omenti

how big is it?

Two days ago I was on a call with one of you.  Somehow "how big is the Universe?" came up.  I spent ten or fifteen minutes talking about it at a very high level.  Here's roughly what I think I said. A few of you worry about this and I'd be interested in comments if this is a good layperson's explanation. 

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Start with the fact that the speed of light is finite and fixed. That you see the Sun as it was about 500 seconds ago, the moon 1.3 seconds and your ring a handful of nanoseconds in the past. The farthest star you can see with the naked eye on a dark and clear night is about 16,000 light years away and the most distant object is the Andromeda galaxy at something over 2 million light years off.

In the past two decades the age of the universe has been pinning down at around 13.8 billion years. Since light travels at the speed of light one might conclude the universe has a diameter of 27.6 billion light years.

But the universe isn’t static. In the late 1920s it became clear it was expanding everywhere.  The farther something is, the faster it's moving away.  The hypothesis that it may have come from something very small was a natural conjecture.  It became known as the Big Bang.  

What a terrible name!  Bang invokes explosion.  Instead it's an expansion of space everywhere.  A neat thing about relativity is that “nothing moves faster than light” only applies to light and matter, and not to space. Space isn't breaking any rules when its expand faster than the speed of light. Distantly separated objects may not be moving much relative to the space immediately around them, but the space between them is expanding and distancing them.

The universe was initially a hot opaque plasma that cooled as it  expanded. Finally, at about 380,000 years, it chilled to about 3,000° K - chilly enough that electrons and protons in the plasma became hydrogen atoms and the universe was transparent to light for the first time. The first color isn’t far from the orange you see on the filament of an old incandescent light - so orange everywhere.  The what might be called the observable universe  had expanded to a sphere with radius of about 42 million light years. We can still see that initial event.  Light coming towards us was encountering an expanding distance to travel and has finally made it here after 13.8 billion years.

So re-stating.... The remnant of that first light that we currently see on earth comes from a sphere that was 42 million light years in radius when it started. Light seen on Earth yesterday was from a slightly smaller sphere, light seen tomorrow from a slightly larger one. The expansion of space has stretched out (red shifted) the wavelength of that light with an initial wavelength of about a half micron to the point where it’s now a microwave with a wavelength of about 1.9 mm. Those primordial photons still light up the universe.. there are about 400 of them per cubic centimeter of space.

Expansion continues. That first glow - the cosmic microwave background - we observe is 13.8 billion years in the past, its sphere has continued to expand (at a slower rate) and is now about 46 billion light years away from us.

So this is the known universe, much of which we can’t observe.

Immediately preceding what is now known as the hot big bang may have been an incredibly rapid inflation. It explains much about the structure of the universe but hasn’t been found in direct observation (yet). It also sets a lower limit on the size of the universe at about 125 million times larger (by volume) than the 92 billion light year universe we sort of know.  It could be much much larger. There’s no reason to think we’re special. It seems likely that volume is filled with stars, galaxies, black holes and (my gut feeling) intelligences beings thinking about this too.

 

the moon's going to be okay

You've probably heard that an old Space X rocket will crash into the Moon on the forth of March.  It's very likely and a good excuse to look at a few other things.

 

The object in question is the second stage of a Falcon 9 that was used to take the Deep Space Climate Observatory to L1, the first Lagrange point in the Earth-Sun system.¹  The observatory monitors the Sun, specifically the solar wind, from a vantage point a million miles closer to the Sun.  In addition to science, it it gives about an hour's warning for satellites in orbit as well as power stations who need to prepare for large solar storms. 

 

The Falcon's second stage has been looping around the Earth and Moon in an unstable orbit making a few close approaches to both Earth and Moon.  This type of orbit crashes into either the Earth or Moon or is perturbed into a solar orbit.  Exactly where is difficult to predict, but almost certainly it will be on the far side of the Moon.  Too bad as it might be visible through a telescope if it were to hit an area in the night side of the Moon's near side.  

 

That brings up another point.  The far side of Moon is the part away from us. We see the dark side, at least some of it, all the time except when the Moon is perfectly full. 

