A very amusing book

Here is yet another book I can thoroughly recommend. It was given to me as an 80th birthday present by friend Lothar, to whom many thanks.

The author is Randall Munroe, probably better known in the internet as cartoonist "xkcd", so the illustrations are in his stick-figure style. I already own three of his previous books, What If ?, How To and Thing Explainer all geeky. This one gives serious scientific answers to the most absurd questions.

The ISBN is 978-1-473-68062-3. Hardback with about 350 pages. Do go get a copy and you will enjoy reading it, as I did.

Copyright ^© Stu Savory on June 28, 2024 permalink Comments Email

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Pythagoras on a Sphere

Back in the old days of ancient Greece many people thought the Earth was flat (been reading too many Discworld^® novels probably). And so we got Euclidean geometry on a plane. Indeed, Pythagoras proved that A² + B² = C² for right-angled triangles only on planes; something we all learned in school. Here's my proof of Pythagoras' theorem :-)

Now imagine if Pythagoras had known that the Earth is a ball, not a plane. What would his theorem look like for a spherical right triangle? Certainly not A² + B² = C² !

First off, we need to define what we mean by a spherical triangle. A great circle on a sphere is any circle whose centre coincides with the centre of the sphere. Arcs of great circles are the shortest distance between two points on the surface. Long distance aircraft thus fly along arcs of great circles (ignoring the effects of winds), and ships sail along them too. There are four great circles in the sketch shown below.

A spherical triangle is any 3-sided region enclosed by sides that are arcs of great circles. If one corner angle is a right angle, the triangle is a spherical right triangle.

In a spherical right triangle, let C be the length of the side opposite the right angle (the hypoteneuse). Let A and B be the lengths of the other two sides. Let R denote the radius of the sphere (or Earth on our case). Then Pythagoras' Theorem on a sphere tells us that cosine(C/R) = cosine(A/R) * cosine(B/R). Now I won't bore you non-maths-geeks with my proof thereof and the maths-geeks can surely derive it themselves. Please note that as R goes to infinity the world gets flat and this equation devolves back to
A² + B² = C², as expected.

So when someone asks you about Pythagoras' theorem, just tell them cosine(C/R) = cosine(A/R) * cosine(B/R), after all, A² + B² = C² is just a special case ;-)

PS: I originally showed you this in 2009, so I am just repeating myself.

Copyright ^© Stu Savory on June 25, 2024 permalink Comments Email

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Dracarys!

"I prefer to think the dragon legends come down to us from a previous civilization that had mechanized, flying war machines like the A-10 Warthog. After that civilization collapsed and the art of heavier-than-air aircraft was lost, how would you explain something like an A-10 to your kids? "There were fire breathing monsters that flew through the air and destroyed everything in their path". That's how."

Later, he did a post detailing how (wing area vs. mass) dragons flew etc, do go read it please. But I decided to follow up on the Warthog idea, as follows.

The A-10 Warthog is a plane carrying a really big Gatling gun. Or it is a really big Gatling gun which happens to be carried by an airplane, in the nose.

The Warthog will do a low-altitude strafing run at 300 Knots and, if it were to use all of its ammunition at once, would use it all up in just 17 seconds. Here is the maths I did. The plane flies at about 300 knots usually (roughly 156 m/sec) and weighs some 19 tons. The magazine can hold 1350 rounds, each weighing about a pound, of which the bullet weighs lets say 200 grams (guessing, in the absence of me knowing the facts). Muzzle velocity is Mach 3 = 1000 m/sec. So 1350 * 0.2 * 1000 = 270,000 kg-m/s of bullets' momentum, divided by those 19 airplane tons implies 14.3 m/sec = about 28 knots of deceleration for firing all that ammo; more when the bigger magazines were later introduced. So 300-28 = 272 knots speed at the end of this example Dracarys run.

