Tensegrity and Tensairity

Structures that hold themselves up with tension, and structures that do it with air

October 17, 2026 · John Peach

Stand under Kenneth Snelson’s Needle Tower outside the Hirshhorn Museum and look straight up. Sixty feet of aluminum tubing climbs into the sky, and not one of those tubes touches another. They hang in mid-air, held apart by thin steel cables, like the blueprint of a building that never got around to becoming one.

Your instinct says it should fall down. In every structure you have ever seen, compression travels a continuous path to the ground: brick rests on brick and column on footing. In Snelson’s tower that path is broken everywhere. The tubes are islands, and only tension connects them.

Snelson’s Needle Tower is an example of a tensegrity structure. It also has a stranger cousin, called tensairity, in which the tension network is replaced by something even less substantial than cable: ordinary compressed air, at roughly one-twentieth the pressure inside a bicycle tire. Bridges built that way have been driven over by trucks.

We’ll look at the history of both ideas, the equations engineers use to design them, and how to build working examples of each from drinking straws, fishing line, and a balloon.

I planned to run the experiments described below but decided to rely on the Pluto notebook instead. The procedures should still work and would make a good school science project.

Tensegrity

Where the idea came from

The word is Buckminster Fuller’s, a contraction of tensional integrity, but the structure came from a 22-year-old art student.

In the summer of 1948, Fuller turned up at Black Mountain College in North Carolina as a last-minute replacement for an architecture professor who had canceled. Among the students was Kenneth Snelson, there to study with the Bauhaus painter Josef Albers. Fuller lectured constantly about tension and compression, and Snelson went home to Oregon that winter and started building.

Over the winter of 1948 to 1949 he made a small sculpture of rigid elements held apart by taut wires, a form he later called the X-Piece. He brought it back to Black Mountain the following summer and showed it to Fuller, who was, by Snelson’s account, amazed and delighted. Fuller went on to name the principle, publish it, and patent it. Snelson’s name appeared on none of the patents.

The two men fell out, and the dispute lasted decades. Snelson never accepted Fuller’s term and preferred his own: floating compression Floating compression — Snelson’s name for tensegrity, emphasizing that the rigid compression members appear to float, since none of them touch one another. He considered it more descriptive and less mystical than Fuller’s coinage. . He spent the rest of his career building the structures and arguing that, whatever the word, the thing itself was his. Fuller worked tensegrity so far into his own cosmology that it became hard to separate from his geodesic domes.

Priority fights like this one are common in the history of technology. Simultaneous invention happens, and influence runs in both directions. Fuller supplied the vocabulary and the obsession with tension, and Snelson supplied the object. Fuller named what Snelson built, and both deserve credit.

What makes a tensegrity a tensegrity

Beyond the sculpture, the three rules of tensegrity are:

1. Compression members never touch each other. Each strut is isolated.
2. Tension members form a continuous network. Every cable connects, directly or indirectly, to every other.
3. The structure is prestressed. Cables are tightened against struts before any external load arrives. Remove the prestress and the whole thing collapses.

The third rule is where tensegrity departs from ordinary engineering intuition. A conventional truss is stiff because its members are stiff, while a tensegrity is stiff because it is pulling on itself. Increase the prestress Prestress — internal force locked into a structure during assembly, present even with no external load applied. In a tensegrity, cables are pulled taut against struts; the resulting self-balanced tension and compression is what makes the structure rigid. and the structure gets stiffer, with no change to geometry or materials. Slacken it and the structure softens toward collapse.

Tensegrity equations

The standard tool for designing these structures is the force density method Force density method — a form-finding technique that replaces each member’s tension with the ratio of tension to length. This turns the nonlinear equilibrium equations of a cable structure into linear ones, which is why it is the workhorse of tensegrity design. , introduced by Schek in 1974 for cable nets and adapted to tensegrity ever since. It turns an otherwise tricky nonlinear problem into a linear one.

