For several months I’ve been in the process of de-cluttering and generally getting rid of stuff. But that has stalled, for reasons that are not entirely clear. And it looks like de-cluttering is going to get somewhat harder from this point forward. Continue reading Post #1667: Döstädning and the problem of small stuff.
For some people, cold winter weather brings thoughts of hot chocolate by the fireplace, cozy comforters, or maybe skiing.
By contrast, I find myself thinking about insulation and R-values.
So, in the spirit of the holidays, here are two R-value calculations that I’ve been meaning to make.
Whenever the weather turns cold, I start getting lots of hits on Post #1412, on making an electrically-heated cover for outdoor faucets. Of late, I’ve been getting more than a hundred hits a day, thanks to this recent cold snap and an offhand reference in an on-line forum for Texas Aggies fans.
One of the interesting findings was how little electricity it takes to keep the inside of the faucet protector warm. For example, a mere 4 watt night-light bulb raised the interior temperature by 28 degrees. That more than meets my needs in any cold snap likely to occur in my area.
But is it really plausible that 4 watts could do that? Or was I (e.g.) mistaking heat leaking out of house for the impact of that small electric light?
Obviously, I could check that empirically by hanging up a standard faucet cover with no added heat, and seeing what the interior temperature was. But, at present, it’s about 15F outside, so I’m ruling that out for now.
Instead, this is a classic cases of “Sure, it works in practice. But does it work in theory?” I’m going to do a theoretical calculation of the temperature rise I should expect, using the R-value (insulating value) of Styrofoam, the dimensions of that faucet cover, and the energy output of a 4-watt bulb.
I’m going to model this as a Styrofoam box with dimensions 4.5″ x 4.5″ x 6″. That effectively covers the open face of the faucet cover with Styrofoam, instead of (in my case) brick. So I’m expecting to see more than 28F temperature increase out of this calculation. The box walls appear to be about 5/8″ thick.
Two final bits of data. The R-value of Styrofoam is listed by most sources as around 5.0 per inch. And 4 watts is equivalent to about 13.5 BTUs per hour (BTUH). (I rounded that down a bit to account for the small amount of energy that escapes from that bulb in the form of light, rather than heat.)
Here’s the calculation, first assuming foam on all sides, and then accounting for one side being brick, with a total R-value (for two inches of brick) of 0.88. (I don’t show the full detail of the brick calculation, only the bottom-line average insulating value of the combined foam/brick container.)
The upshot is that this does, in fact, work in theory. The theoretical temperature rise I get from an all-foam box is 41F, much more than I observed. The theoretical rise I get if I replace one side of the box with brick is 28F, exactly what I observed.
It’s purely a matter of chance that this calculation hits the observed value exactly. The fact that it’s close shows that what worked in practice, does, in fact, work in theory.
I’ve been watching Engels Coach Shop on YouTube for some time now. The proprietor is a self-employed wheelwright whose long-standing business builds and fixes all manner of horse-drawn transportation.
This has absolutely no practical relevance to my life, but is purely a pleasure to watch. Not only for the actual work performed, but also because the guy knows how to film, edit, and narrate a video.
Of late, he installed a 3000-gallon above-ground tank for watering his cattle. To which you might reasonably say, so what? Until you realize that he’s in Joliet, Montana. To put it mildly, the combination of an above-ground water tank and a Montana winter constitutes a freeze risk.
On the one hand, it’s heavily insulated (reported R50 on the sides, R120 on the top), and the water itself stores considerable heat energy.
On the other hand, it’s in the middle of Montana.
Source: Western Regional Climate Center
Apparently his YouTube following is deeply divided on whether or not they think this will work. Mr. Engels seemed kind of amused at the folks who thought he was going to end up with a giant ice cube. For my own part, I’m guessing it will work just fine, based solely on the guy who built it. But I don’t quite grasp why he seems amused by the opposite opinion.
So rather than just guess, let me do a couple of crude calculations. From the standpoint of the arithmetic, it’s really no different from my faucet cover. Just bigger.
First, I wanted to check out the water tower in Joliet, MT. Just to be sure that a big enough tank, with enough throughput, would not freeze in that climate. But when I tried a trick that always works for finding water towers on the East Coast — use Google Earth, set the perspective flat, and look for a water tower to stick up above the houses, because they are all 120 feet tall, more-or-less — that didn’t work. This, despite the fact that there is a municipal water system with a 160,000 gallon tank.
