BalRoc

Solar-Thermal Rocket Design

Last updated 31 May 2002

Copyright 2000, Tom Jolly

Development of the Balloon Rocket (BalRoc, an Air Breathing Inflatable Solar Thermal Rocket

Latest news; component fabrication started for the proof-of-concept model. See it here as it laboriously plods forward.

Cheap Access To Space is heading in a dozen different directions, most of them arguably not cheap at all. The "Space Elevator" would cost numerous billions to build even after it became technically feasible, just in raw materials. Chemical launchers, no matter how efficiently you mass-produce them, require a large structure and lots of propellant to operate; a man-rated launcher is going to cost somewhere in the millions of dollars to produce. What I'd like to see is something on the level of a space-Volkswagen, or better, a "kit airplane" that anyone could buy the instructions for and build by herself.

Can a launchable spaceship be built for under $50,000 that can carry a man into space? Something anybody with a middle-range income could buy and use with a minimal amount of experience (about the level of expertise required to fly an airplane, preferably). A "Cessna" of spacecraft. This document suggests how this might be done.

Sure, these aren't the greatest pictures in the world, but at least they will give you an idea what we're working toward, here.

The balloon rocket will be an eventual entry into the X-Prize competition. The design is very unique and operable, and since it's so far and away different from all the standard chemical models, it has a good chance to revolutionize space travel. Most importantly, I think a man-carrying rocket could be built for well under $100,000 for the prototype, and perhaps $20,000 for production models. Of course, there's the chance that the reason no one else is doing this is because it wouldn't work.

The model presented here is currently only designed to get up to about 1.3 kilometers per second, with potential for design changes for higher speeds. For anybody with a pencil handy, you can easily calculate that this is more than enough to make X-Prize altitude. The main limitation to the model is material thermal limits and heat-dissipation. Better materials will lead to higher maximum speeds, and, eventually, orbital velocities (about 7.5 kilometers per second).

BASIC CONCEPT

The Balroc is a very long tube-shaped balloon that flies along the long axis of the balloon. The initial model I toyed with numerically was 10 meters long by 3 meters wide. The top half of the balloon is clear, the bottom half is a parabolic Mylar reflector that runs the length of the balloon, focusing the light from the sun (assuming you are pointing the right direction) onto a metal tube that runs the length of the balloon, down the center of it. A ram scoop exists at one end of the tube, about the same area as the nose of the balloon. A small nozzle is situated at the other end of the tube. Simply, you move through the air, scoop in air which goes into the tube, gets heated up by the solar heating tube, and exhausts out your nozzle, producing thrust. The faster you go, the more air you scoop in. At some point your drag will equal your thrust, and you will stop accelerating. That, very roughly, is how it will work.

The "break point" of the acceleration sequence, the point where drag=thrust, is modifiable by quite a few factors. To begin with, the higher you go, the thinner the air, but since you are accelerating, you can maintain a fairly constant "chamber pressure" for your rocket. Since the air is thinner, your drag is lower, somewhat, though this is not linear; the drag increases as a function of the square of the velocity, only partially countered by the decrease in density. The bottom line, though, is the higher you go, the thinner the air, and the higher your maximum speed. You can also increase your max V by making the tube hotter, that is, make the balloon longer. This has material limits, since eventually stuff is going to melt, probably the balloon itself (Mylar is good to 300F).

BENEFITS

The nicest benefits of the Balroc are as follows;

1) It's incredibly cheap to build.
2) You don't have any propellant to carry along.
3) You don't need humongous thrust just to get off the ground, it floats in the air (it's a hot air balloon, heated by the rocket tube). Your first few thousand feet of elevation are free.
4) You don't need ablative materials to enter/leave space, it's designed to enter the atmosphere very slowly, using the super-tenuous atmosphere for lift (using small control surfaces attached to the balloon, or the "payload" that the balloon carries).
5) You can use it for local fast transportation from state to state, during the day. Your fuel is free!
6) At low elevations, it's an incredibly safe vehicle. It's not going to blast toxic gases and propellants across the countryside if there's a catastrophic failure. The worst thing likely to happen is the rupture of the balloon, which would probably kill the user unless he's got a parachute; probably a good thing to carry along anyway. If you need to abort your mission for some reason, say, you forgot to bring a lunch along, you just turn away from the sun, lose your thrust, and float gently down to your back yard in Hometown USA. Watching out for power lines, of course.
7) The technology might be adaptable for solar-powered turbine mini-power plants for home power, off-the grid.

TECHNICAL DETAILS

There are obviously some technical bits that I've oversimplified. The balloon has to be fairly rigid in form to maintain a decent parabolic shape, but there's been a lot of work done on rigid inflatables. Using aluminum instead of mylar isn't entirely unworkable, especially since it has a pretty high melting temperature and it's fairly light. The balloon has to carry a pod slung underneath with a man or two inside. It also wouldn't hurt to have a water tank; at some point, outside the atmosphere, you'll reach the "break point" I talked about and you'll want to use your own fuel to bypass the 1.3 kps limit I mentioned. Water is cheap, safe, and easy to pump into the head of the thrust tube. As your elevation increases, too, you can dump some of your balloon-envelope gas into the tube as propellant, also.

You'll want some sort of control surfaces so you can use your velocity at 1.3kps for lift in the upper stratosphere, and to help you gradually slow down as you reenter. You don't want to do a "Shuttle plunge" into the atmosphere, you want to spend as much time as possible skimming along the top of the stratosphere, bleeding off excess velocity just a little bit at a time. The kinetic energy of the gas striking the nose of your ship won't be a whole lot more than the kinetic energy of the gas striking your lift surfaces and keeping your ship up, based linearly on the ratios of the two areas, that is to say, you aren't going to heat up very much at all. For lift, something as simple as a flat plate tilted 6 degrees from horizontal, with an aspect ratio of 2, will give you a lift-to-drag ratio of 6:1. If the scoop has an drag of N, then lift surfaces with a drag of .3N will still give you a lift of 1.8N, versus the 1.3N total drag you have. Your maximum elevation is limited by your lift capability. Since your maximum velocity is limited by Thrust = Drag, your altitude is limited by 0 = Lift + Buoyancy - weight. When total lift plus buoyancy is less than the weight, you stop rising. At some elevation, buoyancy becomes zero. In the example above, the total lift-to-drag ratio will be 1.8/1.3, or 1.38, that is, lift = drag * 1.38. Substituting Thrust for Drag, and plugging this into the formula, we see our limit of lift controlled by 0 = Thrust * 1.38 - weight, or, 1.38*Thrust=Weight. This is an interesting result; it implies that as long as Thrust is more than the .72 * weight of the vehicle, you have lift. You could operate in rocket mode if it Thrust were equal to weight. Increasing the Lift by increasing lift-surface area also increases Drag, limiting your top speed at a given elevation, but requires less thrust to produce lift. Thus, if we continue expounding on the numbers given here, a mass of 2000 kg would require a thrust of 9.8m/s^2*1500kg, or 14,700 Newtons for continuous lift and zero buoyancy. This is pretty unlikely, based on the numbers I get for Newtons of thrust per square meter of collector (see other Balroc page).

The model I'm expecting to work is pretty much just a tube with a scoop on one end and a thruster on the other. The fact that a certain amount of air goes in one end and that same amount exits at a higher velocity at the other end gives you a net thrust. The obvious question arises, "why won't it just come to a stop, since the pressure at either end has to be the same?". I'm suspecting this may not be true; supersonic gas passing through a DeLaval nozzle throat produces a very low-pressure area, so the nozzle area may, in a fashion, suck air in from the front of the vehicle. Anyway, there are technical work-arounds (pumps, or pulsing the input) to avoid this problem if it doesn't work the way I expect it will. Also, the pressure-baffle valve that I will talk about later offers a solution. This is a rather important component for more than one reason.

