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[ 20031031 ]

The Mathematics of Wildfires (II)

Frequent correspondent and contributor Kevin Munden suggested I re-check Joseph Hertzlinger's math. Notwithstanding that Southern California is something of an acquired taste, it hardly seems fair to say that it looks like it's been hit by thousands of small nukes. ;)

But how does the (chemical) energy released by the wildfires compare to other things -- like, for instance, the solar energy falling on the same area over the same time?

Kevin sent a link to this table, which, while not the most intuitive, has lots of useful information; notably, it tells us that ~4.2 kW sec = 1 kCal. Elsewhere, we learn that the solar constant s = 1.37 kW m-2. Actual insolation at Earth's surface and latitude ~33° N, some weeks after the autumnal equinox, will of course be less than this; let's call it an even 1 kilowatt per square meter.

So the 48-megaton (that is, 4.8 × 1013 kCal) estimate works out to 2 × 1014 kW sec (56 billion kilowatt-hours). If the fires have burned 6 × 105 ac = 2.4 × 109 m2, then this works out to 84 kW m-2.

(I note that Joseph's estimate was 20 tons of fuel per acre = 5 kg m-2 and 4 kCal per gram of fuel, implying 20,000 kCal m-2 = 84 kW m-2.)

So, okay, take a cheap magnifying glass about 2½ inches in diameter, with a focal length of about 6 inches, and focus the Sun on a bit of dry wood. The image size will concentrate the sunlight by about the factor we've just derived. Imagine the "hot spot" 35 miles across; that's the Southern California wildfires. Ouch.

Jay Manifold [9:18 PM]

OK, Another Halloween Post

The Four Horsemen of the Arcturcalypse are on display over at Alan Henderson's blog, along with various other luminaries. Something about Sasha Castel's picture seems a little out of proportion, but I'm not sure what it is. ;)

Jay Manifold [9:13 PM]

A Real Halloween Story

-- as forwarded by Bill Walker, is here.

I should add that an All Saints Day story -- one we get to write -- is here.

Jay Manifold [8:14 PM]

A Bush Landslide?

Judging by this, there will be something very much like 1972's "Democrats for Nixon" forming soon. Meanwhile, the inimitable Ted Rall describes why public revulsion at rampaging anti-Bush rioters outside next year's GOP convention will produce a huge backlash and guarantee W's re-election. Of course, that's not quite how he puts it.

Nonetheless, I can imagine an uphill climb for the present-day equivalent of CReEP. My conservative Republican friends -- and in spite of my obnoxious posts on this blog, I still have a few -- are, as far as I can tell, unanimously disgusted with W's profligacy and weakness. All a Democrat would have to do to win is avoid frightening such people, thereby keeping them away from the polls.

Over on BuzzMachine, Dann (of Dain Bramage) has a comment about Bush's real failings, few of which will get attention next year. A possible list:

  1. Hundreds of billions in new spending, mostly on Medicare.

  2. No privatization of Social Security.

  3. Wish-list "anti-terrorism" legislation.

  4. Ludicrous stunts like this.

  5. Imposition of steel tariffs and failure to lower trade barriers.

  6. Failure to confront Saudi Arabia and Pakistan.

  7. Continued destruction of civil society in South America.

  8. Indirectly, through continuing interventionist economic policies, failure to improve the labor market.

Jay Manifold [3:32 PM]

Friday Quagwatch!

Inspired by this earlier post and the example of Alphecca, I've decided to make this a regular weekly feature.

This week's quaggers are (emphases added) ...

That's all for this week. Be sure to check in every Friday to see who's been quagging!

Jay Manifold [3:02 PM]

The Mathematics of Wildfires

Over on Winds of Change, Joseph Hertzlinger left a comment that led me to this post:

If 600,000 acres were scorched and the fuel load is 20 tons ac-1 and the energy release from wood is 4 kCal g-1 (typical of carbohydrates) and the energy in a megaton is 1012 kCal, then the total energy release is 48 megatons so far.

From a purely energetic standpoint, if this was terrorism, it wasn't very efficient. Tens of megatons to destroy a couple of thousand residences? That's well over 10 kT per house. But any such strike would be tremendously nonlinear in its effects -- a handful of people, with almost no preparation, causing billions in damage and drawing down thousands of emergency personnel. Consider also the logistical impact of road closings and the psychological, if not physiological, effects of days of breathing and smelling smoke, all inflicted on millions of people. This is the kind of pinprick, nuisance attack (relatively speaking) that is arguably our greatest post-9/11 risk.

Jay Manifold [11:01 AM]

[ 20031030 ]

New Frontiers in Initiatives & Referenda

-- are being explored in Bolinas, California (hat tip: Beth Elliott):

... the advisory measure in Bolinas ... has everybody's attention. It asks whether the Bolinas Community Public Utility District should adopt the following statement as its policy:

"Vote for Bolinas to be a socially acknowledged nature-loving town because to like to drink the water out of the lakes to like to eat the blueberries to like the bears is not hatred to hotels and motor boats. Dakar. Temporary and way to save life, skunks and foxes (airplanes to go over the ocean) and to make it beautiful."

Jay Manifold [5:37 PM]

Whew! That Was Close!

Well, not really. I dumped four weeks' worth of blog entries in; results:

Words: 8989

(NOTE: The genie works best on texts of more than 500 words.)

Female Score: 8020
Male Score: 21236

The Gender Genie thinks the author of this passage is: male!

Jay Manifold [4:07 PM]

Why The Kyoto Treaty Isn't Worth Fighting Over

-- or even worth discussing, has been diagnosed by Virginia Postrel.

I'm not so sure about that fires vs quakes thing, though. You can see fires coming. (The real answer, of course, would be provided by their respective insurance rates, if purchased separately.)

Jay Manifold [4:06 PM]

[ 20031029 ]

What We Must Not Forget

A reminder from Kris Murray:

Every single woman of your acquaintance spends time alert to her physical situation for safety’s sake. Every single woman of your acquaintance has been accosted in some way at least once in her life. Every single woman of your acquaintance has at least one experience of discrimination under her belt.