For each member $k$ carrying tension $t_k$ over length $\ell_k$, define the force density

Cables in tension have $q_k > 0$; struts in compression have $q_k < 0$. The units are force per length (newtons per meter). That is an odd quantity to think about, but it is what makes the algebra work.

At every node $i$, the forces from all connected members must cancel:

Here $\mathbf{x}_i$ is the position of node $i$, $\mathbf{x}_j$ the node at the far end of member $k$, and $\mathcal{N}(i)$ the set of members meeting at node $i$. Each member pulls its node along the direction of the member, with strength proportional to $q_k$, and balance means the pulls sum to zero.

Equation (2) contains no square roots and no lengths. Because $q_k$ already absorbed the length, the equation is linear in the coordinates. Collected over the whole structure, it becomes

where $\mathbf{C}$ is the connectivity matrix Connectivity matrix — a matrix with one row per member and one column per node, containing $+1$ and $-1$ in the columns of the two nodes that member joins, and zero elsewhere. It encodes which node connects to which, with no geometry. , $\mathbf{X}$ the $n \times 3$ matrix of nodal coordinates, and $\mathbf{D}$ the force density matrix (also called the stress matrix). $\mathbf{D}$ is symmetric.

Equation (3) says the coordinates lie in the null space Null space — the set of all vectors that a matrix sends to zero. Saying the coordinates lie in the null space of $\mathbf{D}$ is another way of writing equation (3): every node is in balance. of $\mathbf{D}$. For a structure that exists in three dimensions and is free to sit anywhere, $\mathbf{D}$ must have a null space of dimension at least four: three for the coordinates, and one for the vector of ones that lets the structure translate:

This is the Maxwell-Connelly rank condition Rank condition — for a tensegrity in three dimensions, the force density matrix can have rank at most $N-4$, where $N$ is the number of nodes. When the rank equals $N-4$ and no eigenvalue is negative, the configuration is unique apart from stretching or shearing the whole structure (Connelly). , the mathematical statement of “a tensegrity can exist here.”

The simplest tensegrity: the prism

A regular prism of $n$ struts has two parallel $n$-sided polygons joined by struts. Before self-equilibrium is possible, the top polygon must be rotated relative to the bottom one by a specific twist angle:

For the three-strut prism, $\alpha = 30°$; for four struts, $45°$. Get it wrong and the structure will not hold. Wind the cables the wrong way round and it collapses.

Given the twist angle, the geometry follows. With base circumradius The circumradius ($R$) is the radius of a circle that passes through all the vertices of a regular polygon, such as a triangle, or touches the vertices of a polyhedron. $R$ and height $h:$

The horizontal cables form the two triangles, and the vertical cables join each bottom node to the nearest top node. The struts run to the far top node, which produces the characteristic twist.

Solving equations (1) to (4) numerically for $n = 3$ confirms the twist angle exactly and returns the force densities in the ratio

The twist angle of $30°$ does not depend on the height-to-radius ratio, so a squat prism and a tall one have the same twist. The vertical cables carry $\sqrt{3}$ times the force density of the horizontal ones and exactly balance the struts. If a cable is going to fail, it will be a vertical one if $h/R \gtrsim 0.86.$

Tensegrity Applications

Snelson’s towers remain the most visible examples in sculpture. Pure tensegrity is rarer in architecture because buildings need floors and floors need continuous compression to spread loads. Tensegrity influenced structures appear in cable domes and tensile roofs, which borrow the prestress logic without the strict discontinuity.

Robotics is where the idea has found the most use. NASA’s tensegrity rover concepts use a strut-and-cable ball that absorbs landing impact by deforming, then moves by changing cable lengths. There is no fragile single point of failure and no landing airbag to discard. The control problem is hard and remains an active research area.

Because a tensegrity’s shape is set by its cable lengths, changing those lengths changes the shape. Prisms that fold flat and spring open have been proposed as deployable satellite antennas.

Chains of tensegrity prisms also behave as strongly nonlinear springs whose stiffness can be tuned by prestress. That makes them candidates for shock-absorbing metamaterials Metamaterial — a material whose behavior comes from its internal structure rather than its chemistry. and for controlling how waves travel through a material.

