Bang Bang, He Shot Me Down Bang Bang, I Hit the GroundBang Bang, That Awful SoundBang Bang, My Baby Shot Me Down

Technically, ballistics is the science of how projectiles travel in flight. Forensic Ballistics is a misnomer since it doesn't concern itself with a projectile's flight but rather about analyzing the firearms used in crimes. Perhaps, ballistic fingerprinting is a slightly better term. Ballistics is actually a subset of the forensic science of Toolmark Analysis. Guns are a tool and ballistics experts study the marks left on bullets by the guns. I'll explain this as we go.

Bullets are made up of three components: primer, propellant (held in a cartridge) and the actual bullet.

The primer is a shock sensitive explosive – it will detonate if struck or if a spark occurs. The primer is kept in a tiny cup in the cartridge's head. The gun's hammer has a pin on it which directly strikes the primer. The detonation goes through a small hole in the cup and ignites the propellant. The explosion in the confined area forces the bullet out the barrel. By Newton's Third Law when the bullet explodes out the barrel, the cartridge must recoil backward. A piece of metal in the gun, called the breech, stops the cartridge from flying into the shooter's face.

Pause for a moment and realize that the hammer striking the cartridge will undoubtedly leave a mark and that you could most likely tell the gun manufacturer from this mark alone. Additionally, The breech will leave a mark on the head of the cartridge. Finally, an extractor will grab the cartridge and eject it also leaving another set of traceable markings. Back to the bullet:

The bullet is now cruising through the barrel. Back when guns were first invented, the projectiles would be very unstable and tumble in the air. This made them extremely imprecise. Rifling changed all this. The barrel of the gun is given a set of helix grooves. The heat from the gun powder causes the bullet to expand slightly. It expands into these grooves and then gets locked into the tracks. When the bullet comes out of the barrel it is spinning! Get it?

Why spinning? Because the spinning adds stability (and reduces air friction apparently). Consider a spinning top. It is very hard to knock off course compared to non-spinning top. We already discussed this when we talked about boomerangs.

But clearly, the grooves have dug into the bullet. By comparing the marks on a bullet found at a crime scene to a bullet fired from a confiscated gun, an expert can determine from these marks whether or not the bullet was fired from the suspected gun.

The data from ballistic forensics is not just class evidence but can also constitute individual evidence. Every time the bullet goes through the barrel it changes the rifling grooves, just as they change the bullet. The scratches and imperfections cause each ballistic fingerprint to be different.

There are a couple of things to be aware of:
Just because two bullets were fired from the same gun does not guarantee that the markings will match. Rust build up can change the stria or repeated firings of the gun will cause an evolution of the stria – imperfections in the bullet alter the groves in the barrel or the barrel of the gun could be replaced or purposely altered.

PS It seems fitting to add that if you want to read about Batman's relationship with guns rather than forensic ballistics you should check out the definitive post over at Silver Age Comics.

Batman's Fingerprints

Pattern evidence (or here) is the oldest branch of forensic science, although it's use as individual evidence. Individual evidence is any object which can be said to come from a one particular source. There is no chance (no whatsoever, wink) that it came from any other source. The pattern evidence covered in Jay Siegel's beginner's guide are:
Finger Prints,
Firearms,
Handwriting,
Accelerant Residue
Blood Splatter

Other kinds of individual evidence include paint chips, fractured fragments of glass and of course DNA. Individual evidence should be compared to class evidence. Class evidence can not be associated with any one particular person or source. Class evidence is still useful of course. Hair and fibers are class evidence. So is ink and dye or certain physical characteristics of drugs. Show prints or tire tracks might be class evidence. Class evidence is tied to groups not to individuals.

Finger prints, forensic ballistics (a term the author has a problem with) and handwriting are all supposed to be individual evidence. They are all supposed to be able to identify whether or not a potential source has produced the piece of evidence.

Despite the fact that forensics has been using certain types of pattern evidence for over 100 years, it can justifiably be criticized. Pattern evidence can grouped into the so called “experience-based forensic sciences”. Since there can be no absolutely quantitative analysis of these, forensic “scientists” who work with these types of evidence rely on experience and judgment. That's hardly what I would refer to as hard science.

Finger Prints
Finger prints are pretty cool. You have them on your fingers, palms, toes and souls. We've all stopped to look at them in our life but have you ever wondered what they might be for? They add traction to your grip so that you can hold on to things better. The ridges appear during the eighth week of a pregnancy and remain unchanged (other than growing in size, unless of course they are artificially altered which by the way just makes identification that much easier, duh) throughout a persons entire life. The root of the ridges is in the middle layer (called the dermal papillae) between your dermis and epidermis.