 

The Moon's rotation is tidally locked with the time it takes to make an orbit.  Initially the Moon wasn't and rotated at a faster rate. Over millions of years tidal forces slowed it down to the point where it became locked.  Roughly speaking the Moon is slightly egg-shaped rather than a perfect sphere.   If the long axis through the Moon isn't pointed at the Earth, a torque is exerted which moves it back into position. Once locked it would take a large force to unlock the rotation. 

 

The Moon's far side is only the dark side when we see a full Moon from Earth.  If you're interested in how bright the Moon's surface is, the far side tends to be much brighter than the side we see.  And the elliptical orbit of the Moon permits us to observe a bit more than half of the Moon's surface over about a month, although only half at once.

 

A few other neat things about the Earth-Moon system.  The two bodies orbit a common point, or barycenter, about 1,700 km below the Earth's surface. (the barycenter for our solar system is sometimes outside the Sun, currently it's on the inside).  

 

And finally the average distance from the Earth to the Moon is increasing at about the rate your fingernail grows. Tidal forces are also slowing the Earth's rotation.  There's a point where a day on the Earth will be the same as the lunar day - something like 46 days long.  It's a bit in the future though..  long after the Sun becomes a red giant and incinerates the Earth and long after before the Sun explodes forming a planetary nebulae.  The Earth and Moon will have vanished long before, but planetary nebulae are beautiful.

 

 

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¹ In a two-body system like the Earth and Sun, there are five points where the gravitational force on an object  exactly equals the centripetal force necessary for that object to move with the bodies.  L1 is closer to the Sun and great for a solar observatory, L2 is behind the Moon and a great place for a telescope like the James Webb Space Telescope. (note the little orbit around L2 - it turns out the JWST orbits L2, rather than sitting there so the Earth doesn't shield it from the solar energy it needs to operate.  L3 is where the anti-Earth of science fiction would live.. (except it's unstable, so not really), an L4 and L5 are useful points on our orbit to put solar observatories that look at the Sun from an angle other than head-on.

 

 

 

 

skiing!

a minipost

With Beijing approaching I started into a piece on skiing, but the number of drawing needed to illustrate carved turns, sidecut radius, reverse camber, self-turning, plowing and so on was daunting.  Looking around I found a good, not very technical, discussion of downhill skiing. The discussion falls apart on freestyle and ski jumping. I'll save freestyle for later as it's a rich area.  But I know a little about ski jumping.

 

The point of ski jumping is to jump as far down a hill as possible while showing style. Contestants are judged on how far their landing is from a critical line know as the K line (kritisch is critical in German).   The main hill at the PyeongChang Olympics was K98 - the K line was 98 meters from the end of the jump.  The long hill was K125.

 

The first phase is the in-run.  A ski jumper releases from a metal bar at the top of the ramp and begins to turn  gravitational potential energy from the height they're at for kinetic energy.  They crouch to lower the area their body presents to the oncoming air.  Aerodynamic helmets and tight fitting suits are used and their arms are out behind them.   Ski jumps have refrigerated ceramic tracks that form a very slippery layer of ice.  New snow or warm sunlight can dramatically change frictional drag and ski waxes are picked for specific conditions.

 

The ski jumper has a good deal of speed and momentum as they reach the takeoff table at the end of the ramp.  It may look angled up, but that's an illusion. It's still slightly down and the jumper needs to change from the crouch they've been in and physically jump into the air.  You don't just fly off.  The timing and power of the jump are critical elements.

 

 The ski jumper/ski combination is a glider at this point subject to three forces:  gravity, aerodynamic drag, and lift.  They've changed from a minimal aerodynamic profile to something more like an airfoil with greater surface area and the best possible shape. The skis move to form a V shape and  with the ski jumper in control of the angle of each ski (a total of six angles) and their hip and chest angles. Their arms are held slightly apart from the body to add some additional area while keeping aerodynamic drag at a minimum.   The best lift to drag in competition is about 1.6 - for every meter a ski jumper drops, they travel 1.6 meters forward. A common sea gull has a L/D of about 10 and modern airliners are in the 15 to 18 range.  

 

The V ski position revolutionized the sport in the mid 80s. Sorting out all of the angles and learning how to  change them for differing conditions is necessary for winning.  The aerodynamic problem is still very computationally difficult, so large low speed wind tunnels as well as racks on top of vans are used for experimentation and training.

