# Ballistic Travel Time

vCalc Reviewed
Equation / Last modified by KurtHeckman on 2018/07/17 19:21
t =
Tags:
Rating
ID
vCalc.Ballistic Travel Time
UUID
e6ccc8b2-da27-11e2-8e97-bc764e04d25f

The Ballistic Travel Time calculator computes the a amount of time an object is in free flight based on height (h) above the horizon of the launch point, initial velocity (V) of the object, and angle of launch (θ), and the vertical acceleration (g). Ballistic flight

INSTRUCTIONS: Choose units and enter the following:

• (h)  This is the initial height of the launch point above the plain.
• (V)  This is the initial velocity of the object that is launched (e.g. muzzle velocity from the gun or cannon)
• (θ)  This is the launch angle above the horizon.
• (g)  This is the acceleration due to gravity with a default of  9.80665 m/s2

Flight Time (t): The calculator returns the time of flight (t) in seconds.  However, this can be automatically converted to other time/duration units (e.g. minutes) via the pull-down menu.

### The Math / Science

t = (V sinθ + sqrt( (V sinθ)^2 + 2gh))/g

where:

This equation calculates the time an object is in free flight based on initial parameters and downward acceleration. The initial parameters are the launch elevation or height (h) above the plane, the launch angle (theta), the initial velocity (V) and the acceleration due to gravity.  A default is provided for the acceleration due to gravity of 9.8 m/s2 which is mean acceleration (at all latitudes) for sea level on Earth.

The Ballistic Flight Time equation calculates the time of flight of an object in free flight.  It only takes into account the initial velocity and launch angle (also knows as the loft) and the effects of gravity through an acceleration towards the ground.  This formula does not take into account other factors such as drag (see below).  A default is provided for the acceleration due to gravity of 9.80665 m/s2 which is mean acceleration (at all latitudes) for sea level on Earth.

#### 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. The international gravity formula provides an acceleration due to gravity based on latitude.