The article discusses the interrelationships of the loxodrome or rhumb line, isometric latitude, and the Mercator projection of the rotational ellipsoid. It is shown that by applying the isometric latitude, a very simple equation of the rhumb line on the ellipsoid is obtained. The consequence of this is that the isometric latitude can be defined using the generalized geodetic longitude and not only using the geodetic latitude, as was usual until now. Since the image of the rhumb line in the plane of the Mercator projection is a straight line, the isometric latitude can also be defined using this projection. Finally, a new definition of the normal aspect of the Mercator projection of the ellipsoid is given. It is a normal aspect cylindrical projection in which the images of the rhumb line on the ellipsoid are straight lines in the plane of projection that, together with the images of the meridians in the projection, form equal angles as the rhumb line forms with the meridians on the ellipsoid. The article provides essential knowledge to all those who are interested in the use of maps in navigation. It will be useful for teachers and students studying cartography and GIS, maritime, or applied mathematics. The author uses mathematical methods, especially differential geometry. The assumption is that the readers are no strangers to mathematical cartography.

This study investigates the impact of extreme rainfall events on soil erosion in the downstream Parnaíba River Basin, located in the Brazilian Cerrado. The analysis focused on rainfall erosivity (R factor) and soil erodibility (K factor) as key indicators. The average erosivity in the region was 9051 MJ mm h⁻¹ha⁻¹year⁻¹, with a variation between 7943 and 10,081 MJ mm h⁻¹ha⁻¹year⁻¹, suggesting a high erosive potential, mainly in the rainiest months, from December to April. The soils of the studied area, mainly Ultisols and Chernosols, present high to very high erodibility, with K factor values ranging from 0.025 to 0.050 t h MJ⁻¹ mm⁻¹. Furthermore, fieldwork revealed areas, near highways, with apparently fragile soils, as well as rills and gullies, identified through photographs taken during fieldwork. These locations, due to the combination of high erosivity and susceptible soils, were considered prone to the occurrence of erosion processes, representing an additional risk to local infrastructure. The spatialization of R and K factors, along with field observations, showed that much of the area is at high risk of erosion and landslides, particularly in regions with greater topographic variability and proximity to water bodies. These results provide a basis for the development of mitigation strategies, being important for the effective prevention of landslides.

Despite Cameroon’s immense sand reserves, several enterprises continue to import standardized sands to investigate the properties of concretes and mortars and to guarantee the durability of built structures. The present work not only falls within the scope of import substitution but also aims to characterize and improve the properties of local sand (Sanaga) and compare them with those of imported standardized sand widely used in laboratories. Sanaga sand was treated with HCl and then characterized in the laboratory. The constituent minerals of Sanaga sand are quartz, albite, biotite, and kaolinite. The silica content (SiO₂) of this untreated sand is 93.48 wt.%. After treatment, it rose 97.5 wt.% for 0.5 M and 97.3 wt.% for 1 M HCl concentration. The sand is clean (ES, 97.67%–98.87%), with fineness moduli of 2.45, 2.48, and 2.63 for untreated sand and sand treated with HCl concentrations of 0.5 and 1 M respectively. The mechanical strengths (39.59–42.4 MPa) obtained on mortars made with untreated Sanaga sand are unsatisfactory compared with those obtained on mortars made with standardized sand and with the expected strengths. The HCl treatment used in this study significantly improved these strengths (41.12–52.36 MPa), resulting in strength deficiencies of less than 10% after 28 curing days compared with expected values. Thus, the treatment of Sanaga sand with a 0.5 M HCl concentration offers better results for use as standardized sand.

The design of effective flood risk mitigation strategies and their subsequent implementation is crucial for sustainable development in mountain areas. The assessment of the dynamic evolution of flood risk is the pillar of any subsequent planning process that is targeted at a reduction of the expected adverse consequences of the hazard impact. This study focuses on riverbed cities, aiming to analyze flood occurrences and their influencing factors. Through an extensive literature review, five key criteria commonly associated with flood events were identified: slope height, distance from rivers, topographic index, and runoff height. Utilizing the network analysis process within Super Decision software, these factors were weighted, and a final flood risk map was generated using the simple weighted sum method. 75% of the data was used for training, and 25% of it was used for testing. Additionally, vegetation changes were assessed using Landsat imagery from 2000 and 2022 and the normalized difference vegetation index (NDVI). The focus of this research is Qirokarzin city as a case study of riverbed cities, situated in Fars province, with Qir city serving as its central hub. Key rivers in Qirokarzin city include the Qara Aghaj River, traversing the plain from north to south; the primary Mubarak Abad River, originating from the east; and the Dutulghaz River, which enters the eastern part of the plain from the southwest of Qir, contributing to plain nourishment during flood events. The innovation of this paper is that along with the objective to produce a reliable delineation of hazard zones, a functional distinction between the loading and the response system (LS and RS, respectively) is made. Results indicate the topographic index as the most influential criterion, delineating Qirokarzin city into five flood risk zones: very low, low, moderate, high, and very high. Notably, a substantial portion of Qirokarzin city (1849.8 square kilometers, 8.54% of the area) falls within high- to very-high flood risk zones. Weighting analysis reveals that the topographic humidity index and runoff height are the most influential criteria, with weights of 0.27 and 0.229, respectively. Conversely, the height criterion carries the least weight at 0.122. Notably, 46.7% of the study area exhibits high flood intensity, potentially attributed to variations in elevation and runoff height. Flood potential findings show that the middle class covers 32.3%, indicating moderate flood risk due to changes in elevation and runoff height. The low-level risk is observed sporadically from the east to the west of the study area, comprising 12.4%. Analysis of vegetation changes revealed a significant decline in forest and pasture cover despite agricultural and horticultural development, exacerbating flood susceptibility.