Math, Engineers, Bridges, and Hand Waving

31 05 2012

By Steve Tung

After seeing the alarming video of the Minnesota I-35 bridge collapse in class today, I’m reminded from my recent reporting on the flattening of the Golden Gate Bridge 25 years ago on how flexible numbers can be. Searching for a simple detail revealed how much hand waving goes on that I hope is reserved for the press and not actual analysis.

In 1987, hundreds of thousands of people crammed onto the iconic Golden Gate Bridge. Image from wikimedia commons, taken by Cary Bass.

To quickly summarize: hundreds of thousands of people crossed the Golden Gate Bridge on foot to celebrate its 50th anniversary. The weight, more than two times of cars in bumper to bumper traffic, was enough to make the middle sag 7 feet, flattening the suspension bridge’s slight curve.

The number I was looking for was pretty simple: just the amount of weight the bridge was designed to support. The original design load of 4,000 pounds per foot of bridge is pretty well documented, but renovations during the mid-80s removed a dense concrete layer and replaced it with lighter and stronger steel frameworks. Those renovations should have boosted the design capacity of weight, and I just wanted to know what it was. But no one I talked to (including officials and engineers that oversee the bridge) could tell me what that new number was. More surprisingly, three of the four engineers I talked to for the story gave me starkly different ideas about the bridge’s strength and how to think of it that day, none of which particularly agreed with the chief engineer’s numbers as reported by the Merc at the time. (The other engineer I talked to recused himself from analysis because he wasn’t familiar with the Golden Gate’s particulars).

Off the bat, all the experts agreed that it would be practically impossible for the Golden Gate to break and drop people to their deaths from simply cramming more and more weight onto it. But they disagreed at the point where

the bridge would start getting damaged– at what load metal might start to permanently bend (like a bent paper clip), rivets might break, joints get overstressed, all which would require maintenance.

According to the Merc’s story in that era, the day after the bridge flattened, the bridge’s chief engineer said that the bridge was no where close to being damaged. He said that the bridge was designed to hold 5,700 pounds per foot of bridge, while the crowd weighed about 5,400 pounds, using rather generous estimates. But even then there’s a buffer where the bridge can gain even more weight without any deleterious effects. Some engineers call it the factor of safety. “There’s no way we could have gotten enough people on the bridge to cause any problem,” the chief engineer said at the time.

But now, one engineer insisted that the bridge was close to being damaged. Partly because the bridge flattened, which should never happen, he said, and also because he estimated that the weight on the bridge was substantially higher than the standards set by AASHTO (the wordy American Association for State Highway and Transportation Officials), which he didn’t think the Golden Gate far exceeded. He said that the load already significantly intruded upon the factor of safety, and was close to completely exhausting it. But he also said that because the bridge went back to its original shape, that was a sign that it wasn’t permanently damaged.

Another engineer, who analyzed the bridge in the years after the bridgewalk, remembered that the load on the bridge was about the same as the design load. But his concept of factor of safety was a little bit different. Dipping into the factor of safety meant that the bridge would start getting damaged, but not completely fall apart. In a way, this idea is similar to the previous idea that the bridge was being close to damage, but the difference of such a simple, standard idea, was a little odd.

The current chief engineer gave me a far different answer, saying that the bridge is and was capable of being completely filled with 36 ton, 28 foot long trucks, which would be far heavier than the 1987 crowd of people. Rough calculations would put that capacity at more than 15,000 pounds per foot of bridge, more than 2.5 times the 1987 estimate. On top of that there’s an additional safety factor which would put that capacity through the roof, before the bridge would begin to get damaged. In short, the engineer said, there was no practical way to put enough weight on the bridge to get it to crack.

Now all of these experts are pretty well established– they’re either professionals who design or analyze bridges for a living, or professors at prestigious universities. What are we to do if they can’t agree on what seems to be a pretty straightforward concept?


Open Source Nuke Hunting

30 11 2011

As my internship at the Monterey Herald came to a close today, I can’t help feel a little a bad for all of the amputeed pages and pages of research in my longer stories that were on the wrong side of the cut.

The latest information to suffer this fate is from a story about Tamara Patton, a graduate student at the Monterey Institute for International Studies, who’s 3d modeling nuclear processing facilities using self-devised methods.

Nuclear Programs Worldwide As of 2005 (Red means a "Nuclear Weapon State" by the Nuclear Non-proliferation Treaty, Orange are other nuclear powers, Yellow are countries suspected of having nuclear weapons or programs, Pink are countries known to at one time have a nuclear weapon or a program. Courtesy of Wikimedia Commons.)

Now, modeling nuclear sites in 3d is not new, she told me. But apparently it is usually used by organizations like the International Atomic Energy Agency to determine where to place surveillance cameras and to plan inspections ahead of time, so they can optimally use the limited time they do have while physically on-site. With a virtual avatar, they can walk around a virtual building, like second-life or a videogame.

