Image credit: SpaceX

Typically, two separate chemical propellants are used, a fuel (such as liquid hydrogen or kerosene), and an oxidizer (such as liquid oxygen or nitrous oxide), which provides the oxygen to sustain a burning reaction. Rockets differ from similar propulsion systems such as gas turbine engines (jets) in that they carry both their fuel and oxidizer on board, thereby needing no intake oxygen to operate. Also, the performance possible with rockets make them ideal for vehicles such as spacecraft, which need to achieve large changes in momentum and high final velocities.

A rocket operates according to Newton’s third law of motion, which states, generally, that for every action there is an equal and opposite reaction. In a chemical rocket, the fuel and oxidizer are combined in a combustion chamber, where they are exposed to a source of ignition, causing a violent chemical reaction which produces hot, rapidly expanding gases. These gases are accelerated through a throat and nozzle, where they are ejected at very high velocity, thereby imparting a change of momentum to the vehicle.

For the purposes of this discussion, there are three major types of chemical rockets: solid propellant, liquid propellant, and hybrid propellant.

A solid propellant rocket, commonly called a “rocket motor,” is likely a composite propellant, with both the fuel and oxidizer pre-mixed together with a firm, rubber-like putty called the binder. This mixture is then formed into the shape of the engine casing itself, and contains an empty space or port down the center of the putty which serves as the combustion chamber. The Solid Rocket Boosters (SRBs) on the Space Shuttle are the most notable of this type of system, using aluminum powder as a fuel and ammonium perchlorate (NH4ClO4) as an oxidizer.

Liquid- and Solid-Propellant Rockets. Note the different combustion chambers and the significant increase in complexity required for a liquid system.

Hybrid Rocket with molded plexiglass fuel module (left) and N20 oxidizer canister (blue, right). (Image credit Hypertek.)

A liquid propellant rocket, commonly called a “rocket engine,” keeps its fuel and oxidizer in separate fuel tanks, then, through a series of pumps, valves and injectors, combines the propellants in a combustion chamber. Liquid systems tend to have better fuel efficiencies (in terms of impulse per unit weight) than solids, but are considerably more complex and thus more prone to failure. The Space Shuttle Main Engines (SSMEs) are the most recognizable implementation of a liquid propellant system.

Hybrid propellant rockets typically utilize a solid fuel and a liquid or gaseous oxidizer. Fuel in a hybrid can be almost anything combustible, but the most common is rubber or, specifically, Hydroxyl-terminated Polybutadiene (HTPB). While rubber may seem a strange choice for use as a rocket fuel, it is interesting to note that the binder used in the shuttle’s SRBs is, in fact, a polybutadiene. Hybrid oxidizers are similar in nature to liquid systems, although N20 (nitrous oxide) is commonly chosen for its ease of handling and storage. Hybrids are seen as being more versatile than solids due to their ability to throttle, stop and restart, and safer than liquids since the propellants are, separately, totally inert. Currently, however, little experimentation has been done with large-scale hybrids.

Most commercial hobby rockets use some form of solid propellant, either black powder or a HTPB-Ammonium Perchlorate composite. A few companies are now producing high-power hybrid motors for the hobby market which are considerably less expensive per flight than composites of comparable performance, but require a complex system of ground support equipment (GSE). The most well-known commercial application of a large hybrid motor is Scaled Composites’ suborbital rocket glider, SpaceShipOne.

Rocket Performance

When designing or selecting a rocket propulsion system for an aerospace vehicle, various performance parameters must be addressed. These include such concerns as final velocity desired, maximum acceleration, maximum altitude, payload and vehicle mass, and fuel mass budget and volume constraints, to name a few. In order to understand and compare the performance characteristics of different systems, the following principles must be discussed.

Force

In physics, a force acting on a body is that which causes the body to accelerate; that is, to change its velocity. The concept first appeared in Newton’s second law of motion of classical mechanics, and is usually expressed by the equation:

F = m a

where

F is the Force, measured in newtons (N),

m is the Mass, measured in kilograms (kg), and

a is the Acceleration, measured in metres per second squared (m/s²).

