May 2005
Our search for a launch site has stalled our program for nine long years! This is the first newsletter in two years! The whole situation has been pretty depressing. It's going to take a lot but I have to get motivated again. My biggest tasks will be to clean the house and cut the yard! A general shareholders meeting needs to be called to go over plans for the launch campaign and the promotion of our new product offerings. More news soon.
THE "POP FLY" ORBIT
Rocket Science for Earthlings #41
a continuing series for the gravitationally impaired
The best orbit is the minimum energy orbit. It's just above the atmosphere at about 100 miles high, and precisely circular. Today it is called a parking orbit, where payloads are parked until they are checked out before being boosted to higher orbit. If something goes wrong with the satellite, atmospheric drag will soon bring the payload back into the atmosphere, safely destroying it. It takes a very precision launch vehicle to hit that minimum energy orbit. Hitting the minimum energy orbit is also a great demonstration of your precision guidance system. Precisely hitting an orbit is a good demonstration of your country's military ability to precisely hit a target with an ICBM. Precision guidance requires a precision inertial system for out of sight control or precision tracking radars and down range tracking stations to control the vehicle, all very expensive. The Soviets demonstrated this ability, the US demonstrated this ability, and now no one questions the need to hit the minimum energy orbit for a satellite launch. Except me of course.
Getting something into orbit cheap is my goal. A precision guidance system is very expensive. So, can you get into orbit with a really cheap guidance system, from one location. MAYBE. Go straight up, like a cheap sounding rocket, way way up, like maybe 115,878 miles up. It takes a lot of energy, more than the minimum energy orbit, but the guidance problem is easy, the vehicle is always in sight, straight over head, well at least during the boost phase. You can use lots of cheap dumb stages and just keep pushing straight up. Now, the fun part is what you do when you get way up there, you turn left. :-) The idea is to hit a highly elliptical orbit with the apogee way out there and the perigee (the close approach to earth) just above the atmosphere. A satellite in a highly elliptical orbit will have very low velocity at apogee and very high velocity at perigee. A sounding rocket coasting out to a very high altitude apogee on a straight up flight path would of course come straight back down. Give a little kick, not much really, 487 ft/sec, to the side, at apogee, and the descent would miss planet earth and go into orbit. Whatever the case, you would want to reach apogee a multiple of 24 hours after the launch, as in the 48 hour case above, then the orbital insertion event would occur in line of sight, directly overhead from your launch facility, very easy to control, cheap. John Eisele gives a good discussion of such an orbit in his book "Astrodynamics, Rockets, Satellite, and Space Travel", well, he discusses actually hitting planet Earth, but he also defines the criteria for missing the planet too. In case you're wondering, you can't get into orbit with a straight sounding rocket, because the point of engine cutoff is always a point on the orbit and sounding rockets finish too low in the atmosphere. The straight up shot would have a safety advantage in that failure to insert into orbit correctly would result in the satellite destroying itself reentering the atmosphere, some multiple of 24 hours later, which also suggests a reentry and recovery possibility but that would need better guidance again. High apogee insertion would also allow access to polar orbits as easily as an orbit with the plane at the launch site latitude, or you could lean south and try for equatorial. While this is probably not a good launch scenario for big commercial payloads, it can be used for a first time launch, by an entrepreneurial launch group, trying to do a launch on the cheap.
PS If you're developing nearly escape velocity anyway, why not go to the Moon, it's actually easier than getting into orbit, no left turn, just launch towards the Sun three days before new Moon, when you get there the Moon will be there and the sphere of influence of the Moon is about 60,000 mile in diameter. Add a little retro fire to slow down and the payload should drop onto the Moon.
Spin, Spin, Spin
Rocket Science for Earthlings number 48
a continuing series for the gravitationally impaired
There seem to be two types of explanations for gyroscopic motion, really really simple or, matrix calculus which is as difficult as it sounds. Simple explanations do not allow you to make the calculations necessary to design spacecraft and the matrix calculus explanations, while they might be absolutely correct and elegant - well it would take me two years of study just to understand the math. So, I've come up with a much simpler system which does make calculations possible but that I can work with. Most explanations of gyros explain the circular precession of a gyroscope due to the Earth's gravitational field, but in Space a spinning spacecraft acts as a free gyroscope. Only the impulse of rocket thrust, either as short bursts of as continuous thrust can act on the spacecraft.
First, lets us pay homage to the law of conservation of momentum which makes it possible to understand gyros. All hail to Newton - or is it Galileo? When a mass is in motion and is acted upon by an impulse of outside force, it's vector direction of motion (momentum) is changed. The vectors add and the mass leaves on the net result vector. The best example of this is the motion of the puck on an air hockey table.
