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`y = a*x^2 + b*x + c`

Enter a value for all fields

The **Ballistic Flight Parabolic Equation** calculator computes the parabolic equation coefficients based on the launch angle above the horizon (**θ**) at an initial velocity (**V**) assuming a constant downward acceleration (**g**).

**INSTRUCTIONS**: Choose units and enter the following:

- (
**V**) Initial Launch Velocity - (
**θ**) Launch Angle above the horizon. - (
**h**) Initial Height above the Plane - (
**g**) Acceleration due to gravity (default is 9.80665 m/s^{2})

**Parabolic Flight Equation**: The calculator returns the equation of the parabola to match the flight.

The formula for the parabolic flight equation is:

y = a•x² + b•x + c

where:

- a = -4 • M / R²
- b = 4 • M / R
- c = h (initial height)
- M is the Ballistic Maximum Altitude without h
- R is the Ballistic Maximum Range without h

The addition of the initial height (h) to the Max Altitude and Range have the effect of shifting the parabola to the right, when all that is wanted is a shift up.

One of the most common representations of a parabola in nature is an object moving in the gravitational field of a massive body, such as the projectile motion of a body affected by the Earth's gravity. The figure shows the parabolic trajectory typifying a projectile that is affected solely by gravity, **g**.

- 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

**Parabola Formula**: This computes the y coordinate of a parabola in the form y = a•x²+b•x+c**Parabolic Area**: This computes the area within a section of a parabola**Parabolic Area (Concave)**: This computes the outer area of a section of a parabola.**Parabolic Arc Length**: This computes the length a long a segment of a parabola.**Paraboloid Volume**: This is the volume of a parabola rotated around an axis (i.e. paraboloid)**Paraboloid Surface Area**: This is the surface area of a paraboloid.**Paraboloid Weight**: This is the weight or mass of a paraboloid.**Ballistic Flight Parabolic Equation**: This provides the formula of the parabola that matches a ballistic flight.

[Figure] Initial velocity of parabolic throwing

Source: Wikipedia / Fizped (modified to include motion equation)

URL: http://en.wikipedia.org/wiki/Projectile_motion#mediaviewer/File:Ferde_hajitas1.svg