Rigi in the context of "Lake Lucerne"

Lucerne (English: /luːˈsɜːrn/ loo-SURN) or Luzern (Swiss Standard German: [luˈtsɛrn] ) is a city and a municipality in central Switzerland, in the German-speaking portion of the country. Lucerne is the capital of the canton of Lucerne and part of the district of the same name. With a population of approximately 82,000 people, Lucerne is the most populous city in Central Switzerland, and a nexus of economics, transport, culture, and media in the region. The city's urban area consists of 19 municipalities and towns with an overall population of about 220,000 people.

Owing to its location on the shores of Lake Lucerne (German: Vierwaldstättersee) and its outflow, the river Reuss, within sight of the mounts Pilatus and Rigi in the Swiss Alps, Lucerne has long been a destination for tourists. One of the city's landmarks is the Chapel Bridge (German: Kapellbrücke), a wooden bridge first erected in the 14th century.

A rack railway (also rack-and-pinion railway, cog railway, or cogwheel railway) is a steep grade railway with a toothed rack rail, usually between the running rails. The trains are fitted with one or more cog wheels or pinions that mesh with this rack rail. This allows the trains to operate on steep gradients of 100% (45 degrees) or more, well above the 10% (5.7 degrees) maximum for friction-based rail. The rack and pinion mechanism also provides more controlled braking and reduces the effects of snow or ice on the rails. Most rack railways are mountain railways, although a few are transit railways or tramways built to overcome a steep gradient in an urban environment.The first cog railway was the Middleton Railway between Middleton and Leeds in West Yorkshire, England, United Kingdom, where the first commercially successful steam locomotive, Salamanca, ran in 1812. This used a rack and pinion system designed and patented in 1811 by John Blenkinsop.

The first mountain cog railway was the Mount Washington Cog Railway in the U.S. state of New Hampshire, which carried its first fare-paying passengers in 1868. The track was completed to reach the summit of Mount Washington in 1869. The first mountain rack railway in continental Europe was the Vitznau-Rigi-Bahn on Mount Rigi in Switzerland, which opened in 1871. Both lines are still running.

Rigi Kaltbad is a resort in the Swiss Alps, located in the canton of Lucerne. The resort sits on a sunny terrace at an elevation of 1,433 metres (4,701 ft), overlooking Lake Lucerne above Weggis in Central Switzerland. The locality is part of the municipality of Weggis.

Rigi Kaltbad is located on the flanks of the Rigi and is connected to Vitznau by the Rigi Railways. It is also connected to Weggis by a cable car.

Rigi Railways (German: Rigi Bahnen) is a railway company that operates a group of railways on the mountain Rigi, located between two of the arms of Lake Lucerne, in Switzerland. They include two standard gauge rack railways, the Vitznau–Rigi Bahn (VRB) and the Arth–Rigi Bahn (ARB), along with the Luftseilbahn Weggis–Rigi Kaltbad (LWRK) cable car.

Reaching a height of 1,752 metres (5,748 ft) above sea level, the Rigi Railways are the highest standard gauge railway in Europe. They are also the highest railway in both cantons of Lucerne and Schwyz. The Vitznau–Rigi Bahn is also notable as the first mountain rack railway in Europe, and even the second in the world, after the Mount Washington Cog Railway in the United States.