Spaceship performance (normal space)

Spaceship performance refers to the flight capability of a spaceship. In this case it's about the performance in normal space only.

Overview
Spaceship performance differs based on technology and the environment. For the sake of simplicity we consider free space as the environment. A spaceship's performance is for example its acceleration capability, range, maneuverability. All things related to active flight and movement in general.

Acceleration
Acceleration is achieved through expended force to create motion regardless of technology. For the most part some sort of reaction thrusters are used which require propellant as fuel.

Maximum velocity
In space speed limitation is meaningless because there is no resistance that counters the force a ship can exert. However, there is a limit set by the amount of propellant aboard if all is meant to be spend just to move it straight forward without care. This limit is given by the Tsiolkovsky rocket equation.

This equation can be rewritten in the following equivalent form:


 * $$ \frac{m_0}{m_1} = e^{ \Delta v / v_e }$$

Know where and when to turn
Knowing the speed limit set by the rocket equation, the condition that engine power and thrust is proportional to propellant consumption without efficiency losses. And for the sake of simplification ignore mass changes due to spend propellant that would reduce consumption for the same amount of acceleration. We also start accelerating from a motionless position. We can easily derive a universal plot or table for quickly obtaining travel distances under acceleration for different acceleration on the same amount of fuel. This is helpful in determining the turning point at a desirable distance in order to deceleration.

The equation is as follows:

$$f(x) = x (1/x)^2$$

where x is the acceleration, and f(x) the resulting distance factor normalized.

As is obvious the reference point is set at 1 g. So if the ship accelerates with 2g the distance it can reach is 0.5 the range and time when it was going for 1g.

Combat acceleration
With what was learned from acceleration it can be applied to practical combat with a little more complexity.