After the strafing run, the Warthog pulls up sharply to get out of enemy ground fire. But just how sharply? Well stall speed for a Warthog in level flight is given as 120 knots, but stall speed increases with the square of the G-loading of the pull-up. Now 272/120 = 2.27 and 2.27²= 5.1529, so let us say a 5G pull-up would stall the plane. Even I could pull 5G when doing aerobatics in the Pitts biplane, but fighter jocks with the G-suits (inflatable trousers) regularly can pull 9 G, so would have to be careful not to stall the Warthog.

BTW, 17 seconds of firing at an average of 286 knots implies the target is a tank/vehicle column about 2.5 km long and straight, unlikely even for Russian tanks (do they have that many left?). So this is an unlikely scenario. And do you know why the Mother of Dragons uses the command Dracarys? Because Supermarine had already taken the English translation "Spit Fire!" ;-) And why Mother of Dragons? Well, Lockheed had already used the name Dragon Lady for their U2 spyplane ;-)

Comments (4)
Chuck added " I added a link to my post." Thanks, man!
Cop Car wrote " The A-10 is among my favorite aircraft, having worked with it on the Rapid Runway Repair program in 1981-1983. Hunky Husband and I saw one in action a few years later at Edwards AFB California. It was impressive how it could rapidly attack the same target by looping between attacks." Nice jock tactic, never occurred to me. BTW, what are female jocks called?
Cop Car wrote again, saying " I asked this question of an A-10 pilot at the Stewart, FL airshow. His response was that the recoil from the guns wasn't noticeable. However, the exhaust generated by the spent shell casings (smoke, particulate) tended to get into the engines and cause issues. Hence the relatively short bursts followed by periods of non-firing to let the engines clear." I was just doing some mental arithmetic, CC.
Pergolator joked "Female Jocks ; Jockettes? Note that male pilots sit in the cockpit while female pilots sit in the box office." That's rather Macho.

Copyright ^© Ole Phat Stu on June 21, 2024 permalink Comments Email

A short history of photography

The oldest photo Wikipedia knows about is from 1826, a French photo of a view from an upstairs window, using bitumen as the medium. Pinhole camera, exposure time was about 9 hours. In 1837 a pinhole camera took the first photo made in Germany; the photo is of the Frauenkirche (Our Lady`s church) in Munich, taken in March of 1837; exposure time was several hours. Sepia.

1860 saw the first aerial photo taken from a tethered balloon over Boston, Mass.

1861 : First colour photo. Tartan Ribbon, taken by no less a person than famous physicist James Clerk Maxwell in 1861, based on his 1855 research.

1882, showing Navajo youth Tom Torlino as he started the Carlisle Indian Industrial School (USA) and 3 years later, first Indian graduate there afaik.

Another Black and White (sic!) photo. George Mclaurin, first black man to be admitted to the University of Oklahoma. It was 1948 and US was still segregated, so he had to sit separated from the white students.

1978 saw the start of Microsoft, who bought 86-DOS 1.10, renamed it MS-DOS.

Our most recent photo, SWMBO and I on my 80th birthday; photo by Andreas.

Comments (2)
Billions of Versions... wrote "The George Mclaurin picture is a sad reminder of the past." Very true.
Cop Car wrote, educating me about college education among Native Americans " First Native American graduate of Harvard University: Caleb Cheeshahteaumuck (Wampanoag) in 1665; First Native American admitted to West Point and first Native American graduate: David Moniac (Muscogee) in 1822; First known Native American person to earn a Western medical degree from Western college: Wa-o-wa-wa-na-onk (Cayuga) in 1844. . . . ." But I do not have a photo of them, CC.

Copyright ^© Ole Phat Stu on June 16, 2024 permalink Comments Email

That pale blue scythe

While I was AFK over the past few weeks the scythe of the grim reaper took Hilde (Prof. Dr. phil), she was just 6 months older than I am and it also took Johannes (67); his ashes were scattered from an ultralight flying over Lake Geneva in Switzerland, a true pilot's burial. RIP both.
Comments (1)
Jenny (Ibiza) said "What makes you think the scythe is pale blue?" Novels by Terry Pratchett.

