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Outward Bound
November 1946 Air Trails

November 1946 Air Trails

November 1946 Air Trails Cover - Airplanes and Rockets Table of Contents

These pages from vintage modeling magazines like Flying Aces, Air Trails, American Modeler, American Aircraft Modeler, Young Men, Flying Models, Model Airplane News, R/C Modeler, captured the era. All copyrights acknowledged.

By 1946, nobody had ever even launched an unmanned rocket into outer space, much less a manned one. Nevertheless, plenty of people were working toward it. With World War II having been over for a year and much of the technology developed being applied toward future wars and societal advancement, the dream of exploiting a presence in orbit around the earth was hotly pursued. The world's superpowers were engaged in a race into space both for prestige and military advantage. As is the case today, countries pretended to get along well enough to cooperate on shared goals, but we all know behind the scenes scheming was going on about how to apply lessons learned to the disadvantage of "them" and to the benefit of "us." It is a survival of the fittest scenario. Unfortunately, when you cannot trust "them" to not do the same to "us," offensive and defensive plans are required - it has always been so and probably always will be ...but, I digress. This article by Will Ley delves into some of the then-anticipated issues that need to be dealt with in order to develop a presence in space - escape velocity, weightlessness, life support systems, navigation, structural integrity, propulsion systems, etc. Back in the day, there were still physicists that doubted rocket engines could provide thrust in the vacuum of space (they must have skipped class when Newton's third law of motion was discussed). It is a very interesting read from beginning.

Outward Bound

Outward Bound, November 1946 Air Trails - Airplanes and RocketsArticle by Willy Ley

Illustrations by Frank Tinsley

This control-room scene may be quite normal during flight outside the atmosphere. The two-deck cabin is a pressurized cylinder with domed ends, similar to the forward compartment of a B-29 set on end. The floor is a thick foam rubber mat upon which crewmen lie prone during the initial acceleration. Spring loaded safety belts hold them in position and two recessed panels carry the necessary controls. Near one wall an airtight hatch leads to the airlock and outer door. Above it another hatch gives access to the automatic instrument compartment. The ceiling is illuminated by fluorescent tubes set in a cove above the instrument panel, and an air grill in the center of the dome connects with the air conditioning system. The room is walled with 24" panels, in which instrument groups alternate with stowage cabinets and double paned ports. One port on either side is fitted with a retractable astro-dome carrying a periscope which reflects a 360° view upon a series of recessed mirrors which frame it. This. arrangement permits all around vision from any part of the control room. When the ship has reached its final flight velocity gravitational effects on the occupants disappear, and they float freely about the interior of the cabin. A gentle push in any direction serves for movement, and rubber grab ropes and foam rubber panel padding prevent injuries. In this scene, the astrogator is braced upright, while the engineer changes a film magazine in a more convenient upside-down orientation. The pilot, meantime, dozes comfortably in midair, exactly like the relaxed citizen in present-day mattress ads.

Control-room scene may be quite normal during flight outside the atmosphere - Airplanes and RocketsThe picture on the cover is, of course, a photograph of a captured German V-2 rocket rising from the White Sands proving ground in New Mexico on a vertical 85-mile journey. If such a picture had appeared twenty years ago, it would have been a still from Fritz Lang's "Girl in the Moon." showing a spaceship on its journey to the moon. True enough, it was a movie spaceship, a model only, but still one conceived by scientists. In another five years the cover might well show a rocket taking off on a trajectory ending among the meteorite craters on the moon, an unmanned rocket at first. But another ten or fifteen years after that it will be a photograph of a real spaceship rising from some place dose to the equator on its outward bound voyage.

The point I am trying to make is that the cover of today and the possible cover of twenty years ago could be interchanged without too many people's noticing it. And the probable covers of five and of twenty years hence will also look like the one of today. The spaceship would be larger than the V-2 rocket, of course, but size is indefinite when there is nothing but sky for a background.

Such predictions are easy to make these days. The idea of space travel is no longer merely a subject of discussion among small and involuntarily exclusive groups. It has even penetrated into official thought. During the first days of August, 1946, a spokesman of the AAF told a conference of newspapermen in Washington that the "AAF would place a guided missile on the moon." The statement that this would take "about eighteen months" was either a mistake on the part of the spokesman, or a bit of premature super-optimism, but it is nice to know that such thoughts exist around the Pentagon. Just a few days before that announcement, Congress, while extending to aircraft the law which makes mail coach and train robberies a federal offense, saved itself future work by writing boldly "airplanes and rocket ships."

