August 30, 2014

Fram and Vasa

On our two-weeks trip across Scandinavia, spending three days each in Oslo, and Stockholm, I got a chance to see two legendary Nordic ships: Fram and Vasa. Separated by 265 years, with one being the first ever to go closest to both geographic poles in human history, while the other sank after sailing only twenty minutes into its maiden voyage. Yet they both capture public’s imagination like few other. In the case of Fram, it is not hard to see why.


Well funded marine expeditions began around mid-nineteenth century to find a new northwest sea passage through Greenland interior or the Canadian arctic archipelago to the Pacific towards the riches of Asia. Successive attempts, however, were met with one disaster after another. Nearly everyone who tried, could not go past frozen waterways of the archipelago. The wooden boats were no match to the formidable crushing pressure of sheet or pack ice.

Despite these challenges, the British explorers managed to chart greater parts of the region from their successive failed attempts, and documented what worked and what didn’t. While this went on, in 1888, Fridtjof Nansen’s early success in penetrating Greenland’s inland ice, at 27 years of age, grew his ambitions of reaching the North Pole. Nansen handed the arduous task of building a custom ship for this extreme adventure to Scottish-Norwegian shipwright, Colin Archer. Archer then went on to design Fram featuring a belly-like hull of extraordinary strength, using strongest oak timbers and well braced intricate system, with an awkward 3:1 length to beam ratio, so it would slip up from pack ice’s wedge-like grip.

In March 1895, Fram (Norwegian for Forward) reached a never-before achieved latitude of 84°4’N. With unreliable drift thereafter, Nansen then made a final dash towards to North Pole on skis and dog sledges. The last mile is excruciating just to read, and I cannot imagine a worse expedition — weather wise. He eventually turned back just shy of 3°46’ — approximately 230 nautical miles south of North Pole. Miraculously or by design, Fram survived the worst on its return voyage before sailing south to Tromsø. It made Nansen and Fram legends, but Nansen would never sail again. The arctic crushes the toughest, as they say. Nansen’s pioneering techniques of travel and survival would come to influence all subsequent explorations.

Inspired by Nansen’s achievements and techniques, Roald Amundsen in 1906, after three years of trying, achieved a break-through in successfully navigating across the Canadian arctic archipelago and found the north west passage in a similarly proportioned 45ton fishing vessel Gjøa, thereby proving to the World that Pacific could be reached via the archipelago. Four years later, Amundsen would take the Fram (used by Nansen for his North Pole expedition) to a South Pole expedition. In this expedition, Fram reached the farthest possible latitude of 78°41’S before Amundsen and team began the rest of the journey on sledges and skis to the South Pole, successfully reaching it on 14 December 1911.1

Standing humble in an understated museum belies their incredible achievements in history. We took the kids to see Fram and Gjøa stand every inch proud at their home in Oslo, the Fram museum this August.2


If Fram was a boat for the nordic polar conquerors, Vasa was an unprecedented tragedy — of very low metacentric height, of over-reliance on geometric proportions, of high ambitions, of immaturity in the art of naval architecture, of fear of breaking unfavorable news to the king of Sweden, and of poor judgement of ballast by its captain.

Sweden was fighting its two great foes: Denmark — to reduce its navigation tax, and Russia — to open up its markets. Prior to Vasa, Sweden lost twelve of its large vessels in the 1620s — one captured, one self-destroyed while resisting capture, and ten ran aground in the Bay of Riga, prompting the king to urgently seek replacements to keep up the pressure in the Baltic.

Armed to gills with two gun decks full totaling an unprecedented sixty-four bronze cannons, specially cast in Stockholm, the ambition and intent of Gustavus was fierce. An operational Vasa as a destroyer would have been a terror of the Baltic, where it was to rendezvous with the king’s fleet, striking fear into the hearts of Sweden’s enemies.

Through changing specifications, an ill shipwright, poor change management, and shortened delivery date due to urgent pleas from the battle field, Vasa is built despite failing a stability test (third run stopped as Vasa begins heeling and heaving violently as 30 men run back and forth on the top deck to test) conducted by Rear Admiral Klas Fleming.

Just as it set sails from Stockholm port on August 10, 1628, catching the southwest squall, Vasa begins heeling hard over its lee side to the extent that lower gun ports begin taking water so much that it finally sinks into seabed. The crux of this tragedy is succinctly summarized in a paper by Richard Fairley and Mary Jane Willshire:

Methods for calculating the center of gravity, heeling characteristics, and stability factors for sailing ships were unknown, so ships’ captains had to learn their vessels’ operational characteristics by trial-and-error testing. The Vasa was the most spectacular, but certainly not the only ship to capsize during the 17th and 18th centuries. Measurements taken and calculations performed since 1961 indicate that the Vasa was so unstable that it would have capsized at a heeling over of 10° it could not have withstood the estimated wind gust of 8 knots (9 miles per hour) that caused the ship to capsize. Recent calculations indicate the ship would have capsized in a breeze of 4 knots. That the wind was so light during the Vasa’s initial (and final) cruise is verified by the fact that the crew had to extend the sails by hand upon launch.