[Review SI Units of Weights and Measures.]

Thrust

Thrust is the force that propels a rocket. The diagram to the right shows a rocket’s combustion chamber with an opening, the throat and nozzle, through which the expanding gases can escape.

(Diagram credit Robert A. Braeunig.)

The thrust force is a product of the exhaust velocity (V_e) and the mass flow rate (q) of the ejected propellant, plus the difference between the atmospheric pressure (P_a) and the pressure of the exhaust gases (P_e). Exhaust pressure (P_e) is affected by the expansion ratio of the rocket nozzle, defined by dividing the area of the nozzle’s exit (A_e) by the area of the throat (A_t).

Thrust is therefore expressed by the equation:

F = q V_e + (P_e – P_a) A_e

A nozzle is said to be optimized for its operating environment when P_e = P_a. Assuming an optimized expansion ratio, the thrust equation can be reduced to its simplest form:

F = q V_e

where

F is the Thrust force, measured in newtons (N),

q is the Mass Flow Rate of the ejected propellant, (kg/s), and

V_e is the hot gas Exhaust Velocity relative to the moving vehicle, (m/s).

This looks very similar to the Force equation above (F = ma), and upon closer inspection it becomes clear that Thrust is simply the acceleration of a given mass of propellant out the back end of the vehicle which, in turn, pushes it forward.

The Thrust Curve

As a rocket motor fires, its instantaneous thrust can be measured and recorded over the duration of the burn. This data can then be plotted on a graph with thrust (in newtons or pounds) on the vertical scale and time (in seconds) on the horizontal scale. This graph is commonly referred to as a “thrust curve”, and is used as a visual means of comparing two different rocket motors. (See Fig. 1)

Typical thrust curve. (Credit ThrustCurve.org.)

You can see from the graph that the thrust spikes sharply at the beginning of the burn, and then gradually begins to taper off. This spike is the point of maximum thrust, and it occurs in this example at about 0.3 seconds into the burn.

Total Impulse

The area under the thrust curve is called the total impulse. It is the product of the thrust force integrated over the burn time, and is expressed by the equation:

or

I = F t (assuming constant thrust)

where

I is the Total Impulse, measured in newton-seconds (Ns),

F is the total Thrust, in newtons (N), and

t is the burn Time, in seconds (s).

Total impulse is the best means of comparing one rocket motor to another. It is proportional to the total energy released by all the propellant in a propulsion system. More total impulse means more velocity and altitude for vehicles of equal mass, or more payload for flights of similar altitude.

You’ll also see in Figure 1 the line of average thrust (F_avg). This number is useful in making approximations of burnout velocity and maximum altitude of a given vehicle, and is also used in the designation of motor types (see next section). Since no rocket motor has constant thrust throughout its burn time, average thrust is computed by dividing total impulse by burn time (F_avg = I / t).

Specific Impulse

Propellant efficiency of a rocket propulsion system is measured by specific impulse (I_sp). Put simply, specific impulse is the total impulse obtainable per unit weight of propellant. This means that the higher the I_sp, the less fuel mass required for a desired total impulse. Specific impulse is expressed by the equation:

I_sp = I / m_p g

where

I_sp is the Specific Impulse, measured in seconds (s),

I is the Total Impulse, in newton-seconds (Ns),

m_p is the Propellant Mass, (kg), and

g is the acceleration of Gravity at the surface of the earth, (roughly 9.81 m/s²).

The next section will describe how these terms are used in the designation and classification of commercial hobby rocket motors.

Rocket Motor Designation

Rocket motor manufacturers designate each of their motors with standardized letter and number codes which approximate total impulse and average thrust. This allows motors built by different manufacturers, possibly having different propellant types and weights, to be classified by their total impulse.

Each motor will have a code similar to the following:

C6-7

The first letter of the code indicates the Total Impulse category. In this case, the letter “C” indicates that this motor has a total impulse between 5.01 and 10.00 Ns. Each successive letter indicates twice the impulse of the previous category (e.g., a “D” motor has an upper limit of 20.00 Ns.)

