Sunday, December 22, 2024

You should hear it in the original Greek!

Singing “Angels We Have Heard On High” in church this morning reminded me of something I thought of some years back when I was first learning Greek: namely, that you can replace the Latin refrain Gloria in excelsis Deo in the carol with the original Greek, Δόξα ἐν ὑψίστοις θεῷ (Doxa en hupsistois theo). It's not quite a perfect fit since δόξα has two syllables to gloria's three, but it's generally less awkward to stretch a syllable slightly than to squash another one in. 

I've mentioned this curiosity to a few people over the years, but today it occurred to me that with LilyPond I could engrave some sheet music to demonstrate it. I brushed off my LilyPond skills (which I found surprisingly fresh for not having been used in a few years) and spent a few hours today making this lovely rendition:

Thankfully, I found a version of “Christ, the Lord, is Risen Today” I'd done a few years ago laying around which gave me a very useful hymn template, including useful features like multiple verses and a refrain; otherwise having to figure out how to do that would've taken me a lot more than a few hours. There are a few small cosmetic tweaks I could still do (the lyrics attach to the soprano voice so there are few choices which simplify the lyrics handling at the expense of nice-looking notes), but it should be performable. I hope. Let me know if you do.

Anyway, Merry Christmas! I know it's been pretty quiet around here, but there are positive developments which I hope to share in the not-too-distant future. A hui hou!

Edit: Actually, I forgot to mention the most interesting thing I learned while doing this, which is that the the way I grew up singing Angels We Have Heard On High is different from how the music reads. I'm short on time at the moment and it really needs some music to show visually rather than trying to explain it in words, so I'll return to this in the future when I have time.

Thursday, November 28, 2024

Sizing koa saplings

Yesterday I went back up to the State Tree Nursery in Waimea to volunteer again (after my first time there three weeks earlier). I had thought we'd be doing the same thing, but discovered we were doing something a little different this time. Instead of transplanting seedlings from their germination beds into individual growing containers, we had trays of already-transplanted saplings several months old, and were dividing them by size (and spacing them out a little more) to help the smaller ones grow better without getting shading out by the taller ones.

(When does a seedling become a sapling, anyway? I guess that's a bit like asking when a baby becomes a child…)

(Oh, and happy Thanksgiving!)

This photo shows the process: on the right, a tray of saplings of various sizes, which I sorted into the four trays on the table. (I started with three size categories, but found four worked slightly better after some experience, which is why they go second-smallest/largest/second-largest/smallest from left to right.) We also gave them a bit of fertilizer, and removed any weeds that had sprouted. It was a rather meditative (and surprisingly satisfying) experience, as I quickly became proficient at sizing saplings and there was a hydroponic setup with some gently recirculating water that made it a very low-stress, soothing time. Perhaps as a result I didn't bother counting closely, but we probably handled some two thousand or so saplings over the course of the morning, finishing about 1:30 in the afternoon.

One other interesting thing I got to see was koa seeds (above). Koa is in the Fabaceae or pea family, and forms little leguminous seed pods which contain the seeds, which are about the size of a soybean, though a lot flatter.

Anyway, that's all the volunteering for the Mauna Kea Forest Restoration Project I have for now; the volunteering opportunities they have aren't spread evenly throughout the year, but tend to bunch up somewhat. I asked about the saplings I helped sort yesterday, and was told they'll probably be planted next spring in a few months, so who knows, I might get a chance to help put them in the ground come that time. We'll see! A hui hou!

Wednesday, November 13, 2024

Transplanting koa seedlings

Last week I had the opportunity to volunteer at the State Tree Nursery over in Waimea. We were helping transplant koa seedling from their germination beds into individual containers, to grow up a bit more before being used for reforestation efforts on Maunakea next year. If you remember when I volunteered to go planting back in the spring, this is where those saplings we were planting came from. It was interesting to see that, a bit like reading a prequel story. 

Here's a photo of what we were working with – hundreds of seedlings, germinated together in a bed on a table.

Each went into its own individual container, to grow until they're about waist height and ready for outplanting.

And here's how many we had left at the end of the day! I know I personally filled six racks of fifty containers each (plus helped fill a few more), so between volunteers and staff that were there that day we probably transplanted over two thousand seedlings, easily. Not all of them will survive when planted in the wild, but that's still quite a few trees that will go out next year! And this was just one day of four – I'll be heading back on the 27th for another day of transplanting.

