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.
The usual solution is to make the rocket into two or three stages, effectively separate rocket engines. After the first (biggest and most massive) stage has consumed all of its fuel, the entire structure of the first stage (engine and fuel tanks and everything else) is jettisoned. After that moment, the remaining rocket thrust does not have to drag along that empty hulk, so the remaining rocket fuel can be used more effectively to produce greater acceleration.
An extension of this concept seems obvious. Rather than having just two or three stages, why not have a rocket that has effectively FIFTY 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 twenty separate pieces of the pipe, each six inches long. When these pieces are stacked up, they still result in a rocket that is ten feet tall and six inches in diameter. 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. 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 fuel is consumed, the fuel in the bottom-most section is used up. 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 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 be traveling vertically upward at 4,694 feet per second, while the segmented rocket would have an upward velocity of almost THREE TIMES as much, at 13,710 feet per second! In addition, where the standard rocket would have attained an altitude of 145,933 feet (28 miles), the segmented rocket would already be at 242,988 feet (46 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.
( http://mb-soft.com/public/othersci.html )
C Johnson, Physicist, Physics Degree from Univ of Chicago