Mission Characteristic Velocity - General Principles

General Principles

The Tsiolkovsky rocket equation shows that the delta-v of a rocket (stage), is proportional to the logarithm of the fuelled-to-empty mass ratio of the vehicle, and to the specific impulse of the rocket engine. A key goal in designing space mission trajectories is to minimize the required delta-v, so as to reduce the size and expense of the rocket that would be needed to successfully deliver any particular payload to its destination.

The simplest delta-v budget can be calculated with Hohmann transfer, which moves from one circular orbit to another coplanar circular orbit via an elliptical transfer orbit. In some cases a bi-elliptic transfer can give a lower delta-v.

A more complex transfer occurs when the orbits are not coplanar. In that case there is an additional delta-v necessary to change the plane of the orbit. The velocity of the vehicle needs substantial burns at the intersection of the two orbital planes and the delta-v is usually extremely high. However, these plane changes can be almost free in some cases if the gravity and mass of a planetary body is used to perform the deflection. In other cases, boosting up to a relatively high altitude apoapsis gives low speed before performing the plane change and this can give lower total delta-v.

The slingshot effect can be used in some cases to give a boost of speed/energy; if a vehicle goes past a planetary or lunar body, it is possible to pick up (or lose) much of that body's orbital speed relative to the Sun or a planet.

Another effect is the Oberth effect - this can be used to greatly decrease the delta-v needed, as using propellant at low potential energy/high speed multiplies the effect of a burn. Thus for example the delta-v for a Hohmann transfer from Earth's orbital radius to Mars' orbital radius (to overcome the Sun's gravity) is many kilometres per second, but the incremental burn from LEO over and above the burn to overcome the Earth's gravity is far less if the burn is done close to the Earth than if the burn to reach a Mars transfer orbit is performed at Earth's orbit, but far away from Earth.

A less used effect is low energy transfers. These highly nonlinear effects work by orbital resonances and by choosing trajectories close to Lagrange points. They can be very slow, but use very little delta-v.

Because delta-v depends on the position and motion of celestial bodies, particularly when using the slingshot effect and Oberth effect, the delta-v budget changes with launch time. These can be plotted on a porkchop plot.

Course corrections usually also require some propellant budget. Propulsion systems never provide precisely the right propulsion in precisely the right direction at all times and navigation also introduces some uncertainty. Some propellant needs to be reserved to correct variations from the optimum trajectory.