Biotensegrity: a genuinely contested idea

Some claim that the human body is a tensegrity, with bones as struts floating in a tensioned web of muscle and fascia. It is an interesting idea, but not one that is widely accepted by the scientific community.

The serious version starts with cells. In 1993 Donald Ingber proposed that the cytoskeleton Cytoskeleton — the internal scaffolding of a cell, built from protein filaments. Microtubules are relatively stiff and resist compression; actin microfilaments are thin and carry tension. is a tensegrity, with microtubules as compression struts and actin microfilaments as tension cables, and that this explains how cells sense and respond to mechanical force. The model made testable predictions, notably that cell stiffness should rise linearly with prestress, and experiments have supported that scaling. Ingber later extended the claim across scales, from molecules to organisms.

The orthopedic surgeon Steven Levin coined biotensegrity for the whole-body version, arguing that the skeleton is a set of struts suspended in a myofascial net rather than a stack of columns.

Tensegrity requires discontinuous compression: struts must not touch. Bones meet at joints. Levin’s response is that cartilage and synovial fluid keep the bony surfaces separated, so the compression really is discontinuous. Critics reply that this stretches the definition past usefulness, since a loaded knee transmits compression across the joint whatever is sandwiched between. At the cellular level the debate has been fought explicitly in the literature. In a published point-counterpoint in the Journal of Applied Physiology in 2000, critics argued that their observations contradicted the global cytoskeletal integration the model requires.

Prestress demonstrably matters in cell mechanics, and the tensegrity model predicts real behavior there. Whether “the body is a tensegrity” is a mechanical claim or a useful metaphor depends on how strictly you hold rule 1, and reasonable people disagree. Treat confident assertions in either direction with suspicion.

Tensairity

Replacing the truss web with air

Take an ordinary truss: a compression chord Chord — the top or bottom member of a truss or beam, running its full length. The diagonal members between the chords are called the web. on top, a tension chord on the bottom, and a web of diagonal struts between them carrying shear Shear — forces that try to slide one part of a member past the next, like scissors. In a truss, the diagonal web carries it. . The web keeps the two chords apart and stops the top chord from buckling sideways.

Now throw the web away and put an inflated tube in its place. That is Tensairity, developed at Empa Empa — the Swiss Federal Laboratories for Materials Science and Technology, in Dübendorf. The Tensairity concept was developed there in the early 2000s, principally by Rolf Luchsinger and colleagues at the Center for Synergetic Structures. in the early 2000s under Rolf Luchsinger. The name follows Fuller’s pattern: tension, air, integrity.

A common misreading is that the air carries the compression. It does not; a slender rigid strut still does that. The low-pressure tube supports the strut continuously along its length, which stops it buckling, and it provides a load path between strut and cable that keeps them apart and the structure deep. The pressure also pretensions the cables.

The payoff is that a very slender strut, one that would buckle immediately on its own, becomes usable, and that is where the weight saving comes from.

Real structures built this way include a parking-garage roof in Switzerland spanning up to 28 meters, and a skier bridge in the French Alps spanning 52 meters. An 8 meter test bridge was loaded to 35 kN before failing, and it failed by shear in the compression element, not by anything pneumatic.

Tensairity equations

Under a bending moment $M$, the strut and cable form a force couple separated by depth $d$, roughly the tube diameter:

$N$ is the compression in the strut and the tension in the cable. For a point load $P$ at midspan of a simply supported beam of span $L$, $M_{\max} = PL/4$, so

A deeper beam has smaller chord forces, which is why the tube diameter matters more than it looks.

On its own, the strut would buckle. A pin-ended column buckles at the Euler load The Euler load (or Euler’s critical buckling load) is the maximum axial compressive force that a long, slender, ideal column can support before it suddenly bows or buckles sideways.