 

You might think that a heavy jumper, coming off the ramp with greater momentum, would have an advantage, but the force of gravity is more important and lighter jumpers fly farther.   There were body mass index requirements, now lighter skiers are penalized with shorter skis that reduce lift.  Ski jumpers still tend to be very thin.

 

The flight is rarely more than four meters above the ground, the flight plath roughly following the hill's downward slope. Landings are highly technical and judged for style.  The transition from the V flying configuration to parallel skis one foot ahead of the other requires timing, strength and balance. 

The longest ski jumping events are on K185 and longer hills - "ski flying"  It's not an Olympic event, but shows off the flying portion:

 

But one of the most memorable performances was that of Eddie the Eagle in the Calgary 88 games.  (it won't embed .. watch at the link) You can place last and be the most celebrated athlete Calgary.  If you've stood at the top of a ramp, you get an appreciation of what it must take to even try it.

 

orbits

It's almost Perihelion Day!   I may wish people Happy New Year, but the beginning of a calendar year is artificial, so I celebrate a specific point in our orbit every year.

 

The orbit of the Earth is elliptical. Not terribly so, but enough we're about 5.1 million kilometers closer to the Sun in early January than we are in early July.  The closest point is the perihelion and the furthest, the aphelion.  The exact time of perihelion varies from year to year - this year it's the 4^th of January at 6:52am UT or 1:52am EST.  Californias get to celebrate on the 3^rd.

 

At perihelion the Earth is at its fastest speed in our orbit - 30.29 kilometers per second.  At aphelion, the slowest point, we've slowed by about a kilometer per second.  Given its closeness, the apparent disk of the Sun has about 7% more area at perihelion than it does at aphelion.  That seems to bother people as it's Winter in the Northern Hemisphere.  In fact the Earth is a bit more than 2°C colder at perihelion than at aphelion - an artifact of the distribution of the continents and a bit of physics.

 

There more land in the Northern than the Southern Hemisphere.  Water has a higher heat capacity than land.  Think about a desert.  During the day it can get scorching hot, but it rapidly cools off at night.  The ground doesn't hold heat as well as water.  In July the Northern Hemisphere has long days that allow the land to heat up for longer periods raising the temperature of the air above it and raising the average temperature of the Earth in the process.   In January the Southern Hemisphere is getting the most sunlight, but most of it falls on water, which doesn't heat up as much as the land. 

 

There are some interesting rabbit holes one can get into and much can be learned by studying the positions of bodies in our solar system and people have been doing it for thousands of year.   Some civilizations were very sophisticated in calculating and predicting astronomical events even though their models of the solar system were wrong.  An early computer that makes your jaw drop is the Antikythera mechanism.  People have been studying it for over a century and Scientific American has a fine summary of what's currently known about the device.

 

In 1900 diver Elias Stadiatis, clad in a copper and brass helmet and a heavy canvas suit, emerged from the sea shaking in fear and mumbling about a “heap of dead naked people.” He was among a group of Greek divers from the Eastern Mediterranean island of Symi who were searching for natural sponges. They had sheltered from a violent storm near the tiny island of Antikythera, between Crete and mainland Greece. When the storm subsided, they dived for sponges and chanced on a shipwreck full of Greek treasures—the most significant wreck from the ancient world to have been found up to that point. The “dead naked people” were marble sculptures scattered on the seafloor, along with many other artifacts. Soon after, their discovery prompted the first major underwater archaeological dig in history.

One object recovered from the site, a lump the size of a large dictionary, initially escaped notice amid more exciting finds. Months later, however, at the National Archaeological Museum in Athens, the lump broke apart, revealing bronze precision gearwheels the size of coins. According to historical knowledge at the time, gears like these should not have appeared in ancient Greece, or anywhere else in the world, until many centuries after the shipwreck. The find generated huge controversy.

...