When hearing announcements of this kind those who failed to follow the admittedly furious (and also largely secret) pace of rocket developments during the last few years are apt to shake their heads and to ask how things could progress to such an advanced point so suddenly.

The answer is, of course, that it was not suddenly, merely unnoticed. The contemporaries of Columbus might also have felt that a great and important discovery had been made "suddenly," since they did not know anything of the many years of planning and propagandizing, of the incredible amount of discussions and disappointments, in short, of the decades of work preceding the event which then became common knowledge.

Not quite three decades ago, in 1919, the now century-old Smithsonian Institute published a thin book by Dr. Robert H. Goddard, a book in which it was stated that it should be possible, under certain conditions, to send a rocket to the moon. A few years later, a young student whose theoretical work was to lead to V-2 in the years to come, published another thin book of some 80 pages. These 80 pages formed an almost unbroken defensive position in the shape of a barbed wire entanglement consisting of interlocking integral and square root signs, and from that fortified position its author stated bluntly that not only the trip to the moon, but space travel in general is possible. While the book was in print its author metamorphosed from student into teacher and became known as Professor Hermann Oberth.

The book landed in the libraries (mostly unread) in the summer of 1923. Later in the same year, on November 1st, Goddard coaxed the first liquid fuel rocket motor of history into feeble and unreliable activity, obtaining a few pounds of thrust for a few minutes. Twenty-one years (minus five weeks) after that date, during the evening hours of September 8, 1944, the first operationally used V-2 crashed down on Chiswick, London, from an altitude of 60 miles, its motor having delivered 27 tons of thrust for 71 seconds.

If two decades of work could trans form a small laboratory model of uncertain value and performance into a 12-ton rocket with a 200-mile range, the moon does not appear so distant any more. It appears hardly as distant as the shores of East Asia were from European ports in 1450 - and though Columbus had long arguments about the width of the ocean there is no argument about the gulf separating earth and moon. Since the Army's radar experiment of a few months ago everybody even knows the figure - 238,000 miles.

Even by terrestrial standards, it is not an impossibly long distance; just about ten times around the equator. There must be thousands of locomotive engineers and train personnel, captains and sailors, pilots and airline hostesses who have traveled a greater distance than that. The difference, the awesome difference, is that even Novaya Semlya to the North of Siberia, even Antarctica in the extreme South, are still places on earth. The moon is not.

Let's Look at the Astronomical Situation

Its dominant characteristic is empty space. From far, far away come the white, yellowish, bluish, and red lights of countless stars, other suns which are so far away that no measuring system in daily use on earth, is even capable of expressing their distances. The very nearest of them, our own sun, is 93 million miles away. Around that sun our earth is moving, once in 365 1/4 days. The earth itself appears as a compact ball, just below 8,000 miles in diameter. If you take those 8,000 miles as a unit of measurement you still need thousands of such units to measure the distance between the earth and its closest sister planets at the time of their closest approach. But only 30 of these units away there is the moon, a much smaller globe, only 2,160 miles in diameter, fallowing the earth in the course around the sun. The two grip each other with mutually interpenetrating gravitational fields.

Not counting occasional meteorites there is nothing solid between them. The earth's atmosphere (the moon does not have one at all) does not count. It extends to just about one. percent of the distance, being about 250 miles high. And only a few miles at the bottom are useful for flying; Man is a deep-air animal and does not change that status by climbing to 35 or 40,000 feet.

The airplane in which Man can climb to these "altitudes" (1/20th of one percent of the earth's diameter) is also a "deep-air instrument." Its engines need the oxygen of the air for combustion of the fuel; its wings need the flow characteristics of dense air to lift its weight. The rocket is not in that class of vehicles depending on the characteristics of a specific environment. Its motor does not need atmospheric oxygen, because oxygen is carried along it) a special tank. The recoil or thrust of the rocket's jet of fire is equally independent of its surroundings. In fact, as external air pressure decreases, the thrust increases: the motor of V-2, capable of delivering 60,000 pounds of thrust at sea level, produced 69,000 pounds at peak altitude. Hence the complete and some what frightening emptiness of the space between earth and moon is actually advantageous. One might say that a rocket, while independent of its environment, does best in no environment at all, in interplanetary space.