Rather than dismiss what I am saying and simply disbelieve me, ask the women in your life.

Jay Manifold [8:01 PM]

The Conspiracy Unmasked


Jay Manifold [6:34 PM]

[ 20031028 ]

Can the Saudis Reform After All?

Unfortunately, registration is required to read this article by Bill Tammeus from Sunday's KCStar:

When I visited Saudi Arabia in June 2002, talk of reforming the brutally run kingdom was muted at best. Now, even amid continuing and embarrassing questions about Saudi Arabia’s widespread and destructive support of terrorism, talk of reform is everywhere there.

Believing as I do that the Saudis are uniquely dangerous and that the risk they pose is not being adequately managed by the Bush Administration, it is incumbent upon me to pass along any good news from that part of the world, however unlikely it seems that the threat can be forestalled by mere diplomatic pressure or internal reform.

Jay Manifold [6:35 PM]

"Never A Candle For The Dark"

Excellent post over on Belmont Club (which Instapundit linked to about something else) highlighting the tragedy of today's world:

The contrast between the youth at Caltech, striving to touch the face of God and the illiterate Muslim boys in a French suburb striving to touch the underpants of their neighbors is a consequence, not of the difference in their natures, but of the contents of their minds. Nothing in the US Army arsenal has been half so devastating to the Muslim world as the Saudi-funded Wahabi madrassa. For where one can injure the body, the other can destroy the mind. Nor is there help in the land of France for those who have managed to leave Arabia yet are never quite permitted to arrive in Europe. The dole for food and a policeman's truncheon, maybe; but never a candle for the dark; nothing whatever from the condemned store of Western values.

Read, follow the links, and recommit yourself to making your country the best place it can be.

Jay Manifold [5:42 PM]

Newspapers and Blogs

Andy Cline pipes up with a retrospectively brilliant idea: "What if newspapers left the old headline ethos to TV, stopped competing with electronic media, and provided deep, contextual second-day coverage?"

This suggests that newspapers -- at least the parts of them that perform this function -- and blogs may largely converge, especially once their technologies converge. It seems to me that "deep, contextual second-day coverage" requires either 1) an enormous amount of text or 2) hyperlinks. So do newspapers turn back into the vast expanses of gray newsprint they were when I was little? Not likely; the advertisers, whatever else we may think of them, won't stand for an aesthetic rout like that.

I think it far more likely that display technology and wireless distribution will combine to create something like Clarke's Newspad, but physically flexible -- capable of being folded or rolled up -- perhaps even disposable. Assuming the requisite hardware and software to exist, what would be the economics of a publication offering primarily "deep, contextual second-day coverage" and leaving immediate reportage to television (or its equivalent)?

Assume labor costs on the close order of $100 hr-1, support by subscription only, and a subcriber base and rate similar to that of the Kansas City Star -- that is, 270,000 (380,000 on Sundays) at, well, let's just average it out to 50¢ a copy. Total revenue would then be $52 million yr-1. Divide this by 2,080 working hrs yr-1, then by $100 hr-1, and we obtain 250 full-time-employee equivalents. Interestingly, this is less than 30% lower than the current newsroom staff of 348.

My scenario assumes, however, that upwards of a quarter of a million households in the KCStar's market would subscribe to something that offered, mostly, news analysis (and had no "dead tree edition" whatsoever). If sports reporting, comics, and classified ads could be added with relatively little overhead, this might be do-able. But another giant step toward feasibility would be provided by farming out the analysis to people something like today's bloggers, but responsible <g>. Labor costs could be significantly lower, thereby either driving down subscription charges or freeing up resources for other areas.

I'll have to remember to check this semi-prediction in about another 20 years. ;)

Jay Manifold [3:38 PM]

Tribulation in Alta California Sur

Over at Purple Tricycle, Carrie recounts a very Californian instantiation of Mark 13:24 -- "with all the smoke blocking the sunlight .... [i]t feels like eclipses feel, a strange level and quality of light."

UPDATE: For the view from Mount Wilson Observatory, click here.

Jay Manifold [3:34 PM]

[ 20031026 ]

Charles Murray Strikes Again

Well, this ought to rattle some cages: in A Cultural Scorecard Says West Is Ahead (registration required), we find Murray in the role of Hari Seldon, asserting in his latest book that "Europeans and North Americans account for 97 percent of scientific accomplishment" -- which is sufficiently lopsided to place cultural relativists in a difficult position, that is, one where they start denying the value of scientific accomplishment. ;)

But it's Murray's identification of the element that "provided all the incentives people need to achieve: not only a sense of autonomy and purpose but a coherent vision of what he calls 'the transcendental goods' — truth, beauty and the good — as well" which is guaranteed to earn him denunciations from the PC mob.

Four comments from a state of relative ignorance, that is, before I buy and read the book:

  1. I think the crucial variable is the ability of societies to create functioning, autonomous institutions, of which the Royal Society (see also here) is the canonical example; but disestablishment of the Church in the US may have been nearly as important. Once those institutions are in place, and for as long as they work well, anyone joining the societies which nurture them is a potential contributor to progress, irrespective of ethnicity -- or religion.

  2. Verges between cultures, and among subcultures, engender progress. See, for example, Vikings vs peasants, 800 AD et seq, drastically (and inadvertently) reconfiguring agricultural plots to make them more suitable for tilling by ox-drawn moldboard plows, thereby multiplying food production.* The modern example that Murray cites is the enormously disproportionate contribution of Jews to Western well-being, occurring within a frequently hostile Christian matrix.

  3. I wonder how great the disparity between the West, which increasingly means the Anglosphere, and the rest of the world can grow before arousing opposition from the "do-nots." Of course, this may be what's going on right now. But what happens when the median US citizen is, say, 5 times wealthier than the median EU citizen?

  4. If you haven't already, read Guns, Germs, and Steel.

As for the predictive part of the model: "Equally provocative, he maintains that the rate of Western accomplishment is currently in decline." By which Murray means that Europe is in decline.