 

A more technical discussion appears in a recent article in Nature (open access)

 

A Model of the Cosmos in the ancient Greek Antikythera Mechanism

Tony Freeth, David Higgon, Aris Dacanalis, Lindsay MacDonald, Myrto Georgakopoulou & Adam Wojcik

The Antikythera Mechanism, an ancient Greek astronomical calculator, has challenged researchers since its discovery in 1901. Now split into 82 fragments, only a third of the original survives, including 30 corroded bronze gearwheels. Microfocus X-ray Computed Tomography (X-ray CT) in 2005 decoded the structure of the rear of the machine but the front remained largely unresolved. X-ray CT also revealed inscriptions describing the motions of the Sun, Moon and all five planets known in antiquity and how they were displayed at the front as an ancient Greek Cosmos. Inscriptions specifying complex planetary periods forced new thinking on the mechanization of this Cosmos, but no previous reconstruction has come close to matching the data. Our discoveries lead to a new model, satisfying and explaining the evidence. Solving this complex 3D puzzle reveals a creation of genius— combining cycles from Babylonian astronomy, mathematics from Plato’s Academy and ancient Greek astronomical theories.

 

Back to now.  Happy Perihelion Day to all of you!

and a comment

I'm  not fond of the idea of the Earth making a circuit every year as, the Earth never comes back to the same spot in any reference frame.  It's roughly close enough for most, but in four dimensional space time it's something of an approximate helix expanding out along the time axis.  You can never go home. Good enough reason to look forward!

 

 

 

 

 

meshes and trees

A few weeks ago an unexpected email arrived from Germany.  A physics postdoc and had come across an ancient transition radiation detector in storage at CERN a few months before.  It seemed like it could be useful in an experiment her group was thinking about. She had a few questions and it turned out I was the best person to talk to.

 

Many people think science is done with sparkling new state-of-the-art kit.  A few pieces perhaps, but very old equipment is updated, repaired and repurposed where it might be useful.  An experiment I was part of in the early 80s required a very large magnet.  The best bet was one that had been a cyclotron at Berkeley fifty years earlier.  It worked well,  but we had to tap into institutional knowledge that had migrated out of physics entirely.  That knowledge combined with technology that hadn't been invented at the time gave us something fantastic.  

 

I have no idea how my old detector made its way from Brookhaven National Laboratories to CERN.  The documentation and lab books were packed with it, but they made assumptions that the people who built it would be involved.   That meant me.  I asked for photos of some of the lab book pages and then it came back.  I listened to her ideas, offered some suggestions and wished we had her experience back then..  Of course that experience came years later.

 

These interactions spanning several decades may not be common, but twenty year interactions of hardware, software and people.  It's all a mesh.  Old apparatus islands that have been repurposed and grafted onto new apparatus.  It's an organic process that's difficult to map out and impossible to predict.   Diagrams it would look like flocks of meshes that are grafted together with a lot of institutional knowledge.  No one has a complete picture and local expertise is critical.  A team sport spanning decades.  It isn't easy, but it works.

 

Last week I came across something by Frank Oppenheimer in the 30s:

 

 

 

It's one of the better commentaries I've seen on how science progresses.  The same is probably true for many other fields.  I suspect it's true for any infrastructure involved in messy and complex endeavors where creativity and insight come into play.  

 

I've been fascinated watching the techno-solutionist approach to cities - the so-called smart city.  These are often based on a "start with internet and build up" model.  They try to measure everything and automate control.  Sensors embedded everywhere and tree-like computational structures making decisions to smooth out - well - everything.  A fundamental problem is we don't know what is being measured and what the biases - social and technical - are.   A simple truth I've learned from my exposure to sports science is you have to know exactly what's being measured and exactly where it is useful. (duh!)   Often current measurements and/or models just don't work.  Something complex like a city is that on steroids with the tree-like information structures introducing a certain rigidity.

 

There are a few types of people who thrive in the messy environment of a city.  Impedance matchers - those who can connect and explain across disciplines, and synthesizers come to mind.  (many others too - artists for example)  They respond to intellectual and system friction and help spark creativity. They're ground zero essentials for  creativity and invention.  I have doubts that the techno-solutionist cities can be terribly creative in the long run.

a song by Malvina Reynolds comes to mind

 

a dive into snowflakes

miniost

Derek Muller interviews Ken Libbrecht.  Ken is an astrophysicist, but like many scientists his curiosity extends past his core interest.  He's a great example of someone making progress in one of those small areas not many people worry about.  His enthusiasm comes through communicating why people do science.

