Well here we are still sheltering in place but can offer a review of a fantastic book and do some physical analysis of some of the issues that go into setting social distancing recommendations.
First up, while stuck inside is this great book by Jim Baggott called " The Quantum Cookbook -- Mathematical Recipes for the foundations of Quantum Mechanics."
|Great book reviewing the derivations of physics equations (Source: Jim Baggott, "The Quantum Cookbook")
What this book is really good at is bringing together in one location some of the derivations of some of the most famous equations in physics. I can sort of recall seeing some of these derivations in previous courses and textbooks, but to have many of them all in one convenient book is really neat. It is really neat to go back and look at how Einstein derived the equivalence of mass and energy. The screenshot below shows some of the topics. All physicist wannabes should check out this book!
|Some of the physics equations and their derivations (Source: Jim Baggott, "The Quantum Cookbook")
For those of you with special interest in astronomy there are other books that do much the same type of thing by identifying how astronomer, amateur and others, can repeat in their own back yards some of the most fundamental and historical astronomical observations. I am reminded of Romer's famous observation of Jupiter and its moons in 1676 to estimate the speed of light. Pretty neat and this is an observation that you can repeat today. Many of these repeatable observations are illustrated in the books by former OCA secretary, Bob Buchheim. His books, which we first reviewed here in posts way back in March 22, 2015 and January 22, 2016, include "Astronomical Discoveries You Can Make, Too!" and "The Sky is your Laboratory." If you haven't checked these books out and even tried to do some of the observations yourselves, do it now while you have the time! You can also see those review comments by looking at those blog posts or just search for "buchheim" on the main page.
Next up, we have some humorous comments on social distancing recommendations as seen on Facebook and emails. For those of you out walking your dogs, or as we say here at the observatory, "Astronomer Assistants", you can use this sign to remind you of the proper distance. Thanks for posting that for us, Cindy!
|Dog Walkers line up their weiners (Source: Facebook post by Cindy)
Next we got an email from the local ham radio club who also have set their recommendation for when you are out and about and not just talking on the radio. Thanks for that Mike!
|Ham Radio Operators do it with precision (Source: SOARA Mike @ AG6VQ)
Ok, let's now return to see what physics principles might be involved in helping epidemiologists set social distancing recommendations. Recall from a previous blog post how virus shedding from infected persons gets out of that person into our environment and for respiratory illnesses it comes out in sneezing, coughing and speaking. Social distancing recommendations are set by looking at each of these situations. We know that the virus can be shed in these ways and so the central idea is how long will the viral particles be suspended in the air before they drop out or come into contact with a person close by.
|Identifying and controlling risk of respiratory secretions (Source: Vincent Racaniello, Columbia U.)
If we want to review how long the virus particles will remain suspended in the air we first of all need to get an idea of how big of a particle we are talking about. This SEM micrograph shows size of the SARS virus, which is also a member of the coronavirus family. So the diameter is about 100 nanometers (nm).
|Size of SARS virus particle (Source: Wikipedia)
Before we get to how long the particles of this size can stay suspended in the air, let's compare the size of the particle to the filter efficiency of the N95 mask. I remember from one of my previous, years ago, work projects of writing and reviewing ISO safety and manufacturing standards for use in my commercial facilities that all Personal Protective Equipment (PPE) use should be covered in a procedure that details how, when, and under what conditions the PPE should and must be used. Writing standards for medical use and applications is even more severe and controlled. Rather than go to some of those standards, an internet search shows the type N95 mask particle filtration efficiency. Hey, it looks like the filter is almost 100% (maybe 95%) for particles down to 0.01 um, which is 10 nm. Yep, the mask should be very effective in protecting the wearer! It is interesting though that the filter efficiency has a dip in efficiency for particles between 0.1 and 1 microns?