* "... heavy moldboard plows could not work effectively in small, squarish fields such as were usual in the older agricultural parts of Europe. Few peasants could put a complete team [of oxen] into the field; and only a pooling of draft animals (together, often, with a reorganization of field shapes and shift of land-management rights) could sustain the improved type of cultivation. It was, therefore, in times when rapine and robbery destroyed established relationships on the land that men became willing to pool their resources and redistribute land rights according to new patterns. In circumstances such as these, the introduction of the more efficient plow and the establishment of co-operative tillage had everything to recommend them. Thus it was precisely in the ninth and tenth centuries, when northwestern Europe was most cruelly harried by Viking and Magyar raids, that the type of agriculture known as 'manorial' achieved the technical basis that soon made it possible for European peasants to produce a considerable grain surplus on lands that had lain waste in earlier ages." -- William H. McNeill, The Rise of the West: A History of the Human Community, II.IX.C (p 452 in the Gryphon edition)

Jay Manifold [7:08 AM]

Leonid Meteor Shower 2003

For most of us, it's coming on the night of Tue/Wed 18/19 November; this article has a good overview.

This applet appears to indicate a spike in meteor flux between local midnight and 2 AM on Wednesday the 19th, at least for locations in the central US, which means going out late Tuesday night the 18th. The peak time for KC (user input as 39° N, 94°30' W) is 1:26 AM CST, and the peak rate is 32 meteors per hour (with "Countryside" viewing conditions).

Jay Manifold [7:07 AM]

Lunar Eclipse, Saturday 8 November

For Western Hemisphere observers, this will be a very child-friendly event, occurring in early evening shortly after Moonrise. As always, Fred Espenak has the scoop; for locals, here's the schedule (all times CST):




5:06 PM

Beginning of Umbral Phase

5:32 PM

Beginning of Totality

7:06 PM

Greatest Eclipse

7:18 PM

End of Totality

7:30 PM

End of Umbral Phase

9:04 PM

End of Penumbral Phase

10:21 PM

Locally, ASKC members are being encouraged to bring their telescopes down to Powell Observatory and set them up on the lawn outside the main dome for the public; a Scout troop has the observatory itself reserved for the evening. Not sure whether I'll go down there (it's almost 40 miles from my house) or just set my 'scope up in my driveway for the neighborhood kids.

Jay Manifold [7:06 AM]

[ 20031025 ]

Hermes Re-Acquired! (II)

(Ref this earlier post.) Hermes is turning out to be the first near-Earth binary asteroid: "The two objects together would cover an area approximately the size of Disneyland." Uh, how does that compare to Worlds of Fun? Seriously, as for the risk of impact, our sister planet may take this bullet for us:

Hermes travels on an elliptical orbit and reaches deep into the inner solar system, crossing Venus' orbit. The new research has made it possible to extend the time interval over which the trajectory can be computed reliably, said Jon Giorgini, a senior engineer at JPL and member of the team.

"As far as impact risk, there is no cause for worry in our lifetimes," Giorgini said. "Over hundreds of thousands, or millions of years, Hermes could impact the Earth, but only if it doesn't hit Venus first."

This statement includes the radar images themselves, which appear to depict a larger, elongated body perhaps 400 m in greatest dimension, and a shorter, rounder body perhaps 200 m across, separated by about 600 m. I will defer my eyeball estimate, however, to that of IAU Circular #8227, which says: "Preliminary estimates of the diameters, based on visible range extents, are 300-450 m. Upper limits to the spin period of each component are 13-21 hr for the above size range."

Let's check that. Suppose that the two components, which I hereby dub Mysteries and Mayhem, are as follows (setting the bulk density
r of both to 103 kg m-3):

Now we need the gravitational parameter m of the overall Hermes (Hermetic?) system. This is simply the gravitational constant G multiplied by the total mass:

(6.7 × 10-11 m3 kg-1 sec-2) × (2.9 × 1010 kg) = 1.9 m3 sec-2

Now we apply P = 2p √(a3 / m), where a = 1000 m, and mass is as above.

Answer: 140,000 sec = 39 hours. So, okay, I'm off by a factor of 2.

Once again, this is where I ask my readers to do the math on their own to get a better answer. Hints: try making both Mysteries and Mayhem spherical, and the maximum diameter as per the IAU Circular; or increasing the density; or both. Send your results here.

The statement linked above also includes the following historical tidbit from Giorgini:

Using radar, the position and velocity of Hermes has been measured to within 300 meters and 50 mm/s; much more accurately than with optical telescopes. Including those measurements in a new orbit solution suddenly allowed us to accurately predict Hermes motion over many centuries, from 1561 to 2103.

During those 542 years, it makes 23 close approaches to the Earth, 29 to Venus, 7 to Mars, and 7 to a large asteroid called Vesta. Hermes' closest approach was in the skies over the Earth in 1942, as World War II was fought underneath, when it passed about 1.8 times further away than the Moon. However, no one noticed it at the time.

Harry Turtledove, call your office.

Additional radar observations are underway at Arecibo today and tomorrow, and more will be conducted from Goldstone over the next couple of weeks.

Jay Manifold [4:33 PM]

[ 20031024 ]

Why Power Lines, High Latitudes, Volcanic Rock, and Solar Storms Don't Mix

Over on ABCNews.com, the generally excellent article Space Weather: How Intense Solar Activity Can Upset Earth-Based Technologies left something partially unexplained:

Researchers believe that portions of the North American power grid that happen to be situated in more northerly latitudes (which is closer to the ring where aurorae are most likely to occur) and atop geological formations that consist largely of igneous rock (which has high electrical resistivity) are especially vulnerable. That would include most of eastern Canada, a good deal of New England, and a big swatch of the Pacific Northwest.

What's electrical resistivity? Why is it higher in igneous rock? Is there a map of the affected areas?

Well, the last question's the easiest: there's a map here; it indicates that a sufficiently severe event could affect not only Montreal but virtually the entire northeastern US megalopolis, and in the west, Vancouver, Seattle, and Portland.