That’s because the Joliet water tower is mostly underground. Like so. I have no idea whether that was driven by economics, or by threat of freezing.
Source: Laurel Outlook
So, is a well-insulated tank, above ground, a problem or not?
The first hint that it’s not a problem is that the total heat loss of this tank is maybe 16 times the heat loss of my faucet cover. This tank is enormously larger. But it’s also enormously better insulated. The combination of having about 300 times the surface area, and maybe 20 times the average insulation, is that, by calculation (below, highlighted in yellow), this tank only loses a bit over five BTUs per hour per degree F. That’s just 16 times the heat loss in my Styrofoam faucet cover.
Here, I’ve assumed a tank shaped like a cube, with an average R-value of 60 on all surfaces. Should be close enough for a rough cut like this:
Well, given that a four-watt bulb would heat my faucet cover, it should be no surprise that even a modest heat input would (eventually) result in a large temperature differential between the inside and outside of that tank. Where four watts was enough to create a 41F difference in my all-foam faucet cover, here, a typical stock tank heater (150 W) would (eventually) generate a massive 94F difference between interior and exterior of the tank.
That’s a big enough difference that (arguably) this simple linear R-value calculation does not exactly hold. I don’t think that much matters. If for no other reason that, given the tiny heat input (about the same as you would use to heat a cup of water to boiling for tea), it would take years to reach equilibrium.
(Well, might as well calculate that roughly. This is about 25,000 pound of water. To raise that by 94F, with zero losses, using a 150W heater, would take just over half a year. With losses, yeah, a couple of years. If then.)
I’m going to go out on a limb and say that, if the tank is well-mixed, running a 150W stock tank heater inside it would, in fact, guarantee that it would not freeze under almost any conceivable circumstances in that climate.
But there’s no electricity at that site. Instead, the tank has to “coast” all winter, using just the energy embodied in the water in the tank itself.
So, how much energy is there in that water? How much heat would you have to remove to take water, at a typical late-summer temperature for that area, and bring it down to 32F?
By definition, a BTU is the amount of energy required to raise one pound of water by 1 degree F. So if (say) the water starts out around 62F (late summer/early fall), it would have to lose over three-quarters of a million BTUs in order to reach 32F. As shown below, bottom line.
Now I’m going to do a little hypothetical calculation. Let me plop that tank down in January, in Joliet, MT, and see how much it cools off over the month. That is, let me start with that tank at 62F, and let it sit for 31 days with an average external temperature of 24F — the actual average temperature for that month and location. This should be a worst-case scenario for temperature loss, because it’s the largest temperature differential you could hope to see. Water temperature from late summer, against dead-of-winter air temperatures.
Here’s the simulation. I just calculate the daily heat loss, and then drop the temperature each day, using that heat loss (in BTUSs) as a fraction of the total heat embodied in the 62F vs 32F water. (That is, I pro-rate the BTUs of daily heat loss over the total 750K BTUs that would take the water from 62F to 32F).
OK, I finally get the joke. Worst case, this tank ought to lose just over 5F per month, in the coldest month of the year. And note that the cooler the tank gets, the slower the additional temperature loss gets. For all practical purposes, the likelihood that the tank will freeze is zero.
(Note that the calculation is linear in temperature, so that it doesn’t really matter if the temperature does up and down in January. The average heat loss is going to match the average temperature. There are more refined physics calculations that will add some slight non-linearity to this, but not enough to matter).
Unsurprisingly, this tank isn’t just built for that climate. It’s over-built. Some of my assumptions might be a bit off. The tank is a cylinder, not a cube. Likely I could have calculated the average insulation value better. I don’t really know the insulation value for the bottom of the tank. And so on. But even with that, this seems to have been built with a huge margin of safety.
I should have expected no less.
Today we get our final bit of hard data for 2022, on the reported number of new COVID-19 cases. If past years are any guide, for the next few weeks, the holidays will scramble the data so badly that we’ll have no clear idea about the trends, if any.
Unsurprisingly, there’s no trend at the moment. Pretty much the same as it’s been for the past few months. Continue reading Post #1665: COVID-19 cases, final post of the year: No change
With all the coverage of the big winter storm sweeping the country, you’d think that the coming cold temperatures were unprecedented. And, for sure, it’s a big storm. And temperatures are going to drop a lot. Might even set some records, somewhere.
