 gr).
BC (Ballistic Coefficient): Drag efficiency relative to standard projectile. Range: 0.1-0.8. Higher = better aerodynamics.
Diameter (inches): Bullet diameter. Used for spin aerodynamics and moment of inertia calculations. Typical: .223 (0.224"), .308 (0.308").
Length (inches): Bullet length from tip to base. Used for moment of inertia and spin aerodynamics calculations. Typical: .223 (0.7-1.0"), .308 (1.0-1.4").
Twist (in/turn): Barrel twist rate. Enter positive for right-hand (RH) twist (e.g., 8 for 1:8 twist), negative for left-hand (LH). Common: .223 (1:7 or 1:8), .308 (1:10 or 1:12). Used to calculate bullet spin rate for spin drift and crosswind jump effects.
Drag Model: G1 (traditional) vs G7 (modern). G7 generally better suited for boat tail bullets, G1 for flat base bullets.
Shooting Parameters
MV (Muzzle Velocity): Initial bullet velocity in fps. Critical for trajectory calculation. Typical: .223 (3000+ fps), .308 (2600-2800 fps).
Zero Range: Distance where bullet hits crosshairs. Common: 100, 200, 300 yards. Affects trajectory shape.
Scope Height: Distance from bore centerline to scope centerline. Typical: 1.5-2.5 inches. Affects trajectory calculation.
Environmental Conditions
Temperature: Air temperature in Fahrenheit. Affects air density - higher temperature = less dense air. Standard: 59°F.
Humidity: Relative humidity percentage. Minimal effect on ballistics. Typical: 20-80%.
Altitude: Height above sea level in feet. Higher altitude = less air resistance. Sea level: 0 ft.
Wind Conditions
Wind Speed: Wind velocity in mph. Always positive value.
Wind Direction (o'clock): Wind direction using a 12-hour clock, describing where the wind is COMING FROM with the target at 12 o'clock. 12 = from target (headwind), 6 = from behind (tailwind), 3 = from right (full-value crosswind), 9 = from left (full-value crosswind). Intermediate positions (e.g., 1 or 11 o'clock) give fractional-value crosswinds.
Spin Effects
Enable Spin Effects: Check this box to include spin drift and crosswind jump in trajectory calculations. Uncheck to disable these effects and use standard trajectory calculation (wind drift is still included, but spin-induced effects are not).
What are Spin Effects? When a bullet spins, it experiences additional forces beyond simple wind drift:
• Spin Drift: A rightward drift (for right-hand twist) caused by gyroscopic precession. This effect increases with range and is independent of wind direction.
• Crosswind Jump: Vertical deflection when crosswinds interact with the spinning bullet, causing it to rise or fall slightly.
Twist Rate: Enter your barrel twist rate (e.g., 8 for 1:8 twist). Positive values = right-hand twist, negative = left-hand twist. This determines the bullet's spin rate, which affects both spin drift magnitude and direction. The calculated spin rate (in RPM) is always displayed in the results, regardless of whether spin effects are enabled in the simulation.
Modeling Approach: Spin effects use simplified, empirically tuned aerodynamics. The model tracks bullet spin and computes lateral/vertical accelerations from wind, spin, and angle-of-attack dynamics. Right-hand twist yields rightward spin drift; left-hand twist reverses the direction.
Accuracy Note: These effects are modeled to illustrate expected trends and add realism. They are not a substitute for live-fire data (dope) and may not match all bullet/rifle combinations precisely. For critical applications, verify with actual range testing.
Trajectory Parameters
Max Range: Maximum distance for trajectory calculation.
Step Size: Distance between trajectory points. Smaller steps = more detailed data. Typical: 25-100 yards.
Angle Units: Units for drop and drift display. MOA (Minutes of Angle) or mrad (milliradians).
Displayed Information
Atmospheric Conditions: The calculator displays calculated atmospheric properties used in the simulation:
• Air Density: Shows in lb/ft³ and kg/m³. Affects drag and bullet deceleration.
• Pressure: Shows in inHg and Pa. Calculated from altitude using the barometric formula (standard atmospheric pressure decreases with altitude).
• Speed of Sound: Shows in fps and m/s. Useful for understanding supersonic/subsonic transitions.
• Temperature: Shows in °F. Confirms the input temperature value.
Bullet Properties: Displays calculated bullet characteristics:
• Sectional Density: Weight divided by diameter squared, shown in lb/in². Higher values indicate better penetration potential.
• Spin Rate: Bullet rotation rate in RPM, calculated from muzzle velocity and barrel twist rate. Displayed regardless of whether spin effects are enabled in the simulation.
Miller Twist Rule: Calculates bullet stability using the Miller stability factor (SG):
• Stability Factor (SG): Indicates bullet stability. Values below 1.0 are unstable (red), 1.0-1.5 is marginal stability (orange), and 1.5+ is good stability (green).
• Ideal Twist Rate: For stable bullets (SG ≥ 1.5), shows the twist rate that would produce the current SG value. For unstable/marginal bullets, shows the minimum twist rate needed for SG = 1.5 (good stability).
• The Miller formula accounts for bullet weight, diameter, length, and twist rate to determine gyroscopic stability.
Results
Range: Distance in yards from muzzle.
Drop: Vertical bullet drop from line of sight. Positive = below crosshairs, negative = above crosshairs.
Drift: Total horizontal deflection including wind drift and spin drift (if spin effects are enabled). Wind drift depends on wind speed and direction. Spin drift adds a rightward component for right-hand twist barrels.
Velocity: Bullet speed at that range. Decreases due to air resistance.
Energy: Kinetic energy in foot-pounds. Decreases with velocity.
Time: Flight time from muzzle to that range.
Technical Tips
Data Sources: Use manufacturer BC values from ballistic tables. Measure MV with chronograph for best results.
Environmental Matching: Set conditions to match your shooting environment for best results.
Wind Reading: Wind direction and speed can change rapidly. Use average conditions for planning.
Technical Details
Model (4DOF): Trajectory is integrated with a 4DOF model that tracks position (x,y,z) and spin rate. Integration uses RK2 with small time steps for stability and performance.
Drag (G1/G7): Uses standard empirical drag tables (G1/G7). Air density corrections are applied from temperature, humidity, and altitude to adjust deceleration along the velocity vector.
Moment of Inertia: When spin effects are enabled, moment of inertia is estimated from bullet weight, length, and diameter. This affects how the spinning bullet responds to wind forces.
Limitations: Spin aerodynamics use simplified models tuned to typical match bullets rather than derived from full CFD or 6DOF data. For critical applications, verify results with live-fire testing.
Disclaimer
Accuracy Limitations: This calculator provides estimates based on mathematical models. Actual trajectory may vary due to bullet manufacturing variations, barrel harmonics, atmospheric micro-variations, and other factors. Always verify critical calculations with live-fire testing (dope) before relying on them for competition or hunting.
Accuracy Degrades With: Longer ranges, longer flight times, and atypical bullet parameters (unusual BCs, very light/heavy bullets, extreme velocities, etc). The model is tuned for typical match bullets at common ranges. Results become less reliable as you move further from these conditions.