To get any thrust at all, the tube wall has to be hotter than the kinetic temperature of the gas hitting it, which is, in effect, the velocity at which you are traveling. At a velocity of 1334 meters/sec, using the formula (1/2)*mv^2 = (3/2) *kT, and assuming we are working with diatomic gases, principally Nitrogen, (28g/mole) the kinetic temperature of the gas at this velocity is about 2000K. Copper melts at about 1356K, so this is well above what we can do with a copper tube. A pure graphite tube, on the other hand, is good to about 3500K, and we could, in fact, push the velocity envelope a little higher (not much, though...keep in mind the temperature rises as a function of the square of the velocity. Note that if we carry a good-sized tank of Hydrogen with us, we can go quite a lot faster; since Hydrogen can give us a molecular mass of "2" versus the molecular mass of "28" for N2. This means (keeping the temperature at about 2000K), we can make V^2 14 times higher, making V about 3.74 times higher (about 5 km/s). Pretty darned close to orbital velocity. Of course, now we're talking about carrying a big tank of Hydrogen along. Interestingly, we can do something similar just using water, though we wouldn't get nearly the delta-V out of it that we could with the same mass of hydrogen. The whole idea of the thrust limits were based on the idea that the kinetic energy of the gas hitting your scoop must be less than the kinetic energy of the gas leaving your exhaust. If you start putting little amounts of water into the tube, your mass out is greater than your mass in, and the balance equation changes in your favor.

(Update, May 2002) The previous paragraph assumes that we are still using kinetic lift and driving hard against the tenuous gas of the upper atmosphere, thus resulting in the speed limits noted. However, if we start dumping water into the tube, and the resulting thrust is high enough, we can go directly to rocket mode and bypass the whole lift-drag-limit scenario, which could conceivably put us into the orbital velocity range. Have to run the numbers; I imagine the mass-ratios will be very favorable, though.

A lot of this is based on the idea that your chamber pressure is kept fairly constant, and your solar flux is fairly constant, and the mass-throughput is constant (a folded tube may also be necessary if the heat transfer isn't fast enough to keep up with the throughput). To keep the mass flow-rate constant, you need to go faster at higher elevations. Initially, your acceleration is very high, but gets slower and slower as you approach the thrust=drag cutoff. Incredibly, if we are cruising at about 1334 m/s, and we manage to point ourselves straight up, then we will come to a halt (v=0) at about 90 km above our starting point, well outside of the "limits of atmosphere" boundary. When we fall, we will once again be going about 1334 m/s as we enter the atmosphere. Of course, the angle of entry would be awfully critical, considering how fragile your vehicle is. The stress of going vertically from your horizontal cruise-mode would likely tear the ship apart. Still, reaching 100 km doesn't seem unreasonable at all.

Maximum Altitude at Steady-state Thrust

This is based on four factors; Lift, Drag, Weight, and Thrust. We assume that at a certain speed the Drag will equal the Thrust, a function of how hot we can run the tube. Our elevation at that point is based on Lift versus Weight. We can increase Lift by increasing the area of the lifting surfaces, which also increases Drag, slowing us down a bit. But, if we design so that a speed of 1m/s is high enough to keep us airborne at sealevel, then at 1334m/s, we should expect the same lift from gas which is about 1000 times as tenuous, which means we should be able to "cruise" nicely at 50,000 meters. This, to say the least, would be great for intercontinental flights.

Delta-P Pressure Baffles.

The whole purpose of the Pressure-Baffle is to create a delta-P across it without using any moving parts. Its success would mean that I could ignore having to use pulse-mode valved-input rockets, or turbine-input, or turbo-pump input, all quite expensive and weighty alternatives. It would also mean a lot of money in the arena of alternate energy sources, possibly supplanting the standard concept of a silicon solar-panel. However, until I test this thing (next few months or so) and file for a patent, I'm not going to go into a lot of details on how it works. If you read this site before, you already know. But, I'll give you a hint; it has to be really hot, and really small, to work.

