physics
Re: physics
"Everything should be made as simple as possible, but not simpler." - Albert Einstein
Re: physics
Momentum conservation.
The fuel is put on fire which creates pressure and then let out from one side. The momentum that's carried out by the burning fuel, creates a momentum in the opposite direction and take the rocket up.
This si the same way airplanes work, except they don't expel fuel, they just use the flow of surrounding air.
The fuel is put on fire which creates pressure and then let out from one side. The momentum that's carried out by the burning fuel, creates a momentum in the opposite direction and take the rocket up.
This si the same way airplanes work, except they don't expel fuel, they just use the flow of surrounding air.
Re: physics
Vaia I think that when a rocket entered in (mohasono),than stop burning.Because ,I think there is no oxygen .Is it right?
Re: physics
MATHEMATICAL THEORY OF ROCKET FLIGHT
BY J. BARKLEY ROSSER, PH.D., ROBERT R. NEWTON, PH.D. AND GEORGE L. GROSS, PH.D.
NEW YORK AND LONDON, MCGRAW-HILL BOOK COMPANY, 1947
DOWNLOAD FREE ROCKET ENGINEERING BOOK:
Mathematical theory of rocket flight
PREFACE
This is the official final report to the Office of Scientific Research and Development concerning the work done on the exterior ballistics of fin-stabilized rocket projectiles under the supervision of Section H of Division 3 of the National Defense Research Committee at the Allegany Ballistics Laboratory during 1944 and 1945, when the laboratory was operated by The George Washington University under contract OEMsr-273 with the Office of Scientific Research and Development. As such, its official title is "Final Report No. B2.2 of the Allegany Ballistics Laboratory, OSRD 5878."
After the removal of secrecy restrictions on this report, a considerable amount of expository material was added. It is our hope that thereby the report has been made readable for anyone interested in the flight of rockets. Two slightly different types of readers are anticipated. One is the trained scientist who has had no previous experience with rockets. The other is the person with little scientific training who is interested in what makes a rocket go. The first type of reader should be able to comprehend the report in its entirety. For the benefit of the second type of reader, who will wish to skip the more mathematical portions, we have attempted to supply simple explanations at the beginnings of most sections telling what is to be accomplished in those sections. It is our hope that a reader can, if so minded, skip most of the mathematics and still be able to form a general idea of rocket flight.
Although this is a report of the work done at Allegany Ballistics Laboratory, it must not be supposed that all the material in the report originated there. We have been most fortunate in receiving the whole-hearted cooperation and assistance of scientists in other laboratories. Many of them, notably the English scientists, were well advanced in the theory before we even began. Without the fine start given us by these other workers, this report could certainly not have been written. However, we were fortunate enough to discover two means of avoiding certain difficulties of the theory. The first is that of using some dynamical laws especially suited to rockets in deriving the equations of motion, and the second is that of using some mathematical functions especially suited to rockets in solving the equations of motion. The explanation and illustration of these simplifying devices take up a considerable portion of the report, although for completeness we have included material not involving them.
In attempting to acknowledge the contributions of other workers, we are in a difficult position. Approximately a hundred reports by other workers were useful in one way or another in the preparation of this report. However, most of them are still bound by military secrecy, so that only the few cited in our meager list of bibliographical references can be mentioned here. Many figures are copied from these unmentioned reports. Sizable portions of our report, such as Chap. II and Appendix 1, lean very heavily on certain of these unmentioned reports, but no specific credit is given. We ask the reader to bear in mind that this report, like any comprehensive scientific report, covers the work of many contributors, and, although we are among the contributors, our present role is that of expositors.
Among the many scientists to whom we are indebted, certain ones have been especially helpful, namely, Leon Blitzer, Leverett Davis, F. T. McClure, E. J. McShane, and R. J. Walker. We regret that we cannot be more explicit as to the nature of their contributions, and the contributions of others.
For their work in computing Tables 1 to 4, and for their assistance with computational matters in general, we wish to thank J. A. Brittain and E. M. Cook.
We wish further to express our gratitude for the willing assistance furnished by our associates in the Allegany Ballistics Laboratory and The George Washington University, and for the encouragement that came from officials of the National Defense Research Committee and the Office of Scientific Research and Development.