What’s remarkable about Vasa though is not how it went down, but after 333 sunken years, when it was raised in 1961 in a televised national effort, it turned out to be over 90% intact! The theory is that the sheltered Stockholm harbor, and Baltic Sea’s low salinity prevented worms from destroying the wooden vessel.

The effort of Vasa’s preservation is admirable, and one can see its majestic stature its exquisite custom wooden carvings and embellished sculptures reveal. Aside from being a deadly machine, it was beautiful art, capturing seventeenth century culture and sophistication. We spent half a day looking at the impressive Vasa this August in Stockholm.

  1. His British counterpart Robert Scott reached over a month late, and unlike Amundsen and team, he and four of his crew did not survive the return journey to base. 

  2. Low light iPhone photography is hard. If not for my lovely wife’s numerous photos of the Fram, I wouldn’t have had a decent picture. 

July 31, 2014

S-N curves

In order to set a suitable design criteria, I was looking to compare two classes of S-N curves for a fatigue design, viz., E and F2, and I could not find a handy plot to refer to. The basic S-N curve equation is as follows, which one may know is from Paris-Erdogan law (fracture mechanics):

N = k1 * S^(-m)

The standard does describe it in its logarithmic form, which is as follows:

log(N) = log(k1) - m * log(S)

and then it goes on to furnish its two sets of key components that form parts of the equation — highlighted below.

Playing with logarithms is fraught with error, as they are not the same as plain algebra — Leonhard Euler’s gift to the world, which reminds me I should jog my memory from high-school. Anyway, not to waste any time, I pulled Calca, punched in the basic equation, and then, case after case, I provided the variables from the table above. Calca, in turn provided me with an equation ready to be pasted in Grapher for a ready plot. Here are those equations for all available S-N curves.1

# Basic S-N curves
# Basic representative S-N curve is of the 
# form (where, x is Number of cycles, and
# y is S Stress range):

log(x) = a - m * log(y)

# a = log(k1).

# Seawater with adequate corrosion protection

For TJ curve:

a = 12.18 # for N =< 1.8E6
m = 3     # -- do --
y => -0.33 * log(x) + 4.06

a = 16.13 # for N > 1.8E6
m = 5     # -- do --
y => -0.2 * log(x) + 3.23

For B curve:

a = 14.61 # for N =< 1E5
m = 4     # -- do --
y => -0.25 * log(x) + 3.65

a = 17.01 # for N > 1E5
m = 5     # -- do --
y => -0.2 * log(x) + 3.4

For C curve:

a = 13.23 # for N =< 4.68E5
m = 3.5   # -- do --
y => -0.29 * log(x) + 3.78

a = 16.47 # for N > 4.68E5
m = 5     # -- do --
y => -0.2 * log(x) + 3.29

For D curve:

a = 11.78 # for N =< 1E6
m = 3     # -- do --
y => -0.33 * log(x) + 3.93

a = 15.63 # for N > 1E6
m = 5     # -- do --
y => -0.2 * log(x) + 3.13

For E curve:

a = 11.62 # for N =< 1E6
m = 3     # -- do --
y => -0.33 * log(x) + 3.87

a = 15.37 # for N > 1E6
m = 5     # -- do --
y => -0.2 * log(x) + 3.07

For F curve:

a = 11.40 # for N =< 1E6
m = 3     # -- do --
y => -0.33 * log(x) + 3.8

a = 15.0 # for N > 1E6
m = 5    # -- do --
y => -0.2 * log(x) + 3

For F2 curve:

a = 11.23 # for N =< 1E6
m = 3     # -- do --
y => -0.33 * log(x) + 3.74

a = 14.71 # for N > 1E6
m = 5     # -- do --
y => -0.2 * log(x) + 2.94

For G curve:

a = 11.00 # for N =< 1E6
m = 3     # -- do --
y => -0.33 * log(x) + 3.67

a = 14.33 # for N > 1E6
m = 5     # -- do --
y => -0.2 * log(x) + 2.87

For W1 curve:

a = 10.57 # for N =< 1E6
m = 3     # -- do --
y => -0.33 * log(x) + 3.52

a = 13.62 # for N > 1E6
m = 5     # -- do --
y => -0.2 * log(x) + 2.72

And finally, here’s the plot I was looking to generate. (The black lines are TJ, green lines are E, and red lines are F2 curves.) Grapher makes it easy to switch curves on and off — using check marks in the equation side bar.

