Tension + Integrity = Tensegrity

The Providence Engineering Academy seeks every year to put skills to use for the benefit of the community. From designing playground equipment to running science lessons, “we have an obligation to turn our skills outward to the world around us; we learn not for our own sakes” (quoted from the Engineering Academy application).

This year, the Advanced Engineering I students took on a challenge from our very own fitness guru, Scott Mitchell. Mr. Mitchell, who teaches middle school P.E. and runs our outdoor education program, is passionate about his craft. He wants students to understand the human body, in terms of both structure and motion. Mr. Mitchell has long used tensegrity structures as an analogy to help students visualize these principles.

What’s a tensegrity structure, you ask? While a formal definition is somewhat elusive, you know it when you see it. Popularized by the architect Buckmister Fuller and his student, sculptor Kenneth Snelson, these structures feature “compression members floating in a sea of tension.” Still confused?

Here’s an animated GIF from Wikipedia’s page:

The engineering class began with some small models, using elastic bands for the tension elements and wooden dowels for the compression struts.

Victor with the most simple of all tensegrity structures: three sticks
not touching
Victor and Todd with a six-member icosahedron
Josh finds a new use for the 12-stick version

As simple as these look, they take a great deal of effort to plan and assemble. But this was not the end goal; our class aimed to build a giant version of the icosahedron, with compression members 8 feet long!

Attempt 1:

A lot of knots tied to create 24 rope members. Attached lag bolts to 20 lb beams. Got it together and realized that everything was way too loose. Too much sag. Took it apart.

Alena carefully loops the non-slip knot over the bolt
Ben gets those bolts secured
Inital success and exuberance, but everything is far too loose

Attempt 2:

All rope connections shortened by 5 inches to tighten things up.  Unfortunate result: humanly impossible to pull together. Mr. Mitchell attempted to complete the final connections under great duress. Failure, bent bolts, and an abandoned attempt.

Attempt 3:

Straightened out bolts. Loosened all rope lengths by 2 inches. Realized that we can do this the easy way, working with the structure and not against it. Beams held in different orientation. Pulled it all together, but some bolts bent again. Much tighter, much easier, good result!

Colby and Todd compare the 8-foot version to the 12-inch!

Attempt 4:

Practice makes perfect! Rechecked all ropes, and found a few that were too long. Replaced all bolts with thicker ones twice as strong in bending. Worked in new orientation and got it together in under 10 minutes! (Compare this video to the last.)

Mr. Meadth tests it out before anyone else–in the name of safety,
of course!

Todd climbs inside once everything is approved

Eva’s turn!

In case it’s not clear from the pictures and videos alone, it has to be emphasized that none of the wooden beams you see are touching each other. Each of them is “floating in a sea of tension”, held in place by the 24 ropes. This is despite the fact that the entire structure weighs about 160 lb (73 kg).

Here’s another interesting observation: in the interest of safety, we strapped a force gauge to the ropes, and measured 150 lb of tension. (These ropes are rated up to 300 lb, so no problem!) But when Mr. Meadth climbed up on top, weighing about 155 lb himself, the rope tension only increased to 190 lb. How fascinating that 155 lb of live weight does not increase the rope tensions by that amount.

In fact, three people at one time were able to climb up on the structure (totalling more than 300 lb), but the max load reading never exceeded 250 lb, with no evidence of any structural problems.

It’s stable, folks! It beautifully and naturally distributes extra load all around to find equilibrium, much like the human body. Even as it moves, it naturally corrects, distorts, and stabilizes. Watch Todd roll a few feet in the following video.

Needless to say, Mr. Mitchell was delighted with the outcome, and brought his middle school P.E. students over to see, touch, and feel its dynamic responses. He taught them that the wooden beams are analagous to our bones, and the tensioned ropes are like our ligaments and tendons and muscles. Inspired by the work of Anatomy Trains, it’s easy to see what happens when our bodies are injured or out of alignment.

Great work, students! Keep on dreaming, designing, calculating, and serving others! Please share this article freely with friends and family.

A good day’s work!

Middle School: A Mechanical Advantage

The second semester of the middle school elective, Intro to Engineering, takes on a special theme each year, and is intended for 7th and 8th Graders who are repeating the class. Last year, the theme was space exploration, and the theme was matched with our first annual Science & Engineering Expo, which was a huge success.

This year, the second semester theme is “Machines”, with a focus on the simple machine types described by Renaissance scientists. We have looked at the history of modern and pre-modern humanity in this area, wrapped around such figures as Leonardo da Vinci, Archimedes, and Vitruvius (not the LEGO wizard–sorry!). As well as the artistry and ingenuity, we’re also studying the idea of the physical concept of work, and how energy is conserved and transmitted in mechanical systems.

One of the simple machines that was studied in antiquity was the pulley–a rope wrapped around a wheel to change the direction of force. The compound pulley is even more interesting, and allows us to dramatically increase our “mechanical advantage”. In everyday terms, this means that we can make ourselves stronger. But to talk about it is not enough: you have to prove this kind of thing outside!

Using Mr. Gill’s outdoor education equipment and some 400 lb pulleys from Ace Hardware, the students themselves arranged the constituent pieces, hanging from the sturdy structure of the outdoor basketball hoop (not the hoop itself). On the previous day, they had worked with small model version indoors, so they knew how to set things up. It didn’t hurt to have some Boy Scouts in the group, too!

Students working out how to set up the equipment

With everything secure and checked, and a safety mat below, the first student was hoisted up into the air.

Julian was our first contestant!

Pedro gets a taste of the air up there

Josh holds on as Pedro slam dunks!

Our particular compound pulley system had two wheels where the hanging student was located. This means that there are four lengths of rope leading away from the load. This gives a mechanical advantage of four, which means that, aside from friction losses, the person pulling is made four times as strong! If a 100 lb student hangs from the pulley, the person pulling only feels 25 lb.

Two wheels at top and two at bottom; the lower pulley moves up with the load,
while the upper pulley stays in a fixed position; note Sam’s bowline knot!

Other notable moments possibly occurred as well…

Chloe representing for the girls!

Tommy and Julian being lifted together at once

Mr. Meadth showing a great deal of trust in Sam


Payback time for Chloe and Belen

More news coming up later this semester, and keep an eye out for this semester’s Science & Engineering Expo in April!

Field Trip: CMC Rescue

Last Friday, the Providence Engineering Academy was given the opportunity to visit CMC Rescue in Goleta. CMC Rescue designs, tests, manufactures, and assembles a wide range of safety and climbing gear, such carabiners, pulleys, harnesses and rope. The class was warmly received by Tyler Mayer, their Engineering Manager, along with several other members of the engineering team.

The Providence Engineering Academy meets with Tyler (far left) in the
conference room; Eva (far right) looks over the latest CMC pulley design

After being introduced in the conference room, and letting the students look over some new products, Tyler and the team brought the students backstage into the testing area. Safety glasses on!

The CMC team had arranged for a live materials tensile test, giving our students a chance to see some real design work in action. A bright red 1/2″ rope was wrapped securely around two ends of a testing rig, and a hydraulic ram was used to stretch it to the breaking point. To make it more exciting, the students were asked to guess how far the rope would stretch before breaking, and mark it on the machine. They also wrote down how much tensile load they thought it would take.

Students watch the rope being pulled to breaking–note the acrylic shield between
the students and the test specimen!

We’re proud to say that Jake in 11th Grade won in both categories, with a ridiculously long length marked off and a tensile load guess of 2,500 lb (more than 11,000 newtons, for us international types). The actual tensile breaking load was around 3,800 lb, which is the weight of a small car! Isabelle, also in 11th Grade, was a close second in the load category at 2,222 lb, so Jake and Isabelle were rewarded with their very own heavy-duty CMC Rescue carabiner—with their name engraved on it by the CMC laser cutter!

The class watches as the rope stretches well past anybody’s estimation!
Aaron and Eva watch as the laser cutter works its electromagnetic magic

From there, the class took a walk through the rest of the testing and manufacturing facility. CMC has constructed an impressive indoor “playground”, welded together out of shipping containers, that allows them to simulate rescue scenarios (escaping out of a burning building, for example). The students peeked inside to see the network of tunnels and a fake grain hopper. Unfortunately, no volunteer equipment testing was enacted!

Tyler shows the class the indoor equipment testing facility

After passing through the in-house sewing manufacturing zone, the students arrived back in the conference room, and were given the chance to put a new pulley design to the test. A broad steel beam ran the width of the conference room, and Aaron (10th Grade) and Eva (9th Grade) were placed into a typical safety harness, and then hoisted up by their classmates. The mechanical advantage of a compound pulley system was made apparent, multiplying force dramatically.

Eva hoists Aaron off the floor; her force is multiplied by a factor of four, but she
has to pull the rope four times as far

As a final test—not to mention a shameless photo opportunity—the class lifted Mr. Meadth up as well. We’re glad to report that the equipment worked as designed!

Mr. Meadth gets a lift!

All good things must come to an end, and this field trip was no exception. Tyler generously gave each student a smaller carabiner as a parting gift, and the students paused for a final photo. We’re hopeful that we might once again take a walk through the company facility someday, and in the meantime, the students are energized for the practical design process. Thanks, CMC Rescue!

(All photos by Tys vanZeyl)