Improved Quantum Theory of Many-Electron Systems. V. The Spin-Coupling Optimized GI Method

The previously developed GI methods have an arbitrary aspect since they are based on a particular representation of the symmetric group. Here we remove this arbitrariness by optimizing the representation, that is, optimizing the spin‐coupling scheme simultaneously with the optimization of the orbitals. The resulting wavefunctions, called the spin‐coupling optimized GI or SOGI wavefunctions, have all of the general properties of GI wavefunctions including the independent particle interpretation and are found as the solutions to a set of coupled differential equations which differ from the GI equations only in that the equations are constructed from a different representation of the symmetric group. We have applied this method to the ground state and some excited states of Li, to the ground states of Be^+ and B^(++) and to the ground state of LiH. In each of these cases, we found that the SOGI wavefunction was only slightly different from the G1 wavefunction and led to very similar energies and other spatial properties. For the spin density at the nucleus, however, SOGI led to much better results. In order to illustrate the effects of spatial symmetry on the SOGI orbitals, we examined the lowest ^1B_(1g), ^3A_(2g), and ^3E_u states of square H_4 and the ^2Σ_u^+ state of linear symmetrical H_3. We find that in three of these cases optimization of the spin representation is crucial to providing an adequate description of the state. To investigate how the SOGI method would describe chemical reactions, the SOGI wavefunctions were computed for several other nuclear configurations of the H_3 system along the reaction path. These calculations showed that the spin coupling changed significantly during the reaction H_2 + H⇆H + H_2 and that the variation of the SOGI orbitals provides a clear description of the changes in bonding which occur during this reaction

Pumping Apparatus For Very Cold Liquids

This invention relates to apparatus for pumping very cold liquids, such as liquid oxygen or liquid hydrogen.. It has been customary to force such liquids out of a closed container by injecting an inert gas, such as nitrogen, under the required pressure. It is found, however, that the gas when in direct contact with such very cold liquids and their metal containers may be condensed and may thus dilute the liquid to be pumped. If not actually condensed, the gas may be substantially reduced in pressure but the excessive lowering of its temperature. It is the general object of the present invention to provide improved pumping apparatus in which the has under pressure has no direct contact with the cold liquid nor with any metal which is directly exposed to said cold liquid. To the accomplishment of this general object, a pumping unit is provided in which the gas under pressure is out of contact with the cold liquid and is also effectively insulated from the cold liquid and from any metal in contact therewith, even when the pumping unit is entirely submerged in the cold liquid.https://digitalcommons.wpi.edu/patents/1075/thumbnail.jp

Combustion Chamber for Aircraft

This invention relates to a combustion chamber particularly designed for use in rockets, rocket planes and other aircraft in which continuous combustion of liquid constituents takes place at a vey high temperature. Effective provision for cooling the walls of such combustion chambers without substantial addition of weight is thus very important. It is the general object of my invention to provide an improved construction in light-weight combustion chambers, such that the chamber wall is effectively cooled; that one of the liquid constituents is simultaneously vaporized, with absorption of latent heat; and the two combustion constituents are intimately mixed adjacent the chamber wall. A further object is to provide a combustion chamber of relatively light weight which is well adapted to resist external pressure.https://digitalcommons.wpi.edu/patents/1062/thumbnail.jp

Propulsion of Aircraft

The present invention relates to the propulsion of aircraft by means of a blast of gas delivered at high velocity from what is commonly known in the art as a rocket and the object of the invention is to provide an improved manner and means for utilizing the energy of the gas blast to obtain a maximum propelling effect for an aircraft. While I am aware of the fact that rockets alone have heretofore been employed for propelling an aircraft, with or without planes, all such previous attempts at aircraft propulsion by means of rockets have depended solely upon the reaction of the gases ejected from the rocket for their propulsive effect. The gases ejected from a rocket travel at great velocity and possess tremendous kinetic energy, and consequently at ordinary low altitudes with pure rocket propulsion most of the heat energy of the fuel, or charge, of the rocket is dissipated as kinetic energy of the ejected gases, leaving a comparatively small proportion of the total energy of the charge available for propelling the carrier on which the rocket is mounted at a relatively slow speed, as compared to the speed of the gases themselves. The present invention proposes to utilize to the best possible advantage the energy of the gas blast to obtain a maximum propulsive effect for the aircraft, under varying conditions of operation resulting from propelling the aircraft at different altitudes. Briefly states, the invention contemplates the utilization of the high velocity gases to drive one or more turbine elements which in turn operate propellers for driving the plane in the usual manner when operating at relatively low altitudes where the air is dense. In this conversion of the energy of the gases into mechanical power, the velocity of the ejected gases is reduced to a low value and the energy of the gases is transferred with high efficiency to the much larger mass of air handled by the propellers. The invention also contemplates means whereby when the aircraft rises to higher altitudes in which the air is less dense, the energy of the gas blast can be used partly to drive the propellers and partly to add to their propelling effect by the reaction of the gas blast itself, or in other words by pure rocket action. And then when the air craft rises still higher, where the air would be so thin as to make the propellers useless, the invention provides means whereby the turbine elements can be moved entirely out of the path of the gas blast, whereupon the aircraft is propelled entirely by the rocket effect. - Robert Goddardhttps://digitalcommons.wpi.edu/patents/1035/thumbnail.jp