But we tend to lose sight of the modern context. Winter nights are much warmer now, on average, than they were just a few decades ago. In the Washington DC area, what we perceive as an outrageously cold night in the 2020s was merely a cold night in 1980s.
In fact, the main temperature impact of global warming is exactly that — warmer nights. And while you can’t infer global warming by looking at temperatures at a single point on the planet, you can remind residents of the DC area that winter low temperatures used to be much lower, on average, than they are today.
Here’s the official temperature data from Dulles International Airport, via NOAA. I’ve simply taken the lowest recorded temperature for each calendar year, and plotted that. (The 9 degrees for 2022 (so far) occurred back in January 2022).
Source: Analysis of weather data via NOAA.
Every year in the 1960s, 1970s, and 1980s had a lower minimum temperature than we are expecting from this super-storm. Almost every year in the 1990s, 2000s, and 2010s, ditto.
Similarly, we can check how common a low of 8F or lower was, back in the day. And the answer is, relatively common. For Dulles Airport, in the 1960s to 1980s, an average year had between seven and eight nights when the temperatures dipped to 8F or colder.
Source: Analysis of weather data via NOAA.
What was once a commonplace wintertime occurrence in this area — nighttime low of 8 or lower — is now a rare event.
When I was a kid, if it only got down to 8F around here, and only did that for a single night? That would have been reckoned as an exceptionally mild winter. But now, that single 8F night is the remarked-upon cold weather event of the year. Such is the slow and subtle impact of global warming.
The sheer area of this storm is unusual. It will be packing some strong winds.
But around here, the “Siberian” temperatures it brings, with all the associated news hype, would not have been at all unusual half-a-century ago. They only stand out in the context of the much warmer average nighttime temperatures that we currently experience. The chill from this storm hardly registers as a blip in the overall trend of rising temperatures.
This is the followup to Post #1661. The problem is that I frequently have to crane my neck to see traffic lights, in my wife’s Prius Prime, owing to the steeply sloped windshield.
The inability to see stop lights is hardly a new problem in the American auto industry. In that prior post, I reviewed the century-long history of inventions that would let you see above the top edge of a car windshield.
I noted that in the modern era, you could solve this problem with a $30 dashcam. But, really, where’s the joy in that?
Instead, I turned my back on that obvious solution and decided to come up with an optical device to let me see above the top edge of the windshield.
The design criteria for this stoplight-viewing device are:
My solution is a negative Fresnel lens, mounted to the sun visor so that you can flip it down when you need it, and flip it up out of the way when you don’t.
In this case, a “negative Fresnel lens” is a flat plastic lens sold as an aid to seeing around blind spots on vehicles. (Negative refers to negative focal length, meaning this isn’t a magnifying glass, it’s a “shrinking” glass.) Typically, these are used by large vehicles as an aid to backing up. The lens allows the driver to see objects that can’t be seen directly through the back window of the vehicle.
Below, note that the top of the cloud is obscured by the roof of the vehicle. Yet, you can see the top of the cloud in the shrunken image in the Fresnel lens. This is precisely what I want to happen, for stop lights obscured by the roof of my car. I want to use a negative Fresnel lens to pull them into view.
Source: The lens I bought for this project, for about $10, on Amazon.
Some variation of this technology is used on the LightInSight. This is an aid to viewing stoplights consisting of a long, narrow Fresnel lens designed to be stuck to the of the inside of the windshield. The product illustration below is completely unclear, but the LightInSight does exactly what the lens shown above does: It pulls images from above the top edge of the windshield down into the driver’s view.
Source: Amazon.
From my standpoint, the LightInSight has a couple of drawbacks. First, it’s permanently in the field of view. I don’t want that. I want it out of the way when I don’t need it. Second, Fresnel lenses fail when viewed at sufficiently shallow angles. The higher the power of the lens, the sooner that happens. I feared that the LightInSight, however well-designed, was not going to be usable on the extremely sloped Prius windshield. Or, if it did, it would have to be a relatively low-power lens, and provide only a modest boost to visibility above the roof of the car.
Instead, I wanted a relatively high-powered negative Fresnel lens, mounted perpendicular to my line of sight. But mounted so that I could put it away when it wasn’t needed.