This is so good!

people beyond the numbers

 

"Track is nothing but numbers. A good mathematician probably could be a good track coach."

 

A quote from the head coach of the University of Oregon's track and field program.   They've picked some metrics that aren't applicable to sport which force young women to endanger themselves mentally and physically.  It turns out to be a way to turn a "fitness goal" into body shaming and performance on the field can suffer.   Here's a good piece on the subject.  Unfortunately Oregon isn't alone. 

 

Just what needs to be measured and how is it analyzed and interpreted.  In this case it's an outdated belief that thin people can run faster and jump higher.  It may be true to a point, but going past that point can reduce performance and lead to Relative Energy Deficiency in Sport.   Sadly RED-S is common among female athletes - often the result of the athletes and their coaches not being aware of the last few decades of health and fitness in sports research.  They may be very good at measuring body fat percentages, but that's barking up the wrong tree.

 

People, it turns out, are complicated.  Traditionally medicine has been based on a biomedical model.  Simply speaking you measure something and react (treat medically or create a fitness goal in sports) based on the number and then repeat the steps.  For many medical conditions measurements and treatments are coarse enough that it works well enough - it's often all there is.  

 

In the past twenty years there's been a recognition that the mind is involved.The mind and body react together to what we forecast might happen in the near future.¹  Sometimes the mental component is small but it's can very large - particularly in competition.   To get a handle on the mental side athletes are often asked to keep detailed training diaries on how they feel at various times of the day .  A coach looks for changes and tries to adjust the training accordingly.   To go deeper here's been explosive growth in the use of sports psychologists in professional and D-I college sports.

 

There's also been an explosion in wearable fitness devices.  They can be great when the simple biomedical model applies.  Using them to improve fitness levels works for many people who aren't at peak performance levels.  Many paths can result in improved fitness and motivation is extremely important.  Professionals find them useful in some areas of training - checking heart rates during aerobics for example,  but don't find them terribly useful outside training.  

 

And back to the amateur.  You may have the twin goals of weight management and improved fitness.  Exercise is almost always great for health and probably worth the price of a wearable if you have motivation issues, but weight management is poorly dependent on exercise.  A device may tell you how many Calories of kilojoules you've used during a session, but sadly it's incorrect to assume that's tied to how much you eat.  Metabolism is very complex and the body and mind adjust it to match new conditions.  So you lose weight at first, but then it comes back even though you're exercising and eating the same.   There are good evolutionary reasons for this that we've abundanced our way out of.

 

Assume you have a device that can measure a few metrics that are well-understood.  How the information is used can be tricky.  We're seeing a lot of amateur mistakes with date analysis in the pandemic - and often by people who should know better.  It's common in fitness training and undoubtedly in many fields.   My friend Greg Blonder put together two pieces of information that presented together are misleading.

 

You plot the amount of ketchup on the horizontal axis, and Tastiness on the vertical.
A hamburger is very desirable with a little ketchup, ever more so slathered. Liver is highly detested, but LOTS of ketchup helps. So more ketchup is better for either meal, but worse overall. The undesirability of liver skews the results when you aggregate data.  

 

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¹ In the literature the mind-body models are sometimes called anticipatory regulation or predictive processing.  Journalist Mike Finch and sports scientists Ross Tucker and John Kiely talk about this and a few other training issues associated with elite sport in episode 26 Tucker's The Real Science of Sport podcast.  If you have any interest in sports science this is one of the best podcasts around. 

 

 

how electrical energy moves..

a quick minipost

Most people don't understand how electric energy flows until they take and Electricity and Magnetism class in college. I've found teaching it without math to be challenging unless your good at drawing or some other type of visualization..    Derek Muller does an excellent job without having to resort to the math! 

