Ballistic Velocity to Achieve Height

The Velocity to Achieve a Ballistic Height calculator computes the initial velocity required to achieve a maximum vertical altitude (M_h) above a plane that is reached by an object launched at an angle above the horizon (θ) assuming a constant downward acceleration (g).

INSTRUCTIONS:  Choose units and enter the following:

• (M) Maximum Height
• (h) Initial Height above Plane
• (θ) Angle above Horizon
• (g) Acceleration due to gravity (default is 9.80665 m/s²)

Velocity (V):  The calculator returns the velocity in meters per second.  However this can be automatically converted to compatible units via the pull-down menu..

The Math / Science

The Max Ballistic Height equation is used to compute the maximum height (h) of an object in trajectory motion above a plane. The range is based on negative vertical acceleration (g), initial velocity (V) and launch angle (θ). This simplified ballistic equation does not take into account any drag or other forces and this equation assumes the launch point (origin) is on the plane. When you solve for the initial velocity, the formula for Velocity to achieve a Max Ballistic Height  is:

               `V = sqrt( (M-h)*2g)/(sin theta)`

where:

• V the magnitude of the initial launch velocity
• M is the maximum achieved height.
• h is the initial height.
• θ is the launch angle (angle from the local horizontal plane)
• g is the acceleration due to gravity.

Note: a default for gravitational acceleration (g) of 9.80665 meters per seconds squared is provided.  This is the approximate SI value at sea level on earth. The user may change the gravitational acceleration constant (g) to accommodate a different body (e.g. moon or a different altitude on the earth, or for other units.

Ballistic Flight Calculators:

• Ballistic Maximum Altitude:  This is the maximum altitude achieved in free ballistic flight.
• Ballistic Maximum Range:  This is the maximum horizontal range.
• Ballistic Flight Time:  This is the time duration of free flight.
• Simplified Ballistic Range: This is the range with no initial elevation above the plane.
• Ballistic Vertical Velocity: This is the vertical velocity at a given time.
• Ballistic Horizontal Velocity: This is horizontal velocity or ground speed.
• Vertical Position (Y) in Ballistic Flight: This compute the vertical position (y) at a given time within ballistic flight.
• Horizontal Position (X) in Ballistic Flight: This compute the horizontal position (x) at a given time within ballistic flight..
• 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
• Velocity to achieve a Max Ballistic Height: This computes the initial velocity required to achieve the max height.
• International Gravity Equation
• Force of Earth's Gravity
• Force of Drag