Ballistic Ejection Max Range
Optimize vacuum ballistic range over launch angle onto a lower horizontal impact plane; distinct from existing fixed-angle/equal-level projectile motion, and aerodynamic drag/terrain or safe distances are not predicted.
Description
Vacuum projectile range depends on launch speed and the impact-plane height.
Vacuum projectile range depends on launch speed and the impact-plane height. A lower impact plane changes the angle that maximizes range.
Optimize vacuum ballistic range over launch angle onto a lower horizontal impact plane; distinct from existing fixed-angle/equal-level projectile motion, and aerodynamic drag/terrain or safe distances are not predicted.
When to use Ballistic Ejection Max Range
Use this tool to optimize vacuum ballistic range over launch angle onto a lower horizontal impact plane; distinct from existing fixed-angle/equal-level projectile motion, and aerodynamic drag/terrain or safe distances are not predicted.
Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
How to use Ballistic Ejection Max Range and understand its results
- Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
- Enter ejectionSpeedMPerSecond, launchHeightAboveImpactPlaneM, gravityMPerSecondSquared using the field table and calculation rules, then run the tool.
- Read maximumVacuumRangeM, optimalLaunchAngleDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| ejectionSpeedMPerSecond | Ejection speed m per second | number | Required |
| launchHeightAboveImpactPlaneM | Launch height above impact plane m | number | Required |
| gravityMPerSecondSquared | Gravity m per second squared | number | Required |
Use positive speed and gravity and nonnegative launch height above a horizontal impact plane. Return range in meters and optimal angle in degrees; equal height gives 45°.1
maximum range = v × sqrt(v² + 2gh)/g; angle = atan(v/sqrt(v²+2gh)) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| maximumVacuumRangeM | Maximum vacuum range m | number |
| optimalLaunchAngleDegrees | Optimal launch angle degrees | number |
{
"input": {
"ejectionSpeedMPerSecond": 10,
"launchHeightAboveImpactPlaneM": 5,
"gravityMPerSecondSquared": 10
},
"output": {
"maximumVacuumRangeM": 14.142135623730951,
"optimalLaunchAngleDegrees": 35.264389682754654
}
}Limitations and assumptions
Aerodynamic drag and terrain are excluded; this does not define a safe stand-off distance.
Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Clast Terminal Velocity Lithic: Balance spherical-clast buoyant weight against caller constant quadratic drag and report Reynolds number for applicability review; not a Stokes viscous law, nonspherical drag solver or hazard trajectory. For a complementary task, use Dome Collapse Block Ash Runout: Translate supplied collapse relief and calibrated Heim-ratio bounds into horizontal-runout scenarios, not probability bounds, a dynamics model or exclusion-zone guidance.
References
-
Ballistic Ejection Max Range — tool.io
Similar or alternative tools
- Clast Terminal Velocity Lithic
Balance spherical-clast buoyant weight against caller constant quadratic drag and report Reynolds number for applicability review; not a Stokes viscous law, nonspherical drag solver or hazard trajectory.
- Dome Collapse Block Ash Runout
Translate supplied collapse relief and calibrated Heim-ratio bounds into horizontal-runout scenarios, not probability bounds, a dynamics model or exclusion-zone guidance.