In fact, as I took Old Saddle Road to Waimea in the morning, I drove by where I'd helped plant saplings earlier this year and caught glimpses of some of them in passing. I don't know how long koa take to grow – I imagine it's on the order of decades – so it'll probably be a while until they're majestic trees, but it was inspiring to see them growing there. Hopefully I'll have more opportunities to help with planting in the future. A hui hou!

Thursday, October 17, 2024

Catching Comet Tsuchinshan–ATLAS

Tuesday evening I drove up Maunakea to the Visitor Information Station to see if I could spot Comet C/2023 A3, a.k.a. Comet Tsuchinshan–ATLAS. I hadn't felt particularly motivated to get up before dawn to see it earlier, but now that it's in the evening sky I figured I'd see if I could spot it.

For an astronomer, I'm a little embarrassed at how few comets I've actually seen. While solar eclipses (which I actually have never seen) either land in very out-of-the-way places or come at inconvenient times when I'm scrambling not to spend money on travel, I haven't lacked for chances over the past few decades to see comets (though a few, like Comet NEOWISE in 2020, did come at times when I wasn't really able to get somewhere dark enough to see them). Still, I don't have much excuse for missing Comet McNaught in 2007 or Comet Lovejoy in 2011. I did see Comet Holmes' remarkable brightening in 2007, though that was an unusual comet since we were seeing it almost head-on, so it didn't really display much of a tail. There are probably a few more I missed in that time span as well which I've forgotten; on the whole, I have a pretty poor track record of seeing naked-eye comets even when presented with the opportunity.

Which is why I found myself yesterday trudging up the path to the top of Puʻu Kalepeamoa in some extremely strong (and frigid) winds, setting up my GoPro for a timelapse, and waiting for the sunset. The timelapse didn't quite work out as planned since it failed to adjust the exposure time properly after it got dark, but I managed to get some photos, at least. 

The setting Sun through a māmane tree. They're in bloom this time of year.
The nearly-full Moon, unfortunately, wasn't doing the comet any favors as it lit up the night sky. I was first able to make it out maybe a half hour after sunset, then as twilight faded it became easily visible for perhaps another hour or so; by the time I left, nearly two hours after sunset, it was getting low enough on the horizon to be difficult to make out again.
Comet Tsuchinshan-ATLAS over Hualālai, with Venus at left.

With that, I can finally say that I've seen a proper, honest-to-goodness hairy star, and I have the pictures to prove it. Speaking of, I got those shots with my Pixel 7 Pro; not as good as a professional camera, but it's still remarkable to me just how good the software and hardware in phones has gotten, that it can capture shots like this in low light. (I did set it up on a tripod for stability, but still.)

Overall it was an interesting experience, and I'm glad I made the effort to see it. (Though after sitting out in those winds, maybe I should've gotten up to see it before dawn from Hilo, where it'd be warm[er] and humid instead of frigid and parched…) It should still be visible for a little while, perhaps the next few weeks; the Moon will start rising later and it'll be getting higher above the horizon, which will both make it easier to see, but it's also receding from the Sun which will make it get fainter, so there's a tension between the various effects. The next few days should still be good, though, and I'd recommend making the effort if you haven't seen it. I probably won't head up Maunakea again, but I'll try to keep an eye out for it from Hilo as it rises high enough now to be seen above the western horizon. A hui hou!

Wednesday, October 9, 2024

Last day at Gemini

Today was my last day at Gemini, officially ending three years since I began there. I found myself leaving with a complex superposition of emotions; sadness at leaving a job I've enjoyed and the friends I made there, yet also a sense of peace that it was finally done, relief that I don't need to wake up to an alarm tomorrow, and – just maybe – the faintest spark of excitement for what comes next. We had a farewell lunch for me (with a cake!) on the lanai, which was nice. Someone found out it was my last day there and said something to the effect of, “Oh! Not taking any vacation days off at the end?” To which I replied (entirely sincerely) that the thought hadn't entered my head when there was still so much work to get done before I left, which our team coordinator told me she got a kick out of afterwards.

The work I've put into DRAGONS won't be coming out very soon; the most recent estimate I heard is that the version containing it might come out September 2025, so it'll be a while before you can be reducing your own near-infrared spectroscopy data using my work. It's somewhat bittersweet to have spent three years working on something and to have to leave before it's even come out for people to use, but I suppose I'm hardly the first programmer to have that happen. And at least it will be released rather than get canceled without ever seeing the light of day, as happens all to often in the programming world. Thankfully things went smoothly and I was able to mostly wrap up what I wanted to and leave the code in a working state; I spent my final three days writing one last test for the GNIRS cross-dispersed data reduction and using it to make one final tweak to make things a bit simpler and more elegant. There are a few remaining issues, but I spent the two weeks prior carefully investigating them and writing down what needs to be done about them (they were a bit too involved for me to start at that point). I know the code's in good hands, at least, though progress will probably be slower now that I've left.

