1. What is the Arrow Trajectory Equation?

The arrow trajectory equation calculates the vertical position (y) of an arrow at a given horizontal distance (x) based on launch angle (θ), initial velocity (v), and gravity (g). This is derived from projectile motion physics.

2. How Does the Calculator Work?

The calculator uses the trajectory equation:

Where:

• \( y \) — Vertical position (m)
• \( x \) — Horizontal distance (m)
• \( \theta \) — Launch angle (degrees)
• \( v \) — Initial velocity (m/s)
• \( g \) — Acceleration due to gravity (9.81 m/s²)

Explanation: The equation accounts for both the vertical component of the initial velocity and the effect of gravity pulling the arrow downward.

3. Importance of Trajectory Calculation

Details: Understanding arrow trajectory is crucial for archers to accurately hit targets at different distances and for predicting the arrow's path under various conditions.

4. Using the Calculator

Tips: Enter horizontal distance in meters, launch angle in degrees (0-90), initial velocity in m/s, and gravity (default is 9.81 m/s²). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the optimal launch angle for maximum distance?
A: Without air resistance, 45° gives maximum range. With air resistance, optimal angle is typically lower (30-40° for arrows).

Q2: How does arrow weight affect trajectory?
A: Heavier arrows have lower initial velocity but maintain momentum better. The calculator assumes point-mass projectile.

Q3: Why doesn't this account for air resistance?
A: The basic equation ignores air resistance for simplicity. Real trajectories are shorter due to drag.

Q4: What's a typical arrow velocity?
A: Compound bows: 70-100 m/s, recurve bows: 50-70 m/s, longbows: 40-60 m/s.

Q5: How accurate is this for very long distances?
A: Less accurate at long ranges where air resistance becomes significant. Best for distances under 100m.