The Ballistic Flight Calculator contains the main equations for distance (range), altitude, flight time and velocity associated with ballistic flight excluding the force of drag. The ballistic flight functions are:
- Ballistic Max Range: This is the maximum horizontal range.
- Ballistic Max Height: This is the maximum altitude in free ballistic flight.
- Ballistic Travel Time: This is the time duration of free flight.
- Velocity for Height: This computes the initial velocity at a launch angle needed to reach a max height.
- Initial Horizontal Velocity: This is horizontal velocity or ground speed.
- Initial Vertical Velocity: This is the vertical velocity at a given time.
- Ballistic Position at Time (t): This compute the position (x,y) at a given time within ballistic flight, where x is distance down range and y is the height above the plane.
- Ballistic Parabolic Equation provides the parabolic flight position equation based on the launch speed, height and angle.
- Acceleration Due to Gravity at Sea Level
The Math / Science
Ballistic flight operates on the premise that there is one primary force working on an object, and that is the force of gravity pulling the object toward the ground. This downward force limits the time that an object can be in free flight. Therefore the key calculation is to compute how long the object will be in the air based on the initial height and the vertical velocity. Based on these two items, the rest of the computation can be made via trigonometry.
Acceleration Due to gravity
The force of gravity pulls masses towards each other. In the case of small objects (e.g. you, an arrow or the Space Shuttle) verses planetary objects (e.g. the Earth or Moon), the difference in masses result in a negligible acceleration of the large object toward the small and small object accelerating toward the center of mass of the large object. Acceleration due to gravity changes based on the mass of the object (e.g. the Earth 9.8 m/s2 verses the moon1.6 m/s2) and the distance from the center of mass. For example, since the Earth is not a perfect sphere, and more closely represented as an oblate spheroid, acceleration due to Earth gravity as Sea Level is more accurately calculated based on latitude:CLICK HERE g=f(lat). The international gravity formula provide an acceleration due to gravity based on latitude. CLICK HERE for the acceleration due to gravity for the other planets in the solar system.