Chapbook

[sasha]

 

Dec 24, 2024 - sometimes math & physics play nice

A long time ago I started chipping away at a barstool problem on old colleague once posed over our Nth beer, where N is an integer >1:

How far does a car travel while braking to a stop?

It obviously depends on how fast you're traveling when you first hit the brakes, and it should be nearly as obvious that the dissipation rate of the car's kinetic energy plays a definitive role as well. The devil lurking in the details is that we know nothing about the temporal profile of the energy curve, other than it's a decreasing function ending at zero from a known starting point. It's not an uncommon dilemma in practical physics, with a common solution: take a guess. (I call it "Physicists' Prerogative".) Start simple - turn it into a toy problem that's easy to solve, then tinker it to make it more realistic. (Back in my lab rat days, I used to say that one had to do every experiment at least twice - once to learn how to do it, once more to get useful data.)

So my first shot assumed that the brakes shed the kinetic energy at a constant rate - the simplest assumption possible. A little first-year calculus led to an elegant (and rather surprising) solution: if this were true (big IF here), then the car travels fully 2/3 the distance it would have without braking at all. It also shows that this distance increases as the cube of the velocity - that doubling your speed octuples the stopping distance. (Direct and inverse square laws are common in physics owing to their geometric interpretations, but cubes and rational powers are considered exotic.)

OK, very nice - but not everything in nature follows a straight line. I've heard the term "brake fade" - the loss of braking efficiency as the disks heat up. Suppose that happens at a constant rate - how does it affect the energy dissipation? Well, what was a decreasing linear ramp becomes a parabolic curve, like a ski slope that gets shallower & shallower nearer the bottom. And with that curvature come a slew of conditions that need to be imposed, boxing in the range of conditions in which such a scenario can even exist.

And the distance calculation...

The final step of the distance calculation is a calculus operation called integration - essentially adding up an infinite number of infinetessimally tiny bits into a finite sum. Knowing how the energy changes macroscopically, it's easy enough to set up the infinite summation - but evaluating it can be quite another matter. When the energy changed at a constant rate, the integral was easily calculated. But once the decreasing energy began to curve, I couldn't even work out the formula for the integral. I had to look it up. And it occupied four lines of text in the handbook.

Still, I dutifully keyed these into a spreadsheet I was building to provide a side-by-side comparison of fading vs non-fading brakes - and I could not get them to work. Buried somewhere in this arcana was a division by zero, or the square root of a negative number, or an infinity where there shouldn't be one - and I simply could not find it. At one point I was beginning to wonder if the book had a typo leading me astray - but an inverse operation called differentiation I applied to the published result brought me back to the starting point, just as it should have. (It essentially "unbakes the pie" - finished apple pie into the oven; apples, sugar, a few cups of flour, a stick of butter out.)

I lost a few months fostering my ex's dog, and when finally freed up to return to it, ran into the same roadblock. Though looking at it afresh, I was running out of ideas - and steam.

I ran a numerical simulation of the fading brakes that produced results consistent with expectations - by tweaking the degree of fade, I could get results approaching those of the original, overly simplistic model. So the physics were sound - the problem lay in the math. And unbaking the pie seemed to say that the math was valid. So it had to be in the coding.

Which I finally resolved yesterday! Oh, there's round-off error, and if I drive the car too fast Excel rounds a tiny quantity to zero and the calculation blows up - but the smaller I make the fade parameter, the closer the results get to the case where the brakes never fade. There's a lot of cleanup yet to be done, but the logs are flowing down the river once again.

If I were still a drinkin' man, I'd've tied one on good last night in celebration!

[saw]

Now you need to add to the equation how dogsitting can save the day

whenever I have gotten stuck with a problem the solution has always been walk away from it ( in this case walk the dog ) and then come back with fresh eyes where the problem has been secretly marinading in a remote corner of your brain without necessarily getting any of your attention.

congratulations roy...and merry christmas....Cheers !

take your foot off the brake and zoom into 2025 with alacrity !

Peace and Harmony and Happy Problem Solving !

[sasha]

Thank you , Steve, hope your day is just what you'd want it to be!

Just a BTW - the title of this post comes from a suggestion you made some time ago - it got me thinking about creating a thread of random minutiae, and I was so excited by this breakthrough, I figured I might as well start there....

[sasha]

 
Christmas Day 2024


     Let's walk...
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     Guiding Light
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     Scott Brook
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     Bridge Over Quiet Waters
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     Quiet Waters
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     Say "hi" to Long Island Sound for me
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     Downstream view
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     Predator vs Prey
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     Habitation
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     Yeah, man... me too...
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     The Way Home
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[sasha]

The lake has officially iced over! It was an expanse of white when I drove past it this morning, except at the boat landing and the girls' camp, where they keep an impeller running under the dock to keep it from freezing. I guess winter can start now.

