Trajectory Calculator Bullet

Ballistic Trajectory Equation:

\[ x = v \cos \theta \cdot t - 0.5 \cdot C_d \cdot \rho \cdot A \cdot v^2 \cdot t / m \]

Initial Velocity (v):

m/s

Launch Angle (θ):

degrees

Time (t):

seconds

Drag Coefficient (C_d):

Air Density (ρ):

kg/m³

Cross-Sectional Area (A):

m²

Mass (m):

Horizontal Distance (x):

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1. What is the Ballistic Trajectory Equation?

This calculator estimates bullet trajectory with drag approximation using the equation that accounts for initial velocity, launch angle, time, drag coefficient, air density, cross-sectional area, and mass.

2. How Does the Calculator Work?

The calculator uses the ballistic trajectory equation:

\[ x = v \cos \theta \cdot t - 0.5 \cdot C_d \cdot \rho \cdot A \cdot v^2 \cdot t / m \]

Where:

\( v \) — Initial velocity (m/s)
\( \theta \) — Launch angle (degrees)
\( t \) — Time (seconds)
\( C_d \) — Drag coefficient (dimensionless)
\( \rho \) — Air density (kg/m³)
\( A \) — Cross-sectional area (m²)
\( m \) — Mass (kg)

Explanation: The equation calculates horizontal distance accounting for both initial velocity components and air resistance effects.

3. Importance of Drag Calculation

Details: Accurate trajectory calculation is crucial for ballistics, shooting sports, and firearm applications. Drag significantly affects bullet trajectory over distance.

4. Using the Calculator

Tips: Enter velocity in m/s, angle in degrees (0-90), time in seconds, and other parameters with appropriate units. Default values represent typical .22 caliber bullet parameters.

5. Frequently Asked Questions (FAQ)

Q1: Why is drag coefficient important?
A: The drag coefficient accounts for the bullet's aerodynamic properties and significantly affects trajectory at higher velocities.

Q2: What are typical drag coefficients for bullets?
A: Typically ranges from 0.295 (standard bullet) to 0.5 or more for less aerodynamic shapes.

Q3: How does air density affect trajectory?
A: Higher air density increases drag force, reducing bullet range. Density decreases with altitude.

Q4: Is this calculation exact?
A: This is an approximation. Exact calculations require numerical integration of differential equations.

Q5: What about vertical motion?
A: This calculator shows horizontal distance only. Full trajectory would require separate vertical calculation.