As to what does come next? No idea. I didn't get the Gemini telescope operator position, and since I haven't heard back from the other two places I'm assuming nothing is forthcoming on those fronts. (From conversations I've had since then, ghosting unsuccessful job applicants seems to be the new standard, even after an interview.) With more free time on my hands and no more stress about wrapping things up successfully, I'm planning to go at the job hunting with more vigor. I've got a few astronomical opportunities that seem a pretty close fit that I've either applied to or am planning to apply to (though they're open till the end of the month so I won't hear back for weeks if at all), and I'm also going to be looking around locally outside of astronomy to see what's available. I've got a few leads and contacts, so we'll see how that goes.

But for the next few days, at least, I plan to rest; considering I went straight from submitting my thesis to working at Gemini, I haven't taken more than about two weeks off at a time for over seven years at this point. I have no lack of hobbies I'd like to take up again, new skills I'd like to learn, and other ways to occupy my time outside of job hunting, and I think it's high time for me to take a well-earned (if externally-imposed) break. Maybe I'll get some more posts out of it too, we'll see! A hui hou!

Monday, September 30, 2024

Some thoughts on the Rings of Power

The title of this post has something of a double-meaning today, as I felt like discussing both Amazon's Rings of Power and the self-same rings of power as Tolkien originally conceived them. Now, I'l begin by saying I haven't actually seen Rings of Power, but I've read a number of articles written about it. From what I've read I am generally of the opinion that I'm not missing much, due to a number of changes from the source material which seem to be made solely for the sake of change rather than out of necessity.  People may defend an adaptation by saying that changes must be made; I don't think any sane person would deny that, but not all changes are equal. Or good. I'm not here to quibble with every change made (indeed, not having watched the show, I can hardly do so, and some are fine), but there are some which seem primarily for the sake of cheap drama rather than from a place of measured consideration of what deeper themes Tolkien intended his work to say.

The particulare change which indirectly sparked this post was this: in Tolkien's work, the three rings of power which end up going to the Elves are completed last, using the knowledge learned from Sauron (in his guise as Annatar, Lord of Gifts), but without him being directly involved as with the previous sixteen rings (which eventually get split up seven to the Dwarves and nine to Men). The three Elven rings – Narya, Nenya, and Vilya – are therefore unsullied by Sauron, and could be used safely as long as Sauron didn't possess the One Ring. 

Rings of Power, instead, has switched things around to have the three be forged first by Celebrimbor with Sauron's direct involvement, in what seems like an attempt to generate cheap drama by having the Elves debate about whether they should use them or not, ultimately deciding to do so and having it (seemingly so far) turn out all right. This, of course, runs completely counter to Tolkien's view, where the instruments of evil (such as the One Ring), even if wielded for the best of purposes and with the purest of motives, inevitably corrupt their wielders with a desire for ever-more power and domination. We need look no further than Gandalf and Galadrial's reactions to being offered the One Ring; they both are wise enough to recognize that while they would initially take it up with the best of intentions, in time they would become tyrants to rival Sauron.

But how, in Tolkien's work, did Sauron get the Elves of Eregion to work with him in forging the rings of power in the first place if they proved so dangerous? I was recently thinking about this (read: my brain obsessively decided to focus on this at 4 AM in the morning when I woke up one night after reading Tolkien's essay On Fairy-stories before bed), and I have some thoughts.

The Second Age, in Tolkien's legendarium, was an age of, if not necessarily decay, at least a bit of a slow burn; after the high and heroic deeds of the First Age, ending in the fall and banishment of Morgoth, the Second Age starts out hopeful: the Númenóreans have their island home of Númenór (granted by the Valar as reward for their help), and after the cataclysmic battle against Morgoth the rest of Middle-Earth has peace again, with evil seemingly defeated. But over the centuries and millennia, it become clear that cracks are forming in this idyllic vision; as the average lifespan of the Númenóreans slowly dwindles, they start to become more and more afraid of death, ending ultimately in Ar-Pharazôn's catastrophic attempt (provoked by Sauron) to invade the Undying Lands. Sauron, having escaped the overthrow of his master, lay low for centuries but eventually begins to stir again, fortifying Mordor as his stronghold and seeking to extend his power and influence. The Elves, in general, are not doing a whole lot during this time (though the friendship between the Elves of Eregion and the Dwarves of Khazad-Dûm is notable); after the great deeds of the First Age, they seem to enter something of a holding pattern, more interested in preserving what is rather than making new things.