Finger prints are not determined by your genes (cough... not completely determined by your genes). Identical twins have easily distinguishable prints. People argue that it is impossible for two people to have the exact same set of finger prints (although how they would have legitimate statistics on this is beyond me). In any case, finger prints are usually an acceptable form of individual evidence.

When the surface of your skin comes in contact with a surface (glass, plastic but even paper and fabric) biological (like perspiration, skin cells or proteins) and alien (like ink or oil) material is left behind forming a latent print. If the print is visible to the naked eye and needs no amplification, it is called a patent print, such as if it were left in paint or blood. If the print is actually impressed into some matrix (like wax) then it's called a plastic print.

When they are latent (i,e, invisible) they must be found. Smooth surfaces can be dusted or fumed with superglue. Magnetic powders can be used for surfaces with fine texture. Dusting isn't the only way. Chemical fuming with iodine creates temporary reddish images which must be photographed. Silver nitrate can be applied to latent prints as a aqueous solution but therefore can't be used on surfaces that can't get wet. Ninhydrin can be sprayed onto latent prints. It reacts with amino acids to forms a a colored compound. Ninhydrin even works on porous surfaces (i.e. paper!). Laser luminescence can also be used.

So they can find them but what do forensic scientists see? Fingerprints are made up of various topographical elements.

1) The print will have a sort of pattern. There are four major patterns: either the ridges loop, arch, tent or whorl. The four general types are typically broken down into eight patterns which can be seen in the figure.

2) Besides the general pattern there are little details in the ridges, called “minutiae”. Ridges can do all kinds of things:
Bifurcations - when ridges split (trifurcations occur too)
Ending Ridge – self explanatory
Dot – a tiny round island
Short Ridge – a small isolated segment
Enclosure – when a ridge bifurcates and then reconstitutes

3) And looking at even more detail (under a microscope) gland pores, the shape of edges or little scars can help to compare prints

As a final note finger prints can be used to identify some sorts of drug use by individuals.

This was a little more extended than I would have like. Tomorrow I'll cover handwriting and ballistics.

Batman The World's Greatest...Forensic Scientist?

I picked up an introductory book on forensics this weekend and thought I would recapitulate and review it for you. Batman is undoubtedly well versed in forensic science. I have read an online discussion or two on what kind of scientist Batman is.

Like a few people state: He's a forensic scientist. And it's true! Forensic scientists are multidisciplinary just like Batman. And really anybody who applies the techniques and methods of science to solving crimes is a forensic scientist.

Here at Building Batman, I'm introducing myself to everything that someone would need to know to be Batman. And so, on with forensics. Because as everybody (who's read the last paragraph) knows Batman is the world's greatest forensic scientist!

The book I picked up is generically titled 'Forensic Science' and it's written by Jay Siegel who is the “Chair of the Department of Chemistry and Biology, and Director of the Forensics and Investigative Sciences Program, at Indiana University-Purdue University”. I read “ Chemistry and Biology” as a single department and “Forensics and Investigative Sciences Program” as a supplement to a diploma of some kind. Otherwise, this guy must not sleep.

In any case, he seems to have recognized the public interest in forensics due to fiction like the CSI franchise. As such, he doesn't really explain anything in the book but rather just introduces concepts and basic ideas. His intent is only to inform the general public on the topics and limitations of forensic science. He discusses the “CSI-Effect”, the exaggeration of forensic science's ability to magically and quickly collect and analyze all the evidence needed to convict bad guys. Furthermore, the CSI-Effect means that juries expect prosecutors to present incriminating forensic evidence. They tend to discount evidence that doesn't have the Authority of Science (notice the capital letters, please) backing it up.

But not only does forensic science have limitations but so do forensic scientists. Observer Bias (<---that's a great link) can creep in and corrupt the scientific method. Extra information (that may not even be true) can (and presumably does) influence the way that a forensic scientist interprets their results causing the scientist to get in the way of the science. Perhaps, forensic scientists should only be given the evidence and asked to apply scientific techniques to discover what they can. But if you think about that, it's not a very practical way of doing business. How should they know what to search for? or what tests should they apply? Perhaps the some piece of withheld information could be the key in solving a crime. Who decides what is “domain irrelevant”? It's a big question. Even wording in reports can cause subtle bias. There are other kinds of bias. There is Conformational Bias, where the results of one forensic scientist influence another's toward agreement. Or even a pro-prosecutor bias. The author certainly seems to think that regulatory bodies are lacking and that certification and supervision are needed.

