Tunnel Book: Cut Panels on Folded Side Strips, as in 1851

A concertina fold, in a 1982 Library of Congress dictionary of bookbinding terms by Matt Roberts and Don Etherington, folds a sheet “first to the right and then to the left,” so it opens and closes the way the instrument does. In the tunnel book modeled on this page, one such strip runs down each side, and the panels sit between its folds.

What is a tunnel book?

As this page uses the name, a tunnel book is a stack of panels, each cut with an opening, behind a front cover with a window. Look in through the window and each layer is framed by the one in front of it. The back cover closes the stack.

One surviving example is Lane's Telescopic View, published in 1851 and now in the Johns Hopkins University library; Wikimedia Commons files its photographs under tunnel books. The library's catalog record, quoted on its Commons file page, says it opens with a concertina action and is viewed through a small peephole in the cover.

This site groups the tunnel book with hand-operated paper mechanisms. A 2011 geometric study of pop-ups by Xian-Ying Li, Tao Ju, Yan Gu and Shi-Min Hu lists, as one property of a pop-up, that it opens and closes with no force beyond holding and turning the two pages. A tunnel book does not work that way: the reader pulls the covers apart. A V-fold pop-up is the opposite case, lifted by the turning pages alone.

How two concertinas hold the panels apart

The model on this page uses paper logic: every piece is a rigid sheet with no thickness that turns only at its folds. Each side strip is made of 12 mm panels, two between each pair of neighboring layers. The two panels are hinged to the layer edges and to each other at a fold that points outward, so the folds alternate mountain and valley down the strip.

As the covers draw apart, each pair of strip panels opens like a hinge. At full stretch the pair lies straight, so each gap is 2 × 12 = 24 mm. Four gaps make 96 mm from front cover to back cover.

Closed, every pair folds shut and all five panels lie in one plane. The strips then poke out to 72 mm from the center line. The covers reach 75 mm, so the strips stay inside.

Scroll sideways →

Open the diagram full size

Why it has no fixed half-open position

At a pull of 48 mm, the strips no longer decide where the middle panels sit. Each gap can take any value from 0 to 24 mm, as long as the four gaps add up to the pull. In the model, layer 2 can then sit anywhere from 0 to 48 mm behind the cover. Only at 0 mm and at 96 mm does every gap have one value, so the figures on this page show only those two states.

The model leaves out paper stiffness and friction, so it says nothing about where a real book's layers settle part way open, only that the folds alone do not decide it. The Miura fold is different: in its rigid model, every panel moves together in one linked motion.

Download the tunnel book model (CSV) (what the file holds)

Why the windows shrink toward the back

Every opening edge has to show past the edge in front of it, or part of that layer hides. The check puts the eye 300 mm in front of the cover, a viewing distance chosen for the model. It scales each edge for its distance: an edge w mm from the center, d mm behind the cover, looks like w × 300 / (300 + d) at the cover.

With half-widths of 50, 42, 34 and 26 mm, the edges look like 50, 38.9, 29.3 and 21.0 mm from the center line. Each one falls inside the one before, so every edge shows. Distance alone shrinks a back window a little: a 50 mm half-width set 24 mm back looks like 46.3 mm. What counts is the edge as the eye sees it, and cutting each window smaller than the one in front keeps every edge clear.

Scroll sideways →

Open the diagram full size

How it fails: wide strips and oversized windows

The checks reject two designs. In the first, each strip panel is 20 mm instead of 12 mm, so the closed strips fold out to 80 mm from the center line. That is 5 mm past the 75 mm cover edge. The closed book no longer fits inside its covers.

Scroll sideways →

Open the diagram full size

In the second, layer 1's window is wider than the cover's: a 50 mm half-width behind a 40 mm one. From 300 mm away, that edge looks like 46.3 mm, outside the cover's window, so the cover hides it.

Scroll sideways →

Open the diagram full size

A third limit sits at the end of the pull. At full stretch the strips have no more to give, because each pair of panels already lies straight. The model has no position at the next 2 mm step, 98 mm. Going farther would take strips longer than the book has, and the model does not say how real paper or glue would give way.

An 1851 example, fully open

The same Lane's Telescopic View, drawn out all the way, shows the structure from the front. The printed cover reads “Designed by Rawlins” and “1851,” with a small round peephole in the middle. Behind it, a row of cut layers with arched openings stands between the side strips, which zigzag in and out between the layers.

The photograph shows the build, not its measurements. This page does not measure the strip widths or the spacing in this copy, so the model's numbers do not describe it.