And this, I think, gives a clue as to how Sauron was able to trick the Elves' best and brightest into forging what would become some of his most potent weapons. His endgame was always Domination; the forceful overwriting of others' wills with his own, as seen most vividly with the Nazgûl, or Ringwraiths. But he could disguise this desire by presenting the rings as agents of Preservation, which the Elves were interested in. The error of the Elves lay in not recognizing that Preservation of things beyond their natural state or lifetime is but little removed from Domination. Preserving may seem to be “freezing things in time,” but what it must actually be is a series of changes undoing those done by time, just as a pure tone may be canceled out by playing another of the same frequency but 180° out of phase with it.

Sauron thus essentially had a backdoor in every ring that was forged; they were already latent instruments of domination, of the imposing of the will upon Nature and Others beyond the natural state. In forging the One Ring to control them he simply, as it were, revealed their true nature and the trap the Elves had fallen into. While the Three were forged without his direct involvement and thus bore no direct taint, even they had the fatal flaw of the others (and could be suborned) because they were built on the same principles and along the same lines. When the Elves perceived this treachery on Sauron's part they removed their rings, and did not wear them again until Sauron was overthrown and the One Ring was lost (closing out the Second Age in the process), but he was able to use the sixteen already made – to devastating effect in the case of the Ringwraiths.

(As an aside, the rings given to the Dwarves don't seem to have had much effect on them, beyond inflaming their natural desire for gold and perhaps extending their lives somewhat. Sauron, as a Maia, was once the student of Aulë, the Vala who created the Dwarves in anticipation of the coming of Men; and perhaps here we may see where the pupil's craft proved unable to surpass the master's.)

It's a shame that Rings of Power doesn't seem interested in telling this arresting tale – of Sauron cunningly working on the Elven smiths of Eregion, promising (real) knowledge and power to help keep things as they are and arrest their natural decay, while secretly sowing the seeds of destruction and domination. A nuanced discussion of when to Preserve and when to let go could have been had, and what the proper place of Magic (really, Technology) is in so doing; but instead we get a flipping of the rings' forging order seemingly for the sake of some cheap drama and uncertainty, without any deeper thought as to what the ramifications of such a change would mean or how the lesson imparted might end up entirely at odds with Tolkien's intended one. It is not (from what I have gleaned) the first such change in Rings of Power, and it will probably not be the last.

What should we take away from all this? One possible moral might be that since Preservation is not so far removed from Domination we shouldn't try to preserve Tolkien, and accept whatever changes others make. I feel, however, that this would be missing a key point: that there is a proper and an improper use of, and time for, preservation. The rings' powers only became problematic when they tried to preserve something beyond its natural state or limit; they did not provide more life, but merely an extension of it, being stretched ever thinner. As Bilbo said, beginning to feel the effects, it was like being “butter, spread over too much bread,” a discomfort which would eventually stretch into a torment had he not freely given up the ring.

But there is still a use for Preservation, when it does not seek to preserve things too far. Elrond in Rivendell and Galadrial in Lórien both preserve their respective locations throughout the Third Age, but when the One Ring was unmade, the Third Age ended, and the Elves knew that the time of Men was come and the time of the Elves was ending, they willingly surrendered their attempts at preservation to higher powers and departed Middle-Earth for Valinor. Tolkien knew and accepted that people would build upon the foundation he laid; but I think there is still room to critique the additions and see if they measure up to what came before, without declaring the entire edifice untouchable and eternally fixed. Preserving Good in the world and not letting it fall into ruin before its time is good, as long as the focus remains on the Good and not solely on the Preserving, as such; a trap, as Tolkien reminds us, all-too-easy to fall into.

Friday, September 27, 2024

Touring an oceanic research vessel

Back on the 11th I had the opportunity to take a tour of the NOAA ship Okeanos Explorer, the only federal ship dedicated to mapping and exploring the deep sea and sea floor while it was in port in Hilo. (This was through Gemini; some of the ship's crew got a return tour of the telescope a few days later.) The ship itself is a converted former Navy submarine hunter, making it perfect for running quietly while carrying out sonar mapping.

View from in front of the bow.

