Robert H. Goddard - A Method of Reaching Extreme Altitudes: The seminal text on rocket science that foretold the Space Age

Digital Edition by Sibyl Publishing, 2017
Edited by Markus Amalthea Magnuson

ISBN: 978-91-88547-01-9

Sibyl Publishing is not affiliated in any way
with the Smithsonian Institution.

Preparing and publishing a century-old text that is a classic in its field has to strike a balance between truth to the original and readability according to current best practices. In very few cases have significant changes been made to the language itself, but some writing conventions are altered, as well as certain aspects of the typography, as compared to the 1919 edition published by the Smithsonian Institution. To never distort the authors intentions, such adjustments have been checked against the 1916 typescript, including its handwritten notes and equations. When the typescript was prepared, its figures were renumbered, but a few instances were missed and made its way into print; these are now corrected. A summary of other changes that might be noticed is as follows:

All units are abbreviated and written as outlined by the National Institute of Standards and Technology (NIST) in their Guide for the Use of the International System of Units (SI) (NIST Special Publication 811, 2008 Edition), including non-SI units in the manner they are referred to in the same publication. For example, feet per second as Goddard would have written ft./sec. is changed to ft/s. In general, the old convention of having a period after such abbreviations, even mid-sentence, has been disregarded for the sake of readability.

These are all symbols used in the present edition of the text:

cal/g = calories per gram

cm = centimeter

dm = decimeter

ft = feet

ft/s = feet per second

g = gram

kg = kilogram

km/s = kilometers per second

lb = pound

mi = mile

mi/s = miles per second

min = minute

mm = millimeter

oz = ounce

s = second

T = ton (note this is short ton, not metric ton, which would rather be t)

An exception is made for inch that instead of being abbreviated in is most of the time written out to avoid confusion with the regular and common English word.

Mathematical expressions have sometimes been simplified to linear form, if possible without losing clarity, to lessen the effect on line height and other formatting. For example, some fractions are written in special form (e.g., ) or piece/solidus form (e.g., 1/2) instead of built-up form.

All variables are in italics as you would expect from a modern text, that seems to have been Goddards intention when underlining them in the typescript, but somehow got lost when typeset.

Bibliographic references in the endnotes have been expanded into Chicago style citations including article name, more specific page numbers, full author names, and so on, and in cases where the referenced source is readily available on the Internet, the name of the article is hyperlinked to such an online resource.

Last, a short comment on geocoronium. This was the name coined by Alfred Wegener in 1911 for a hypothetical chemical element, with an atomic weight of 0.4, which he believed the upper atmospheric layer to mostly consist of. By inferring its properties, this light gas was supposed to explain certain unidentified lines found in the spectrum of the aurora borealis, but these were later shown to be part of the oxygen spectrum, and the geocoronium theory was laid to rest.

The theoretical work herein presented was developed while the writer was at Princeton University in 191213, the basis of the calculations being the assumption that, if nitrocellulose smokeless powder were employed as propellant in a rocket, under such conditions as are here explained, an efficiency of 50 % might be expected.

Actual experimental investigations were not undertaken until 191516, at which time the tests concerning ordinary rockets, steel chambers and nozzles, and trials in vacuo, were performed at Clark University. The original calculations were then repeated, using the data from these experiments, and both the theoretical and experimental results were submitted, in manuscript, to the Smithsonian Institution, in December 1916. This manuscript is here presented in the original form, save for the notes at the end that are now added.

A grant of $5 000 from the Hodgkins Fund, Smithsonian Institution, under which work is being done at presented, was advanced toward the development of a reloading, or multiple-charge rocket, herein explained in principle, and this work was begun at Worcester Polytechnic Institute in 1917, and was later undertaken as a war proposition It was continued, from June 1918, up to very nearly the time of signing of the armistice, at the Mt. Wilson Observatory of the Carnegie Institution of Washington, where most of the experimental results were obtained.

In connection with the present publication, I take pleasure in thanking Dr. A. G. Webster for the facilities of the shop and laboratory at Clark University, used in the preliminary experiments herein described. I also take this opportunity of expressing my gratitude to the Smithsonian Institution, for its support and encouragement in the later work.

Robert H. Goddard

Clark College,

Worcester, Massachusetts,

May 26, 1919.

A search for methods of raising recording apparatus beyond the range for sounding balloons (about 20 mi) lead the writer to develop a theory of rocket action, in general, taking into account air resistance and gravity. The problem was to determine the minimum initial mass of an ideal rocket necessary, in order that on continuous loss of mass, a final mass of one pound would remain, at any desired altitude.

An approximate method was found necessary, in solving this problem, in order to avoid an unsolved problem in the Calculus of Variations. The solution that was obtained revealed the fact that surprisingly small initial masses would be necessary () provided the gases were ejected from the rocket at a high velocity, and also provided that most of the rocket consisted of propellant material. The reason for this is, very briefly, that the velocity enters exponentially in the expression for the initial mass. Thus if the velocity of the ejected gases be increased five fold, for example, the initial mass necessary to reach a given height will be reduced to the fifth root of that required for the lesser velocity. (A simple calculation shows at once the effectiveness of a rocket apparatus of high efficiency.)

It was obviously desirable to perform certain experiments: first with the object of finding just how inefficient an ordinary rocket is, and secondly, to determine to what extent the efficiency could be increased in a rocket of new design. The term efficiency here means the ratio of the kinetic energy of the expelled gases to the heat energy of the powder, the kinetic energy being calculated from the average velocity of ejection, which was obtained indirectly by observations on the recoil of the rocket.

It was found that not only does the powder in an ordinary rocket constitute but a small fraction of the total mass ( or ), but that, furthermore, the efficiency is only 2 %, the average velocity of ejection being about 1 000 ft/s (). This was true even in the case of the Coston ship rocket, which was found to have a range of a quarter of a mile.