What is unusual is that she’s done this all using publicly available tools and resources. Google SketchUp provides the interface to push and pull shapes around to make three dimensional objects. Google Earth provides satellite images that she uses as the templates for her models. Though the overhead view by Google Earth doesn’t provide as much detail as close-up, on-site photography, Patton analyzes the shadows from the limited photographs combines them with time of day and location to accurately determine height.

She’s used her techniques to provide evidence that a textile factory is really just a textile factory and to help determine the production capacity for a nuclear facility of Pakistan.

It’s part of a new wave of intelligence where citizens without access to special tools or restricted information can participate, said Assistant Secretary of State Rose Gottemoeller of the Bureau of Arms Control, Verification and Compliance, in a speech at Stanford on Oct. 27 titled “Arms Control in the Information Age.”

There she asked:

Can we incorporate open source information technologies and social networking into arms control verification and monitoring?

What does she mean by this? She thinks that large groups of people can work together to either generate new sources of information gathering of dangerous weapons or provide deeper analysis of existing information.

Looking for nuclear materials in the digital age (Courtesy of Wikimedia Commons)

For information gathering, she cites the Defense Advanced Research Projects Agency Red Balloon challenge as an example, where the agency offered a $40,000 reward to the first team to find 10 identifiable red weather balloons moored throughout the country (Out of 4,300 teams, an MIT team won in under 9 hours).

Then she extrapolates it to arms control:

Now, how could something like this work in an arms control context? Let’s just imagine that a country, to establish its bona fides in a deep nuclear reduction environment, may wish to open itself to a verification challenge. It could seek to prove it was not stashing extra missiles in the woods, for example, or a fissile material production reactor in the desert.

Of course, it sounds like there are a lot of potential holes in the challenge– blocking access, intimidating participants, fabricating results, plus the entire idea of offering an incentive not to find something– but she invited the audience, future members of the intelligence community, to come up with solutions.

The other half of her proposal was to use open source solutions to analyze publicly available information. In addition to Patton’s work, Gottemoeller cited the work of Laila Shereen Sakr, who predicted the fall of Libyan towns and cities hours beforehand, by building software that analyzed tweets from twitter and finding trends in hashtags.

It’s a far different way to do intelligence.

Bigger Birds in Central California?

11 11 2011

By Stephen Tung

Ever since I wrote that mongabay article about the invasion of monster King Crabs that will apparently wreak havoc on life on the Antarctic shelf, I’m a little apprehensive of any climate related changes that cause different, potentially disastrous, animal behavior or morphology.

Big Birds may eventually take over? (Courtesy of wikimedia commons)

So I was a little worried when I read that birds are apparently getting bigger in the central Californian area.

A team led by Rae Goodman from San Francisco State University studied data of bird populations of 40 years at one site and 27 years at another and found that, slowly but surely, bird wing length increased. Body mass didn’t always change, but when it did it went up at about the same rate as wing length.

Don’t panic yetthe rates seem to be fairly small: wing span increases 0.024 – 0.084 percent per year, while body mass seems to increase at most 0.040-0.112 percent per year, which means at that rate, they’ll only grow as much as 11.8 percent in a century. But what is more noteworthy is that it seems to go against an established idea that bird size decreases as temperature increases.

The strange thing is that it doesn’t seem to be happening across the United States. A paper published in 2010 studied passerines populations in Pennsylvania spanning 40 years and found that wing size actually decreased.

According to the paper published online on Oct. 12 in Global Change Biology, there are competing interpretations of how climate change affects what is known as Bergmann’s rule. The 1847 rule states that for animal populations of the same genus, body mass is higher the farther away from the equator. Some researchers have taken that to mean that larger birds can conserve heat better and do better in cooler climates, and so body size of observed populations will decrease as it warms as birds migrate to cooler weather.

A Maryland passerine in Great Falls National Park (Photo by Stephen Tung)

Some have interpreted that to mean that larger birds do better in more severe weather because they can fast and stay sheltered longer. If climate varies more often, then birds need to be able to store more food in case of extreme events.

On top of that, other researchers have interpreted it to mean that food availability is the primary cause of Bergmann’s rule. Under this interpretation, it depends on the region of whether body size would increase or decrease due to climate change.

To get to the bottom of it, researchers studied data of bird populations from two sites: 14,735 birds from Palomarin Field Station, and 18,052 from the San Francisco Bay Bird Observatory. Data spanned 40 years for Palomarin site (from 1971-2010) and 27 years for the Bay site (from 1983-2009).

They studied a variety of species of passerines (perching birds that make up 60 percent of all species of birds, and 40 percent of all families), finding that wing size increased over time. Body mass increased in some cases over time, but not significantly for some groups. The researchers suspected body mass varied more than wing size, even after compensating for fat levels and time of day.

According to the researchers, temperatures steadily increased at both of the sites. They reason if changes body size responded only to temperature then they would have expected the results to be the same as those in Pennsylvania. They concluded that it couldn’t just be temperature that determines species size and that it’s likely that the other two explanations play a part, which would be caused by climate change.