The next number indicates the Average Thrust of the motor throughout its burn time. In our example, the number “6″ indicates that the average thrust of this motor is roughly 6 N. [Note: Motors of equal impulse will often have different average thrust values. Assuming equal total impulse (e.g. two "C" motors), a greater average thrust value will produce greater acceleration over a shorter burn time. This is helpful for getting heavy rockets off the pad and flying quickly.]

The number following the dash (-) is not always present, as it represents the Delay, in seconds, between motor burnout and the recovery system ejection charge. Here, the number “7″ indicates a seven-second delay between motor burnout and chute deployment. Longer delays allow a longer coast phase between burnout and apogee. [Note: Many high-power motors ("G" impulse and higher) will have no built-in delay, allowing the user to tailor the delay length to vehicle mass and predicted coast time, either with a modular delay charge or a flight computer. A motor with a -0 designation is intended for use as a first stage motor on vehicles with multiple stages.]

The following table lists standardized impulse categories by their alphabetic designator. Specific information on each motor type, including thrust curves, can be found at the NAR Certified Motors page.

Model Rocket Flight Profile

Diagram credit NASA Glenn Research Center.

Copyright © 2000 Aerospace America.   Reprinted with permission.

Image credit: SpaceX

But turbopump engines, whether high pressure or low, were a mistake from the very beginning. They simply are not worth what they cost in time and money. In all the early development efforts, pump-fed systems were preceded by a pressure-fed version. In every case, the mission was accomplished and the program goals met before the development of the pump system was completed. After the X-I broke the sound barrier with its pressure-fed rocket engine, who ever heard of the D-558-2 — powered by a pump-fed engine?

Technically simple two-stage launchers with pressure-fed engines and ocean recovery offer the economical operations that have escaped our high-technology turbopump rockets for more than four decades.

Economic considerations

How could an entire industry have gone so far astray? The answer is simple. In the commercial world, when technologies mature they eventually reach a point where further refinement is not economically justified. However, rocket development in both the U.S. and the Soviet Union had always been government-sponsored. It never had the benefit of the primary limiting influence — economic shakeout.

Development trends were dictated by engineers who strove for high performance. Most often they neither knew nor cared about the cost impact of their designs. High performance and light weight invariably led to complication and high cost. No development really focused on the economic aspects of high performance. No one wanted to. The engineering of complex systems is fun, and most programs were done on almost inexhaustible budgets. No one bothered to ask, "Is it worth the price?"

Back in 1959 I noted, to my great surprise, that the Agena, only one-fifth the size of the Thor intermediate-range ballistic missile, cost more, not less, than the Thor. Here were two liquid-propellant rockets, each comprising one set of tanks, one pump-fed engine, one autopilot, etc. The Agena was almost a scale model of the Thor. Following the accepted practice of the time, we had gone to great lengths to make both of them as small as possible so the mission could be accomplished.

For most missions, a less efficient rocket can do the job of a more efficient one by making the former a bit bigger. With the Agena/Thor situation, we had data that said that efforts to make a given rocket as small as possible might be grossly misdirected.

Another example of such misdirection was the Titan intercontinental ballistic missile (ICBM). The first stage (in 1959) used two engines of about 150,000 lb of thrust each. The single second-stage engine developed 60,000 lb. Again, I found that the smaller engine cost more. The size factor was only little over two, not five as in the case of Thor/Agena, but it still reflected the difference in launch weight between a simple vehicle and a sophisticated one. The absurdity of excessive emphasis on keeping the rocket small became clear.

A third example is the Atlas ICBM. For years the Atlas program had been kept on the back burner because it required a liftoff weight of almost 500,000 lb to throw a hydrogen bomb 6,000 mi. When the weight of the bomb was halved, the Atlas was suddenly considered practical. For some reason, cutting the liftoff weight from 500,000 lb to 250,000 lb made it acceptable.

