Beginning Space Technology

My projection is that we have a 70% chance of developing hyperdrive without first destroying ourselves, that we are 12% along in developing hyperdrive, and that we should have it developed in 2043. Read my reasoning at the following link:

http://issuu.com/eanbardsley/docs/7250821_forecast_hyperdrive

Ian Beardsley
June 10, 2009

I think the most important aspect of the sciences, is design. Is what I mean by that, is the concept that with good design, you can make something that does a lot for little cost to natural resources in manufacture of the tool if you have a good idea. Buckminster Fuller invented what he termed "design science". He made the very important point that anyone designning a technology should have in mind while they are doing it, what exactly a technology is. He said it is something that in some way gives us more degrees of freedom. I find that a very important definition, because given global warming, peak oil, droughts, and so forth, his definition means technology can save us. Also that it can bring world peace, because ultimately I believe wars are due to famine caused by draughts, as we see in Africa, or, wars in the Middle East are for oil. Buckminster Fuller did say it would be a "touch and go relay race to the finish." Just what are some examples we see of technology solving environmental and political problems to possibly bring more peace and a better life for all? Desalination machines are now going to become a viable reality, as the Dutch have made filtration cheap through design, imitating life, the way cells in some oceanic life filters out salt between cells: it is in the geometry of the molecular structure of the cell wall that has allowed them to do do it cheaply, that is with little electricity, pass salt water through a filter. This means clean drinking water for a lot of people in the Middle East and Africa. They are learning to grow meat in giant sheets with bioengineering, and such factories can be put in Africa (Countries in Africa have said we can set them up there when the technology is mastered). So we see how technology can bring peace and freedom to the world. Ofcourse that is determined by how we manage such technologies politically, that we do not use western technologies to control people. In my opinion, only in love and respect of fellow humans across the globe can we be a successful worthwhile species. Also, it is interesting that the desalination machine's design came from imitating nature, for, it was Buckminster Fuller who said that human design was nothing compared to that of nature. It is no doubt important to understand what Isaac Asimov said, that the Earth is finite in mass, which means there are finite resources. This means design becomes at the crux of the most important issues, because we will not have anymore resources until we can easily travel in space and mine other planets in the solar system, unless we learn to make elements from energy (as Einstein pointed out matter is another form of energy in his famous E=mc^2). Or learn to make resources from more abundant elements (nuclear chemistry).

If the Earth is pulling on a mass towards its center with an acceleration given by

(g) = (GM_e)/(r^2)

from Newton’s Universal Law of Gravitation:

F=ma=G(M)(m)/(r^2)

where G is the universal constant of gravity equal to…

then it must have a tangential velocity given by

(v^2) = gr

to keep from falling in towards the Earth and maintaining a circular orbit (r is its orbital distance).

We can see intuitively that Newton’s law of gravitation is an inverse square law because a sphere’s surface area increases with the square of its radius times 4(pi), where (pi) is the ratio of the circumference of a circle to its diameter, equal to 3.141… and is directly proportional to the mass of the body doing the pulling.

Newton’s Law of Gravitation can be derived from Kepler’s laws of planetary motion:

1. A planet moves in an ellipse, the Sun as a focus.
2. The planet sweeps out equal areas in equal times.
3. The square of the planets orbital period is proportional to the cube of the major axis.

We launch a rocket vertically and only begin to gradually curve its trajectory a little way into the flight. There are several stages of burn (three) each tank ejects appropriately after burn out. We don’t begin to approach a horizontal trajectory until the rocket is above the atmosphere to reduce adverse effects of drag on the structural system.

We transfer orbits of a rocket by increasing the tangential velocity putting it into an elliptical orbit. After the rocket has completed half the elliptical orbit and is at aphelion, we boost its tangential velocity appropriately.

If the mass flow out the nozzle of a rocket is constant, the thrust increases with altitude due to the drop in atmospheric pressure. This causes an increase in the specific impulse (I_sp). It is a common practice to take an average for specific impulse in calculating rocket velocity at burn out where not terribly precise maneuvers are required. Increase in pressure with altitude is usually less than 20%. Specific impulse has units of time, and has been researched for many propellants for given ranges of atmospheric pressure with respect to for example, liquid oxygen and liquid hydrogen (H_2) in the percent mixture of the fuel and oxidizer. Since the mass flow rate through any cross-sectional area is constant, a decreasing nozzle diameter will increase exhaust velocity. The nozzle must then widen where the gas can expand and flow at supersonic velocity. The optimum nozzle contour is then convergent-divergent, and there is a minimal cross-sectional area. The optimum nozzle has been designed by Carl G.F. de Laval, called a Laval nozzle.

Image of Laval Nozzle:

The equation for the motion of a rocket in a straight line is:

(1) (ma) = F – D + mg cos a

Where a is the angle made with the path of the rocket and the vertical, D is the drag, and F is the thrust.

To integrate this let us look at impulse.

IMPULSE

Impulse is the integral of force with respect to time. That is

I = int [F dt] = int [m dv/dt]dt = int [m dv] = mv = delta p, the change in momentum.

SPECIFIC IMPULSE

Thrust is force caused by mass flow at the nozzle of a rocket in the opposite direction. It is standard practice to write thrust in terms of the specific impulse of a propellant denoted, I_sp. Specific impulse is impulse per weight, and allows us to express the thrust as:

F = g I_sp (dm/dt)

In other words, thrust can be expressed in terms of the change in mass as the rocket burns its fuel. (g) is gravity, dm/dt is change in mass with time. Dividing (1) through by m, we have:

(dv/dt) = g(I_sp)(dm/m(dt))dt + g cos a

int [dm/(m)] from mass empty to mass full = ln [(M_full)/(M_empty)]

where M_full is the mass at take off and M_empty is the mass after total burn. We can neglect the drag:

(2) V_bo – V_0 = g(I_sp)ln (M_full/M_empty) + gt_p cos a

t_p is the duration of the flight while in burn, V_bo is the velocity at burn out.

For steady mass flow, use the equation for thrust, F to obtain:

(t_p) = (M_full – M_empty)g(I_sp)/F