Why Rockets Work in Space

Why Rockets Work in Space - Airplanes and RocketsThe perennial argument all rocketeers encounter is, "How can a rocket work where there's no air or anything to push on?" Suppose a standard welder's oxygen tank were somehow dropped in space, where there was no air, and the valve opened. Inside the tank there is a pressure of 2,000 pounds per square inch; outside, a perfect vacuum. Will the gas escape through the open valve? Naturally. But - how can it? What does that gas push on to get moving outward, when there's nothing to push on? But there is! It gets started outward by pushing on the inner wall of the tank. Obviously, if the escaping gas pushes on the tank, and the tank, being in airless space, has nothing to push on in turn, the tank simply has to move. And if the gas doesn't push on the tank - how does it get started moving out?

Ideally, the rocket should, for maximum fuel economy, consume all its fuel almost instantly. In this way, all the fuel energy would be used in accelerating the rocket ship; no fuel-energy would be consumed in lifting tons of fuel to be used later. The tin-can-and-firecracker system, in other words, is efficient, since the can, but not the "fuel," is lifted. Machines can stand such an almost instantaneous start. Human beings, however, can't take the tin-can take-off.

The human ideal, therefore, would be a rocket ship that took off slowly, with a gentle acceleration like a freight elevator. Even modern high-speed elevators are less comfortable than slower ones. But that brings up the fuel-energy problem. A long-range plane uses two gallons of gas carrying the weight of the one gallon that it must have at the end of its long flight; a slowly accelerating rocket ship would have to use 10 tons of fuel lifting 1 ton for later use.

A compromise is necessary, and perfectly practicable. Men would like a 1-g take off; the ideal rocket engine efficiency calls for a 1,000-g take-off. But men can readily stand a 4-g start, and with that acceleration, the rocket ship is sufficiently practical. The more energy-per-pound in the fuel, the slower the take-off of the rocket ship may be. Atomic fuels will yield about 4,000,000 times the energy-per-pound of gasoline-oxygen fuel, making elevator-slow takeoffs perfectly practicable. The moon rocket ship is already possible.

Hypothetical spaceship, based on the V-2 design - Airplanes and Rockets

The artist shows here a hypothetical spaceship, based on the V-2 design, and incorporating many fully tested devices and principles. The hull is essentially a cylindrical, stressed skin structure, 80' long and 10' feet in outside diameter. It is double walled, with very efficient insulation. The extreme nose contains a series of glass fiber parachutes to be used for vertical stabilization in atmospheric landings, with actual deceleration effected by the main jet. Below the chute hold is space for recording cameras, cosmic ray detectors, and other instruments. Beneath this is the upper deck of the pressurized control cabin. Next is a compartment packed with mechanisms; autopilot, gyrostabilizer, air and temperature control plant, radio and radar installations, etc. An airlock gives access to the outside through a two-piece door, the lower port of which serves as a platform when open. Below the crew space the fuel and oxidizer tanks occupy more than a third of the ship's length, and beneath them is the rocket engine, with its pumps and plumbing. Worm gear driven tubular legs in the fins permit leveling the ship on rough ground for the return take-off.

If the emptiness of interplanetary space permits the rocket motor to work at its best, it also does not impede the movement of the rocket itself. But before interplanetary space is reached, the rocket has to traverse the atmosphere and it is at this point that another inherent advantage of the rocket becomes obvious. A rocket can acquire very high velocities, higher than the velocities of high-velocity artillery projectiles. But unlike those projectiles, the rocket acquires its high velocities gradually. It is easy to say that a projectile, fired vertically with such and such a muzzle velocity, would reach interplanetary space and, if aimed correctly, the moon. That is easy to say, but the facts of reality are that it wouldn't. Any projectile moving with a velocity of several miles per second would encounter such incredible air resistance that all its energy would be used up producing shock waves.

A rocket accelerates gradually; to the great good fortune of rocket designers it is slowest near sea level, where air density is highest. As the velocity of the rocket increases, the air resistance decreases (assuming a vertical or near vertical path); it might be possible to find an acceleration for the rocket where the two factors, the increase of rocket velocity and the decrease of external air resistance, balance each other at least approximately. Once the densest layers have been passed the velocity could increase faster, the acceleration could go up.

