The Cold Equations Of Spaceflight

Space Daily.com ^ | 9/9/05 | Jeffrey F. Bell

[nuke rocketeer]

In the past month, we have been blessed with numerous leaks from NASA of various study documents relating to the new boosters that will be needed to carry out the new manned moon program. I've been monitoring the large volume of Web chatter about these plans, and have noticed a disturbing theme therein. Many Space Cadets are expressing dissatisfaction with these leaked NASA plans. They say that the Shuttle-derived boosters are too primitive, too expensive to develop, too expensive to operate, and not inspiring enough. They can't understand why we will be returning to the Moon with rockets and space capsules that look like minor variations of those used in the Apollo program 40 years ago.

[general_re]

At mile marker one I place one baloon, at mile marker two I place two baloons, and so on, I pop all the balloons at once. The pressure readings are going to differ for some time after. No matter what scale you use this is the way it works.

We're talking about just a bit more air than that, and hence, "some time after" is going to be quite a bit shorter than with your balloons. After you open your door, there is going to be some point where the pressure at the bottom of the tube is still zero - no air has reached the bottom yet - but is something else, some non-zero pressure, higher up the tube.

Now, if you happen to be standing in the middle of the tube, there is going to be a point where the pressure around you increases from zero to something, and rather rapidly too. The farther away from the mouth of the tube you're standing, the longer you're going to have to wait for that to happen, because the air has to travel down at the tunnel to get to you. But it will happen, because that air is coming, whether you paid attention to Boyle's law or not.

[SauronOfMordor]

The world's longest extension cord, huh. Someone oughtta do the math for how heavy it would need to be in order to carry the requisite current... shoot, even to support itself against high atmospheric winds.

The thing I was proposing was only for interplanetary travel, so no winds to deal with in vacuum. It would be a nuke propulsion unit trailing a tether that would drag the payload capsule along with with it, so no extension cord either. At 0.01 G, the load would not be high, but a unit that could maintain that indefinitely could build up considerable velocity

[general_re]

In your model, how does the front of the wave "know" what the final equalized pressure will be?

It's not going to be zero, and that's just about all that matters, innit?

If the pressure behind them isn't as great, as it was at the beginning, a forgone conclusion...

Do you imagine that this is enough to stop the flow to the zero pressure area farther down the tube? After all, whatever the pressure is behind the leading edge, it's not zero, right?

Basically, what you're telling me is that turbulence and M. Bernoulli - and presumably special relativity - are going to conspire to keep the molecules of air from accelerating to c. Well, that's fine, but they're still going to the zero pressure parts of the tube, and they're still going to meet up with your railgun sled somewhere in that tube as they go one way that the sled goes the other.

[meema]

Well said. We also need a new near miraculous type of power before intending to go beyond where man has never gone before.

[Ronaldus Magnus]

The rocket equation tells you that an SSTO booster using LH2 fuel and LO2 oxidizer needs a fuel mass fraction of around 0.92. That means that 92% of the take-off weight needs to be ascent propellant, and only 8% is left for everything else.

NASA needs to get outside the box. Chemical propulsion should be an anachronism. From your great link:

"The mass of the vehicle on takeoff would have been on the order of 10,000 TONS (28); most of this mass would have gone into orbit. The bomb units ejected on takeoff would have yielded 0.1 kiloton; initially the ejection rate would have been one per second. As the vehicle accelerated the rate would slow down and the yield would increase until 20-kiloton bombs would have been going off every ten seconds (29). The idea seems to have been for the vehicle to fly straight up until it cleared the atmosphere so as to minimize radioactive contamination."

At a time when the U.S. was struggling to put a single man into orbit aboard a modified military rocket, Taylor and Dyson were developing plans for a manned voyage of exploration through much of the solar system. The original Orion design called for 2000 pulse units, far more than enough to attain Earth escape velocity. 'Our motto was 'Mars by 1965, Saturn by 1970', recalls Dyson."

[Larry Lucido]

Has anyone figured out how they are going to get through the Van Allen Radiation belt alive?

There are still folks trying to figure out how to get through the Van Wyck Expressway alive.

[Phsstpok]

Basically an atom bomb with wings??

We don't need no stinkin' wings!

You put a nuke under a big steel plate and I guarantee you that sucka will FLY! You just gotta make sure you set off the next one before you fall back down and crash. Two, maybe three "pulses" and you're well out of the atmosphere, assuming you start in the atmosphere.