The Okeanos Explorer can carry and deploy underwater vehicles equipped with lights, video feeds, arms for grabbing samples, and more, and livestream their underwater expeditions. I've come across clips from them on YouTube before, so it was really neat getting to see where those discoveries came from.

Starboard side of roughly the latter half of the ship.

You might have heard about the Okeanos Explorer from when their discovery of a mysterious golden-colored egg on the ocean floor briefly went viral earlier this year. It was about the size of an emu egg and had a hole where something had hatched, but no one was able to identify what species it might have come from, which gave it an evocative, mysterious appeal that made it briefly famous. So far it still hasn't been identified; I asked our guide about it, and found out she'd been the one who bagged it up when it was collected for study, so “all the world was going crazy about this thing, and I had it in a Zip-loc bag full of ethanol,” as she put it.

The control room for the underwater vehicles, and livestreaming the expeditions.

We got a lot of interesting information over the course of an hour and a half; the ship had been in the Pacific several years ago, but had then been in the Atlantic the past few years, and is now back in the Pacific for a few years on its first expedition of several (though it doesn't have underwater vehicles for this one, it's a mapping expedition instead). It left harbor sometime over the weekend on a ten-day voyage to where it will have begun its mapping by now in the Papahānaumokuākea Marine National Monument to the north-west. It was supposed to leave at 0830 Saturday morning, and I was hoping to catch it with my drone when it did from the lookout point on the west side of the bay, but something must've come up since it still hadn't left the dock after an hour and a half. I found out I could zoom in with my phone and make it out at dock (from several kilometers away!), which resulted in some shots like the one below artistically framed by a vine in the foreground.

The Okeanos Explorer at dock (the white ball near center is its radar dome).

Overall it was a really interesting tour and I'm glad I got to go. One thing that struck me was how a number of aspects of running a science ship like that mirrored running an observatory; one major parallel was how the weather dictates the schedule for both, but there were a number of other little similarities as well. It was fascinating to hear about the work they do, especially with having previously seen video clips taken from the ship. I guess that's another parallel to astronomy: trying to engage the public and share the knowledge they're gaining. Which I thought was pretty inspiring. A hui hou!

Saturday, August 31, 2024

Painting a solar filament

I haven't done much painting since moving back to Hawaii. I'm not sure why, other than that I just haven't felt very motivated to do it; perhaps because it started as something of a social activity in Australia and I haven't replicated that feeling here. However, back in May, the Astronomy Picture of the Day website had an image of the Sun from the Solar Dynamics Observatory which really inspired me. It showed the limb of the Sun with a filament stretching out from behind it towards the foreground, which gave it a strong sense of three-dimensionality – something often lacking in astronomical images. I thought I'd take a shot at painting something like it, leading to the painting below:

Solar Filament, 12"×18", acrylic on canvas.

I'm not entirely happy with how it turned out – especially when comparing to the infinitely more dynamic and vibrant inspiration – but I've learned that sometimes it's best just to draw a line under something, take the lessons learned, and move on, rather than striving in vain for perfection. Though for being the first moderately intricate thing I've painted in a few years now, I'm also not too unhappy with it. I learned (and relearned!) multiple things about painting while working on it, which I'm sure will come in handy the next time I feel like painting a star.

I tried to replicate the colors from the reference images somewhat, such as having the hottest parts of the surface be white. It didn't quite come out like I'd hoped, which actually characterizes a fair amount of my color-mixing experiments over the course of this painting – but in the process I remembered how much fun it is mix colors, to arrange them as I like, and the physical application of paint on a surface. Speaking of surfaces, that's one thing I think did go well: before coloring the Sun, I laid down a thin layer of flexible modeling past, then lightly tapped all over it with my finger to create an appropriately fractal, rough surface. (I later realized I should've done something similar where the filament goes beyond the solar limb and had to improvise with some stiff paint, but that's part of the learning process!)

In-progress image showing the texture on the Sun's surface.

I thought about using glass beads like some of my previous stars, but it didn't quite feel right for this painting, and I think that was right call in the end. Overall, I'm happy enough with it to share it here, and it has reminded me of the simple joy of painting. I don't know what I'll paint next, or when, but I do have a few ideas rattling around in my head, so we'll see where things go. A hui hou!

Tuesday, August 27, 2024

Windy wet weather

This weekend was wet and windy as the center of tropical storm/hurricane Hone passed just to the south of the island. (It upgraded in status a short while before its closest approach.) According to the 48-hour rainfall map I saw Hilo got about 8-10 inches, so the rivers have been running high. After work yesterday I drove up to Waiʻale Falls, and found the lighting rather evocative above the raging river:

Waiʻale Falls, swollen with recent rain.