Continuing to work backwards, we find this imperfectly translated article (warning: 214 kB *.pdf), which says:

Electric current primarily flows through the underground water found in the gaps (pore) between the minerals that compose the ground. Igneous rocks, which are hard and fresh with fewer pore, indicate a high resistivity, while, sedimentary rocks that are comparatively young in terms of geological age indicate low resistivity, because of more pores filled with groundwater. Furthermore, the lower the resistivity of the groundwater (pore water) in pores, the lower the resistivity of the rock.

So we see that it is a physical, rather than chemical, property of igneous rock that gives it high resistivity. Indeed, the chemical composition of some igneous rocks tends to lower the resistivity; as Delius, Bartetzko, and Pechnig note (warning: 763 kB *.pdf):

The highest density, velocity and electrical resistivity values are recorded from the massive lava flows and gabbros. [but] In-situ physical properties of oxide gabbros are controlled by the mineralogical composition of the rocks. The high amount of heavy and electrically conductive iron and titanium oxide minerals in the rocks causes the electrical resistivity to decrease and density to increase.

Measuring electrical resistivity in soil and rock turns out to be quite useful. But what is it, exactly?

I found a definition here, one that distinguishes it nicely from "resistance":

Both are measurements of the extent to which the flow of electricity is hindered when passing through a substance. The difference is that resistivity is a property of a kind of material while resistance is measured for a particular object.

More formally, resistivity is defined as the resistance of a 1 meter path through a cubic meter of a substance.

Resistivity is the resistance of a conductive material 1 meter long with a cross-sectional area of 1 m2.

It is measured in ohm-meters (not ohms per meter!) -- well, that's the SI unit; 1 ohm m = 1011 Abohm cm. This source notes that "[t]he reciprocal of the electrical resistivity [of a substance] is [its] electrical conductivity."

In short, power lines strung over especially non-conductive (ie, insulating) rock and near the "auroral zone" 10-20° from the magnetic poles are more prone to buildup of induced currents in the event of big solar storms. Fortunately, on this occasion, the effect seems to have been modest. The geomagnetic storm scale mentioned in the Reuters article is defined here; for a G 3 ("Strong") storm like the one in progress as I write this, the effects are:

Power systems: voltage corrections may be required, false alarms triggered on some protection devices.

Spacecraft operations: surface charging may occur on satellite components, drag may increase on low-Earth-orbit satellites, and corrections may be needed for orientation problems.

Other systems: intermittent satellite navigation and low-frequency radio navigation problems may occur, HF radio may be intermittent, and aurora has been seen as low as Illinois and Oregon (typically 50° geomagnetic lat.).

Finally, just for fun, graze on over here for near-real-time images of the Sun at lots of different wavelengths.

Jay Manifold [8:31 PM]

Friday Quagwatch!

Inspired by this earlier post and the example of Alphecca, I've decided to make this a regular weekly feature.

This week's quaggers -- fewer but more verbose -- are (emphases added) ...

That's all for this week. Be sure to check in every Friday to see who's been quagging!

Jay Manifold [8:41 AM]

[ 20031023 ]

International Travel

Last weekend, I traveled to another nation to witness this event. Impressions:

Besides an unpayable debt to Dave and Deborah, I owe a good deal of hospitality to Beth Elliott for providing crash space (not to mention dinner) and Jon Osborne for taking me on a tour of Stanford and introducing me to his 20-month-old daughter.

Jay Manifold [3:55 PM]

[ 20031022 ]

With Allies Like These ...

This (currently tied for #16 on Blogdex) is such incredibly bad news that even though it reinforces my existing prejudices, I'm unwilling to believe it without substantial additional confirmation. But if it holds up, forget all the other "scandals" getting whomped up out of next to nothing by desperate Democrats. The only question that will matter in the 2004 election is: are you safer now than you were four years ago?

It's the civilization, stupid.

UPDATE: We've got a domestic problem, too. See Me and My Muslim Friends Neighbors (hat tip: Glenn) and If You're On The Lookout For Anti-Semitism .... Grim but necessary reading. "It takes but one foe to breed a war, not two ... and those who have not swords may yet die upon them." - JRRT

Jay Manifold [9:55 AM]

[ 20031021 ]

Redirects Finally Diagnosed

By way of answering several inquries over the past couple of months: the occasional odd redirect you may experience when grazing in here -- well, it's the outfit that provided the snippet of code that makes the "Special welcome to our visitors from [wherever]" message appear over in the left sidebar. They want money from me to make the redirects stop: "Remove the advertisement from your GeoPhrase .... Pricing starts from just $9.95 for 10,000 requests." My initial reaction to this is not favorable. More developments as (or if) they occur ...

Jay Manifold [1:50 PM]

Space Elevators vs Linear Accelerators

In a comment to this post over on Transterrestrial Musings, Alan Henderson continues to demonstrate an ability to ask the right questions:

How does the space elevator concept compare to building a linear accelerator large enough to launch payloads? Is that comparing apples to apples, or would each be useful for different purposes?

Heinlein may have been right about building rail guns on the Moon. No sonic boom problem there, and only one-sixth gee. Sound would travel through the crust - would that present a problem for lunar colonists?

I've heard that a rail gun could be suitable for (survivable) human launch if it were built long enough. Assuming that the launch site is on the equator in the Ecuadoran Andes (and not without seismograph-triggered shutoff switches for that tectonically active location), how far east would the rail gun have to extend?

The hint that space elevators and linear accelerators are economically complementary is correct. Space elevators can lift large, finished assemblies (with people in them if desired) at relatively long intervals (hours to days) and low accelerations; linear accelerators are best for inserting small amounts of raw materials into orbit at short intervals (seconds) and high accelerations.

I would expect a lunar railgun to be entirely inaudible, as the items being launched are themselves in physical contact neither with the ground nor with the railgun's structure while they are being accelerated. There might be some low background noise associated with the power consumption of the overall device. In any case, safety concerns are likely to require that railguns be placed well away from habitation, analogous to (new) airports on Earth. Machinery would have to be pretty loud to be heard through several kilometers of rock.

