Space Transport and Engineering Methods/Methodologies

Methodologies

Systems Engineering

Individual humans are not smart enough to design complicated space hardware. An engineering process known as "systems engineering" has been developed over time as a way to get the job done. It allows breaking down a complicated project in such a way that the smallest pieces are simple enough for humans to design, then putting the pieces back together so that the total system does what you wanted. The systems engineering process can be used for any complicated engineering project, but aerospace projects are particularly suitable. The steps in the systems engineering process include:

• Defining the goal
• Determining the evaluation criteria
• Selecting alternative approaches
• Optimization and evaluation
• Flowdown of requirements and interfaces
• Detailed design
• Production of components
• Assembly and test to requirements

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The traditional job of the rocket designer has been to find the best compromise between high cost and small payload when going to Earth orbit. Larger payloads can be achieved by making a rocket last a single flight (thus using lighter structures than ones built to last many flights), and by dropping parts of the propulsion system (as fuel is used up less thrust is required to maintain acceleration, so you can drop engines). These measures are expensive (you have to replace or re-assemble the rocket), but were necessary in the past because of the weight of structures and the low performance of chemical rockets.

Today the job of the space transportation system designer is much more complex. There are many more propulsion concepts available (over 60 in this document alone), and missions are not limited to getting into Earth orbit. Technology (such as strength of available materials) is progressing rapidly, and the market for space transport has expanded beyond the mostly government customer of the past to include a substantial commercial element. Selecting the optimal transportation system design is a primarily a function of the mission model, and secondarily a function of the risk level you choose and available capital you have to work with..

Mission Model

In space transportation system design, the "Mission Model" refers to the information on what you want to transport in terms of quantity, size, mass, type of cargo, etc. and when you want to transport it. A mission model is developed from a project goal to define specific operating characteristics that the transportation system must meet. For example, the Apollo Program had a goal of landing a man on the Moon before 1970. This is not sufficient information to design a transportation system from. A mission model developed from this goal would be something like:

Cargo characteristics:

Number of crew to the lunar surface: 2/mission Maximum Stay time: 4 days/mission Additional science equipment: 250 kg./flight Lunar samples returned: 100 kg/flight

Mission Schedule:

First Flight: as early as possible but before Jan 1, 1970 Flight quantity: 10 to lunar surface (this was the original plan) Flight rate: 4 flights/year

Basics of Space Transport Design

The rocket equation

Some numbers will illustrate the problem. A good chemical rocket has an exhaust velocity (the speed of the gases coming out the nozzle) of 4500 m/s. The velocity to reach orbit is about 9000 m/s. The basic equation of rocketry, the "rocket equation" tells you that the ratio of rocket mass when full of fuel to rocket mass after burning the fuel is:

m(i) / m(f) = exp ( dV / v(e) )

Where:

m(i) = intial mass m(f) = final mass dV = velocity change (9000 m/s in this case) v(e) = exhaust velocity (4500 m/s in this case)

So in our example, dV/v(e) = 2, so m(i)/m(f) = exp(2) = 7.39. Therefore 1/7.39, or 13.5% of the initial weight is left on reaching orbit. In the past (before 1980s), the structure would be about 15% of the takeoff mass, so there was a negative payload (i.e. you couldn't get to orbit), even with a throw-away structure.

The rocket equation is generally valid for any type of reaction engine with any velocity change.

Staging

In an attempt to increase the payload fraction, staging (dropping part of the rocket during the ascent) has been used. The vehicle is much lighter as it burns off fuel. Less thrust, and hence fewer or smaller engines are required in the later part of the launch. As propellant tanks are emptied, they can be dropped off. A set of engines and tanks dropped as a unit is called a 'stage', and they are numbered in the order they are used and dropped (hence first stage, second stage, etc.). The drawback to staging is that your vehicle must be re-assembled before the next flight. This makes operating the vehicle more expensive.