After the impulse the puck is on a new course, with just a little more speed. Now consider the example of a spacecraft in orbit. An impulse (small of course) applied at a right angle to its course will not cause it to fly off into deep space but will change the plane of it's orbit. The same is true of the gyro, this is precession.
Now let's give an example from a historical spacecraft. Syncom was a spinning disk shaped spacecraft which had full attitude and translational control with just two thrusters as opposed to the usual twelve needed for a non spinning spacecraft. A very neat and simple design that had a lot going for it. Both thrusters were pulse fired, the attitude thruster could precess the spacecraft into any attitude, and the translation thruster would push at right angles to the spin axis. You just had to pick the timing of the firing pulse to change the attitude or push the spacecraft anywhere you wanted it to go. The firing dwell could be up to 60 degrees of rotation.
But how to calculate? The equations, yes math! The equations for rotational math are exactly like linear math with different symbols;
* LINEAR FORCE = MASS * ACCELERATION
* VELOCITY = ACCELERATION * TIME
* MOMENTUM = MASS * VELOCITY
* ROTATIONAL TORQUE = INERTIAL MOMENT * ROTATIONAL ACCELERATION
* ROTATIONAL VELOCITY = ROTATIONAL ACCELERATION * TIME
* ANGULAR MOMENTUM = INERTIAL MOMENT * ROTATIONAL VELOCITY
* and TORQUE = FORCE * RADIUS FROM CENTER OF MASS
You need two things, the moment of inertia around the spin axis, and the moment of inertia at right angle to the spin axis (this has to be averaged if the masses inside the spacecraft are not distributed equally) these are different. Once the spacecraft is spun up (leave this to the booster rocket) the moment of inertia about the spin axis times the rotational velocity (one revolution is 6.28 radii or radians) gives you the rotational momentum. This is the momentum vector. Now divide the torque of the thruster impulse by the moment of inertia at right angles to the spin axis times the duration of the thrust times the inertial moment at right angles to the spin axis, this gives you the impulse momentum vector. Do the vector addition and measure the angle of the precession. This is basically a graphical or trigonometry approach but much easier than matrix calculus. I hope it works, as usual I working without a net here, this method will probably work if there is a large difference between the spin and impulse momentums.
Now, how do you measure the moment of inertia? There are formulas for basic types of objects, see a good college physics book, but spacecraft don't fit into those models, so you must measure the moment with a trifilar pendulum. Take two triangles, one fixed to the ceiling, one hung below on three wires. This system will rotate around a vertical axis with a period defined (so I've been told) by; time = 2 * pi * radius of gyration * square root of (the hang length divided by gee times the moment of inertia). I'm going to have to build one of these and try it out. First add a small mirror to the bottom platform to give you a reflected light beam spot on the wall to measure the timing, then measure the empty oscillation rate, then put several test items on the platform to get a good idea of how the system reacts. Simple point masses with radius from the rotational axis r have an inertial moment defined as I= M*r^2. Soon you should have enough information to design your own spinning spacecraft!
Go Figure - Growth Factors
Rocket Science for Earthlings number 49
A continuing series for the gravitationally impaired
The Devil is in the details - No, the Devil is in the Mass Ratio at least for rocket scientists. You get your ISP number when you choose the propellants and you don't have a lot to say about it, but the mass ratio depends on how much money you have to spend. There is always going to be a minimum cost point in rocket design, too heavy is expensive and too light is expensive. Of course upper stages will have better mass ratios than lower stages, but how do you get an idea of what weights will be for each pound of payload?
First find out the velocity needed for the mission and divide it by the number of stages to get an average Delta Vee for each stage. Plug this and the expected ISP into the rocket equation (V=ISP*lnMR*G) and you will come up with a mass ratio number greater than (>) one. There are two ways of expressing mass ratio, > one and < one, and we need a mass ration number less than one, so, (MR - 1)/MR=(MR < one). Or the other way 1/(1-MR)=(MR > one).
Now we can figure the growth factor. Each stage will have two mass ratios, the stage mass ratio, equal to the propellant divided by the propellant plus the stage structural mass (MR=PR/(PR+ST), and the working mass ratio, which includes the mass of the payload (PL) which the stage is pushing, (MR=PR/(PR+ST+PL). The working mass ratio is always lower because of the added mass of the payload. These two mass ratios determine how big the stage should be, the growth factor. The Growth Factor = the working mass ratio / (the stage mass ratio - the working mass ratio), or GF=WMR/(SMR-WMR). Example, for a payload of 1, with a working mass ratio of 0.5, and a stage mass ratio of 0.66, the stage would have a mass of 3.125 the growth factor, 2.0625 of propellant, 1.03125 of structure, and 1 payload.
