
Computing DeltaV required

References:
Space
Vehicle Design
by Griffin, referencing Fundamentals
of Astrodynamics
by Bate, Mueller and White
PreCalculated Delta V requirements for Ballistic Missiles on EarthNotes: These were calculated with the equations below. 

Missile 
Range /Apogee (km) 
DeltaV required 
Atlas F ICBM 
12,570 km range 
5,680 m/sec 
Thor IRBM 
2,400 km range 
4,257 m/sec 
Iraqi Al Hussein 
644 km range 
2,420 m/sec 
Equation Explained
Burnout_{Velocity} = Final Velocity (Deltavee) required by the missile to achieve it's range in km/sec.
G_{Rad}: Solved independently below to simplify equation.
Range_{Angle}: Solved independently below to simplify equation.
G_{Rad}: = (Gravity_{Parameter} / Burnout_{Radius})
Gravity_{Parameter}: Gravitational Parameter
of planet in km^{3}/s^{2}.
Burnout_{Radius}:
See Equation Below
Gravitational Parameters of 

Earth 
398,600.4418 
Moon 
4,902.7779 
Mars 
42,828 
Titan 
8,978.2 
Pluto 
871 
Ceres Asteroid 
63.1 
Range_{Angle}: = (Range_{Surface} / Planet_{Radius})
Range_{Surface}: Missile range in
kilometers.
Planet_{Radius} = Radius of
planet in kilometers.
Burnout_{Radius}: = (Planet_{Radius} + Burnout_{Altitude})
Planet_{Radius} = Radius of planet in
kilometers.
Burnout_{Altitude} = Burnout
altitude of missile in kilometers.
EXAMPLE: We want to calculate the ∆v required for a 7,000 km ICBM. The first step is to begin calculating the subvariables, using a burnout altitude of 330 kilometers. For Burnout_{Radius}, since we know Earth's radius is 6,378 km; Burnout_{Radius} solves for: Burnout_{Radius}: = (6378 + 330) = 6,708 For G_{rad}, since we know Earth's Gravitational Parameter is 398,600, and because we solved for Burnout_{Radius} earlier; G_{rad} solves for: G_{Rad}: = (398,600 / 6,708) = 59.42 For Range_{Angle}, since we know Earth's radius is 6,378 km, Range_{Angle} solves for Range_{Angle}: = (7,000 / 6,378) = 1.097 Now that we have solved the subvariables; we can solve the main equation: Thus, our hypothetical 7,000 km ICBM would require a ∆v of 6.05 km/sec². However, it is a good rule of thumb to add an extra 0.5 km/sec² to your estimates to take into account air drag during the inatmosphere phase, and to provide a margin for underperforming components. 