Copyright ^© Ole Phat Stu on June 14, 2024 permalink Comments Email

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Monday, June 10

Biker Birthday Bash

S aturday afternoon our street was permeated by the sound of rolling thunder as a dozen biker friends (un)surprisingly came to celebrate my 80th birthday. Luckily we had good weather and so could use the back garden. Here are some of my photos.

L2R: Matthias, Andreas, Dieter, the other Matthias.

On the left: Peter and Rüdiger

Frank with Marion

L2R: All in profile, Thomas, Marion, Dirk, Hans-Jürgen

Marion, Matthias, Dieter, Hans-Jürgen, Dirk, Volker, Thomas listen as ...

..... Matthias reads his self-written Laudatio poem.

And I just bask in the sunshine as his Laudatio is read.

After all had gone, SWMBO relaxes in the hammock.

Comments (1)
Billions of Versions... asked " Where's the picture of all the bikes?!" Didn´t take one, sorry. They were all too, too, too clean!

Copyright ^© Ole Phat Stu on June 10, 2024 permalink Comments Email

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Saturday, June 8

Octogenarian

Turned 80 today. Hurrah! Having been ill recently, I didn't think I was going to make it. Subdued party tomorrow, so photos to follow.

Comments(12)
Cop Car wrote " Happy Birthday, Stu, somewhat late. It’s my computer’s fault. Knowing that I had a full month scheduled for June, I had input your birthday on my calendar so as to be reminded. Of course, I managed to wipe out the whole calendar and did not get that date re-input. Hope you had a good one, even if you don’t sound as if you are at top form. We octogenarians welcome you to our fold." Thankyou.
Kate (UK) wrote " Hi Stu just wishing you a very happy 80th birthday...." Thankyou.
Mostly Cajun wrote " Happy birthday, my friend. I’m six years behind you. Best wishes for your next year." Thanks, Dale.
Monika und Bernhard (D) wrote " wir gratulieren Dir sehr herzlich zu Deinem heutigen Geburtstag. Dir alles Gute fürs nächste Lebensjahrzehnt." Ich danke euch.
Jenny (Ibiza) said "You beat me there, well done!" Stay safe, lass!
Anon sent this explanation :

Peter Harris (UK) wrote "Happy Birthday, Octoman!" Thanks.
Dirk R. (B) whom shares with me an obsession with cryptography, wrote " Happy birthday… although, that’s historically and mathematically, long time ago, in some maternity ward. Still an odd phrase/expression. I whish you many more years alive and kicking, but since your still young, you have at least 20 years ahead before becoming adult ;-]..... ....this on one big KL-7 page (fortunately with a menu). See One big KL-7 page . Hoooooowever, If you prefer to polish your motorcycle, no problem." Sold my motorcycle, due to my arthrose. Now have a Porsche 944 Oldtimer.
A couple of dozen bikers turned up (un)surprisingly for a beer etc and several people called on the phone. Photos of the bikers tomorrow.
Billions of Versions... wrote " Happy belated birthday. I'm about 2 1/2 years behind you. " Thanks Mike.
Marie (A) sent this piccy she found on the web of other octogenarians :

Bruce wrote "80? So you've caught up with Keith Richards. I'll catch up with you in September, but tS06:43:16 AM then Keith jumps ahead in December. For me saying 80 is a shock. A little pride that I'm that bad because the good die young. A little sad because it's a clear signal to the ladies that I'm out of the running. So happy belated birthday and wishing you many reruns." Thanks, stranger.
Comrade Misfit wrote " Belatedly, happy birthday Stu." thanks, Stinson Gal! Fly safe!

Copyright ^© Ole Phat Stu on June 8, 2024 permalink Comments Email

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Link to the previous month's blog.

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