The publishers have agreed that ten years after the date on which this volume is issued the copyright thereon shall be relinquished, and the work shall become part of the public domain.
CONTENTS
- THE EQUATIONS OF MOTION OF A ROCKET
- MOTION AFTER BURNING
- MOTION DURING BURNING
- BOUNDARY CONDITIONS
- PROPERTIES OF THE ROCKET FUNCTIONS
CHAPTER I - THE EQUATIONS OF MOTION OF A ROCKET
It is often stated that the motion of a rocket can be derived from Newton's laws of motion. In the strict sense, to do so would require considering the motions of all the molecules of gas within the rocket blast, as well as the motions of those air molecules with which the rocket comes into contact. This would involve intolerable complexity.
Accordingly, some simplified theory is necessary, both for the gas flow inside the rocket and for the air How outside the rocket. The simplified theories presented herein have been developed by a combination of theory and experience. We have tried to explain these simplifications fairly fully and have tried to indicate their background and shortcomings as well as explain their usefulness.
1. The Jet Forces on a Rocket
Preliminary Ideas. In Fig. I.l.l we picture the essential features of a rocket. The gas generated in the chamber at high pressure expands rapidly and so rushes out of the nozzle at a great velocity, forming the jet. The burning of the rocket propellant fuel continually furnishes more gas to the chamber, maintaining the gas supply and the high chamber pressure.
In small rockets, such as the bazooka rocket, current practice is to use solid fuel. The chamber is filled in advance with solid pieces of powder of composition similar to that used in large guns. When the powder is ignited, it burns rapidly, furnishing a continuous supply of gas at high pressure. A typical chamber pressure P c might be 2,000 lb/in. 2 With such a high chamber pressure, the pressure at the exit P ( . is fairly high, for instance, 220 lb/in. 2 A typical value for the velocity at the exit v,. might be 6,200 ft/sec.
In large rockets, it is more common to use liquid fuel. For instance, in the German Y-2, which was used against London in the fall of 1944, alcohol and liquid oxygen are continuously pumped into the chamber, where they combine chemically to produce an ample supply of gas at high pressure. A typical chamber pressure for a liquid fuel rocket might be 300 lb/in. 2 With this smaller chamber pressure, we have a smaller exit pressure, say perhaps approximately sea-level atmospheric pressure, or 15 lb/in. 2 For liquid fuels, a typical value of v e might be 6,000 ft/sec.
We shall not be concerned further with the mechanism by which gas is supplied to the chamber at the proper pressure and in the proper amounts. This is part of the "interior ballistics" of rockets. We merely state that rockets are commonly designed so that the chamber pressure is constant. However, this is not always desirable or feasible; instead, some rockets burn progressively, that is, the pressure increases as the rocket burns, while other rockets burn regrossively, that is, the pressure decreases. Nevertheless, for a first approximation, it is usual to assume a constant chamber pressure.
We shall need certain information about the behavior of the gas in the jet. To supply this information we have given in Appendix 1 a simplified theory of the motion of the gas through the nozzle. We here present a few high points of this theory. At the throat, the velocity of the gas is the so-called "local velocity of sound." This is the velocity with which a normal disturbance in the gas, in particular a sound wave, would be propagated through the gas. The adjective "local" is adjoined because the velocity of sound depends on the condition of the gas (mainly the temperature), and this is changing as we proceed along the nozzle. Incidentally, the condition of the gas at the throat is such that the local velocity of sound there may run as high as two or three times the velocity of sound in normal air (see Appendix 1).
Before the gas gets to the throat, its velocity is below the local velocity of sound; after the gas passes the throat its velocity is above the local velocity of sound. This fact is of the utmost importance, since, as a result, conditions outside the rocket usually do not affect conditions in the nozzle or interior of the rocket. The explanation is very simple. If a variation of conditions or other disturbance in the gas outside the rocket is to be felt inside the rocket, this disturbance must be propagated through the gas in the nozzle to the gas inside the chamber. That is, the disturbance must move upstream against the blast of the rocket jet. As the jet at the exit of the nozzle has a velocity well above the local velocity of sound, whereas the disturbance is propagated at the local velocity of sound, the disturbance will be swept downstream and so cannot affect conditions inside the nozzle or chamber.
Accordingly, in computing jet forces, we need not consider external circumstances at all.
