**1. Introduction**

The work presented in this article was developed within a research project on the work of Agustín de Betancourt [1–3], analyzing his best-known inventions both from the point of view of engineering graphics [4–7] and from the point of view of mechanical engineering [8–12].

The article shows the static analysis carried out on the inclined plane for the transport of vessels that operated in Coalbrookdale (Shropshire, England) at the end of the 18th century. This historical invention, popularly known as '*The Hay inclined plane*', and the work of the Englishman William Reynolds, made possible the transportation of boats between channels located at different levels.

This invention was the object of a very detailed study from the point of view of engineering graphics [13] that allowed us to obtain a reliable 3D model, from which the research presented in this article was carried out. There is no study from the point of view of mechanical engineering worldwide of this historical invention, a fact which underlines its novelty and scientific interest. The invention had a remarkable influence on the socioeconomic development of the region, as it was of considerable benefit for the coal mines and blacksmiths of the zone, since it allowed the commerce of their products through the river Severn, and the fluvial port Coalport on this river grew to be an important industrial hub [14].

The Shropshire canal was created in 1790 and closed to river traffic in 1944. This bi-directional inclined plane, which had a length of 350 yards (320 m) and allowed vessels to ascend and descend, was put into operation in 1792, and negotiated a difference of 210 feet (64 m).

Meanwhile, Agustín de Betancourt had dedicated much of his research to the study of navigation channels [1], and during his stay in England (1793–1796) he copied in detail the mechanism as it was built, drawing a color sheet of the inclined plane with much detail and a three-page handwritten account explaining the parts of the plane and its operation. These are the only documents of which there is evidence in reference to the inclined plane of Coalbrookdale [15]. The advantage of this historical invention was that it allowed a large drop to be negotiated without loss of water in the process of the ascent and descent of the boats.

Later, Agustín de Betancourt published his work 'Mémoire sur un nouveau système de navigation intérieure' written in Paris in 1807 [16], in which he proposes a channel navigation system for France very similar to the English navigation system: shallow channels and with an advanced system of locks that avoid loss of water in the ascent and descent of the boats. In this account, Betancourt applies his plunger lock to the inclined plane, and mentions the previous work of Robert Fulton [17], indicating that his inclined plane is designed according to Reynolds' procedure.

At present, only ruins remain of the inclined plane of Coalbrookdale. Some photographs [18] still show the inclined plane and the remains of the rails, although it is also possible to distinguish the upper cargo basin and the remains of the brick building that housed the steam engine.

The ultimate goal of this research is to perform a static analysis [19] of the *Hay inclined plane* using the finite element method (FEM) [20] under real operating conditions, in order to determine whether it was well dimensioned and functioned properly. Its scientific interest lies in the fact that from the point of view of industrial archaeology and the study of technical historical heritage, there is no existing study, worldwide, on this outstanding example of industrial historical heritage, which marked a historic milestone in the Industrial Revolution (1760–1840). This underscores the utility and originality of this research.

The remainder of the paper is structured as follows: Section 2 presents the materials and methods used in this investigation; then, Section 3 includes the main results such as von Mises stresses, displacements, deformations and safety coefficient; and Section 4 shows the main conclusions.