Alan's final question may be answered by imposing an upper limit on acceleration and doing a bit of math. Historical manned launches have demonstrated a steady decline from Mercury (8 g) to the Shuttle (3 g); this source (warning: 694 kB *.pdf) notes that jet airliners accelerate at 0.2-0.7 g at takeoff. So suppose we work two cases: existing capability, that is, 3 g; and mass-market comfort, that is, 0.5 g.

Not to overlook the obvious, what's a g, anyway? Well, here's what:

g = G M / R2

G = 6.673 × 10-11 m3 kg-1 sec-2
M = 5.976 × 1024 kg
R = 6.378 × 106 m

g = 9.803 m sec-2

Now we need to know the orbital velocity at Earth's surface:

Vorb = √(G M / R)

with values as above

Vorb = 7.907 × 103 m sec-1

This result may slightly overstate the actual requirement, since the payload will be several kilometers above sea level when it is released from the linear accelerator. Other complications I'm ignoring are air resistance, which by introducing drag would effectively increase the velocity needed, and Earth's rotation, which by providing some velocity to start with would reduce the velocity needed (at the equator and high altitude, these come close to canceling each other out).

In any case, with final velocity established, here is how much time it takes at our selected accelerations to reach that velocity:

T = Vorb / A

A1 = 3 g
T1 = 268.9 sec

A2 = 0.5 g
T2 = 1613 sec

The final step is to apply the distance formula:

s = ½ a t2

s1 = 1.063 × 106 m
s2 = 6.376 × 106 m

So the 3 g linear accelerator would have to be over a thousand kilometers long, and the 0.5 g one would span the US. Neither of them are going to fit in Ecuador, I'm afraid. Working the problem backwards -- starting with the length of the accelerator and deriving the necessary g force -- is left as an exercise for the reader.

(Looking at the topography of the area around Cayambe, it seems unlikely that less than 60 g would suffice, and the true figure may be much higher. Feel free to let me know what you come up with.)

Jay Manifold [1:34 PM]

[ 20031017 ]

Formatting Workaround

Thanks to Professor Hall over at Spacecraft for the link, and for helping me fix the high-order character display problems in Dance of the Moons. He sent me a tip in e-mail about how to make the degree symbol show up, and eventually I thought to Google "ampersand character codes." Here are some useful sites for anyone needing to display diacritical marks, mathematical symbols, etc:

Jay Manifold [10:09 AM]

Friday Quagwatch!

Inspired by this earlier post and the example of Alphecca, I've decided to make this a regular weekly feature.

So let's see who's been quagging, as of late morning Central time today (emphases added) ...

That's all for this week. Be sure to check in every Friday for your quagmire update!

Jay Manifold [10:07 AM]

[ 20031016 ]

Hermes Re-Acquired!

The asteroid, that is, which went missing shortly after its initial discovery in 1937, when it flew by Earth at only twice the distance of the Moon; Bill Hanson of the Space Frontier Foundation writes:

The Halloween season has produced other notable asteroid encounters in the past. Perhaps the most dramatic of these took place several decades ago when, on October 28, 1937, Karl Reinmuth at the Konigstuhl Observatory in Heidelberg, Germany, discovered a very fast-moving asteroid on a photograph he had just taken. This object showed up on a handful of photographs taken elsewhere in the world -- the earliest of these being on the 25th -- and it was detected for the last time on the 29th. This handful of observations over a span of only four days could not produce an especially accurate orbital calculation, but these were enough to show that the asteroid had passed just over 450,000 miles from Earth -- slightly less than twice the moon's distance -- on the 30th, and then had moved into the daytime sky. Reinmuth christened the asteroid Hermes, after the fleet-footed messenger of the gods in Greek mythology.

And S & T senior editor Roger Sinnott recalls:

Shortly after the Hermes flyby of October 1937, the American Museum of Natural History created a spine-tingling exhibit for public display. Poised above a model of New York City was Hermes, represented by a ball the size of Central Park. Pictures of the scene appeared in many astronomy books of the day.

NewScientist.com has the scoop; congrats to Brian Skiff (whom I met at the Texas Star Party in the '90s) on the rediscovery.

Jay Manifold [3:27 PM]

Dance of the Moons

Time to return to my roots and do some spaceblogging. Today we're going to visualize the sky from the Uranian moon 1986U10, whose orbit lies between that of two other moons whose orbits are themselves less than 500 kilometers apart!

First of all, an excerpt from the news item that got me started:

The newly discovered moons are temporarily designated as S/2003 U 1 and S/2003 U 2 until the IAU formally approves their discovery. S/2003 U 1 is the larger of the two moons, measuring 10 miles (16 km) across. The Hubble telescope spotted this moon orbiting between the moons Puck, the largest satellite found by Voyager, and Miranda, the innermost of the five largest Uranian satellites. Astronomers previously thought this region was empty space. S/2003 U 1 is 60,600 miles (97,700 km) away from Uranus and whirls around the giant planet in 22 hours and 9 minutes.

The smallest Uranian moon yet found, S/2003 U 2, is 8 miles (12 km) wide. Its orbital path is just 200 to 450 miles (300 to 700 km) from the moon Belinda. S/2003 U 2 is 46,400 miles (74,800 km) away from Uranus and circles the planet in 14 hours and 50 minutes. The tiny moon is part of a densely crowded field of 11 other moons, all discovered from pictures taken by the Voyager spacecraft.

A brief search led me to this table, which I quickly converted to a spreadsheet to which I added the newly-discovered moons. Uranus (which we all learned how to pronounce recently, remember?) has three groups of satellites, the innermost of which contains 13 moons with orbital radii ranging over only 48,000 km. So they routinely approach within 4,000 km of each other (Earth's Moon is nearly 100 times that far away from us).

But some of them are much closer; quoting again from the article:

"The inner swarm of 13 satellites is unlike any other system of planetary moons," says [Jack] Lissauer[, a research scientist at NASA Ames]. "The larger moons must be gravitationally perturbing the smaller moons. The region is so crowded that these moons could be gravitationally unstable. So, we are trying to understand how the moons can coexist with each other."