Development of the 0.5-million-lb Atlas was well along when the order came to downsize it. The original design used five engines of the same size. Cutting the vehicle size in half required a complete redesign, and an entirely new sustainer engine had to be developed. Downsizing the Atlas was an unfortunate mistake. The smaller version cost more, took longer to develop, and provided a vehicle of half the capability.

Apparently, nobody thought of the idea of putting two warheads on an ICBM — that idea came along much later. Had we developed the full-size version, we could have orbited both the Mercury and Gemini astronauts on the same vehicle. Actually, the Atlas never was any good as an ICBM; it came into its own only as a space launch vehicle.

Simplicity, not size, is the key

Truax Sea Dragon concept

Why wings?

Image Credit: Wikipedia

Today, at last, there seems to be an effort under way to develop low-cost launch systems. But most people and organizations in the space community do not really want to develop cheap rockets. Fancy ones are more fun, and, at least at first blush, make more money, create more jobs for more people, and require large organizations to develop, manufacture, and use them.

However, in commercial space, as in most business ventures, cost is the primary consideration. Although perhaps not so obvious, cost is also of great importance in both the exploration of space and in using space for military purposes. It is long past time to stop designing and building engineering tours de force that produce marvelously intricate machines but make access to space more costly.

Many are also obsessed with the idea of flying into space. Why put wings on a space launch vehicle? Perhaps because there are so many airplane pilots in important positions. Perhaps because the Air Force runs the space end of national defense. Perhaps because NASA wants a bigger role for the first A in its name.

The only justification is the unproven (and I believe unfounded) assumption that if the configuration looks and acts like an airplane, it will have operating costs like an airliner's. This is the argument that NASA used for the Space Shuttle, but there was no background of experience to support that assumption. It has been proven to be a very costly error: The Space Shuttle represents a truly marvelous implementation of an absolutely absurd concept. Its development and use have cost some $20 billion-$40 billion, and it has set back economical access to space about 35 years.

Shuttle's costly lessons

Many flawed design choices were made in arriving at the Shuttle's final configuration:

• Wings and landing gear are the heaviest of all possible methods of recovery.
• Parallel staging is less efficient than tandem. More importantly, it also prevents the upper-stage engine from being optimized for vacuum operation.
• Use of two boosters doubles the probability of catastrophic failure. Multiple main engines increase probability of catastrophic failure by a factor of three, even though they may reduce the probability of noncatastrophic failure.
• Opting for segmented booster cases increases the probability of case failure by unnecessarily complicating case design. Monolithic cases were proposed but rejected because Thiokol, a Utah company with no access to water transportation, had to propose a take-apart design.
• Putting a crew on the first flight requires a very high reliability based on ground tests alone. A more sensible procedure would have been to fly the vehicle unmanned for cargo missions until an adequate degree of reliability could be demonstrated, as was done with the Saturn V (the Soviets, incidentally, did fly their shuttle Buran, for the first and only time, without a crew).
• Use of solid propellants in the boosters minimizes the savings that can be had through recovery and reuse. Pressure-fed liquid-propellant boosters, as initially recommended by NASA-Marshall, would have required little more than a wash-down and refueling before reuse. Solids require disassembly and return to the factory, along with replacement of many parts. The cost of solid propellants runs about $7/lb vs. an average of about 10 cents for liquids.
• Throwing away the largest part of the system, the main fuel tank, adds about $50 million to the cost per flight.
• People and cargo should never be mixed. Payloads to be transported to orbit, even for missions requiring a human presence, are 95% "stuff' and at most only 5% "meat." The provisions and safety requirements for the latter cost an order of magnitude more than for the former. Mixing the two burdens cargo flights with the same elaborate safety measures required for people.

Parallel staging, incidentally, led to the need for extremely high engine chamber pressure-3,000 psi. The consequent requirement to pump hydrogen to 6,000 psi created a nightmare of ongoing problems. Had designers chosen to ignite the liquid-propellant engines at booster burnout there would have been no need for high chamber pressures. In fact, the chamber pressure could have been so low that no pumps would have been needed at all.

