Riding the Sag: How Far Does a Vinpearl Cable Car Cabin Really Travel?
The Vinpearl cable car crosses more than 3km of open sea between Nha Trang and Hon Tre Island in Vietnam, hanging from just seven towers in the water. Between each pair of towers the cable sags into a curve, so a cabin travels further, at a changing speed, than the straight line between the towers suggests.
Where this idea comes from
Start here — these are the sources that inspired this exploration.
Introduction
The Vinpearl Cable Car, near Nha Trang, Vietnam, connects the mainland to Hon Tre Island. At its longest it ran 3,320 m, supported by just seven towers standing in the sea (the tallest reaches 115 m, with 40 m of that underwater), and held the Guinness World Record for the longest cable car crossing open sea. The system has since been rebuilt, so look up its current length and journey time before you start, rather than assuming the original figures still apply. Between each pair of towers, the cable is not straight: like any cable hanging under its own weight, it sags into a curve. The honest curve is a catenary, which sits beyond the IB syllabus, but a parabola is a good approximation for a shallow sag and is syllabus content. Start with the parabola, and use it to work out how far a cabin actually travels along one span, and how its speed changes as it goes.
Guiding Questions
- Look up the cable car's current total length, number of towers, and journey time, then use them to find the cabin's average speed over the whole crossing.
- Model a single span between two towers using a parabola — a good approximation for a shallow sag, and the version of this curve that is on the syllabus. What do you need (span length, sag depth, tower heights) to write down its equation?
- The honest curve for a hanging cable is a catenary, not a parabola. Look up its equation and compare it with your parabola over one span. How different are the two curves for a sag this shallow?
- Using your model, find the actual length of cable in one span, and compare it with the straight-line distance between the two towers. How much extra distance does a cabin travel because of the sag?
- If the cabin moves along the cable at constant speed relative to the cable, is its horizontal speed constant too? Where in a span is it climbing or descending fastest?