All the members of the inner swarm are in almost perfectly circular orbits and are quite dark:

Astronomers stretched the limit of Hubble's ACS to find the tiny satellites. "These moons are 40 million times fainter than Uranus," Showalter says. "They are blacker than asphalt, if their composition is like the other small, inner moons."

The members of the inner swarm frequently appear the size of a Full Moon from one another -- though of course far darker; Uranus is over 19 times farther from the Sun and therefore receives only about 1/370 the sunlight Earth gets, and the moons themselves reflect only about half the light that our Moon does. So a typical close approach would have one of the moons shining at about magnitude -5, still brighter than any star in the sky, but much fainter than the moonlight we're used to seeing. Uranus itself, by comparison, could shine as bright as magnitude -17, over 50 times as bright as a Full Moon seen from Earth.

By far, the three moons closest to one another are 2003U2, 1986U10, and Belinda. The interval between the orbital radii of 2003U2 and 1986U10 is only 200 km, and from the orbit of 1986U10 to that of Belinda is only 260 km. Their orbital velocities differ by only about 12 and 15 meters per second, respectively.

So stand at the "north" pole of 1986U10 (the entire Uranian system is tilted 98° to the plane of Uranus' orbit around the Sun), and what do you see?

The "north star" is Sabik (
h Ophiuchii), which is one-third fainter than Polaris; but Antares, the 15th-brightest star in the sky, is only about 14° away.

Uranus is on the horizon; you are circling it every 14 hours and 53 minutes -- faster than its own rotation of 17:14, so you would "lap" any point on its (somewhat arbitrarily defined) surface every 5 (Earth) days or so. It is, as noted above, some tens of times brighter than a Full Moon, but it is nearly 40° across, so its surface brightness is over 100 times fainter, and you can look directly at it without discomfort.

If 1986U10's density resembles that of Miranda, the smallest of the five main satellites whose mass was established by the Voyager 2 flyby on 24 Jan 86, then it's about 1,200 kg m-3. Assuming it to be spherical and applying V = 4/3
p r3 and g = G M / R2, we obtain V = 2.7 × 1014 m3, M = 3.2 × 1017 kg, and (with G = 6.673 × 10-11 m3 kg-1 sec-2) g = 13 cm sec-2, which is just about 1/740 of Earth's gravity. You'll only weigh a few ounces. In fact, you'd probably need crampons in order to walk. An object dropped from waist height would take almost 4 seconds to fall to the ground (on Earth, a 4-second fall is over 250 feet!).

Also, the surface temperature is down around 80° Kelvin, colder than liquid oxygen, and perhaps needless to say, there is no atmosphere. So you're wearing a pressure suit with somewhat better thermal control than is necessary on Earth's Moon, where it only gets down to about 120° K at night.

The surface itself, as noted above, is quite dark, but it's just a thin coating of something like soot over ice. Not slushy -- at these temperatures, ice is the consistency of concrete. Since 1986U10, like most other small solar system bodies, is probably a rubble pile, however, you're not walking on a solid slab; more like gravel. The horizon (X = √[h2 + 2 h R]) is less than 400 meters away.

The orbital velocity at the surface of 1986U10 (Vorb = √[G M / R]) works out to all of 23 meters per second, and its escape velocity (Vesc = √2 [Vorb]) is 33 m sec-1. You could probably throw a chunk of ice completely off it into an independent orbit around Uranus. Do it just right, and you might be able to hit one of the nearby moons.

And nearby they are. 2003U2, at closest approach, is only 200 km away and, being 12 km in diameter, subtends nearly 3½° of sky, almost 7 times the size of a Full Moon, but -- for reasons described earlier -- only about 1/15 as bright. With the unaided eye, you could spot details on it only about 40 meters across.

Since its relative velocity is only 12 m sec-1, it would take over a quarter of an hour to move its own length across the sky -- silhouetted against Uranus (which would appear more than 10 times larger) at closest approach. An "inferior conjunction" like this would happen about once every 250 orbits, or 155 Earth days. 2003U2 would take about 4 hours to transit the disk of Uranus as seen from 1986U10.

Belinda is only 260 km farther out, and at 68 km in diameter would subtend just under 15° of sky. Due to its diameter, which is more than one-fourth the minimum separation between it and 1986U10, its peak brightness would be about that of a Full Moon in spite of the dim sunlight falling on the Uranian system.

Belinda is moving only 15 m sec-1 slower than 1986U10. Superior conjunction should occur about every 200 orbits of Belinda, or 125 Earth days. At closest approach, you could see details 55 meters across with the unaided eye, and Belinda would be moving across the sky at 12° per hour.

All the other moons in the inner swarm, plus the five main satellites farther out -- totaling at least 17 -- would at least occasionally be close enough to 1986U10 to appear as disks; even the innermost moon, Cordelia, should subtend 3½ minutes of arc at closest approach, the size of a dime at 57 feet. Besides 2003U2 and Belinda, Juliet, Portia, Rosalind, and Puck in the inner swarm, and Miranda (mentioned above) and Ariel among the main satellites, would occasionally appear larger than a Full Moon as seen from Earth.

Ironically, the rings would most likely be invisible, since they are only ~100 meters thick; seen edge-on from nearly 24,000 kilometers away, this thickness translates to less than 1 second of arc.

But from your viewpoint on 1986U10: an enormous gas giant, 8 large moons, and 9 small moons, all in the sky at once!

Jay Manifold [10:22 AM]

[ 20031015 ]

Jargon Meme (II)

Regular contributor and Friday lunch bunch attendee Leo Johns read this earlier post and promptly got to work:

Interestingly enough, "quagmire" is the rare amplified-by-self-redundancy English word. Roget's says that quag = mire; Thesaurus.com says quag = mire = quagmire.

Slightly ironic, because it's a word usually chosen in a weak attempt to amplify the strength of a sentence - usually a lead or headline.

quag (NOUN) A usually low-lying area of soft waterlogged ground and standing water
mire (NOUN) 2. A usually low-lying area of soft waterlogged ground and standing water

Now, let's Google the synonym ...