Thankfully, damage was fairly minor within Hilo from what I've seen. Around 5,000 people lost power according to HECO, but that seems to have been mostly outside Hilo in more rural areas, and all but about 400 had it restored by this morning. I heard a transformer blow not too far away (it made a tremendous noise), but never lost power. We've got another storm (Gilma) projected to pass by north of this island later this week (perhaps hitting the rest of the chain more square-on), but it was just downgraded from a hurricane in the last day or so and is expected to get weaker and not cause any significant effects here. All just part of hurricane season in Hawaii!

In other news, I found out last week that I didn't get the Gemini telescope operator job; from the message I got they went with someone currently working as a telescope operator, which certainly makes a lot of sense. That's pretty much the last nail in the coffin for me sticking on with Gemini, so I've been adjusting to that. I'm still waiting to hear back from the other two interviews I had, despite sending some gently querying emails about a week ago. I know things can move slowly, and no news can be good news at this stage, but I'm a bit surprised not to have heard anything. Still, not much to do for it except wait (and maybe see about putting in some more applications…). A hui hou!

Wednesday, July 31, 2024

Calculating collision damage as falling damage in D&D

I recently saw a discussion on a forum I visit about how much damage a creature would take in Dungeons & Dragons from running into a wall at a hundred miles per hour, with someone noting that there's no formal rules covering collisions, but that it could be modeled using the rules for falling damage. This sparked my curiosity, and I ended up deriving a formula for collision damage as a function of velocity which I thought was interesting enough to share here.

First, our starting assumptions: falling damage in D&D is modeled fairly simply as 1d6 per 10 feet fallen, up to a maximum of 20d6 at 200 feet. We're going to take this model as a given (including ignoring air resistance) rather than investigating it more closely here (though while looking things up I found a post examining it which suggests it's actually a decent approximation). However, it models damage in height fallen rather than speed of impact at the end of a fall, which is the value of interest for modeling (horizontal) collision damage.

Here's where the equations of motion come through for us: we assume a creature falling from some height \(r_0\) with an initial velocity \(v_0\) of zero comes to a stop at a height \(r\) of zero with a final velocity \(v\) entirely under the acceleration due to gravity \(g\) (\(-9.8\) m/s², or \(-32\) ft/s²). Equation [4] has all the variables we need:

\[v^2=v_0^2+2a(r-r_0)\]

We can rearrange this (substituting \(g\) for \(a\)) to get

\[r_0=\frac{v^2-v_0^2}{2g}-r,\]

and since both \(v_0\) and \(r\) are zero in this situation, it becomes even simpler:

\[r_0=-v^2/2g.\]

(Remember that \(g\) is negative so the final result is positive.) It then becomes a matter of unit conversions, since \(r_0\) needs to be in feet. With \(g\) in ft/s², we just need to convert velocity from the more familiar miles per hour into feet per second. 5280 ft/mi / 3600 s in a hour equals a conversion factor of 1.47, so for velocity in miles per hour we have (leaving out the units):

\[r_0=\frac{(1.47\cdot v)^2}{64}.\]

(If you want to use it with ft/s, just don't multiply by 1.47.) Putting in 100 mph for \(v\) gives a starting height of 337.6 feet, which is above the 200 foot cutoff for maximum damage; one could either rule that a creature hitting a wall at that speed just takes 20d6, or keep extending the model out and take 33d6. (If you use the maximum damage model, the cutoff point is almost exactly 77 mph or 113 ft/s – anything moving faster just takes the max damage.)

How applicable is this in normal combat? Probably not very; the normal move speed of a player character is typically 30 feet per round. Rounds are 6 seconds, so that comes to 5 ft/s, or a leisurely 3.4 mph, slightly faster than normal walking speed. Generally players can run at twice that speed (at the expense of not performing other actions), which is still only 10 ft/s, or 6.8 mph, a gentle jogging pace. How much damage would a player take from running full-tilt into a wall at that speed? None, it turns out, as it would be equivalent to a fall of a mere 1.5 feet, nowhere close to the minimum 10-foot threshold to take damage. The original hypothetical was about a flying dragon, which makes a bit more sense to be speeding around, but most creatures probably aren't moving fast enough to warrant collision damage in most circumstances. Still, the formula above will allow you to calculate it should the situation ever arise, and I present it to do with as you will. A hui hou!