I think the most rational use of Orion is exo-atmospheric, however. But then you're still left with the problem of getting out of this gravity well before you can really get started.

By the way, I think the best fictional description of Orion I've seen is in Niven and Pournelle's Footfall. That's where the "this sucker will move" line comes from. Pournelle is a long time proponent of the "big dumb booster," including "old bang bang."

We WILL go back to the stars, riding a fire in the sky!

[Phsstpok]

Project bang bang was in Footfall, not Lucifer's Hammer

Those two are Niven and Pournelle's best.

[SampleMan]

Well, you're meandering argument has finally found its way into my court. Thank you for agreeing with me, even if belatedly.

My original point was that pressure rise would be linear, not instant. Thus the onset of load to the vehicle would be somewhat cushioned.

It was never my point that simply opening the end of the tube and letting air rush in was a "great idea", just that it would also result in a linear onset of pressure. However, the turbulent airflow near the muzzle might be a problem. Mr. Boyle's law certainly states that increasing volume decreases pressure, so I think I've got that one covered. The Bernoulli effect supports my argument, but only as far as pressure goes, when in actuality I'm concerned about the mass of the gas more than its static pressure. As the gas would be moving quickly, its measured static pressure would be lower than its mass would create under, well, static conditions. As the vehicle hitting it would create a whole new dynamic, it would be unfair of me to use Bernoulli as my supporting element. However, Bernoulli certainly would NOT support your original posts, which were maintaining a solid flow of air at 1 atmosphere, as the leading edge of the wave would be moving the fastest, with incidentally ever decreasing mass. Why? Because gas molecules bounce around at random. They turn when they hit something including each other.
Your point that no matter what it would eventually reach equilibrium wasn't ever contested. However, if the door were to open for even ten seconds (an eternity for the given dynamics) the air that rushed in would have the entire 100 mile tube to fill. Under your original premise a wave of air (unaffected by the flow dynamics in its wake) would be a 1 atmosphere puff that went all the way to the end, and then I assume bounce back.
Completely academic however, as letting atmospheric oxygen into a container where it would get so greatly compressed would be a bad idea. Bleeding nitrogen in as I suggested, before opening the door would be much better.

[Doe Eyes]

Let private enterprise do it. They're already doing brilliantly in near space.

Private enterprise hasn't given us little spaceships to fly around in (like George Jetson).

Some things things are not yet economically viable.

On the other hand, our "communicators" are very advanced.

[Balding_Eagle]

Aside from the fabulously profitable comsat market, private enterprise hasn't got much incentive to go into space right now.

Well that's not true. Virgin Airlies, or some spin-off, is already placed orders for spacecraft and is selling, or plans to sell, 'space vacations'.

[NicknamedBob]

"The approach that seems to make the most sense to me is using a progressive rail gun built into an equatorial mountain slope, to shoot a vehicle into space. Thus allowing a theoretical 0% usage of on board fuel to attain orbit."

" Entering the atmosphere already above 10,000 (half of the mass of the atmosphere) would decrease structural loading. A high energy laser could also super heat the flight path just before to lesson resistance (like lightning splitting the air). "

Quite early in the discussion, you described an elegant suggestion. I have only two things to recommend to make it even more useful.

First, I would not make it an equatorial mountain. I know the reasoning behind this, to take advantage of Earth's rotation. But I would place the rail gun in Antarctica. The cladding necessary to prevent damage to the ship -- the ablative material which would protect it, would be ice. Maybe even a lot of ice.

The idea about using a laser to heat the air ahead of the vessel is also a good one. That is why I used it in a Science Fiction novel published last year. "...high output laser energy is sent forward to prepare the undisturbed atmosphere in front of the ship to expand and get out of the way, so we can slip through without pushing the air..." (page 189, Chapter Sixteen)

My second reason for locating in Antarctica is a commercial one. Once the ramp is set up to launch "packages" (electro-magnetically) toward the edge of the atmosphere, one could contract with governments or individuals in desert areas of Australia or Northern Africa, or any desert on Earth, to deliver fresh water on a contractual basis for irrigation purposes. This should pay for the overall enterprise, and allow up to five million square miles of desert to become productive agricultural zones.

[RightWhale]

Better plan on building up the new gravel pad at NO a couple more inches to compensate for the extra rise of sea level.

[NicknamedBob]

I didn't want to go into my whole plan...

[general_re]

My original point was that pressure rise would be linear, not instant. Thus the onset of load to the vehicle would be somewhat cushioned.

