The delta height for ballistic range formula computes the difference in ballistic range (dx) based on the difference in the initial height.  It uses the same velocity(v) and launch angle (`theta`) but two different heights, initial height (h₁) and the final height (h₂).Ballistic Flight  The result is the difference in the range cause by changing the initial height.

Inputs

• `h_1` - the initial height above the launch origin
• `h_2` - the initial height above the launch origin
• `theta` - initial launch angle at h = 0
• `v_0` - magnitude of the initial velocity
• g - gravitational acceleration constant (defaults to Earth's gravitation acceleration constant)

Usage

This equation simply provided the difference in range based upon changing the elevation (height) of the initial launch point.  It could tell you how much further or nearer your object will go out in the plane if the launch point is raised or lowered.

History and the High Ground

Historically, the high ground has been coveted on the battle field, because of the principle demonstrated in this equation.  If the elevation is higher for one combatant, their munitions have a longer effective range, and their rocks, arrows, bombs or missiles will reach the enemy before the enemy's reaches them.  This is why the high ground is sought on the battlefield and why defensive positions (e.g. castles) are typically placed on high ground such as mountain tops.

See Also

• Ballistic Range
• Ballistic Travel Time