Jay Manifold [7:46 PM]

Trains, Planes, and Actual Distances (Reader Reaction - II)

Marc of Lay Lines writes (after pointing out various complications in trying to figure the exact delays associated with train travel; this is a slightly edited excerpt):

One other problem with both flying and trains is that you won't have your car with you at the far end of the trip. When I used to live in Los Angeles, I would visit my brother in the Bay Area. To fly there, I would have to drive 45 minutes (on a good evening with minimal traffic) away from my destination, to waste 1½ hours at the airport (and pay for parking), to fly to Oakland to wait 25 minutes for my bag, and then drive 40 minutes to my brother's house (which is on near the driving route I would take), and then be dependent on my brother and his wife to get around. I only did that once.

UPDATE: It's a first-ever readers' spat on Arcturus! Brett writes:

I've written to you before, so if you don't know who I am, I'm a forgotten reader, not a new one. :)

Regardless, I just thought I'd pass along that, Marc, with all due respect, is on crack. My in-laws live in San Diego (which is about an hour and a half south of LA). I live in the Bay Area. The first year we lived here, my wife and I drove to San Diego for Thanksgiving - about twelve hours. The second year we lived here, I realized that for $95/person (thank you Southwest!) and $200 for car rental, we could cut that to about five hours. If you time everything right, that's an extra day of work. If you make a reasonable wage in the Bay Area, an extra day of work pays for the travel. It's even better if we don't rent a car and spend our spare time sitting by my in-laws' pool, but that's a relatively unique perq.

In Marc's defense, he did say "I only did that once."

Jay Manifold [7:46 PM]

"As We May Think"

-- the pathbreaking essay by Vannevar Bush, may be found online here; thanks to PunditMania for the tip.

Jay Manifold [6:38 PM]

It's Missouri Day!

Really! So fellow Missourians are invited to raise a toast with me to the land of Twain, Truman, and Heinlein ...

Jay Manifold [9:20 AM]

Jargon Meme

I just thought this up. Help me 1) determine whether or not it's original and 2) in any case, spread it around:

Quagged it -- analogous to "blogged it," which means "placed a news item or personal communication in a weblog entry and posted for public reading." A journalist or commentator who has described an American military operation as a "quagmire" in a news story, column, or weblog entry has quagged it. Also, quagging means the regular practice of inserting "quagmire" in news stories, columns, and weblog entries.

To see who's been quagging recently, click here. Looks like I need to add "Israeli" to "American," above.

Jay Manifold [6:56 AM]

[ 20031014 ]

Trains, Planes, and Actual Distances (Reader Reaction)

Previously unknown reader (the best kind) Charles R Martin wrote in to tweak my coefficients:

My experience -- as someone who used to do 200,000 mile years, and who has lived in both NYC and out here in the middle -- is that the breakeven is around 400 miles.

I think the difference is accounted for largely by underestimating the amount of time spent dealing with airports. For example, when I lived in NYC, Penn Station was less than 15 minutes away, and I could depend on boarding within 15 minutes, so the total time was 30 minutes or so (plus whatever time I left myself for the news stand). On the other hand, LaGuardia was nearly an hour away, plus you needed to allow two hours for ticketing and check in, security, and so on. Time from arrival to destination was rarely less that 2 hours; thus the overhead is closer to 5 hours.

I expect that actual values vary widely. One variable is airport design; this one allows passengers to be dropped off less than 100 feet from the airplane itself, and a large portion of the parking facilities are immediately adjacent to the terminals. Airport accessibility is another issue; Midway and Love Field, for example, are quite handy, thanks to their location near their respective city centers. Denver, D/FW, Dulles, KCI, etc, are out in the sticks. On balance, yes, I underestimated the time penalty incurred by using an airport. Argument from observation beats algebraic estimation!

Meanwhile, equally previously unknown reader Joe Markham suggests a grim equalizer may be in the offing: "... as soon as some nutball blows up a train full of people in some highly public place, you'll have the same 2-hour penalty applied to trains." Virginia Postrel has made the same prediction, for buses as well as trains.

Jay Manifold [7:22 PM]

Proof That Brains Aren't Everything (II) - Free Riders

I got to thinking about this earlier post and realized that, due to the mobility of Americans, many of the states become winners and losers by virtue of the lack of correlation between their efforts at public education and the actual behavior of their economies. Big winners, defined as states in the bottom 10 of "smarts" but the top 10 of "dynamism," are Arizona, California, and Florida; big losers are Montana and Wisconsin. Locally, Missouri (28/14) is something of a winner, and Kansas (15/34) is something of a loser.

This is an argument for Federal imposition of uniformity in public education across all states. It's not a very good argument, unless they also do something to flatten out everyone's economic performance, which would be idiotically destructive (shades of Harrison Bergeron). But the question of "free riders" remains an interesting one, especially in light of voucher proposals. How much money should a state give parents to educate their children if most of them aren't going to stick around?

Jay Manifold [6:01 PM]

Rush (not the band)

The depths to which some people will descend in their frantic attempts to distinguish Rush Limbaugh from the hundreds of thousands of other Americans who run afoul of narcotics Prohibition every year are nicely pointed out by Alan Henderson; some right-winger over on NewsMax extruded this:

In Rush's case the drugs were legal and prescribed for the management of pain. He had no reason to question his doctor about the propriety of their use. There was no need for him to wrestle with any moral question in the beginning. By the time morality became an issue, the drugs had pinned him to the mat.

Apparently junkies and alcoholics aren't experiencing pain, just having fun. Yeah, sure thing. No pain in their lives at all. And that's some fun, pal. Especially when you haven't eaten for a week or bathed for a month.

But Rush, of course, couldn't help himself. Of course.

I knew there was a reason I can't stand NewsMax.

This column, by contrast, is spot on (and has the additional virtue of an extra level of irony, given Clinton's pathetically inadequate impulse control).

I admire Rush's "I am not a role model" statement, which indicates a level of self-awareness we would all do well to emulate. The great question right now is whether an attitude of humility will carry him through being sentenced to 5 years in prison. The closest Rush has ever come to advocating anything other than the harshest Prohibitionist approach is this incoherent rant (thanks to Dave Tepper for the link) in which he appears to be attempting to criticize all the alternatives at once.

Thirty days of rehab will chemically detoxify him, but emotional sobriety takes much longer to achieve. I think the great test of his recovery will be his attitude at the trial. Will he, like Socrates, refuse to plead for clemency?

And will his fans learn the lesson of Prohibition?

Jay Manifold [5:36 PM]

Public, Private, and Secret

There's an interesting insight over on Danny O'Brien's Oblomovka, and you don't have to care much about the Californian techno-sub-sub-culture in question (I certainly don't) to enjoy it. I think I understand, now, what's behind all the boneheaded "progressive" ideas about making private organizations subject to "public" (government) oversight. "Progressives" literally don't understand what "private" means -- they recognize only "public" and "secret," and, of course, consider all "public" things good and all "secret" things bad.

Jay Manifold [5:35 PM]

Another One Of Those Lists

Currently tied for #29 on Blogdex, Robert McCrum of the Observer weighs in with The 100 greatest novels of all time: The list, which actually isn't nearly as bad as such things usually are, partly because it's chronological by publication date rather than an attempt at ranking by quality. I'll confine myself to commenting that it has a decent number of SF or fantasy entries (Pilgrim's Progress; Gulliver's Travels; Frankenstein; Alice's Adventures In Wonderland; Dr Jekyll and Mr Hyde; Brave New World; Nineteen Eighty-Four; The Lord Of The Rings; Lord of the Flies -- plus several children's books), but none from the past half-century or so.

In answer to the obvious question, I've read 13 of the 100. For my earlier remarks on the subject, and a much shorter list of my own (which if I were to write today, would probably include Niven's PROTECTOR somewhere), see this post. Enjoy!

Jay Manifold [5:37 AM]

[ 20031013 ]

Carnival of the Capitalists

-- a Jay Solo venture, is now in operation. Graze on over to BusinessPundit to catch the inaugural "issue," which just happens to include a certain book review that was itself reviewed elsewhere, earning the accolade: "Differential equations -- the sure route to a bestseller."

OK, I'm keeping the day job for now.

Jay Manifold [5:09 AM]

[ 20031011 ]

Trains, Planes, and Actual Distances

Recalling this post, I got the idea of figuring out the average and median separations of large US cities and comparing air travel with trains. This is by way of developing ammo against arguments for reviving passenger rail as a substitute for jets. Such arguments are surprisingly popular in the northeastern US. Unfortunately for their adherents, they don't work in the real world.

Here's a mileage table for the ten largest US metropolitan areas:











Bay Area






















































The shortest distance is New York City to Philadelphia, 110 miles; the longest is Boston to the San Francisco Bay Area, 3,130 miles. The median is Washington, DC to Houston, 1,370 miles; and the average is just slightly greater than the Dallas/Fort Worth to Los Angeles distance of 1,400 miles.

Assume a 2-hour penalty for using air travel, due to security check-in procedures and baggage retrieval, and that travel times to and from airports and train stations are identical.

Assume that the aircraft averages 360 mph and the train averages 45 mph. I got these values by looking up an LAX-to-LaGuardia flight on Newport Beach Travel and a NYC-to-Chicago train on Amtrak.

Then Tair = 2 hours + (distance/360) hours, and Ttrain = (distance/45) hours. Algebraic manipulation establishes that the breakeven point is only 103 miles! No pairs of large cities in the US are this close together.

What could make it worthwhile? Cheaper rates -- if the traveler's time isn't worth too much. Taking median annual household income and dividing it by the number of working hours in a year yields a figure close to $20 hr-1. Every train trip longer than the breakeven distance would need to charge $20 less than plane fare between the same two points for each extra hour of travel.

So a Boston-to-DC train, at 10 hours, vs a Boston-to-DC shuttle, at 3¼ hours, would need to charge $135 less. That's pretty steep, and outside the Northeast, it quickly becomes impossible; at the median distance of 1,370 miles, the discrepancy is over 24½ hours and the cost of the extra time is around $490. That's close to the round-trip airfare for that distance, let alone one-way. Over typical intercity distances in the US, train travel would have to be free of charge to make up for the value of the extra travel time.

Now suppose we expand the Acela Express to connect these cities with 150-mph trains. So Ttrain = (distance/150) hours, and the breakeven point rises to 514 miles.

Better, but still not great: only 9 of the 45 combinations of the 10 largest metro areas in the US are closer together than that. And outside of the various Boston-NYC-Philadelphia-DC pairs, the only possibilities are Chicago-Detroit, D/FW-Houston, and LA-Bay Area. Total track to be laid would be about 1370 miles -- the existing Acela system is 450 miles, but its track is not optimized for high speed and would have to be replaced also. The Federal Rail Administration's cost estimate for such upgrades is $5 million per mile, implying construction costs of $~7 billion.

In the real world, this would barely get the project started. Here's another estimate, this time from Amtrak, of "$7 million to $12 million per mile," which pushes the cost of 1,370 miles into the range of $9.6 billion to $16.4 billion. (And comparisons to highway costs are misleading, since highways are used by orders of magnitude more people; a highway with an average density of only ten persons per mile in each direction will handle [at 60 mph] 28,800 persons every day. Actual densities are much higher; rush-hour traffic with three lanes in each direction and vehicles 2 seconds apart implies 10,800 persons per hour. But the Acela Express ridership is well under 10,000 per day.) The California high-speed rail segment alone, less than one-third of the overall system, could cost $20 billion (admittedly with some frills). Reasonable estimates for the total would start at $50 billion -- for something that would carry only about one-fifth of the passenger traffic between just the ten largest cities.

It all makes about as much sense as going back to these. Hey, they'd work fine for the Midwest ...

Jay Manifold [7:21 PM]