To begin with, the rocket sitting on a launching pad has VERY substantial weight (mass). After one second of burning, the mass that must still be accelerated is slightly less, due to the fuel that was used up in that second. However, the rocket body that had contained that fuel is still part of the mass that must be further accelerated. This is rather wasteful of energy.
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An extension of this concept seems obvious. Rather than having just two or three stages, why not have a rocket that has effectively FIFTY or A HUNDRED stages! These wouldn't be discrete stages in the traditional sense of rocket stages.
Imagine a simple normal rocket body that is made out of a six-inch diameter piece of pipe, ten feet long, that is filled with solid propellant fuel. (Put a nose cone on top for aerodynamic reasons and to contain the gyroscopic guidance system, parachute and payload.)
Now imagine a very similar rocket, but with one difference. Where the first rocket had a one piece pipe body, this one would be made up of one-hundred-twenty separate pieces of the pipe, each just one inch long. These sections are each stepped sections of pipe where they each drop into the section just below it. When these pieces are then stacked up, they still result in a rocket that is ten feet tall and six inches in diameter. It would still then be filled with solid propellant rocket fuel. Each small piece would have a small piece that fit reasonably tightly inside the piece just above it. This friction fit would keep the rocket from falling apart during handling of it. The solid propellant would be packed down inside the rocket so that each short section would be filled with the solid propellant fuel.
It may be desirable for each of the short sections to have minimal external fins to assist in developing dynamic stability during flight.
The fuel is ignited at the bottom, as normal. As the rocket rises, and the bottommost fuel is consumed, the fuel in the bottom-most section is used up first. As the fuel in the next section above starts burning, the thrust pushes against a small crossbar at the top of the bottom-most section. This would push that section of pipe away from the remainder of the rocket.
Rather than using the available thrust to lift the entire length and weight of the pipe body of the rocket, each section would automatically drop off as its fuel was consumed, continually lightening the remaining rocket body, allowing greater and greater acceleration to result.
Both rockets would have an initial vertical accelerating thrust of 230 pounds (500 pounds thrust minus 270 pounds weight). This would give an initial vertical acceleration of (230/270) about 0.8 G.
Using simple Newtonian analysis and the values given above, we get the following results:
After 80 seconds, when the fuel is entirely used up, the standard rocket would then weigh 110 pounds and be traveling vertically upward at 2,694 feet per second, while the hundred-segment rocket would be down to around ten pounds final weight, and would have a final upward velocity of MORE THAN FIVE TIMES as much, at 15,957 feet per second! Note that the ending acceleration of the standard rocket would be (500 - 110) or 390 pounds thrust applied to 110 pounds, or over 3 Gs. In contrast, the same 500 pounds of thrust would be accelerating a 10-pound remaining craft in the segmented rocket, so (500 - 10) 490 pounds of thrust would be accelerating a 10 pound craft, or around 49 Gs of acceleration. Incredibly different!
In addition, where the standard rocket would have attained an altitude of 145,933 feet (28 miles), the segmented rocket would already be at 382,728 feet (72 miles)! Each rocket would continue to coast upward due to its vertical velocity. They would peak out at around 49 miles and around 350 miles!
The benefits of not carrying any more weight along are extremely obvious! This approach should have value for amateur rocketry as well as for satellite launches by governmental rockets. The value of the segmenting concept depends on the relative weights of rocket body, payload and fuel, and on the Specific Impulse of the propellant fuel being used. The figures above are representative for realistic applications.
Please realize that if air friction is calculated and if the variation in the strength of the Earth's gravitational field is included, the true performance of this extremely cheap and simple rocket would be less than the numbers here. But still spectacular!
I had considered entering the X-Prize contest in the late 1990s but I truly hate doing massive paperwork and they seemed to insist on it and also my method would not have qualified for one of their conditions. I would have made sure not to spend more than $10,000 on the entire project, and did not have interest in refining it with controls or any capability for a soft landing! But where each of the competitors spent many millions of dollars to try to get their entry into space, I was pretty sure that I could have sent a smaller object a LOT farther into space than any of them expected to do,
But I have great confidence in the accuracy of Newton's laws and of the sort of rocket fuel that I felt I had access to, and I did not really see what benefit might be achieved by spending $10,000 to do this. There would certainly be a lot of complaints in that a hundred small pieces of metal would fall out of the sky during my effort, while the other X-Prize competitors expected to lose relatively few parts! As far as I am concerned, I could have done it, and sent a small object far higher than the International Space Station! Big deal, I guess!
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago