Vacuum Trajectories

Vacuum Trajectories

Horizontal Range

Range = R₁ * R₂

R₁ = Velocity * Cos(Angle_Fire)

R₂ = (2 * Velocity * Sin(Angle_Fire) ) / Gravity

Where:

Range: Horizontal Range in meters

Velocity: Velocity of the projectile in m/sec.

Angle_Fire: Launch angle of the projectile in radians (convert from degrees to this).

Gravity: Gravitational constant of whatever planet you are on in m/sec.

Time of Flight

Time = (2 * Velocity * Sin(Angle_Fire) / Gravity

Where:

Time: Time of flight in seconds

Velocity: Velocity of the projectile in m/sec.

Angle_Fire: Launch angle of the projectile in radians (convert from degrees to this).

Gravity: Gravitational constant of whatever planet you are on in m/sec.

Computing Vertical Velocity

Velocity_Vert = Velocity * SIN(Angle_Fire)

Where:

Velocity_Vert =Vertical Velocity in meters/sec.

Velocity = Velocity of projectile in meters/sec.

Angle_Fire: Launch angle of the projectile in radians (convert from degrees to this).

EXAMPLE: What is the vertical velocity of a projectile fired at an angle of 90 degrees (1.57 Radians) with a muzzle velocity of 180 m/sec?

180 * SIN(1.57) = 180 m/sec.

Maximum Vertical Height in Trajectory

Height = Velocity_Vert² / (2 * Gravity)

Where:

Velocity_Vert =Vertical Velocity in meters/sec.

Gravity: Gravitational constant of whatever planet you are on in m/sec.

EXAMPLE: What is the maximum vertical height of a projectile with a vertical velocity of 17.45 m/sec on a planet with 1.7 m/sec gravity?

17.45² / (2 * 1.7) = 89.58 meters