|Filter efficiency for N95 mask (Source: blogs.cdc.gov)
Ok, now let's go back and try to estimate how long viral particles that are expelled by an infected person will remain in and travel through the surrounding air. This is the time to go back to our old friend, Stoke's Law, which describes how particles and aerosols can remain suspended in air. As you can see in this Wikipedia page screenshot, Stoke's Law can be used to evaluate particle size and drop out rates for particles suspended in air.
|Stoke's Law (Source: Wikipedia)
Well I looked up the values for the constants involved and assumed the particle size at 100 nm and the density of the particles to be about the same as water. My back of the envelope calculation shows the terminal velocity to be 2 times 10 to the minus 10, meters per second. Hmm, that is so low that the particle would remain suspended almost permanently. Hmm, some other factors must be applicable because other internet reviews indicate the virus only stays in the air for a number of hours. One possible addition to the calculation might be that the viruses are expelled along with small water particles, like in a fog for example. So, we see that other factors probably need to be included in our back of the envelope need to be included.
So, for now, let's go on and look at the airflow dynamics of people sneezing and just breathing affect the air conditions around us. This paper study shows the distance and velocity associated with just nasal breathing. So for nasal breathing we see maximum distances of about 0.6 meters with exit velocities of say up to 1.5 meters per second.
|Propagation Distance and Velocity for Nasal Breathing (Source: J. Tang, et al, "Airflow Dynamics of Human Jets..."
But we also breath through our mouths and speak with our mouths and the airflow dynamics in those cases is found to be a little more forceful.
|Propagation Distance and Velocity for Mouth Breathing (Source: J. Tang, et al, "Airflow Dynamics of Human Jets..."
Now, I have no idea about how reliable these studies are, but they do seem to be authentic. What I see in this is that this could be the basis for not recommending restaurant eating with a bunch of people at your table. If anyone has the virus in their breath and you are sitting in that area for an hour or so, then it just seems possible that the virus particles could end up in your breath intake zone.
But, how many virus particles are we talking about in cases like this? Another paper from 2014 gives us some idea about the number of particles that could be present. So read through the screenshot from that paper that says that during tidal breathing there could be 10,000 particles per liter of tidal volume.
|Viruses in Exhaled Breath (Source: N. Nikitin, et al, "Influenza Virus Aerosols in the Air and Their Infectiousness", 2014)
That same paper by Nikitin, et al, provides one other key needed parameter and that is the amount of viral particles that need to be inhaled to cause an infection. So, if I am interpreting the paper correctly it seems that infectious dose for influenza virus is between 2000 and 3000 particles per liter.
Ok, enough on trying to use Stoke's Law to understand how its application and other principles and data from other experimenters too can be used to set social distancing guidelines. Other news shows that work on many space programs is being delayed, like the JWST, for example, bu other programs in China and the SpaceX Starship SN3 continues making progress. The fuel tank assembly has been moved out of the high bay and moved across the Texas Highway 4 to the launch site. Here you can see the assembly mounted atop the launch structure. The next tests that are thought to take place shortly are the cryo pressure testing verification of the new thrust puck design. If those pass, then a short static firing of the engines could take place. It is not known when the rocket nosecone will be transported across the street and then lifted atop the rocket stack, but progress is moving so quickly there. I guess we can say that if you are working in a crane on a rocket you can be said to maintain good social distancing. Sadly, some of the spring breakers that went to south Texas, and which started to really get together after we were on out way back from South Padre Island, have contracted the infection. But for now, Go Elon and thanks for the update BocaChicaGal!
|Fuel tanks for Starlink SN3 installed on SpaceX launch pad (Source: @BocaChicaGal)
Finally, we shouldn't forget that we can still enjoy some of the simpler beauty in the world just by walking outside and watching the sunset. Here, I was out just a few minutes late, and didn't grab the DSLR, bu used to smartphone to photograph the sunset. So, remember to continue to enjoy he simple little pleasures that are right there in your immediate neighborhood!
|Finish off the day with beautiful sunset (Source: Palmia Observatory)
Until next time, here from our burrow, stay sane, stay safe,