Vacuum Trajectories |
Horizontal Range
Range = R_{1} * R_{2}
R_{1} = Velocity * Cos(Angle_{Fire})
R_{2} = (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_{Vert}^{2} / (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? 17.45^{2} / (2 * 1.7) = 89.58 meters |