$E$ is the material’s stiffness, $I$ the second moment of area Second moment - also called the area moment of inertia - is a geometric property of a 2D shape that measures its resistance to bending or twisting (torsion). A higher second moment of area means a shape resists deflection and bending stress better. This is why structural elements like I-beams place most of their material as far away from the neutral axis as possible. (how the cross-section resists bending), $L$ the unsupported length and $K$ an end-condition factor. The important term is $L^2$ in the denominator. Halve the unsupported length and the buckling load quadruples; double it and the load falls to a quarter.

That $L^2$ is fatal for long slender struts, and the air removes it. A strut supported continuously along its length by an elastic medium of stiffness $k$ (force per unit length per unit deflection) buckles instead at

Length does not appear in equation (12): a strut on a continuous elastic foundation keeps its buckling capacity as it gets longer. This is why Tensairity scales to 52 meter bridges while a bare strut of the same slenderness would be useless at 2 meters. Breuer et al. give $k \approx \pi p$ where $p$ is the gauge pressure Gauge pressure — pressure measured above the surrounding air pressure. A water manometer reads it directly. .

The membrane has its own limit. An inflated cylinder resists bending only while its whole wall stays in tension. Past a critical moment the compressed side goes slack and wrinkles, and stiffness drops sharply. The classical wrinkling moment is

with gauge pressure $p$ and tube radius $r$. Because of the $r^3$, radius is worth far more than pressure. Doubling the pressure doubles $M_w,$ but doubling the radius multiplies it by eight, so a fat, softly inflated tube beats a thin, hard one.

The hoop stress Hoop stress — tension running around the circumference of a pressurized tube, trying to split it lengthwise. It is twice the stress along the tube’s length. in a wall of thickness $t$ is

This sets how much pressure the fabric, or the balloon, can take.

For a three-point bending test, midspan deflection is

Rearranged, it converts measured load and deflection into an effective $EI$ for the whole assembly, which lets you compare configurations against each other.

Tensairity Applications

Bridges and roofs are the strongest use case: long spans that must be transported flat, erected fast, and taken down again. Temporary vehicle bridges, event roofs, and the alpine skier bridge already mentioned all fit that description.

In aerospace, inflatable wings using the Tensairity principle have been investigated. The attraction is a wing that packs into a small volume and deploys in flight. Empa’s group also worked on Tensairity kites for pumping-cycle wind power, where structural mass is a direct penalty on performance.

More generally, Tensairity finds applications in temporary construction wherever the ratio of erected span to packed volume is important.

Results from the notebook

The numbers in this section come from the companion Pluto notebook. The tensegrity half solves the equilibrium equations directly. The tensairity half evaluates the formulas above for a 0.6 meter beam built on a 260-size balloon, with $r = 25$ mm and $d = 50$ mm. The material properties of the straw, skewer, and fishing line are assumed typical values that have not been measured, so the tensairity numbers show orders of magnitude and the ratios between configurations more reliably than they show absolute loads.

The tensegrity prism

The notebook does not assume the twist angle of equation (5), but searches for it. For each twist angle from 0° to 180°, it builds the three-strut prism and asks whether any set of member forces can hold that shape in balance with no outside load. The test is the smallest singular value Singular value — a measure of how strongly a matrix stretches vectors in a particular direction. A smallest singular value of zero means the matrix sends some nonzero input to zero; here, that input is a set of member forces in perfect balance. of the equilibrium matrix, which reaches zero only when such a self-stress Self-stress — a set of member forces that balance at every node with no external load. Prestress is a self-stress scaled to a chosen level. exists.

The curve in Figure 8 stays near 1 almost everywhere and falls by about sixteen orders of magnitude, to the level of rounding error, at exactly 30°. There is no other dip between 0° and 180°. Repeating the search at height-to-radius ratios from 0.25 to 4 puts the zero in the same place, so the twist angle does not depend on the prism’s proportions.