The above comforting generality, like all generalities, is untrue in extreme cases. If the chamber pressure is loss than twice the external pressure or if the exit pressure is less than the external pressure, the flow pattern presented in Appendix 1 breaks down, and then external conditions can affect conditions inside the rocket. This would have an adverse effect upon the behavior of the rocket, so that rocket designers take pains to avoid such extreme conditions. Accordingly, we shall proceed with full confidence that external conditions do not affect the thrust of the jet.
BY J. BARKLEY ROSSER, PH.D., ROBERT R. NEWTON, PH.D. AND GEORGE L. GROSS, PH.D.
NEW YORK AND LONDON, MCGRAW-HILL BOOK COMPANY, 1947
DOWNLOAD FREE ROCKET ENGINEERING BOOK:
Mathematical theory of rocket flight
PREFACE
This is the official final report to the Office of Scientific Research and Development concerning the work done on the exterior ballistics of fin-stabilized rocket projectiles under the supervision of Section H of Division 3 of the National Defense Research Committee at the Allegany Ballistics Laboratory during 1944 and 1945, when the laboratory was operated by The George Washington University under contract OEMsr-273 with the Office of Scientific Research and Development. As such, its official title is "Final Report No. B2.2 of the Allegany Ballistics Laboratory, OSRD 5878."
After the removal of secrecy restrictions on this report, a considerable amount of expository material was added. It is our hope that thereby the report has been made readable for anyone interested in the flight of rockets. Two slightly different types of readers are anticipated. One is the trained scientist who has had no previous experience with rockets. The other is the person with little scientific training who is interested in what makes a rocket go. The first type of reader should be able to comprehend the report in its entirety. For the benefit of the second type of reader, who will wish to skip the more mathematical portions, we have attempted to supply simple explanations at the beginnings of most sections telling what is to be accomplished in those sections. It is our hope that a reader can, if so minded, skip most of the mathematics and still be able to form a general idea of rocket flight.
Although this is a report of the work done at Allegany Ballistics Laboratory, it must not be supposed that all the material in the report originated there. We have been most fortunate in receiving the whole-hearted cooperation and assistance of scientists in other laboratories. Many of them, notably the English scientists, were well advanced in the theory before we even began. Without the fine start given us by these other workers, this report could certainly not have been written. However, we were fortunate enough to discover two means of avoiding certain difficulties of the theory. The first is that of using some dynamical laws especially suited to rockets in deriving the equations of motion, and the second is that of using some mathematical functions especially suited to rockets in solving the equations of motion. The explanation and illustration of these simplifying devices take up a considerable portion of the report, although for completeness we have included material not involving them.
In attempting to acknowledge the contributions of other workers, we are in a difficult position. Approximately a hundred reports by other workers were useful in one way or another in the preparation of this report. However, most of them are still bound by military secrecy, so that only the few cited in our meager list of bibliographical references can be mentioned here. Many figures are copied from these unmentioned reports. Sizable portions of our report, such as Chap. II and Appendix 1, lean very heavily on certain of these unmentioned reports, but no specific credit is given. We ask the reader to bear in mind that this report, like any comprehensive scientific report, covers the work of many contributors, and, although we are among the contributors, our present role is that of expositors.
Among the many scientists to whom we are indebted, certain ones have been especially helpful, namely, Leon Blitzer, Leverett Davis, F. T. McClure, E. J. McShane, and R. J. Walker. We regret that we cannot be more explicit as to the nature of their contributions, and the contributions of others.
For their work in computing Tables 1 to 4, and for their assistance with computational matters in general, we wish to thank J. A. Brittain and E. M. Cook.
We wish further to express our gratitude for the willing assistance furnished by our associates in the Allegany Ballistics Laboratory and The George Washington University, and for the encouragement that came from officials of the National Defense Research Committee and the Office of Scientific Research and Development.
The publishers have agreed that ten years after the date on which this volume is issued the copyright thereon shall be relinquished, and the work shall become part of the public domain.
CONTENTS
- THE EQUATIONS OF MOTION OF A ROCKET
- MOTION AFTER BURNING
- MOTION DURING BURNING
- BOUNDARY CONDITIONS
- PROPERTIES OF THE ROCKET FUNCTIONS
CHAPTER I - THE EQUATIONS OF MOTION OF A ROCKET
It is often stated that the motion of a rocket can be derived from Newton's laws of motion. In the strict sense, to do so would require considering the motions of all the molecules of gas within the rocket blast, as well as the motions of those air molecules with which the rocket comes into contact. This would involve intolerable complexity.