 

Maxwell's equations are often the first place a physics student has the wind knocked out of them by sheer beauty. 

opportunity++

Now it's posh, but London's Soho district was a rather unfortunate place in the mid 19th century.  The region was experiencing dramatic growth, but it didn't connect to London's sewer system.  Residences crammed in with slaughter houses and rendering plants overloaded a primitive sewer system that was unable to serve everyone.  Cesspools ran over and untreated waste flowed directly into the Thames.  This was taking place during a worldwide pandemic. London had seen outbreaks before, but the 1854  outbreak on Broad Street changed the course of history.

 

John Snow is famous for mapping out cholera deaths in the area and noting a cluster served by a water pump on Broad Street. The pump drew water from a well that was contaminated by human and animal sewage. The Broad Street pump was removed from service, but didn't make much of a dent in the three or four thousand cholera deaths in London.  What made a difference was what he did next. - an analysis of deaths in regions served by water pumped from the Thames.  He set up a double blind experiment and showed cholera was carried by an agent in the water rather than the dominate theory that it was "bad air" (miasma).  It was the beginning of scientific epidemiology and modern public health. 

 

There's a pub named in his honor near the location of the pump that started his line of reasoning.

 

Over the last year and a half we've been  learning just how important public health is.  It seems odd to unquestionaingly spend so much on a war industry when a pandemic mixed with politics and a fear of science has prove more lethal than war.  That aside we're learning fresh air is critical with airborne spread diseases.  During an outbreak that means masks universally worn as a first and final line of defense and frequent air changes.  With the delta variant of SARS-CoV-2  it looks like you need at least fifteen air changes an hour to qualify as safe with minimal masking.  Outside of clean rooms and operating theaters that's a tall order indoors.  We can get part of the way there with in-room air cleaners, upgraded HVAC systems and opening windows when you can.  I've been spending some time doing this to learn a bit and have come to the conclusion that, although effective, it's sort of a piano wire and chewing gum approach.   Real fixes require an architectural design approach informed by science to create new spaces as well as retrofit existing ones.  Very few people do the science and much needs to be done.  New technologies probably need to be developed and there needs to be a better understanding of what can be done with what exists.. 

 

Creating clean spaces goes well beyond the current pandemic.  Clean indoor rooms can have an impact on the flu plus there are a number of chemicals that outgas that we mostly ignore.  And many of us have had to deal with PM 2.5 pollution from forest fires and combustion.    The question is how do you make this desirable enough that we learn how to make and implement better designs than we have?   How do you spark a revolution in public health that involves architecture design and retrofit on a massive scale?

 

Unfortunately successful public health measures are often seen as expensive overkill.  Perhaps carbon dioxide concentration is the answer.  Over the years studies have shown decreases in cognitive functions and alertness linked to higher  CO₂ concentrations.¹ Generally 1000 parts per million is seen as a boundary, but some studies show decreased mental ability around 800 ppm.  Many offices and schools regularly exceed 1000 when occupied.  Your car is probably several thousand in a half hour  if you aren't bringing in outside air.  How much would a school spend to upgrade the mental ability of its students?  Would a company pay extra for more alert workers who function at higher cognitive levels and get sick less often? And what about homes?  Many homes are worse than offices - maybe working from home should be rethought or at least certified.   

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¹ A fairly recent study on cognitive function associated with CO₂ and VOC exposure 

 

 

getting to clean enough

It's becoming clear that the SARS-CoV-2 virus will be around for a long time.  We're probably much closer to the beginning than the end.   Hotspots will shift and new variants arise so it makes sense to be ready to mitigate risks as much as possible.  Vaccinating the world should be a high priority along with next generation vaccines, better treatments, testing, high quality masks when the risk is high, etc. etc.  

 

Improving local air quality is low hanging fruit.  To first order that means high quality masks in hotspots along with fresh air.   Room air filtration and circulation can be a powerful tool.  As living animals we exhale carbon dioxide.  In pristine location, say a mountain top in Hawaii, you can measure the baseline concentration. Air is about 420 ppm (parts per million) carbon dioxide - a bit over 0.04%.  Enclosed spaces with people have higher concentrations.  You're breathing some of the air from other people.  If people are the only source, you can calculate the percent of the total air in the room that's exhaled:

        CO₂ concentration (ppm)        % of total air that is exhaled 

                    420                                                  0%

                    600                                                0.5%  

                    800                                                1.0%

                    1000                                              1.5%

                    2400                                               5.0%

 

With these numbers it was believed the risk is low for up to an hour if everyone was wearing a simple cloth mask and one person was infected with the alpha variant with carbon dioxide concentrations as high as 800 ppm.  The delta variant changes the threshold.   Now the one hour number is about 600 ppm with everyone wearing a surgical mask.¹  Of course the probability of an infected person being in the room is low if you're in an area where the infection rate is low.  