The pressure baffle, in the context of the BalRoc, would mean I could develop a positive chamber pressure without having to worry about back-pressure neutralizing my thrust. And, the higher the chamber pressure, the better the efficiency of the rocket (generally speaking). If it doesn't work the way I expect it to, I'll have to go to something like a turbine or pulsed-input. If it does work, it will be an incredibly cheap alternative to both.

Magnetic propulsion.

Rough calculations predict that under ideal circumstances, the "Balroc" rocket will lose its ability to accelerate at about 1.3 kilometers per second. I based this on a 10-meter balloon, 3-meters wide, if I remember correctly. At this speed, the kinetic energy in (KE=0.5*mv^2)equals the kinetic energy out. If one was going for the X-Prize, this would easily be fast enough to pop up out of the atmosphere up to 100 kilometers, and come back down again. And, the vehicle would be immediately reusable. One of the nicest aspects of the vehicle is that it never goes like a bat out of hell through thick atmosphere, like the Shuttle does, so it doesn't need any sort of heat shields. It reenters very, very slowly, producing just a little less thrust than drag, and actually using the tenuous atmosphere for lift. A launch thrust cycle, instead of lasting 3 minutes like some modern boosters, would last for many hours, gradually going higher and higher into the tenuous stratosphere. You'd actually be using some sort of little "wing" to get non-aerodynamic lift from the super-thin air you're hitting, since you aren't up to orbital speed. The only way to get higher, and thus faster in the even thinner atmosphere, is to use the "fluid" of the plasma at that altitude to push against.

So what's this got to do with magnetic propulsion? One of the ways to go faster than 2kps (besides carrying water), is to use a system that can stand a lot higher heating than normal metals can. Ultimately, if you want to achieve orbit, you have to plow through super-thin atmosphere at 7.5kps, and since the kinetic energy is a function of the square of the velocity, and the temperature is a function of (1/3k)*mv^2, then the kinetic temperature of your gas has to be up around 63,200K, which is a lot hotter than molten diamond. This is a bad thing. Of course, this is a very thin gas distributed over a large thermally radiating scoop, so this isn't an insurmountable engineering problem.. At 2kps, your temperature is only about 4500K. At temperatures of 63,200K, you're probably going to need magnetic containment fields to act as your tube, collector, and thruster nozzle. Of course, you aren't *really* running into gas that's heated to 63,200K, it's *you* that's travelling along at 7.5kps, not the gas, making the gas kinetically equivalent to that temperature, but it also means that very little of the gas is ionized (1 part in 100,000,000 in the ionosphere). So, while magnetic confinement might give you some control over the gas you encounter, you'd still need some way to ionize the gas as it goes through your magnetic-tube so you could magnetically control it, and then you'd need some way to convert your solar collector into a magnetic gas-rail-gun.

Pulling negative g's in the atmosphere to get to 11KPS.

So, once you've overcome all these other technical difficulties, you can tackle the tricky act of pulling negative g's as you zoom around the Earth. Anything greater than normal orbital velocity is going to send you off into the wild blue, but since you want to achieve escape velocity, you stay IN the atmosphere using control surfaces that will allow you some maneuvering, slowing pumping up your velocity using solar heated air! Once you get to about 11kps, you let yourself out of the forced orbit and let fly to your next destination, Mars, perhaps. Forcing yourself to stay in orbit while pushing 11kps will produce an interesting effect; it will seem to you that "gravity" is pointing away from Earth, that is, everything on Earth should be falling away from it. Hopefully this won't happen any time soon.

Useful design data, such as Elevation Vs. Air Density, can be found here. I'll add more to this page as the design process moves along, such as formulas for nozzle design criteria and my data for other design characteristics of the BalRoc.


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