To continue the example above, let us split the vehicle into two stages, each of which provides half of the velocity to orbit. Using the rocket equation, each stage has a ratio of initial to final mass, or mass ratio, of exp (1) = 2.72:1. Thus after the first stage burns it's fuel, 1/2.72 = 36.8% of the initial vehicle remains. The fuel for the first stage represents 85% of the total first stage mass. The other 15%, the structure and engines, is 11.1% of the total vehicle mass. So the first stage in total is 74.4% of the total vehicle. The second stage and payload is then 25.6% of the takeoff mass.

Similarly, the second stage has the same mass ratio, and so 36.8% of it's mass is left after it burns it's fuel. Taking 15% for the structure, we have 21.8% of the second stage+payload for the payload alone. Thus the payload = 21.8% of 25.6% = 5.6% of the total vehicle mass. This is a positive figure, unlike the single stage case, which is why all rockets so far have used more than one stage.

Structures

The non-fuel mass of a stage can be grouped into engines, tanks, and 'other'. Engines produce 40-100 times their weight in thrust. For liftoff from the ground, you want about 1.3 times the vehicle weight in thrust, so the engines are about 1.3-3% of the total weight. A large tank, such as the Shuttle External Tank, can weigh 4% of the fuel weight, but other tanks can range up to 10% of the fuel weight. 'Other' inlcudes plumbing, parachutes (if you want to use it again) guidance systems, and such non-propulsion parts. It can range from 1% up to 10% of the total weight.

Older materials required 15% of the total weight for one-use structures. Modern materials require about 10% of the total weight for re-useable structures. Structures tend to get heavier at the rate of 10% for each factor of 10 in life. So a 100-use structure will be about 20% heavier than a one-use structure.

Orbit equations

The circular orbit velocity, v(circ), for any body can be found from:

v(circ) = sqrt ( GM/r )

Where:

G = Gravitational constant M = Mass of body orbited r = radius to center of body orbited

G is a univeral constant, and the mass of the Earth is essentially constant (neglecting falling meteors and things we launch away from Earth), so often the product G*M = K = 3.986 x 10^14 m^3/s^2 is used.

Escape velocity = sqrt ( 2GM/r ), or sqrt(2) = 1.414 times circular orbit velocity.

Ascent Trajectories

Circular orbit velocity at the earth's surface is 7910 meter/sec. At the equator, the Earth rotates eastward at 465 meters/sec, so in theory a transportation system has to provide the difference, or 7445 meters/sec. The Earth's atmosphere causes losses that add to the theoretical velocity increment for many space transportation methods.

In the case of chemical rockets, they normally fly straight up initially, so as to spend the least amount of time incurring aerodynamic drag. The vertical velocity thus achieved does not contribute to the circular orbit velocity (since they are perpendicular), so an optimized ascent trajectory rather quickly pitches down from vertical towards the horizontal. Just enough climb is used to clear the atmosphere and minimize aerodynamic drag.

The rocket consumes fuel to climb vertically and to overcome drag, so it would achieve a higher final velocity in a drag and gravity free environment. The velocity it would achieve under these conditions is called the 'ideal velocity'. It is this value that the propulsion system is designed to meet. The 'real velocity' is what the rocket actually has left after the drag and gravity effects. These are called drag losses and gee losses respectively. A real rocket has to provide about 9000 meters/sec to reach orbit, so the losses are about 1500 meters/sec, or a 20% penalty.

Combining Methods

There is no law that says you have to use the same method of propulsion all the way from the ground to orbit. In fact, it makes sense to use different methods if one does better in the atmosphere and another does better in the later, vacuum part of the ascent.

In past rockets, this has been done by using different type of fuel for different stages in a rocket. In the early part of the flight, air drag is important, so a dense fuel is preferred. A dense fuel means smaller fuel tanks, and hence less area to create drag. Thus the Saturn V used liquid oxygen/kerosine and the Shuttle uses solid rockets for the first stage, both being dense fuels. Both use liquid oxygen/ liquid hydrogen for the second stage. This has the highest performance in use for a chemical rocket fuel.

The Pegasus rocket uses an aircraft to get above the bulk of the atmosphere. A sub-sonic jet engine has about ten times the performance of a chemical rocket, mostly because it does not have to carry oxygen to burn.

Many, many propulsion combinations are possible in getting to Earth orbit and beyond. A large part of space propulsion design is choosing which methods to use and when to switch from one to another.