Accordingly, some simplified theory is necessary, both for the gas flow inside the rocket and for the air How outside the rocket. The simplified theories presented herein have been developed by a combination of theory and experience. We have tried to explain these simplifications fairly fully and have tried to indicate their background and shortcomings as well as explain their usefulness.
1. The Jet Forces on a Rocket
Preliminary Ideas. In Fig. I.l.l we picture the essential features of a rocket. The gas generated in the chamber at high pressure expands rapidly and so rushes out of the nozzle at a great velocity, forming the jet. The burning of the rocket propellant fuel continually furnishes more gas to the chamber, maintaining the gas supply and the high chamber pressure.
In small rockets, such as the bazooka rocket, current practice is to use solid fuel. The chamber is filled in advance with solid pieces of powder of composition similar to that used in large guns. When the powder is ignited, it burns rapidly, furnishing a continuous supply of gas at high pressure. A typical chamber pressure P c might be 2,000 lb/in. 2 With such a high chamber pressure, the pressure at the exit P ( . is fairly high, for instance, 220 lb/in. 2 A typical value for the velocity at the exit v,. might be 6,200 ft/sec.
In large rockets, it is more common to use liquid fuel. For instance, in the German Y-2, which was used against London in the fall of 1944, alcohol and liquid oxygen are continuously pumped into the chamber, where they combine chemically to produce an ample supply of gas at high pressure. A typical chamber pressure for a liquid fuel rocket might be 300 lb/in. 2 With this smaller chamber pressure, we have a smaller exit pressure, say perhaps approximately sea-level atmospheric pressure, or 15 lb/in. 2 For liquid fuels, a typical value of v e might be 6,000 ft/sec.
We shall not be concerned further with the mechanism by which gas is supplied to the chamber at the proper pressure and in the proper amounts. This is part of the "interior ballistics" of rockets. We merely state that rockets are commonly designed so that the chamber pressure is constant. However, this is not always desirable or feasible; instead, some rockets burn progressively, that is, the pressure increases as the rocket burns, while other rockets burn regrossively, that is, the pressure decreases. Nevertheless, for a first approximation, it is usual to assume a constant chamber pressure.
We shall need certain information about the behavior of the gas in the jet. To supply this information we have given in Appendix 1 a simplified theory of the motion of the gas through the nozzle. We here present a few high points of this theory. At the throat, the velocity of the gas is the so-called "local velocity of sound." This is the velocity with which a normal disturbance in the gas, in particular a sound wave, would be propagated through the gas. The adjective "local" is adjoined because the velocity of sound depends on the condition of the gas (mainly the temperature), and this is changing as we proceed along the nozzle. Incidentally, the condition of the gas at the throat is such that the local velocity of sound there may run as high as two or three times the velocity of sound in normal air (see Appendix 1).
Before the gas gets to the throat, its velocity is below the local velocity of sound; after the gas passes the throat its velocity is above the local velocity of sound. This fact is of the utmost importance, since, as a result, conditions outside the rocket usually do not affect conditions in the nozzle or interior of the rocket. The explanation is very simple. If a variation of conditions or other disturbance in the gas outside the rocket is to be felt inside the rocket, this disturbance must be propagated through the gas in the nozzle to the gas inside the chamber. That is, the disturbance must move upstream against the blast of the rocket jet. As the jet at the exit of the nozzle has a velocity well above the local velocity of sound, whereas the disturbance is propagated at the local velocity of sound, the disturbance will be swept downstream and so cannot affect conditions inside the nozzle or chamber.
Accordingly, in computing jet forces, we need not consider external circumstances at all.
The above comforting generality, like all generalities, is untrue in extreme cases. If the chamber pressure is loss than twice the external pressure or if the exit pressure is less than the external pressure, the flow pattern presented in Appendix 1 breaks down, and then external conditions can affect conditions inside the rocket. This would have an adverse effect upon the behavior of the rocket, so that rocket designers take pains to avoid such extreme conditions. Accordingly, we shall proceed with full confidence that external conditions do not affect the thrust of the jet.