And here it comes: freezing rain in the forecast again - we don't get snow any more. Just freezing rain. Sleet. Power outages lasting days. I've already booked a room at the Best Western for the weekend, before Eversource grabs them all for their restoration crews. The forecast has since been downgraded to possible freezing rain during the day Saturday, chased by probable (unfreezing) rain overnight. I've got until tomorrow afternoon to cancel my reservation - let's see where the NWS moves the goalposts in the meantime.

[saw]

Great start on the Chapbook as well as wonderful photos

looks like the weather is getting treacherous .....be safe....falling at our age is a bad idea.....

matter of fact today is my birthday...76 big ones !.....I'm working on a little project ( impossibly slowly )

adding toilet in my pantry on the first floor....I let a master plumber do the tricky plumbing work...the rough in

now it's my turn to do the carpentry....wish me luck...I can't get my body to bend the way I want it to....

[sasha]

76 laps, well done! If I make it to May, I'll complete my 75th.

Hats off to for tackling that pantry conversion project. My carpentry is rudimentary at best. I managed to install stool caps in all of the windows when we moved here, replaced the front steps, and have built a bit of rustic furniture of my own design, but woodworking is NOT my strong suit.

I decided not to bail out last night. It was the right call - the storm tracked largely to our south, & the lights stayed on. What little ice we got has already melted. The next few days are supposed to mild & foggy - great days for photography! I think a road trip could be in order tomorrow...

Speaking of photos, thanks for going along on my Xmas day jaunt. Something about late afternoon light in the woods this time of year... austere yet ethereal... I've never been able to capture it...

[saw]

some things remain elusive
Winter Light is like trying to capture a fairy
we see her flitting around our head
like a sparkling hummingbird
but our nets are far too porous
to capture the prize
nonetheless
your photos say a great deal
thank you

[sasha]

 
Thanks. I took one New Yr Eve that captures just a whiff of that elusive something, just a suggestion of it:
 

 

... but it doesn't quite convey that cathedral-like essence of pines illuminated from the side rather than from above...

Oh well. Maybe next time.

==================================================================================================

December 31, 2024

I stand at the edge of the road gazing at the waters rushing past in their eagerness to get beyond the rocks, where they can then slow to a more relaxed pace in the marshland just beyond. I hear its music, its joyful shouts of excitement; I smell its cologne, and I watch its dance among the bouulders and fallen trees in its path. I observe the convergence of its flowlines as it squeezes through a narrowing along the shore, I marvel at the waves reflecting off submerged obstacles, and the futility of their attempted march back upstream, the speed of the torrent just enough to keep them in place. Hydraulic jumps, they're called - standing waves whose natural propagation velocity in one direction is precisely balanced by the bulk flowrate in the opposite.

I've attended a couple of seminars in fluid dynamics, the physics of flowing liquids. At the center of the subject lurk the notorious Navier-Stokes equations: a dozen or so 2nd-order partial differential equations - with crossterms - that need to be solved simultaneously. It's never been done. Trust me, you do not want to fuck with these bad boys. Best you can do is whittle them down by ignoring the bits you think (hope) you don't need, and solving what's left for a rough sketch at best of the process - not so much a portrait as a stick figure, a reasonable caricature of the fluid's overall behavior. "Only interested in steady-state? Then just ignore all the time-dependent terms!" "No rotation to speak of? Then throw away anything involving theta!" With a simple wave of the hand, four-dimensional geometry becomes three or less.

If it's enough to help you design a rocket engine that won't suffocate on its own exhaust, or build a spillway that won't collapse the minute you open a gate, then it's enough. Maybe not as intellectually satisfying as an exquisitely detailed score of the ballet, but that's just how it seems to go - all of physics seems to be built on assumptions that can only approximate our imperfect perceptions of this wondrous cosmos we just happened to awaken in one morning.

I was raised Catholic, and for a while I went along with it. But it didn't take too many years for me to realize that "because it's God's will" really meant "because we just don't feel like figuring it out"; and my discovery of mathematics when I was 13 or 14 started a spirituality construction project that is still going strong, and is unlikely to end before the biological machine I inhabit breaks down for good. Turning water into wine is cool and all, but nowhere near as cool as the intricate flow of water along an ordinary country stream.

[saw]

a fine chapbook offering roy
sometimes we can clearly see the importance of simplicity

Catholism scared the shit out of me
I remember asking sister Elinore,
the huge nun that actually hit me with things
and made me sit in the corner after I asked my question
and stare at the wall, which I found more enlightening
"Well in our Catechism it talks about the importance
of the Love of God, but it also stresses we must learn
The Fear of God, and well I was just wondering how
can a boy love someone he is afraid of ? "
I paid the price for that dumb question and well
everything after that fell apart for me, this was third grade
and I don't remember if I knew the word bullshit
but that's was I was thinking

[sasha]

I never had much to do with the nuns - my dad was Catholic only because my mom was, and did the bare minimum to keep peace in the household. So we kids all attended public schools. We did have one parish priest who was a serious alcoholic, but to my knowledge he never had any inappropriate contact with anyone - maybe that's why he drank. For me, math & science just supplied the epiphany that religion never quite managed to. (Dad was an engineer & indoctrinated me early...) I treasure those "aha!" moments...