Strangely enough, a rocket of sufficient size takes care of even that condition automatically. If we say, for example, that a rocket weighs ten tons at take-off and its motor produces a thrust of 20 tons it will rise with an acceleration of 1 gravity, or 1-g, for short. Its rise will be a reversed fall, its velocity upward would increase in precisely the same measure as the velocity downward of a falling stone would increase. It would increase in precisely the same measure, that is, if the weight of the rocket remained unchanged. But, of course, the weight does change, fuel is being used up steadily. After some time the rocket will weigh only five tons, but the thrust of the motor will still be 20 tons (actually, because of the effect mentioned earlier, it would he about 23 tons, but we'll ignore this), hence its acceleration will then be 3-g. This increase in acceleration is literally "just what we wanted," - we only have to watch out that it does not happen too early. (Just for the sake of illustration it may be mentioned that the acceleration of V-2 at take-off is slightly higher than 1-g, while the acceleration near the end of the burning period is about 8-g.)

We can get a good idea about the altitude where the rocket might begin to be really fast from an observation made over a decade ago. When the Stratosphere Balloon, Explorer II, hovered at its peak altitude of 72,395 feet on November 11, 1935, the men in the airtight spherical gondola had 24/25th of the total mass of the atmosphere under their feet. Since the height of the atmosphere is customarily taken to be about 250 miles, there were still about 1,200,000 feet of so-called air above the balloon. But that million feet amounted to only 1/25th of the total mass.

Taking all the foregoing fads together we can safely conclude that the natural performance of a rocket, functioning" as a plain rocket unhampered by wings, is such that it may be expected to penetrate the atmosphere and to reach interplanetary space. Provided, of course, that it is large enough.

There is just one point where we may wonder a little bit. Our conditions are that the final velocity must be high, that the final acceleration should be high (it should be high as far as the rocket itself is concerned, hut there is an obvious limit to the acceleration if the rocket is a spaceship. i.e. if a man is to be carried), but that the velocity must be fairly low at take-off and until the dense layers of the atmosphere have been penetrated. The question is: Is there such an acceleration which will combine these features?

That question can only be answered by calculations, by trying a few likely accelerations and seeing how they work out. If we pick an effective acceleration of 3-g and, for the sake of a quick first approximation, assume that the acceleration will not change and that there is no air resistance, we find that the rocket, after twenty seconds of burning, will be at an altitude of about 20,000 feet, moving at the, end of the 20th second with 1,900 feet per second. The latter is less than the velocity of an artillery projectile - in short, the acceleration of 3-g effective just before fills our needs.

Now we can look at the problem of the guided missile to the moon, as an introduction to the problem of the spaceship to the moon. The essential difference between the two is that the latter is manned, which imposes a limitation on acceleration. The complicating point is that the spaceship is expected to come back, while the fate of the missile is not so important.

The first question is not how big the missile would have to be, but how fast. We can approach that question by looking at a well-known device, the anti-aircraft gun.

Everybody knows by now that the altitude to which an anti-aircraft shell will carry depends on the muzzle velocity of said anti-aircraft shell. The higher the muzzle velocity, the higher the altitude reached. If air resistance did not confuse the issue, a simple and clear relationship would be obvious: The muzzle velocity required to fire a shell to an altitude of, say, five miles, is the same figure as the impact velocity of a bomb dropped from an altitude of five miles. If somebody could drop a bomb from the distance of the moon - which is large enough to be called "infinity" for purposes of calculation - its impact velocity would be 11,200 meters per second, which happens to be almost precisely 7 miles per second. Conversely, to send a missile to that distance requires a velocity of 7 miles per second.

This is what the missile designer has to strive for; at least, it is the most efficient way by far to make the missile attain that velocity as soon as possible after the densest layers of the atmosphere have been traversed. Once that velocity has been attained no further power application is required; the missile will go on coasting with slowly diminishing velocity. We will look at that phenomenon more closely a little later.

Naturally, nobody will try to sit down with a logarithm table (the slide rule is not good enough for these calculations) ,and handbook and make plans for a moon missile; neither "Mr. Wright nor Monsieur Bleriot sat down to design a B-29. There will be many intermediate steps and a look at probable intermediate steps is interesting because it will show what a little more velocity will do.

Rocket velocity / altitude reached table - Airplanes and RocketsIn the following table it is assumed that a rocket which has an acceleration of 3-g is permitted to burn until it has reached the velocity in the left hand column; the right hand columns then show to what altitude it would coast before falling back. (Air resistance has been ignored.)