At that twist the force densities come out in the ratio $1 : \sqrt{3} : -\sqrt{3}$, as equation (8) states, and the ratio is the same at every height tested. The force density matrix $\mathbf{D}$ has rank 2, which is $N - 4$ for the prism’s six nodes, and none of its eigenvalues Eigenvalue — a number describing how a matrix scales vectors along one special direction. A negative eigenvalue of the force density matrix would signal a direction in which the structure could buckle. is negative. Together these two results satisfy Connelly’s condition for super stability: the prism is stable at any level of prestress, whatever the stiffness of its members. Figure 9 shows the equilibrium shape. With 200 mm struts, the horizontal cables are 159 mm long and the vertical cables 104 mm, and the assembled prism stands 92 mm tall.

Force density is not the same thing as tension, and a cable fails in tension. Multiplying each force density by its member length gives the ratio of vertical to horizontal cable tension as $\sqrt{(h/R)^2 + 2 - 2\sin(\pi/n)}$. For the three-strut prism the two tensions are equal at $h/R \approx 0.86$ (Figure 6). At $h/R = 1$ the vertical cables carry 1.13 times the tension of the horizontal ones, and the gap widens as the prism gets taller. In a squatter prism the horizontal cables carry more tension than the vertical ones, so the weakest cable depends on the prism’s proportions.

Figure 11 shows how stiff the prism is under a vertical load at different levels of prestress. The model pins the three bottom nodes, pushes evenly down on the top three, and computes the initial stiffness from the tangent stiffness matrix Tangent stiffness matrix — relates small node movements to the small extra forces needed to produce them. It has one part for members stretching and one for the stiffening effect of prestress, like a taut guitar string resisting a pluck. , which accounts both for members stretching and for the extra resistance their prestress provides against sideways movement. The result is a straight line through the origin, rising by about 0.1 N/mm for every newton of compression in the struts. At zero prestress the stiffness is zero, which means the unstressed prism folds under any load, as the third rule of tensegrity says.

The line cannot be followed all the way. In this model the struts are 3 mm bamboo skewers, which buckle at about 9.8 N over 200 mm, so the useful prestress range ends there, at a stiffness of roughly 1 N/mm. The model is also linear: it gives the stiffness at the start of loading. A real prism twists as it is pressed, so its stiffness should change as the load grows.

The tensairity beam

Figure 12 compares the buckling load of a polypropylene straw, assumed 6 mm in diameter with a 0.15 mm wall, with and without support from a tube at 10 kPa. The foundation stiffness is $k \approx \pi p$, following Breuer, Ockels and Luchsinger (2007). On its own, the straw follows the Euler curve of equation (11) and loses strength with the square of its length; at the 0.6 m span it buckles at about 0.5 N. With the air support, the curve levels off once the straw is longer than about 5 cm and settles at the long-strut limit of equation (12), about 47 N. At the beam’s span that is close to a hundredfold gain. The small ripples in the supported curve appear where the strut switches from one number of buckle waves to the next as its length increases.

Equation (10) converts strut force into midspan load. With $d = 50$ mm and $L = 0.6$ m, the strut carries three times the applied load, so a straw that buckles at 0.5 N limits the beam to about 16 g, and one that buckles at 47 N allows about 1.6 kg.

The balloon alone wrinkles at a load that rises in proportion to pressure (Figure 13). Equation (13) gives 33 g at 2 kPa, 167 g at 10 kPa, and 334 g at 20 kPa. The dashed curve shows the classical collapse moment $\pi p r^3$, twice the wrinkling moment, which has not yet been checked against its primary source.

At 10 kPa the three results compare as follows:

The 1.6 kg figure is an upper bound. It assumes the straw is attached to the balloon continuously, or with tape bands no more than about 60 mm apart, so that it cannot lift off or slide sideways. It also assumes a perfectly straight strut and a membrane that carries shear without wrinkling or slipping at the end rings. Latex adds two further problems that the equations ignore: it stretches far more than the fabrics the wrinkling formula was derived for, and a modeling balloon’s pressure is set by the rubber, so pressure and radius cannot be varied independently. None of these predictions has been tested against a physical model.

Experiments

You can build and measure both structures with a ruler, a kitchen scale, and a few dollars of materials. Predicted values come from the equations above, and the point of the exercise is to find out where they hold and where they do not. I didn’t run the physical experiments, but they could be done with household items.