  1. It’s just awesome to punch in any equation in Calca, even if it’s a complicated LHS in order to get a solved output. MathCAD cannot do this; Matlab cannot do this; and Maple cannot do this — at least the last time I checked. 

July 27, 2014

OS X on external volume

Maintaining hardware, the women in our lives have assumed, is a man’s job. So, just when the handyman (i.e., I) took his hands off maintaining the family iMac was when things started going south. It was barely a day after a full rsync backup of Users folder to an external FAT drive — no time to fuss around with permissions crap, and since SuperDuper! decided it couldn’t/wouldn’t (I don’t care) do this job; I am so not kidding! — that the computer’s hard drive failed completely. No recovery volume, no primary volume. Kaput, as they say. Lost NVAlt notes, kiddy journals in Day One, et al.

I installed OS X via the internet recovery, not knowing it was the hard drive, since Disk Utility gave the drive a clean chit, and it failed again the very next day. The boot would take 5 hours. My wife actually turned the iMac on, and for her dogged loyalty decided to wait for 5 hours just to print something, when I had already pulled out our backup computer running Elementary OS that literally boots in 5 seconds and ready for use on a 2GB Intel Atom D525 Processor — for heaven’s sake! (The iMac has 8GB and is Core i5 2.x something; for the household work, this is my new measure of efficiency.)1

I called up a local authorized reseller, who also provides some sort of unofficial Genius support, and this is the conversation I had on the phone:

Me Hello. Hi, could you connect me to the service please, I have an issue with my iMac?
Operator Hold on.
Service Yes?
Me Hi. I am having booting issues with my 27” iMac (Mid 2010). It takes a long time to start. I’ve already formatted the drive, and reinstalled OS X afresh. The problem persists.
Service You have to bring it in, and we take a look.
Me If in case it is the hard drive, would you be able to replace the normal hard drive with an SSD?
Service No. We look at it first, get the serial of the component and order the same again. It will take two weeks to place the order.
Me Not even if I am willing to pay for an SSD?
Service No.
Me I see. OK, thank you.

At this point, I was about to trash the iMac, power it down, and leave it near the trash can, when I decided to have one last go to see if this thing could be powered by a USB powered external hard drive as its primary volume.

  1. Initiated Recovery with Cmd + R upon the boot sound — holding it until the system entered a recovery mode.
  2. The recovery mode then downloaded OS X Basic system to perform necessary disk operations.
  3. I attached an external hard drive and followed these instructions.
  4. Further, I also formatted the internal problematic hard drive to FAT, so the iMac wouldn’t mistake it every time as the first drive to boot from.
  5. Once installed, the iMac now automatically boots from the external drive.

It’s been five days since, without fuss, and it’s working more or less as it has been for the last four years.

One immediate conclusion I can draw from this experience is that no system is immune to failures of the hard drive — they are never built to last longer than five years on average, especially the spindle-platter-head types.2 The other and perhaps more interesting conclusion is that OS X, like linux, supports running the OS from an external hard drive, which it should be noted, without the need for any hacks (even supported officially), which Windows is incapable of. The beauty of an OS on a stick or an external drive is often understated. Pull it out of one system and connect it to another, and the OS effortlessly remaps the new hardware, and preps it ready for you to use. That’s only possible with modular operating systems like linux or BSD upon which OS X is built.

PS: My real complaint with Apple is that with Genius support not universally available, making computer’s hardware3 inaccessible for replacement without special tools that are not easily available is really a bummer. Given its care for the environment, despite being a hardware company looking to sell, I do not believe Apple wants people to upgrade to a new computer just because one crucial component fails. This is perhaps a legacy of preventing hacks from Apple’s early days — Jobs’s hands-off-the-internals finger to the user. It has run its course; these days the people who really want to try doing this are largely doing it not to tinker with the hardware, but for economic, speed, and to a lesser extent, environmental reasons.4 So, I think new hardware casing design should allow easy upgrade of parts like RAM, and hard drives — at least in large computers that cannot be easily hauled to the shop, and for people that do not want to get rid of computers they love just because of the commonly failing component like the hard drive.5

  1. By putting processor speed against hard drive performance, it should be obvious that I am ranting (because they are not comparable) — just getting my frustration out. 

  2. My first laptop died of a hard drive failure. Windows could not run on a USB, and linux bought me time when I could not afford a new computer. 

  3. Especially integrated desktops like the iMac, where there’s an incentive to keep the computer longer for its well functioning large screen, and most of other good parts. 

  4. There are better avenues these days for idling. So, the person looking for the right set of screw drivers instead of browsing facebook is really looking to solve his or her problem. 

  5. I have rarely heard of parts other than the hard drive that is most consistent in failures.