## Section B: Propulsive Forces List

This section lists the forces that can be used for propulsion. The forces can be broken into two classes. The first class is reaction force from an expelled material. The second class are forces created by interaction with an entity outside the vehicle. The law of conservation of momentum (i.e the sum of changes in mass x velocity is zero) requires that the force you impart to the object you want to move is matched by an equal and opposite force on something else.

### B.1 Reaction Against Exhaust

This is the classical rocket propulsion method. Part of your initial mass is expelled at high velocity in one direction, so that your vehicle will move in the other direction.

The reaction law is Force = Mass x Acceleration (F = ma). Acceleration is change in velocity per time (dv/dt), so we can move the dt term tothe mass and re-write the reaction law as F = (dm/dt)v (Force equals mass change per time times velocity). In this form we can see the factors that affect propulsion performance. If we want more force (thrust), we can either increase the mass flow rate, or increase the velocity, or some combination. Since a rocket by definition carries its own fuel, which is a finite quantity, to get more performance we generally want as high an expelled velocity as possible.

In the list that follows, the range of reasonably achieved velocities is provided, and the list is generally in order of increased exhaust velocity. Note that what we mainly use today (combustion gas) is among the lowest in performance.

B.1a Bulk Solid (0-5 km/s)

Solid pellets or slugs expelled via mechanical devices (such as a rotary flinger), or mass driver (electromagnetic accelerator with recirculating buckets).

B.1b Powdered Solid (0 - 10 km/s)

May be accelerated by electrostatic forces.

B.1b Heated Gas (0.1 - 10 km/s)

This item includes ambient temperature gas such as the Nitrogen "cold gas" thusters used in spacesuit maneuvering backpacks. Cold gas thrusters are useful when you don't want to damage things with a hot exhaust plume, but they are very low performance (~0.5 km/s).

Heating the gas, and using a low molecular weight gas (i.e. Hydrogen) allows much better performance. Methods of heating the gas include electric discharge through the gas (arcjet), concentrated sunlight, electric filament heaters, or heat from a nuclear reactor.

B.1c Combustion Gas (2 - 5 km/s)

The hot gas is generated by chemical reactions in the propellant. The propellant then becomes the expelled mass. A monopropellant has a single ingredient which is decomposed and heated by passing over a catalyst bed. A bi-propellant has two ingredients, a fuel and an oxidizer, which are generally mixed and burn in a combustion chamber. In a liquid rocket the two ingredients are in liquid form in the propellant tanks (although one or both may be converted to gas before reaching the combustion chamber). In a hybrid rocket, one of the ingredients is in solid form (usually the fuel), and the other in liquid. In a solid rocket all the ingredients are in a finely mixed powder which has been cast into a solid form. A typical solid rocket formulation has an oxidizer like ammonium perchlorate, and a complex fuel containing powdered aluminum, rubber, and epoxy.

B.1d Plasma (5 - 20 km/s)

The propellant is heated to the point that the atoms disassociate into charged components. This can be a vigorous electric discharge, or internal heating in a fusion plasma.

B.1e Ion (2 - 200 km/s)

The propellant is first disassociated, then the positive ions are accelerated across a voltage gradient to high velocity. To maintain overall charge balance across the vehicle, an electron gun separately emits negative charges.

B.1f Atomic Particle (1000 - 299,000 km/s)

Whereas an ion exhaust typically has a single voltage gradient, a particle accelerator has multiple chambers that add successive amounts of energy to the propellant particles, enabling velocities up to near lightspeed. Another method is direct emission of atomic particles from fission decay or fusion reactions.

B.1g Photon (299,792 km/s)

Direct emission of photons, while low in thrust, has the highest possible exhaust velocity. For practical use, an extreme high energy source needs to be used, such as fusion or antimatter decay. Fairly simple blackbody emission and reflector arrangements collimate the light beam to produce useful thrust.

### B.2 External Interaction

B.2a Mechanical Traction

B.2b Cable Tension

B.2c Friction

B.2d Gas Pressure

B.2e Aerodynamic Forces

B.2f Photon Reflection

B.2g Solar Wind Deflection

B.2h Magnetic Field

B.2i Gravity Field