Experiment 1: The straw tensegrity prism

Materials. Three straight drinking straws (avoid the corrugated bendy section), monofilament fishing line, clear tape, a lighter, and a craft knife.

Build. Wrap a 10 mm band of clear tape around each straw end before cutting anything. The tape stops the slit from tearing lengthwise down the straw, which is the main failure mode. Cut a slit 2 to 3 mm deep in each taped end. Slide the fishing line into the slit and secure it with a knot, then melt the tag end into a small bead with the lighter, since a bare knot in monofilament will pull back through. Hot melt glue is another option.

Cut lengths. For 200 mm straws at a height-to-radius ratio of 1, equations (6) and (7) give six horizontal cables at 159 mm node to node and three vertical cables at 104 mm, for an assembled height of 92 mm. Add 40 to 60 mm per cable for knots and adjustment. Make at least one cable per triangle adjustable with a slip knot; you will need it.

Measure.

1. Measure the twist angle between the top and bottom triangles and the assembled height. Compare them with $30°$ and 92 mm.
2. Stand the prism on a kitchen scale, press down on the top triangle with a flat book, and record force against height measured alongside with a ruler. The scale reads in grams, so force in newtons is $F = mg \approx m/102$. Repeat at three different prestress levels by adjusting the slip knots.

The expectation is that stiffness rises with prestress, but a conventional pin-jointed truss does not behave this way at all, so this measurement shows what makes tensegrity different.

Expect trouble. Assembly is awkward because the structure is floppy until the last cable is tensioned, so enlist a second pair of hands. Monofilament also creeps Creep — slow stretching of a material under constant load. In nylon line it gradually lets prestress bleed away. , and prestress bleeds away over hours. Build with monofilament, which stretches and forgives cut-length error, then switch to braided line for the stiffness runs.

Experiment 2: The balloon tensairity beam

Materials. 260-size modeling balloons (nominally 2 in × 60 in), a drinking straw or bamboo skewer as the strut, fishing line as the bottom cable, strapping tape, and clear vinyl tubing for a manometer.

Build a pressure gauge first. None of the equations can be tested without knowing the pressure. Bend a length of clear vinyl tubing into a U, part-fill it with water, and connect one end to the balloon neck. The height difference gives the pressure, $p = \rho g h,$ so 1 kPa lifts the water 102 mm.

Assemble. Do not tape directly to the latex. Strapping tape adheres poorly to talc-dusted latex and, being inextensible, constricts the balloon and pops it. Instead, make two tape rings near the ends and anchor everything to those, letting the balloon bulge freely between them. Run the strut along the top and the fishing line along the bottom, both ending at the same two end rings.

The controlled comparison. Test four configurations with the same span and the same loading Mechanism — an assembly that can move without stretching or compressing any member, so it carries no load in that direction. An unprestressed tensegrity is a mechanism. :

Load continuously with water. Support both ends, hang a cup at midspan, and add water slowly; 1 mL of water weighs 1 g. Continuous loading catches the exact onset of buckling instead of bracketing it between two washers. Photograph the midspan against graph paper as you go, and put a bucket underneath.

Predictions to test. For a 0.6 m span with $r = 25$ mm, equation (13) gives wrinkling at roughly 33 g at 2 kPa, 167 g at 10 kPa, and 334 g at 20 kPa (requires a 2 meter water manometer). A 200 mm polypropylene straw buckles at about 3 N by equation (11), and equation (10) says a 16 g midspan load on a 0.6 m span puts about 0.47 N into the strut. So the bare strut should fail at roughly 16 g, while the balloon-stabilized strut should carry well past it. The experiment is designed to show that gap.

Safety. Wear eye protection, because balloons under tape fail suddenly. Check for latex allergy before starting. Budget a dozen balloons, since the first several builds will fail.