 

It would be good to know the concentrations where ever you go:   offices, classrooms, stores, theaters, taxis, airplanes etc.²  Consumer grade carbon dioxide meters can be purchased for $100 to $300.  If you're really interested I can make a recommendation, but I've only used a few.  We'll probably see a rapid improvement as these are going to be essential tools.  Japan is requiring them in many public places and school rooms.³  It's important to have an NDIR sensor (basically it's doing spectroscopy with an infrared laser to measure concentration  - there are many other techniques, but this is the cheapest with enough accuracy and repeatability).  These are accurate to about 50 ppm, so ignore the more exact looking reading and just round up to the next multiple of 50  - if it reads 537 just call it 550.    It takes about two minutes to get a stable reading and you'll want one that stores measurements.  The model I like talks to an iPhone app which gives you a nice chart of the day.   For businesses and schools it's a good way to check if the rooms are getting good airflow.   I saw one schoolroom that exceeded 3000 ppm when students were present. It turned out an air return duct was blocked - a thirty minute fix gave the students clean air again.

 

High carbon dioxide concentrations make people drowsy and sap cognitive abilities.  It hasn't been carefully studied, but readings over 1000 ppm can make you drowsy and perhaps a bit feeble minded.  One Army study suggests 800 ppm should be a warning level.  Half-jokingly I told a superintendent that he could justify the cost of measurement though improved test scores.  It turned out that's what sold him.  Maybe it's a way to upgrade the collective intellectual capacity of an office.  Another benefit is a possible reduction in airborne diseases like the flu.  

 

You can't always open windows and doors to get a solid draft, but HVAC systems can often have their fan settings increased and room vents adjusted. High quality filters can capture viruses along with other particulate like some from a fire.  MERV-13 is a sweet spot for price,  the ability to snare virus sized particles and not requiring more powerful fans.  And you can buy or build portable air cleaners.

 

The hot ticket for rolling your own is a very simple design known as the Corsi-Rosenthal cube.  Here's the public domain diagram we used to build 84 of them for about $5,000  (the cost shown in the drawing doesn't involve much shopping around).  We used the cardboard from the shipping boxes the fans came in.  The shroud is very important.  Square corners disturb the airflow and can drop the unit's efficiency by about a third. A normal sized classroom for 30 to 40 students probably needs two units.  Keep them away from walls, doors,  and openable windows.  The filters will probably last the school year if you turn them off when people aren't in the room.  Most of the classrooms are showing readings under 600 ppm with these and the school's HVAC system fans all on high.  The boxes make a big difference.  Commercial air cleaners with good filters probably make more sense in offices and schools if they want to go long term, but 600 cfpm MERV-13 filters are about $500 and in short supply these days.   Like carbon dioxide meters I suspect we'll see some movement on air filter and fan design. 

 

Some learnings:

Duct tape is frustrating!

Schools have mountains of duct tape.

Eighth graders are the perfect people to enlist if you want to build a lot of them.  Eighth grade girls if you want them to be semi-presentable.

_________

¹ These are rule of thumb numbers based on empirical evidence.  But it's complex with many confounding factors. 

² A closed car can be spectacularly high. I sat in my car for fifteen minutes with one other person and recorded 3800 ppm!  You can drop this by opening the windows.  Opening them diagonally makes a lot of sense for creating airflow.  Airliners have good general circulation, but a given row can be bad.  A flight is probably much safer than a half hour Uber ride if the driver has the windows up.

³ People are already taking measurements in gyms, restaurants, etc and putting them online with locations and business names. It's ad hoc and not very standardized, but there are over 100 locations in NYC the last time I checked.  It makes much more sense for a business to do their air handling homework and post numbers in their establishment as well as their website.  Hopefully at some point a respectable aggregator will step in.