Analytical solutions for the equations of motion of a space vehicle during the atmospheric re-entry phase on a 2-D trajectory

A practical and important problem encountered during the atmospheric re-entry phase is to determine analytical solutions for the space vehicle dynamical equations of motion. The author proposes new solutions for the equations of trajectory and flight-path angle of the space vehicle during the re-entry phase in Earth’s atmosphere. Explicit analytical solutions for the aerodynamic equations of motion can be effectively applied to investigate and control the rocket flight characteristics. Setting the initial conditions for the speed, re-entering flight-path angle, altitude, atmosphere density, lift and drag coefficients, the nonlinear differential equations of motion are linearized by a proper choice of the re-entry range angles. After integration, the solutions are expressed with the Exponential Integral, and Generalized Exponential Integral functions. Theoretical frameworks for proposed solutions as well as, several numerical examples, are presented.     

Multiple solutions in preliminary orbit determination from three observations

Charlier’s theory (1910) provides a geometric interpretation of the occurrence of multiple solutions in Laplace’s method of preliminary orbit determination, assuming geocentric observations. We introduce a generalization of this theory allowing to take into account topocentric observations, that is observations made from the surface of the rotating Earth. The generalized theory works for both Laplace’s and Gauss’ methods. We also provide a geometric definition of a curve that generalizes Charlier’s limiting curve, separating regions with a different number of solutions. The results are generically different from Charlier’s: they may change according to the value of a parameter that depends on the observations.     

Using micro-catchment experiments for multi-local scale modelling of nature-based solutions

The Q-natural flood management project has co-developed with the Environment Agency 18 monitored micro-catchments (~1 km²) in Cumbria, UK installing calibrated flumes aimed at quantifying the potential shift in observed flows resulting from a range of nature-based-solutions installed by local organizations. The small-scale reduces the influence of variability characterizing larger catchments that would otherwise mask any such shifts, which we attempt to relate to a shift in model parameters. This paper demonstrates an approach to applying donor-parameter-shifts obtained from modelling two of the paired micro-catchments to a much larger scale, in order to understand the potential for improved distributed modelling of nature-based solutions in the form of additional tree-planting. The models include a rainfall-runoff model, Dynamic Topmodel, and a 2D hydrodynamic model, JFlow, permitting analysis of changes in hillslope processes and channel hydrodynamics resulting from a range of distributed measures designed to emulate natural hydrological processes that evaporate, store or infiltrate flows. We report on attempts to detect shift in hydrological response using one of the paired-micro-catchment moorland versus forestry sites in Lorton using Dynamic Topmodel. A donor-parameter-shift approach is used in a hypothetical experiment to represent new woodland in a much larger catchment, although testing all combinations of spatial planting strategies, responses to multiple-extremes, failure-modes and changes to synchronization becomes intractable to support good decision making. We argue that the problem can be re-framed to use donor-parameter-shifts at multi-local-scale catchments above communities known to be at risk, commensurate with most of the evidence of NbS impacts being effective at the small scale (ca. 10 km²). This might lead to more effective modelling to help catchment managers prioritize those communities-at-risk where there is more evidence that NbS might be effective.     

NaCl溶液饱和膨胀土的压缩特性及其微观机制

孔隙溶液浓度及组份改变会影响膨胀土颗粒间作用力,改变微观孔隙结构,从而影响土体的物理力学特性。为此,以宁明膨胀土为研究对象,采用不同浓度NaCl溶液制备泥浆预固结重塑样开展一维压缩试验和压汞试验,研究化学作用对重塑天然膨胀土的压缩性和微观孔隙结构的影响规律。结果表明：随着渗透吸力增加,颗粒间水化能力降低,物理化学力使土颗粒由分散状态转变为集聚体状态,形成了集聚体内孔和集聚体间孔,土体表现出双峰孔隙分布特征。预固结样（压力为20 kPa）的初始孔隙比随渗透吸力增加而减小,进而导致固结屈服应力增加;但是渗透吸力对压缩性影响不大,压缩指数和回弹指数基本不变。此外,利用固结系数计算了土体的渗透系数,随着竖向压力增加渗透系数降低;当竖向压力小于200 kPa时,随着渗透吸力增加,渗透系数先增加后减小,但是竖向压力超过200 kPa后,渗透系数变化不大。分析发现,渗透吸力增加导致大孔隙增加,渗透系数增加,但同时密实度增加会导致渗透系数降低,低竖向压力下渗透性受密实度和微观孔隙结构变化耦合作用控制。     

一个采用多种支护技术的基坑工程

基坑支护是一种临时施工措施,目的是挡土挡水,为地下室施工创造条件,同时控制好对周边环境的影响。以一个基坑工程为例,介绍根据其不同的周边环境采用不同的支护技术及在施工过程中发生问题的解决办法,供类似基坑支护工程参考。     

Determination of the fault plane using a single near-field seismic station with a finite-dimension source model

We explore the possibility of determining the actual fault plane of an earthquake from the inversion of near-source displacement seismograms of one station when a finite-dimension source is used instead of a point source model and when the complete displacement is taken into account, including near-field waves. Tests on synthetic seismograms and real data recorded at local distances show that this is possible even with a single, three-component station. A single accelerogram available for the Erzincan, Turkey, 1992 March 13, M _s = 6.8 earthquake is inverted and the solution found is compatible with other seismological studies and with the mechanism expected for the North Anatolian Fault.     

Distribution and environmental impact of coal-mining wastes in Upper Silesia, Poland

 About 50 million tonnes/year of waste rock from coal-mining is generated in the limited area of the thickly populated Upper Silesian Coal Basin (USCB) in Poland. There are 380 coal-mining waste dumps, including 76 active dump sites covering over 2,000 ha. About 15-16 million tonnes/year of waste rock is being reused for civil engineering purposes in the same area. This brings about a problem of ground water deterioration by constituents leached from waste rock exposed to atmospheric conditions. The major factors determining the ground water contamination potential from waste rock are chloride salinity, sulfur content and acid generation potential. The concept behind the presented studies was to provide data for correct evaluation and prediction of contaminant release from the waste rock, based on the characterization of coal-mining waste properties, as well as on long-term laboratory, lysimetric and field studies. The results show that coal-mining waste dumps can be a long-term source of ground water contamination, lasting for decades and increasing with time. Ground water down-gradient from the disused 15–30-years-old part of the studied dump displays high and increasing acidification, high TDS, SO₄, and the highest, still increasing concentrations of Mn, Fe and Zn. Cost-effective and efficient pollution control measures, similar to the presented design and construction elements of the dump site, can mitigate the negative environmental impacts. Received: 3 July 1997 · Accepted: 9 September 1998     

变荷载下双层地基一维非线性固结近似解析解

目前考虑土体非线性压缩及渗透特性的双层地基非线性固结解均假定土体固结系数保持不变,能反映固结系数变化的双层地基非线性固结解还很鲜见。引入经典的e- 和e- 非线性关系描述土体的非线性压缩、渗透特性,在假定双层地基上、下土层压缩指数与渗透指数比值 相等且不等于1的基础上,得到变荷载下考虑土体固结系数变化的双层地基一维非线性固结近似解。该解答在 1条件下可退化为已有的 1时双层地基一维非线性固结解。基于此解探讨了双层地基上、下土层参数的相对比值对非线性固结性状的影响。结果表明：单面排水条件下 越小,下层土与上层土的相对压缩性越低、相对渗透性越高,则双层地基非线性固结速率越快;减小 值,增加双层地基中压缩性小、渗透性高的土层的厚度,会加快地基的固结速率。