Further questions

• Does measured stiffness scale linearly with prestress, as the tensegrity model predicts, or is the relationship nonlinear at low prestress?
• Does wrinkling load scale with $p$ as equation (13) says, when you vary pressure over a factor of five? Repeat the wrinkling test with a fabric or bicycle inner-tube sleeve, where pressure can be varied.
• Build a four-strut prism ($\alpha = 45°$). Is it stiffer or softer than the three-strut version for the same material?
• Wind the prism cables in the opposite direction. What happens, and why?
• Replace the straight bottom cable in the tensairity beam with two helical cables, as in the original Empa geometry. Does it improve the load capacity, and by how much?

Conclusion

Both structures get their stiffness from something set during assembly. In tensegrity it is the prestress: cables tightened against struts before any load arrives, and a prism that goes limp the moment you slacken them. In Tensairity it is the air pressure, which pretensions the cable, holds strut and cable apart so they act as a deep beam, and supports the strut along its whole length. That support is what lets a very slender strut carry load. Equation (12) has no length in it, which is why Tensairity can span a 52 meter skier bridge with members that would buckle on their own.

The mathematics is simpler than the structures look. Writing each member’s tension as a force density turns tensegrity equilibrium into linear algebra, and the 30° twist of the three-strut prism follows from it. Tensairity design rests on a few classical formulas, and the wrinkling moment of equation (13) carries the most practical lesson: because it grows with $r^3$, a fat, softly inflated tube beats a thin, hard one.

The notebook puts numbers on both ideas. The three-strut prism’s stiffness rises in proportion to its prestress, by about 0.1 N/mm for each newton of strut compression, and falls to zero when the cables go slack. At the 0.6 m span, air at 10 kPa raises a drinking straw’s buckling load from about 0.5 N to about 47 N, so a beam that would fold under 16 g as bare straw and cable could in principle carry around 1.6 kg, nearly ten times what the balloon alone supports before it wrinkles. That figure assumes a strut held firmly against the balloon along its whole length and material properties that were never measured, so the experiments described above remain the way to find out how much of it survives contact with real straws and latex.

Code for this article

The calculations are worked in a Pluto notebook (download from GitHub). I found that Firefox didn’t render the notebook well, but Chrome did. If your default browser doesn’t cleanly generate equations, try starting Pluto from a Julia terminal,

using Pluto
Pluto.run(launch_browser=false)

then copy the URL into the browser of your choice. Copy the whole URL Pluto prints in the terminal, including its ?secret=… part. Pluto needs that token for access.

The notebook should have a table of contents in the right column so you can browse through the sections. If it doesn’t appear immediately, click the “Run Notebook Code” button in the top area of the notebook interface.

The notebook covers:

• Prism geometry from equations (5) to (7), with cut lengths for any strut length
• Verification that the force densities of equation (8) satisfy the equilibrium condition (3), with a residual at machine precision
• Euler buckling (11) for straws and skewers across plausible moduli
• Wrinkling moment (13) and predicted wrinkling load against pressure
• Manometer conversion and hoop stress (14)
• Reduction of measured load-deflection data to effective $EI$ via (15)

Software

• Julia - The Julia Project as a whole is about bringing usable, scalable technical computing to a greater audience: allowing scientists and researchers to use computation more rapidly and effectively; letting businesses do harder and more interesting analyses more easily and cheaply.
• Pluto - Pluto is an environment to work with the Julia programming language. Easy to use like Python, fast like C.

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Image Credits

• Hero: Kenneth Snelson Needle Tower: Wikimedia Commons by Onderwijsgek.
• Tensegrity prism: by Cmglee — Own work, CC BY-SA 3.0.
• Simple Tensegrity Prism: Marcelo Pars, Tensegrities.
• Tensairity bridge: Breuer, J. C. M., et al. An inflatable wing using the principle of Tensairity.
• Skier bridge in French Alps: Galliot, C. and Luchsinger, R., Non-linear properties of PVC-coated fabrics used in Tensairity structures.
• Tensairity kite: Breuer, J. C. M., Luchsinger, R. Inflatable kites using the concept of Tensairity.