Launch and Propulsion

Draft

Orbital Mechanics established how much velocity change a mission needs. This section is about producing it: the equation that governs what that costs, the propellants and engines that deliver it, and the economics of not throwing the hardware away.

Reading order

The first page is a prerequisite for everything else. Chemical propulsion, cycles and nozzles form a group covering how a conventional engine works. The last four are alternatives and applications.

The results this section turns on

Tsiolkovsky rocket equation

\Delta v = I_{sp}\,g_0 \ln\frac{m_0}{m_f}

Delta-v is logarithmic in mass ratio, so propellant demand grows exponentially with mission requirement. Everything about vehicle design follows from this.

Payload fraction of a stage

\lambda = \frac{1/\text{MR} - \varepsilon}{1 - \varepsilon}

When the mass ratio’s reciprocal falls below the structural coefficient, the payload fraction goes negative and the stage cannot lift itself. This is why single-stage-to-orbit does not close.

Thrust equation

F = \dot{m}\,v_e + (p_e - p_a)A_e

The second term is why the same engine produces more thrust in vacuum, and why sea-level and vacuum nozzles are different hardware.

Thrust in the power-limited regime

F = \frac{2\eta P}{I_{sp}g_0}

For electric propulsion, thrust is inversely proportional to specific impulse. This trade has no analogue in chemical systems and defines the whole field.

Four things worth knowing

Specific impulse is the wrong figure of merit for a first stage. Density impulse reverses the ordering completely: hydrogen is best on $I_{sp}$ and worst on density impulse, solids the reverse. That inversion explains the propellant choice of every stage on every vehicle.

Two stages turn an impossible mission into a viable one; three barely help. The jump from one stage to two takes payload fraction from negative to 3.6%. The third stage adds 0.7 points, and each staging event adds failure modes.

Reuse is a refurbishment problem, not a durability problem. If refurbishment approaches the cost of a new vehicle, no number of flights makes it pay. That is what the Shuttle demonstrated, and what Falcon 9 was designed around.

Most alternatives to rockets fail on the atmosphere. About 97% of the energy of reaching orbit is velocity rather than altitude, and any ground-based accelerator must impart it at sea level. On the Moon, with no atmosphere and a seventh of the velocity, the same concepts become the obvious choice.

Pages

01The rocket equation

Derivation from momentum conservation, what specific impulse actually measures, the staging analysis that rules out single-stage-to-orbit, and the gravity, drag and steering losses.

02Chemical propulsion

Propellant combinations and real performance, why density impulse decides a first stage, storability and handling, and the four reasons methane took over new designs.

03Engine cycles

Pressure-fed through full-flow staged combustion, what each cycle costs in complexity, why expander cycles cannot scale past about 300 kN, and how the cycle is matched to the stage.

04Nozzles and thrust

The thrust equation and pressure thrust, expansion ratio and optimum expansion, flow separation as the structural limit on sea-level nozzles, and why altitude compensation never flies.

05Electric propulsion

The power-limited regime and its inverse thrust relation, how gridded ion engines work, the optimal specific impulse problem, and the missions that could not have flown otherwise.

06Hall thrusters

The crossed-field discharge, why quasi-neutrality removes the space-charge limit, the erosion problem that capped life, and how magnetic shielding solved it.

07Nuclear propulsion

Why low molecular mass doubles specific impulse at lower temperature, what Rover and NERVA demonstrated, thermal against electric, and the constraints that keep both grounded.

08Reusable launch systems

The recovery sequence and its payload penalty, the break-even analysis, why the Shuttle failed it and Falcon 9 passed, and the unsolved upper stage.

09Launch vehicles

The operational fleet, how to read a performance figure, fairings as the binding constraint, launch site geography, and the rideshare model.

10Alternative launch concepts

Air launch, centrifugal launch, mass drivers, elevators, tethers and beamed energy, assessed against the physics that defeats them on Earth and permits them on the Moon.