A novel approach to hybrid propulsion transfers

This paper introduces a hybrid propulsion transfer termed a Hohmann Spiral, incorporating low and high-thrust technologies, analogous to the high-thrust bi-elliptic transfer. To understand this transfer fully it is compared to a standard high thrust Hohmann and a bi-elliptic transfer. Two critical specific impulse ratios are derived independent of time that determine the point this novel transfer consumes the exact amount of fuel as the two compared transfer types. It is found that these ratios are valid for both a circular and elliptical starting orbit so long as the apogee of the elliptical orbit coincides with the target orbit radius. An expression representing the fuel mass fraction is derived dependent of time in order to allow a bound solution space. The final part of this paper investigates two orbit transfer case studies, one is a Geostationary Transfer Orbit to Geostationary Earth Orbit based on the Alphabus platform specification and the other is from Low Earth Orbit to an orbit near the Moon. It is found the thrust required to complete the former transfer in a specified duration of 90 days exceeds current technology and as such provides a technology requirement for future spacecraft. It is found however, for spacecraft of significantly smaller mass, in the region of 1000kg, compared to Alphabus (Max. mass at Launch =8100kg), the transfer consumes the same fuel mass as a standard high-thrust Hohmann transfer with realistic low-thrust propulsion values (150mN, 300mN and 450mN) within the set duration of 90 days. In addition, it is shown that utilising uprated thrusters (210mN, 420mN and 630mN) a fuel mass saving can be made. This could provide a potential transfer alternative for future smaller spacecraft. The second case study is bound to a maximum thrust of 150mN, but the mission duration is not specified to highlight the variation. It is found that the HST offers fuel mass savings of roughly 5% compared to a standard high-thrust transfer and approximately 1.5% compared to a bi-elliptic transfer for different scenarios

Hohmann spiral transfer with inclination change performed by low-thrust system

This paper investigates the Hohmann Spiral Transfer (HST), an orbit transfer method previously developed by the authors incorporating both high and low-thrust propulsion systems, using the low-thrust system to perform an inclination change as well as orbit transfer. The HST is similar to the bi-elliptic transfer as the high-thrust system is first used to propel the spacecraft beyond the target where it is used again to circularize at an intermediate orbit. The low-thrust system is then activated and, while maintaining this orbit altitude, used to change the orbit inclination to suit the mission specification. The low-thrust system is then used again to reduce the spacecraft altitude by spiraling in-toward the target orbit. An analytical analysis of the HST utilizing the low-thrust system for the inclination change is performed which allows a critical specific impulse ratio to be derived determining the point at which the HST consumes the same amount of fuel as the Hohmann transfer. A critical ratio is found for both a circular and elliptical initial orbit. These equations are validated by a numerical approach before being compared to the HST utilizing the high-thrust system to perform the inclination change. An additional critical ratio comparing the HST utilizing the low-thrust system for the inclination change with its high-thrust counterpart is derived and by using these three critical ratios together, it can be determined when each transfer offers the lowest fuel mass consumption. Initial analyses have shown the HST utilizing low-thrust inclination change to offer the greatest benefit at low R2 (R2 - R1) and large AI (AI > 30º). A novel numerical optimization process which could be used to optimize the trajectory is also introduced

Novel numerical optimisation of the Hohmann Spiral Transfer

As the revenue of commercial spacecraft platforms is generated by its payload, of which the capacity is maximised when fuel-mass is minimised, there is great interest in ensuring the fuel required for the trajectory to deliver the satellite to its working orbit is minimum. This paper presents an optimisation study of a novel orbit transfer, recently introduced by the authors through an analytical analysis, known as the Hohmann Spiral Transfer . The transfer is analogous to the bi-elliptic transfer but incorporating high and low-thrust propulsion. This paper has shown that substantial fuel mass savings are possible when utilizing the HST. For a transfer to Geostationary Earth Orbit it is shown that a fuel mass saving of approximately 320 kg (~ 5 - 10% of mwet ) is possible for a wet mass of 3000-6000 kg – whilst satisfying a time constraint of 90 days. Several trends in the gathered data are also identified that determine when the HST with high or low-thrust plane change should be used to offer the greatest fuel mass benefit

An extension and numerical analysis of the Hohmann spiral transfer

This paper extends previous work on the Hohmann Transfer Spiral (HST) by introducing a plane change into the analysis. An analytical expression determining the critical specific impulse incorporating a plane change is derived for both a circular and elliptical initial orbit. This expression determines the point at which the HST is equivalent in terms of fuel mass fraction to the compared Hohmann transfer. The expression assumes that the inclination change is performed by the high-thrust system. The numerical approach uses a blending method coupled with optimised weighting constants to deliver a locally optimal low-thrust trajectory. By comparing the analytical and numerical approaches, it is shown that the analytical can deliver a good estimation of the HST characteristics so long as little orbit eccentricity control is required. In the cases where orbit eccentricity control is required, the numerical approach should be used. A case study from an inclined Geostationary Transfer Orbit, equivalent to a high-latitude launch site, to Geostationary Earth Orbit has shown that the HST can offer a fuel mass saving approximately 5% of the launch mass. This equates to the mass penalty associated with this high-latitude launch site and therefore mimics the advantages of a low-latitude launch site at the expense of a longer transfer duration

Market Competition, Institutions, and Contracting Outcomes: Preliminary Model and Experimental Results

Contracts, Competition, Market Power, Enforcement, Institutions, Agribusiness, Industrial Organization, Institutional and Behavioral Economics, Production Economics, C91, D02, D43, D86,

Solving eigenvalue problems on curved surfaces using the Closest Point Method

Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on rather general curved surfaces. Our algorithm, which is based on the Closest Point Method, relies on an embedding of the surface in a higher-dimensional space, where standard Cartesian finite difference and interpolation schemes can be easily applied. We show that there is a one-to-one correspondence between a problem defined in the embedding space and the original surface problem. For open surfaces, we present a simple way to impose Dirichlet and Neumann boundary conditions while maintaining second-order accuracy. Convergence studies and a series of examples demonstrate the effectiveness and generality of our approach

The United States and World Cotton Outlook

Crop Production/Industries,

The United States and World Cotton Outlook

Crop Production/Industries,

Pieri resolutions for classical groups

We generalize the constructions of Eisenbud, Fl{\o}ystad, and Weyman for equivariant minimal free resolutions over the general linear group, and we construct equivariant resolutions over the orthogonal and symplectic groups. We also conjecture and provide some partial results for the existence of an equivariant analogue of Boij-S\"oderberg decompositions for Betti tables, which were proven to exist in the non-equivariant setting by Eisenbud and Schreyer. Many examples are given.Comment: 40 pages, no figures; v2: corrections to sections 2.2, 3.1, 3.3, and some typos; v3: important corrections to sections 2.2, 2.3 and Prop. 4.9 added, plus other minor corrections; v4: added assumptions to Theorem 3.6 and updated its proof; v5: Older versions misrepresented Peter Olver's results. See "New in this version" at the end of the introduction for more detail