Engine Models and Related Concepts

Constant Thrust and I_sp Engine Model

In the Constant Thrust and I_sp Engine Model, you enter a constant value for thrust T and for the I_sp (specific impulse). Exhaust velocity V_e is calculated on the basis of I_sp and the gravitational acceleration constant at sea level, g, as follows:

V_e = I_sp(g)

Constant Acceleration and I_sp Engine Model

In the Constant Acceleration and I_sp Engine Model, you enter a constant value for acceleration and for the I_sp (specific impulse). The thrust level is given as a function of time through the relationship:

T(t) = mdot( m(t), a, g, I_sp ) * g * I_sp

where the mass flow rate is calculated from the mass, m(t), at a given time and a, g, and I_sp are constants.

Pressure Mode

If you select the Blow Down mode, pressure is decremented by the ideal gas law:

where P = pressure in fuel tank, V = volume of fuel tank, and = density of fuel.

Thrust Efficiency and Effects

Thrust efficiency E is related to final thrust (T_final) and engine thrust (T_engine) as follows:

Acceleration due to thrust depends on T_final and spacecraft mass m:

Mass flow rate is a function of thrust (defined below) and exhaust velocity V_e:

In the above equation, if you elect to have thrust efficiency affect mass flow with acceleration,

T = T_final

Otherwise, if you opt to have thrust efficiency affect acceleration only,

T = T_engine

Mass Decrement Based on Fuel Usage

If you opt to have mass decremented on the basis of fuel usage, the decrement is governed by the rocket equation:

where V_e = exhaust velocity, m_i = initial mass and m_f = final mass. This is equal to:

Given that m_f = m_i - m, and solving for m: