More than just O-rings.

 

More than just O-rings. 

When the space shuttle Challenger exploded shortly after launch on 28th Jan 1986, killing all the seven people onboard, a Presidential Commission was formed to investigate the disaster, it was headed Neil Armstrong, Sally Ride (The first woman in space), and none other than Richard Feynman (Nobel prize winner physicist).

The Challenger exploded because of a leak from one of the solid rocket boosters. Each weighed around 500 tonnes, used metal as fuel: they burned aluminum.

Once the fuel was spent at an altitude of over 40 kilometers, boosters got jettisoned by the shuttle and eventually deployed a parachute so they would splash down the Atlantic Ocean. Re-use was the name of the shuttle game, So NASA would send boats out to collect the boosters and take them off to be reconditioned and refueled for the next take-off. 

As the booster slammed into the ocean, the boosters were basically empty tubes. They were built with a perfectly CIRCULAR cross-section, but the impact could distort them slightly and added stress during the transportation. They were dismantled into four sections, checked to see how distorted they were, reshaped into perfect circles, and put back together. Rubber gaskets called O-rings were placed between the sections to provide a tight seal (we have the same gaskets in LPG cylinders).

It was these O-rings that failed during the launch of Challenger, allowing hot gases to escape from the boosters and start the chain of events that lead to that disaster. 

Famously, during the investigation, Richard Feynman demonstrated how the O-rings lost their elasticity at low temperatures. But Feynman also uncovered a second problem with the seals between the booster sections. Checking if a cross-section of a cylinder is still circular is not that easy. For the boosters, the procedure for doing this was to measure the diameter in three different places and make sure that all three were equal. But Feynman realized that this was not sufficient. 

Feynman recalled as a child seeing in a museum ‘non-circular, funny-looking, crazy-shaped gears’ which remained at the same height as they rotated. Despite not being circles, they always have the same-sized diameter from any direction you wish to measure it. You could make thousands of diametric measurements of a shape of constant widths, such as a Reuleaux triangle, they would all come out exactly the same, despite the shape being very much not circular.

So, if a booster had been distorted into a Reuleaux triangle cross-section, then the engineers would have been able to spot this easily, it might not be visible to the naked eye but still, be enough of distortion to change the shape of the seal. 

The final report bears that performance of the rubber O-rings was definitely the primary cause of the accident. But there was a recommendation and 'finding #5': by investigating the team for how the NASA engineering and management team missed a ‘Significant out-of-round conditions existed between the two segments’. 

NASA undone by simple geometry. 

Feynman's shape with three identical diameters next to a shape of infinitely many identical diameters. Both are obviously not circles.

Kennedy Space Center, Florida - Space Shuttle Challenger launches from launchpad.
Pic courtesy - Wikipeida.org.

Space Shuttle Challenger explodes shortly after take-off.

Pic courtesy - Wikipeida.org.

This blog is written based on a chapter from the book "Humble Pi: A Comedy of Maths Errors

Book by Matt Parker"

Book's link - https://www.goodreads.com/book/show/39074550-humble-pi

Perspective

 perspective 

 

As mum had to be admitted at the heights of the lockdown during the Covid-19 Pandemic, that week in intensive care was a bit of a rollercoaster ride, with doctors and nurses needing to keep a close eye on her vitals, and her life was under the support of BiPAP (Non-invasive ventilation), meanwhile, her Covid-19 test result was awaited, a Positive result in the covid test could have opened another Pandora box. 

The oxygen level reached worrying lows, thanks to those God's sent nurses, who would let me see her through video calls, My worry about mum stripped everything else away.

I didn't care about any urgent emails or the calls, I hadn't gotten back to. I didn't have the temptation to check anything which was a periodic task until she was admitted. Even the world news seemed so irrelevant when you are sitting outside the door of an intensive care unit hearing the wails of grief and those ICUs are full of activity and its disturbing noises of equipment beeping, the commotion of nurses and doctors inside the intensive care, raised my heartbeat. 

Intensive care units are bleak places, sometimes, but those sterile rooms full of health care people alight between life and death can be also hopeful ones. The nurses and doctors were my inspiration in the time of darkness. 

The ignominy of this event, I suppose that it takes us such a major event in our lives or the people we love, for perspective to arrive. invariably we take things for granted. I imagined that I could keep hold of this perspective, I would always keep my priorities right, even during good and happy times. I imagined if we could always think of our loved ones the way we think of them when they are in a critical condition. If we always keep the love for them, Love that is always there... So close to the surface, I imagined the love of life and gratitude towards life. 

Well, I am trying now, when my life gets too jam-packed with redundant and stressful junk. I remember that room in the hospital. Where mum was thankful to have a view out of the window or a momentary video call,  I was giving her assurance, everything will be alright mum, you will be fine.