Space Transport and Engineering Methods/Forces

Propulsive Forces

Space transport methods can be categorized by the forces used, the energy sources, and by the state of development. This page will discuss the first of these three. 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.

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 (a = dv/dt), so we can move the dt term to the 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 practical exhaust velocities is provided, and the list is generally in increasing order. Note that what we mainly use today (combustion gas) is among the lowest in performance. To achieve higher velocities than the characteristic ones, you can use large amounts of propellents, stack multiple stages of the same method, or use multiple methods.

A. Bulk Solid (0-5 km/s)

Solid pellets or slugs expelled via mechanical devices (such as a rotary flinger), or electromagnetic accelerator.

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

In addition to the methods in A., it may be accelerated by electrostatic forces by first charging the solid particles. That only works in a vacuum or non-conducting medium.

C. Gas Flow (0.1 - 10 km/s)

In theory you can eject a liquid to obtain thrust, but in almost all cases better performance can be gotten using a gas due to the higher average molecule velocity and ability to extract energy from the gas expansion, so liquid is skipped over here in the solid/liquid/gas progression. Gas flow includes ambient temperature gas such as the Nitrogen "cold gas" thrusters 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) allow much better performance due to the higher average molecule velocity. Methods of heating the gas include electric discharge through the gas (arcjet), concentrated sunlight, electric filament heaters, or heat from a nuclear reactor.

D. Combustion Gas (2 - 5 km/s)

The hot gas is generated by chemical reactions in the propellant. The propellant then becomes the expelled mass, normally via a supersonic nozzle in order to reach the highest velocity. Performance is limited by the reaction energy in the fuel, which is a maximum of about 15 MJ/kg for non-exotic fuel combinations, and thus a maximum of about 5 km/s exhaust velocity. When heating comes from an external source, as in other methods, it is not limited in this way, so higher exhaust velocities are possible. 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 burned in a combustion chamber. In a liquid rocket the two ingredients are stored 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 form. 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.

E. Plasma (5 - 50 km/s)

The propellant is heated to the point that the atoms disassociate into charged components (ions and electrons). This can be via a vigorous electric discharge, intense microwaves, or internal heating in a fusion plasma. Plasma temperatures are high enough to melt most materials, such as the rest of the engine, so they are usually confined by a magnetic field. Alternately the plasma density (and hence the thrust) can be kept low enough that the engine can disperse the heat gained. There is no theoretical limit to how hot a plasma can be, but practical ones like how large an energy source you have and heating of the engine components will limit a practical design.

F. Ion (2 - 200 km/s)

Ions are atoms from which one or more electrons have been removed. The propellant is first disassociated, then the positive ions, which represent nearly all the mass, are accelerated across a voltage gradient to high velocity. To maintain overall charge balance across the vehicle, an electron gun separately emits negative charges. Compared to a plasma, an ion beam is not electrically neutral, and can thus be directed with electrostatic voltages.

G. Atomic Particle (1000 - 299,000 km/s)

Atomic particles include nuclei of atoms from which all electrons have been removed, single electrons, neutrons, or protons, or more exotic particles such as muons. Whereas an ion exhaust typically has a single voltage gradient, a particle accelerator has multiple chambers that add successive amounts of energy to the particles, enabling velocities up to near the speed of light. Another method is direct emission of atomic particles from fission decay, fusion reactions, or antimatter decay. Charged particles (generally those besides neutrons) can be directed by magnetic or electric fields.

H. Photon Emission (299,792 km/s)

Direct emission of photons, while low in thrust, has the highest possible exhaust velocity. For practical use, an extremely high energy source needs to be used, such as fusion or antimatter decay. Fairly simple thermal (black body) emission and reflector arrangements can align the light beam to produce useful thrust. A laser aligns the light very accurately, but the gain is small compared to a light beam with a width of a few degrees. The momentum contribution for an off-axis photon is cosine(a), where a is the off axis angle. For small angles that is very close to 1.0.

Discussion for reaction against exhaust:

Some kinds of exhaust-reaction propulsion have independent sources of mass and energy. With these systems, there is a tradeoff -- to get a given desired total velocity change ΔV, one can either use a lot of energy to accelerate a small amount of mass, or one can use less energy to accelerate a larger mass of propellant. The kinetic energy required goes as the square of the propellant velocity. Depending on how efficiency goes with velocity, the energy source power level then also tends to go as the square of velocity. Higher power sources have more mass, and represent overhead beyond the cargo you are delivering. Depending on if you want to complete the mission in the least time, or least propellant used, the optimum exhaust velocity will vary.