Mechanism for Feeding Combustion Liquids to Rocket Apparatus

This invention relates to rocket apparatus of the type in which flight is sustained by continuous combustion of suitable liquids, such as gasoline and liquid oxygen. In this application, wherever reference is made to oxygen, it is to be understood that the oxygen is in a liquid state unless otherwise specified, and the term gasoline is to be understood as including other liquid fuels having similar characteristics. It is the general object of my present invention to provide improved means for continuously feeding gasoline or other liquid fuel and oxygen under high pressures to a combustion chamber. A further object is to provide improved means for developing power to produce such high pressures and to return condensed products for further use. I also provide improved and novel means for maintaining substantially uniform pressure in the oxygen and liquid fuel containers as the liquids therein are gradually withdrawn. Further features of my invention relate to automatic control of pressures in my improved feeding mechanism, to provision for automatic closing of certain valves on exhaustion of the liquids in said containers, and to certain safety devices to be describedhttps://digitalcommons.wpi.edu/patents/1072/thumbnail.jp

Seal for Centrifugal Pumps

This invention relates to centrifugal pumps and particularly to pumps designed for handling low temperature liquids, such as liquid air, at or near their very low boiling points. In pumps designed for such purposes it is obviously necessary to reduce all heat losses to a minimum. It is the general object of my present invention to provide a construction in a centrifugal pump by which the friction of solid bodies in running contact is entirely avoided. More specifically, I provide a construction by which a liquid is rendered effective by centrifugal force to serve as packing for the pump and shaft, all other packing being avoided.https://digitalcommons.wpi.edu/patents/1055/thumbnail.jp

Gyroscopic Apparatus for Directing Flight

This invention relates to apparatus for directing the flight of aircraft in outer space and beyond normal atmospheric conditions. While the invention is of somewhat general application, it is more particularly adapted to aircraft which are propelled by the discharge of gases or vapors therefrom, such as rockets or rocket planes… A more specific object of the invention is to provide means for operatively connecting each pair of gyroscopes to the aircraft only during periods of angular adjustment of the rotating gyroscope members relative to the selected axis. In the preferred embodiment of my invention, the frame which supports each pair of steering or control gyroscope members is normally mounted for free angular movement about three mutually perpendicular axes, but said frame is automatically held from movement about one selected axis during any angular adjustment of the planes of rotation of said two gyroscope members in said frame and relative to each other.https://digitalcommons.wpi.edu/patents/1063/thumbnail.jp

Vaporizer for Use with Solar Energy

The general object of the invention is to provide means by which radiant energy from the sun may be used to convert a liquid into vapor in a limited space or area, but at which area the rapid flow of the liquid prevents an excessively high temperature, notwithstanding the high concentration of solar energy. A further object is to provide improved means for localizing the heat absorption and for preventing re-radiation thereof. - Robert Goddardhttps://digitalcommons.wpi.edu/patents/1033/thumbnail.jp

Liquid Storage Tank

This invention relates to tanks in which liquids are stored and from which said liquids are delivered, usually at atmospheric pressure. When such tanks are subject to angular displacement or to changes in acceleration as in an aircraft, it has been found difficult to maintain continuous liquids discharge therefrom, as the discharge outlet of such a tank may be partly or wholly uncovered from time to time, or the depth of the liquid above the outlet may vary widely. It is the general object of my invention to provide a construction in a liquid storage tank which will effect continuous liquid discharge from the tank in any angular position of the tank or under substantial changes in acceleration or deceleration. To the attainment of this general object, I provide a plurality of separate discharge valves, together with means for opening each valve when submerged and when in a definite relation to the mass of liquid in the tank. I also provide a construction by which the liquid which passes out through all of the valves is discharged from the tank through a single discharge connection.https://digitalcommons.wpi.edu/patents/1071/thumbnail.jp

Rocket Apparatus

This invention relates to a rocket apparatus and particularly to a form of such apparatus adapted to transport photographic or other recording instruments to extreme heights. Certain features of the invention are also applicable to the display of signals or to the project of explosives.https://digitalcommons.wpi.edu/patents/1019/thumbnail.jp