Engine performance at altitude is almost exclusively a function of the area ratio of the nozzle, and almost independent of combustion pressure. Low-chamber-pressure engines are larger, but no heavier, than those using higher pressure; nor need they occupy more space. If the pressure is low enough, the nose of the first stage can be inserted into the nozzle of the second, reducing (and possibly even eliminating) the interstage structure. Very high area ratios, even those having exit bells extending beyond the diameter of the first stage, can be obtained by corrugating the thin exit cone into a cylinder and draping it over the first stage. Since low-pressure nozzle skirts can be radiation cooled, they can be made of thin stock, and hence are very light.

The vacuum specific impulse calculated for the realistic case of shifting equilibrium changes by no more than 1.5% for chamber pressures ranging from 75 psi to 3,000 psi. True, at the lower pressures the equilibrium changes from shifting to frozen at a lower nozzle area ratio, but even so, the difference in specific impulse almost certainly will not exceed 5%. For a two-stage-to-orbit configuration, with an upper-stage ideal velocity change of 20,000 ft/sec, a 5% difference in specific impulse would change the payload by about 15%. A launch vehicle using a pressure-fed upper stage would therefore have to be only 15% larger to carry the same payload.

Since the relationship of cost to size is very flat, this small increase in size would produce a virtually undetectable increase in cost. It was for this piddling difference that we developed the enormously expensive Shuttle main engines. The payload increase gained by igniting the pressure-fed engine after burnout of the boosters would have more than offset the 15% loss resulting from the slightly lower specific impulse. Thus the Shuttle could have lifted more payload to orbit with a simple, low-cost, pressure-fed main engine.

There simply is no justification for using pumps on a stage that operates in a vacuum. Moreover, even with a first stage, although the difference in performance is somewhat greater, there is no economic justification for using pumps. If a pressure-fed first stage has to be a bit larger, the slight difference in cost attributable to the larger size will be overwhelmed by the incremental cost of developing, building, and using the more complex system. A completely reusable, pressure-fed two-stage launch vehicle can be built with a gross-weight-to-payload ratio of 35. The same ratio for the Space Shuttle is 68. All that cost and complexity produced a product only half as good! The ratio of parts count is at least a hundred to one; the disparity in cost would be at least as great.

Recovery costs

t/Space CXV

Drawbacks of SSTO

Lockheed Martin X-33. Credit: Wikipedia

Formula for cheap access to space

Getting into space is a simple problem. It need not be very expensive. It can be done with a simple rocket at very low cost. It takes a lot of energy, but that energy costs only about $6/lb of payload. No new technology at all is needed. But we have to use the right technology, most of which has been around for four or five decades. We must stop trying to do it the hard way. The formula for cheap access to space involves only a few rules:

• Make the rocket bigger than it has to be.
• Use two stages to orbit, with a single engine per stage.
• Make it simple, using pressure-fed propulsion for both stages.
• Conduct launch operations from the ocean, well offshore.
• Recover the first stage by parachute in the ocean.
• Probably recover the second stage by parachute in the ocean. (Some believe that launch vehicles can be made so cheap that there is no point in recovering them. While recovery of first stages by parachute is so easy that there is no question about the payoff, the jury is still out on upper stages. We have never tried to recover an upper stage using a heat shield plus a parachute.)
• Fly it without a crew, at least initially.

Sea launches and recoveries impose no limit on size. We must build our launchers big to achieve the really important uses for space, such as orbiting solar power stations, space factories, and manned missions to the planets. The technology to get us into space for $30/lb has been around for 40 years. In our infatuation with "high tech," we have simply refused to recognize it. We should throw out 90% of the "improvements" in liquid rockets made in the last four decades, refine pressure-fed rockets a little, and apply the technology of the '50s to recovering both vehicles as well as payloads.

We appear to have learned nothing from the Shuttle program, and are getting set to repeat the error. I hope this trend will not prevail.