Finally, I rejected the use of a cheap positive (magnifying) Fresnel lens. That would have made fabrication a lot easier and cheaper, but it would have produced an image that was upside-down and side-to-side reversed. To me, typically facing a string of lights at a multi-lane intersection, that just seemed like a recipe for an eventual disaster.
The rest is just tinkering.
Other than the Fresnel lens, I tossed this together from scraps lying around the garage. Size, shape, and method of attachment were therefore more-or-less determined at random.
Here are the materials. The flexible Fresnel lens needs some sort of clear, hard plastic sheet to be affixed to. I decided to tape the lens to the plastic sheet with clear packing tape. And I decided to have this rest above the sun visor, held on with a couple of pieces of elastic, run through holes drilled in the hard plastic.
The only thing that is even remotely tricky is that the Fresnel lens is not uniform. By design, the bottom and side edges do a much better job of pulling images into the field of view, compared to the top edge. And after you cut it, you want to be looking through that external edge to find your stop light, not through the (much weaker) center of the lens. The upshot is that you want to cut your piece out of the bottom of the Fresnel lens, and you want to mount that so that the edge of the original lens ends up where the holes are drilled in the plastic.
Below I show the first test. It sits above the sun visor, held in place with two piece of elastic. To deploy it, pull it forward and let it hang off the front of the sun visor. When you are done, slide it back into position above the sun visor.
In the three pictures below, I’ve circled the one-way arrow to keep you oriented.
The first picture is the intersection, as seen when sitting up straight in the driver’s seat. The light is obscured by the roof.
Second picture show the traffic light from the “slouch and crane” position. Normally, I’d slouch in the seat and crane my neck to watch the light.
But with the Fresnel lens, I can see the light without slouching. This may not look like much in the photo, but it was perfectly adequate for monitoring the light to see when it turned green. No slouching required.
This will win no beauty awards, but it works, and it’s unobtrusive. When not in use, all you can see of it is the thin pieces of elastic circling the sun visor.
This could definitely use some tweaking if there were any need for an improved version. First, it’s far larger than it needs to be. Second, I’d probably glue the lens down, rather than tape it. Third, I’d probably cut a section from the less powerful portion of the lens (the top), as the lens is far more powerful than it needs to be to provide a clear image of the light.
By far the biggest drawback — totally unanticipated — is that you have to focus your eyes on the Fresnel lens, not on the road. Beyond being an annoyance, that means you aren’t focusing on the roadway in front of and around you. When the light turns green, you then have just a split second to refocus on the roadway and check conditions. This strikes me as a significant safety drawback to this device. Enough that maybe I want to rethink the whole thing.
But the bottom line is that this does what it’s supposed to do. It provides a usable image of a stoplight that would otherwise be obscured by the roof of the car. Thus, I carry forward the century-old tradition of ad-hoc “signal viewing devices” that let you avoid craning your neck to see traffic lights.
I’m checking the new case a couple of times a week, consistent with most states now reporting data about once a week.
There’s nothing new to report. Depending on how I choose to gap-fill the spotty state data, the new case rates are either level or falling slightly.
Per the CDC, we still have about 350 COVID-19 deaths a day. It’s been around that level for months now.
And we’re back over 4000 new COVID-19 hospitalizations a day. That figure had gotten down close to 3000 a day, as of a month or so ago. But respiratory (and cardiovascular) hospitalizations always increase with colder weather. So that increase is likely as much a result of winter as of any new spread of COVID.
In short, we’re stuck in neutral. No winter wave. But no fading away, either.
Briefly:
Continue reading Post #1661: When you can’t see the traffic light ahead of you. Part 1, the setup.
This is a brief followup to Post #1658., where I checked the UV protection provided by some eyeglasses, sunglasses, and car window glass.
Here, I’m validating that using an actual UV meter, marketed for safe tanning practices.
Nothing new to report. The 2022 winter wave of COVID-19 remains a dud. We had a little blip in cases (here and in Canada) following U.S. Thanksgiving. But that’s it. No hotspots, no strong trends. Just an annoyingly high background level of daily new cases.
Recall the goal of this: I want to see how well my eyeglasses, sunglasses, and car windows block ultraviolet (UV) light. See my recent Post #1654 on this topic if you wonder why anyone would care about that. Continue reading Post #1658: Testing eyeglasses and sunglasses for UV protection. Part 2, the initial tests