For a fixed propellant mass and a fixed ΔV, it takes less total energy to "dump" the early exhaust mass at a lower exhaust velocity V_e, and then eject the later mass with a higher V_e, than to eject at a constant V_e. If the goal is minimum time and you have a fixed energy source, this is optimum. For missions which use solar power as a source, where the power varies with distance from the Sun, the optimal operation is more complex. Usually the best thrust plan in that case is found using a numerical simulation which divides the mission into small time steps and adjusts the variables looking for an optimum.

Combustion gas rockets have a finite amount of fuel, which provides both mass and reaction energy. For combustion gas rockets, the Tsiolkovsky rocket equation shows that higher V_e is always better.

External Interaction

In this group, rather than expelling some material from the vehicle, force is applied by or against some external object.

I. Mechanical Traction (3 km/s)

This method uses devices like a cable or net to accelerate/decelerate the vehicle. They function via atomic bonds in the materials used, so are limited by the strength of the materials.

J. Friction/Traction (2 km/s)

This method is friction/traction against a solid surface. If your intent is to slow down on, for example, the Moon, you can have a flat paved runway and simply use mechanical braking against the runway to stop. Space velocities generally represent more kinetic energy than it takes to heat and melt most materials, so friction is of limited use except for small bodies or velocity changes.

K. Gas Pressure (9 km/s)

This method encompasses all types of guns, where gas pressure in a tube applies force to the vehicle. It also all types of jets, where the pressure difference between an incoming gas flow and the outgoing one generates net thrust. In this category is the Bussard Ramjet, which is a kind of fusion rocket that, rather than carry fuel on-board, uses a huge electromagnetic field as a ram scoop to collect and compress hydrogen from the interstellar medium. The field compresses the hydrogen until fusion occurs, then directs the energy as rocket exhaust, accelerating the vessel.

L. Aerodynamic Forces (2 km/s)

These forces include lift, buoyancy, and drag. Wings and fan blades develop lift by pressure difference across the upper and lower surfaces as a fluid such as air flows across them. Buoyancy develops lift by having a lower density than the surrounding fluid, such as in a balloon. Drag generates forces by accelerating the surrounding fluid in the direction you are moving, thus producing a force opposite your motion. A parachute, for example, is shaped to capture and accelerate the maximum amount of air, thus producing the maximum amount of drag to slow you down.

M. Photon Reflection (299,792 km/s)

Compared to H. Photon Emission above, this uses an external source of photons, such as a star or laser. Reflection produces nearly twice the force as emission, because the photon changes velocity by twice the speed of light from forward to backward. It is slightly less than twice because no reflector is 100% efficient, and off-axis cosine losses. The quantity of light (photons) is not limited by an internal power source, so can reach relatively higher forces than emission, but still generally low compared to other methods. A solar or light sail uses thin but very large mirrors in order to reflect the maximum amount of light.

N. Solar Wind Deflection (100 km/s)

The thin plasma and gas emitted by the Sun's heated outer layers is called the solar wind. Typical velocities are 100km/s relative to the Sun. The force per area due to light pressure is much greater than due to solar wind flux. A magnetic sail or magsail is a proposed method of spacecraft propulsion which would use a magnetic field to deflect charged particles in the plasma wind. Since the field itself is non-material, in theory it can be large enough to get useful thrust, even though the area density of the solar wind is very low.

O. Magnetic Field (20 km/s)

By using a current carrying wire or coil to generate a magnetic field, you can react against other magnetic fields (natural or man-made). In this category fall maglev, coilguns, railguns, and electrodynamic thrusters. It can be used both for net thrust, or torque forces to rotate your vehicle. Magnetic flywheels are often used to orient or rotate spacecraft. The Sun and many planets have a magnetic field.

(Many satellites also use the magnetic field to rotate the satellite to a desired orientation using a "magnetorquer".)

P. Gravity Field (20 km/s)

Gravity functions to accelerate objects towards any nearby mass. Besides simply falling towards an object if that is your destination, a gravity flyby can be used to change the direction, but not total amount, of your velocity. Since a planet, for example, is moving with respect to the Sun, changing direction relative to a planet via a flyby can change the velocity relative to the Sun. By conservation of momentum, the planet also must change velocity, but since it is much more massive, the velocity change is small enough to ignore in most cases.

Gravity changes as the inverse square of distance from an object. If your vehicle or object is elongated, the difference in gravity between the near and far ends can be used as a torque to stabilize your orientation.

External Interaction Discussion:

External interactions do not consume a finite supply of reaction mass as in the exhaust methods in the previous section. So they would be preferred, all other factors being equal. Reaction mass, though, can be expelled under a wider range of circumstances in most cases, and usually with a higher thrust/mass ratio. So it is not possible to state a general conclusion as to which approach is better, it will depend on the detailed circumstances.