To reach the velocity of 11,200 meter per second, or 7 miles per second, that particular rocket would need a burning time of about 8 minutes, say 500 seconds for the sake of getting a round figure.

What Then?

After having burned 500 seconds the rocket is far above what is euphemistically called the fringes of the atmospheres. It is in empty space, traveling without power now. Without any other power, that is, than its kinetic energy, the product of the square of its enormous velocity and of half of its mass. There is no air resistance anymore to slow it clown, but there still is the earth's gravity, trying to pull it back.* It loses some 30 feet per second of velocity for every second that elapses. It is no longer the full force of close to 32 feet per second per second which holds true at sea level; it is already somewhat less. And it grows less and less as the distance from the earth increases. In due course, the loss of velocity for every second elapsed amounts to only 28, 27, 26, 25 feet per second, later to 16 15 14 13 feet per second, still later to only 6. 5. 4, feet per second. After 300,000 seconds have gone by, things approach a balance. The velocity losses are down to fractions of an inch per second now, the velocity of the missile is down to a few feet per second.

But by that time the point has been reached where the gravitational fields of the earth and the moon, interpenetrating each other, as gravitational fields have a habit of doing, are about equally powerful. Theoretically, there is a line where they balance each other perfectly. Whether the ship crosses that line or not, it will begin to fall after about 300,000 seconds after take-off. The only difference is this: If the ship, or missile, still has enough velocity left to cross the line of perfect balance, it will fall toward the moon.

If it fails to cross. the line, it will fall back to earth, entering the atmosphere with 7 miles per second after about 300,000 seconds. But we'll assume that it did cross the line and falls in the moons gravitational field. It will need 50,000 seconds to get to the moon from the line of equal gravitational force and crash with an impact velocity of 2,370 meters per second or 1.45 miles per second. From take-off to crash there would be total time interval of 350,000 seconds, or about four days.

Looking at this performance, we now realize why it is more efficient to reach the so-called "escape velocity" of 7 miles per second fast. There is always the earth's gravity, trying to pull the missile back. If somebody decided that the-rocket-motor-is-after-all-very-powerful and why-strain-the-ship-with-high-acceleration, consequently let's-take-it-easy-and-just-burn-a-little-more-fuel, he would run no other risk than not getting anywhere. To begin with, the efficiency of the rocket motor itself depends to a very great extent on the velocity of the rocket. If the acceleration is kept low and the velocities stay low the efficiency of the rocket motor stays low too. It means nothing more serious than higher fuel consumption. More important even, the rocket would linger for a much longer time in regions where a higher gravitational pull would cause much greater velocity losses.

The fundamental difficulty involved can be seen most easily by going to extremes. Suppose the rocket pilot decides to maintain just a normal 1-g acceleration from take-off. At the end of twenty minutes his fuel is exhausted - and the rocket will, of course, be at an altitude of 0.00 miles, and the rocket's velocity will be 0.000 miles per sec. He has expended all his fuel in simply holding the rocket at a fixed altitude against Earth's gravity.

Taking the other extreme, suppose the pilot of the rocket is a mechanism built like the V-T fuse mechanism used in artillery shells, a device that can function happily at 20,000-g accelerations. This mechanical pilot wouldn't mind burning all the fuel almost instantaneously and executing a take-off at 20,000-g. When this pilot's fuel is all gone, the rocket will still be only a short distance from the ground - but it will be traveling at terrific speed. In this case, none of the energy of the fuel will have been used in lifting part of the fuel; all of the fuel energy will have been used in accelerating the rocket.

There is literally no upper limit to the fuel consumption which would be caused by trying to keep the velocity low. The whole problem bears a strong resemblance to the problem of carrying a leaking container of liquid to an upper floor in a house. The slower it is done, the more of the liquid will leak away before it gets to the point where it will do some good.

Fine, But What Is the Fuel Consumption?

There is no single answer to that question; there are a lot of them.

It depends on the fuel, or, more precisely, on the exhaust velocity of a fuel. The solid powder bars used in bombardment rockets produce an exhaust velocity of about 3,300 feet per second (1,000 meters per second), or a little better. The alcohol-water mixture in V-2, burning with liquid oxygen, produces an exhaust velocity of close to 7,000 feet per second (slightly above 2,000 meters per second). Hydrogen burning with oxygen can be expected to produce about 4,000 meters per second. There exists a substance known as "monatomic hydrogen," which is hydrogen where two atoms do not form a molecule of hydrogen as usual, but where they are (very temporarily) single atoms. Theoretically, that substance would produce an exhaust velocity of 20,000 meters per second; actually, one might expect about 10,000 meters per second. But so far nobody has succeeded in producing monatomic hydrogen and keeping it in that condition, and nobody knows how it could he stored if large amounts could be produced.