For the next stage, the payload would be 3.125+1=4.125, times the growth factor of 3.125, its mass would be 12.890625. Things just keep adding up from there on down. At some point it's a good idea to stop staging and start refueling, Low Earth Orbit is a good place.
The High Cost of Staging
Rocket Science For Earthlings # 51
A continuing series for the gravitationally impaired.
Statement of unknown origin, but widely used and believed, and often repeated; "The cost of a rocket goes up exponentially with the number of stages." I hear this nearly every time when presenting Minimum Cost Design launch vehicle projects. And, I suppose that it is true for the person who originally stated it, probably a NASA bureaucrat. The effect of using multiple stages on launch vehicle cost can be represented by the formula; Cost = X (to the n), where X is the number of stages, and n is the inefficiency of the launch organization. For NASA every new stage means, a new contractor, another oversight contractor, another auditing contractor, more environmental studies, new technology development programs, stage interface committees at each end of the stage, and lots of consultants. All a good recipe for exponential cost growth.
It's sort of like walking a dog. One is an easy enjoyable walk, two is much, much more difficult, three or more is a nightmare! However, it should be remembered that an Inuit, (Eskimo), can easily handle twenty half wild sled dogs in almost impossible conditions. He is very good with a whip, and does not allow middle managers to come between him and the dogs.
Commercial organizations don't need all that bureaucracy, and they can fire people. They can take of the two great advantages of staging, a smaller vehicle, and lower technology level.
The Soviets used multistage vehicles often, but kept the cost down by using common technologies for most stages, and working a small number of people very hard. The Soviet manned vehicle Vostok was a two and a half stage system, while the U.S. Mercury / Atlas was a one and a half stage vehicle.
How much is a brick worth?
Rocket Science for Earthlings # 43
We train our engineers to build airplanes, then we ask them to build rockets, is it any wonder that our rockets look like airplanes stood on end.
So, take a brick, one pound in weight, and stick it somewhere in the airframe of a Boeing 737. How much is it going to cost you? Just doing some back of the envelope figuring, with current fuel costs, and over the long life span of a 737, about $1890.48. Pretty expensive brick. It would pay you to have somebody go look for that brick. If you have a fleet of Boeing 737s you should hire somebody to make sure that people don't leave bricks on your aircraft. You should certainly demand that Boeing remove any useless brick shaped objects from any new 737 you might want to buy.
The problem is that on an airplane you're going to haul that brick around for many years and many many miles. On a Minimum Cost Design rocket you're only going to look at that brick for a few seconds on the booster, and a few minutes on an upper stage. That makes a big difference. On a booster that runs for 50 seconds, the brick will cost you ........ 10 cents. Not even worth worrying about. A ratio of 18904.8 to 1. Of course if you noticed someone loading a truck load of bricks onto a MCD booster you might be slightly concerned.
In structure, the Apollo Saturn V is very similar to the Boeing 747. They were both designed at about the same time by the same people, aeronautical engineers.
P.S. This also applies to automobiles, one pound = $10.
THINGS FALLING FROM HIGH ALTITUDE
RSE # 36
If you want to break a stack of things, put a space between them, that's how the karate guys break a stack of bricks, they put spaces between them. Example; A single clay skeet tile breaks when a 1 oz steel rod dropped from 3 inches hits it. Two clay skeet tiles stacked with nothing between them will both break at 18 inches, which is a little better at 2.44 times the momentum. But, put sand between them and it requires 36 inches or 3.46 times the momentum to penetrate both tiles. Make the stack three layers of tiles with sand between them and it takes 4.28 times the momentum of the two sand buffered tiles or 14.83 times the momentum of a single tile to penetrate through all three tiles. Now why is this important. Well, if you're sitting in a bunker with a heavy steel missile headed directly at you from a high altitude, you really really want a lot of energy absorption between you and the rocket. Multiple layers of steel reinforced concrete with sand and gravel buffers between them will work best to absorb that energy. I'm thinking four layers with a layer of old auto cylinder heads thrown in for good luck.
THE LATEST ON THE NASA CREW EXPLORATION VEHICLE
There seems to be very little information available on plans for the NASA Crew Exploration Vehicle that will be the replacement for the Space Shuttle. What little I have seen of the designs combines the worst parts of the Shuttle with the worst parts of the old Apollo capsule. This strategy is probably planned to support keeping the Space Shuttles in operation, forever. NASA is so enamored with the Space Shuttles that it is now in the business of failure, producing designs that are so bad that the only alternative is to continue operating the shuttles.