[sasha]

January 2, 2025 - a wasted gallon of gas

What happened to the specialty hobby shops? Have we really settled for the bland uniformity of WalMart and its ilk who sell a little of everything but not a whole lot of anything?

I need a new camera bag. The clasp on my old Tamrac has broken - I can still latch the bag shut, but can't reopen it without tools and more finesse than I can muster barehanded on a cold day out on a trail somewhere. At 15 years old it doesn't owe me anything, so I figured I'd hie over to Peterborough Camera where I bought the thing, and scope out a new one. Then I could swing by Market Basket for my weekly grocery run & maybe put $20 of gas in the car. And it was a nice day. Thus was a plan born.

But Peterborough Camera is now Copies & Photos R-Us, or some such. There are still a few shelves devoted to medium-grade camera lenses, but the only camera body on display was a fist-sized device with a single fixed lens and an ON/OFF switch - a camera for people uninterested in photography. Two camera bags big enough to double as carry-on luggage... another made of cardboard clad in a veneer of cheap fabric. As their new moniker suggests, they are now primarily a copy center dabbling in photo finishing. Camera gear is so, you know, last century.

When I returned home, I did what I should have done before I left: google "Tamrac". Plenty of offerings from Amazon, et al, but I couldn't tell from the glamor shots if any met my particular requirements. I need to see, to handle, to try the merchandise before committing to it. You know, like our brutish ancestors used to. I knew of only one other similar brick & mortar establishment less than an hour away, Monadnock Imaging in Keene. But they've apparently gone out of business. Like Perfecta Camera before them.

So I still need a new camera bag.

Perfecta Camera... Melody Shop, Turn It Up (music)... Audio Lab, Interface (high end audio)... all gone the way of Lafayette Electronics & Radio Shack - not only gone, but with nothing equivalent to replace them. Sure, there are online outlets (like ShowMeCables.com), but without being able to heft a potential purchase in your hand, it's a throwback to shopping blind, like from the Sears catalogs of yore. Place your order & hope it's what you want. Convenience at the cost of Certainty. Now it's WalMart et al, one size fits all - sort of. Not well, but well enough to suit those who've never known anything else. It's the new normal. Mediocre adequacy vs Just Right.

Ahh, shuttup, Boomer. What do you know?

[saw]

aah you had me pining for Coopers Camera Mart in Hamilton
I spent a myriad of hours fondling paraphernalia
waitin to talk to the developer about how I wanted my film processed
the cropping, the finishes, the enlargements
all part of a nice day, and the excitement of picking up the finished products

you are so right
it's a one size fits all kind of world ulitmately for the custom goodies we once enjoyed
just pick one of these and be satisfied
they're cheaper to make, and well just.... Cheaper
that's why a love to buy used tools at the flea market
Now that's the steel that they built the Brooklyn Bridge with

and not just tools
hardware is now ..well....softer
they are good at disguising crappy alloys to look substantial
be careful hanging the porch swing on the back porch with a WalMart eyebolt
you may end up on your keister
out in the garden, and crawling back on all fours into the house for some horse liniment.

[sasha]

It's all about profit. Much cheaper to vomit out a zillion of one item that can be coerced into multiple functions than to shut the lines down for changeover after a limited run of some specialty item.

And there's something ADHD about the notion that Newer is always Better. It's a persistent false equivalence. I came of age computing with a slide rule, and writing up lab reports on a Smith-Corona portable typewriter - and no way would I willingly go back to either. But there's just something about the relentless evangelism of Convenience that has the stink of marketing about it. Once you've saturated the market with some shiny object, it's time to introduce another one. I was also heavily into open-reel recording back in the day, and only reluctantly transitioned into cassette - not for their "convenience", but because they'd managed to elbow RR into obscure specialty niches. (I've since gone digital, and LOVE it - there was no Undo when editing mag tape!)

There's a great sci-fi story by Arthur C Clarke on the theme called "Superiority", and gets it just right. You might enjoy this audio rendition of it: https://www.youtube.com/watch?v=iTLPref3ke0&t=4s

[saw]

great story...thanx for the link

another thing that strikes me is our devotion to our "stuff".....

the great Gerorge Carlin did a nice bit on "stuff"


https://video.search.yahoo.com/search/v ... tion=click


the fastest growing segment of the commerciaal real estate industry over the past 40 years is offsite storage

there are currently upward of 50,000 storage facilities in the US