It is obvious that a ton of fuel with a higher exhaust velocity will impart a higher velocity to a rocket than a ton of fuel with a lower exhaust velocity; what is needed at this point is a kind of permanent yardstick for purposes of comparison. That yardstick is found in the ratio:

Rocket mass equation - Airplanes and Rockets 

and the ratio M0/M1, is generally called "mass-ratio." The yardstick is the exhaust velocity itself for a standard mass-ratio and the most useful standard is, obviously, the mass-ratio where the rocket velocity becomes the same as the exhaust velocity. The V-2 weighs about three times as much at take-off than it does after all the fuel has been burned.

Rocket required exhaust velocity  - Airplanes and RocketsBy means of a mathematical formula * it is possible to calculate the mass-ratio which is needed for attaining a desired velocity, provided you know the exhaust velocity of the fuel. For the moon missile we have a desired velocity of (in round figures) 12,000 meters per second. the 11,200 meters per second mentioned earlier plus some extra velocity for overcoming air resistance. Assuming a set of exhaust velocities we can then write the following table:

By sheer coincidence. the table contains a mass-ratio which IS that of V-2, the figure 3.2. But the exhaust velocity belonging to that mass-ratio is 10,000 meters per second, about 32,800 feet per second. If we had a fuel with such an exhaust velocity a V-2 could reach the moon. With the actual exhaust velocity of V-2 it is a sheer impossibility. There is no way of building a rocket that will weigh 402 times as much when fuelled as it weighs when empty. The 7.4 (to 1) mass-ratio which belongs to the 6,000 meters per second exhaust velocity might still be built as a single rocket and possibly, just possibly, even the 11-to-1 mass-ratio belonging to the 5,000 meters per second exhaust velocity.

This would be most comforting if we could attain such an exhaust velocity by the use of chemical fuels. But while we may hope for such fuels or hope for an application of atomic energy, we have, as of August, 1946, to face the fact that 4,000 meters per second is all we can expect to get, burning hydrogen with oxygen. The mass-ratio belonging to that exhaust velocity is 20 to 1. It cannot be built as a single rocket, but it can be built as a so-called step rocket, one rocket carrying another one, only the second rocket, the "upper step" reaching the goal. (The Nazis planned the "America Rocket" on that principle.)

In a step rocket the velocities attained by the single steps add up; it is the same, in effect, as if the individual mass-ratios were multiplied. Hence (with a little simplification) , if you have a lower step with an effective mass-ratio of 5 to 1 and an upper step with 4 to 1, the result, we'll call it "ideal mass-ratio," will be 20 to 1.

We can build such mass-ratios after some practice and experimentation. We can also, again after some practice and experimentation, count on an exhaust velocity of 4,000 meters per second.

Because of these two facts the guided missile to the moon is a distinct possibility.

* The formula reads:  M0/M1 = ev/c

where v is the desired velocity, c the exhaust velocity (available or assumed) and e the base of the so-called "natural logarithms." If v = c the ratio becomes simply e = 2.71828; v = 2c the mass-ratio becomes e2 (7.4); if v = 3 c the mass-ratio becomes e3 = 20.0 etc. etc. The reader will have to accept my assertion that this relationship actually holds true, proof is rather difficult and space-consuming. As for the value of e, it is the result of a mathematical series, but it can also be derived in a rather amusing elementary manner, by way of "progressive percentages." If you take the figure 100 to begin with and add one percent of it you get 101. Now you add another one percent, but not on the original base 100 but on the new base 101. You get 102.01. Add one percent of 102.01 to that and continue in the same manner until you have added one percent one hundred times on that progressive base. The result of the addition will be 271.828 ...

* Contrary to an ingrained popular belief, the earth's gravitational field does not stop at one point; it goes on and on into infinity. Of course, at a sufficiently large distance it will get so weak that it can be ignored. If the case earth-moon is under consideration, the earth's field "stops" when that of the moon becomes more powerful.



Posted March 14, 2020

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