LOL. Setting aside the fact that an "instant" rise is linear - it's merely a line with an infinite slope - I really don't think you can claim any sort of "cushioning" at all until you figure out just how much air is coming at you and how fast it's going. Basically, you want folks to believe that if you drop a column of air weighing, oh, 2 million pounds or so onto an object traveling the opposite direction at 8 km/s in the opposite direction, it's okay, because the rise in pressure is going to take at least a few milliseconds or so. Gotcha. LOL.

It was never my point that simply opening the end of the tube and letting air rush in was a "great idea"...

Was that really so hard? Really, now.

Mr. Boyle's law certainly states that increasing volume decreases pressure, so I think I've got that one covered.

Still didn't do the math, I see.

However, Bernoulli certainly would NOT support your original posts, which were maintaining a solid flow of air at 1 atmosphere...

They were? You must be thinking of someone else - I don't recall claiming anything specific about the actual pressure of the column, other than that it would be non-zero, and indicating that you could expect an approximate atmospheric pressure of 0.3 atmospheres at 29000 feet. Perhaps before we continue, you'd like to review what I've actually said, instead of responding to what you imagine I've said.

...as the leading edge of the wave would be moving the fastest, with incidentally ever decreasing mass. Why? Because gas molecules bounce around at random.

You can't be serious. Individual water molecules bounce around at random too, but that doesn't obviate the fact that they're all going over the waterfall sooner or later. If you'd like to try calculating the position of each individual molecule, be my guest, but I can save you some trouble by stating that the column of air is headed down the tube. Period.

[SampleMan]

You're a lost cause, arguing in vain attempt to prove to somebody that your original unfortunate comment is holds water, despite any amount of science. Its evident you don't even read my posts. Luckily you're not in charge of driving science forward. Or perhaps given our stellar success at NASA you are in charge.

Now going from a vacuum to atmospheric pressure over say 12 miles at 7000 mph would mean a cushioning of 6 seconds. If you don't think an engineer considers that significant to instantaneous onset, then again I can't help you, simply don't respond to this and finish junior high.

If you still can't wrap you mind around the concept of gas expansion as a particle to particle interaction, then I can't help you. I've made it as simple as I can. Vacuums are not a force in nature. Only positive pressure is. Particles only move when they have more pressure on one side than they do on the other side. Thus if air is moving into the tube AND moving down the tube the air mass cannot be of constant density. IT JUST CAN'T. Each element of the moving air must have more behind than in front or it wouldn't move, it would be static. ITS THAT SIMPLE.

Suggest you move on to arguing that the Earth is flat.

[general_re]

Now going from a vacuum to atmospheric pressure over say 12 miles at 7000 mph would mean a cushioning of 6 seconds. If you don't think an engineer considers that significant...

I don't think anyone considers that significant, insofar as it appears to me that you've simply invented numbers in an attempt to wield them the way villagers wield a cross to ward off Dracula. Any time you feel like putting a little meat on those bones, I'll be around. In the mean time, those of us who've ever felt a blast of air while standing on a subway platform will continue to wonder just what in the hell you're babbling about.

Particles only move when they have more pressure on one side than they do on the other side.

Hello, McFly? Anyone home? Open the window. Observe all that air. All that air creates air pressure outside the tube, whereas there's none inside the tube. Hence, air moves from high to low pressure, into the tube. I don't think I can do this monosyllabically, so please don't make me try.

Thus if air is moving into the tube AND moving down the tube the air mass cannot be of constant density.

As convenient as it is for you to "refute" arguments I haven't made, it's really a touch dishonest. See ya round.

[SampleMan]

I've decided to outsource your argument. Call your local HVAC people. Ask them how big a blower you need to move air through 50 feet of tube. Then ask them how big a blower you need to move it through a 300 ft tube to keep the same volume of air moving. When they tell you it will require a bigger blower, you may begin your argument, and tell them what morons they are. I'm sure they will be just as impressed with you as I am.

[general_re]

Ask them how big a blower you need to move air through 50 feet of tube. Then ask them how big a blower you need to move it through a 300 ft tube to keep the same volume of air moving.

I take it all back - science isn't your problem, literacy is. When you feel like actually reading my posts, do drop me a line, and we'll pick up where we left off.

[Interesting Times]

Excellent article.

For those who aren't science fiction fan, the title plays on the classic 1954 short story The Cold Equations by Tom Godwin.