Rocket - Physics - Delta-v (rocket Equation)

Delta-v (rocket Equation)

The delta-v capacity of a rocket is the theoretical total change in velocity that a rocket can achieve without any external interference (without air drag or gravity or other forces).

When is constant, the delta-v that a rocket vehicle can provide can be calculated from the Tsiolkovsky rocket equation:

where:

is the initial total mass, including propellant, in kg (or lb)

is the final total mass in kg (or lb)

is the effective exhaust velocity in m/s or (ft/s)

is the delta-v in m/s (or ft/s)

When launched from the Earth practical delta-v's for a single rockets carrying payloads can be a few km/s. Some theoretical designs have rockets with delta-v's over 9 km/s.

The required delta-v can also be calculated for a particular manoeuvre; for example the delta-v to launch from the surface of the Earth to Low earth orbit is about 9.7 km/s, which leaves the vehicle with a sideways speed of about 7.8 km/s at an altitude of around 200 km. In this manoeuvre about 1.9 km/s is lost in air drag, gravity drag and gaining altitude.

The ratio is sometimes called the mass ratio.