And bias is definitely not the only human error that can hinder forensic science. Somehow, the evidence has to get from the scene of the crime to the lab. Only rarely do forensic investigators accompany detectives and police investigators to crime scenes. All evidence must be searched out and collected without damage, which can be tough if say the evidence is a single fiber or buried under the debris from and explosion or liquid blood that will putrefy. The author makes a very tight analogy. Crime scene investigations are immediate archaeological digs. Investigators sift through the evidence and clues to reconstruct a past event.

Forensic also should be limited by the courts. Not all evidence is relevant or competent and so not all evidence should be allowed to be admitted.
- Evidence must be material meaning it must have something to do with the case at hand.
- Evidence must be probative meaning it must prove something and not just be a fact.
- Evidence must competent meaning that it must abide by a set of rules – a spouse may not have to testify against their partner or a religious confession might not meet competence constraints.

Forensic scientists have expert witness status when they testify which simply means that they have knowledge or skills to draw conclusions from a set of facts that your average juror could not. This means that not only must they be good scientists but they must also be good teachers. Despite all this, we should remember that just because a scientist has arrived at some conclusion does not mean that it is de facto truth. People tend to believe scientists and so if they testify in a court case jurors may accept their words without question.

That's the background information. Over the next couple of days, I will summarize the material covered in “Forensic Science” by Jay Siegel. We'll talk about

Pattern Evidence
Evaluating PMI
Serology
DNA
Drugs
Fires and Explosions
Trace Evidence

Another Man's Treasure

Walking home from work tonight at midnight (it's tough to be Batman when I spend so much of my time doing real people stuff) I found a boon. Someone is doing renovations to an old apartment building and there were a few pieces of scrap wood lying against the fence. It was clearly no good to anyone else but the blocks are quite thick (maybe 4' in width and depth) and maybe only 2"6' long. They might work perfectly as a target for the shuriken I should be receiving in the mail any day now.

Now all I have to do is find a hammer... I bet the real Bruce Wayne doesn't have to ask his neighbors if he can borrow a hammer.

Batman: Arkham Asylum

I finished Batman: Arkham Asylum last night. The dream is over and it only lasted three days. Too bad. Now that I'm done the game, I don't really feel like the Dark Crusader. Too bad. So I'm back to my training: 20 laps in the pool during lunch, a 25 mile bike ride this morning and Jiu Jitsu in the evening. But before I get back into it here at Building Batman why don't I review the game for? Just a few comments.
I'll do it in a Pro-Con format and start with cons because the good drastically outweighs the bad and so I want to finish on the positive notes:
Cons:
1) The game was too forgiving. They made this soundtrack and setting that are as creepy as could be. It's really tense BUT because Batman just re-spawns whenever you screw-up, there are no consequences for my actions and therefore I'm not scared. Why did Resident Evil work so well so long ago? Because not only was it scary in all the ways that a scary movie was but if you as the player screwed up there were terrible consequences: you might not have anymore ammo for hours, or maybe you would die and have to start from a point that felt like it was at the very beginning of the game. Batman: Arkham Asylum lacked that. Since I wasn't concerned about any consequences, the tension that they worked so hard to make so good was diffused.

2) The game was very linear. Although it was placed on an island and you could theoretically go anywhere, in actuality there was only ever one path and it was always right in front of you. I'm not asking for a game like Fallout but give the world's greatest detective multiple ways to go about solving a problem.

Pros:
1) You couldn't have this game without Batman. In many ways, it's not just 'another Batman game' but it's a game about Batman. You couldn't just be anyone with a boomerang. The game actually explores his character.

2) It's not the rogue gallery vs Batman. It must have been so tempting to just trot every Batman character in and say, "Everyone against Batman!" Instead, Batman is stuck in a crazy storm. It's all about him and the Joker. When other villains show up they are there on their own terms and for their own reasons, not just as super-henchmen in the Joker's scheme.

3) Paul Dini wrote it (really the last two just boil down to this).

4) Mark Hamill is amazing.

Final Post

This will be my last post. I will no longer need to continue my Batman training.

You see, I am Batman. Buying Arkham Asylum has instantly transformed me into the Caped Crusader. And so I will nor be learning any more of the skills Bruce Wayne acquired before becoming the Batman:

Because they're all really easy on my computer.

Batman's Shuriken

I ordered shuriken today.

Shuriken...

Looking up shuriken online is a tougher than you might think. The internet seems to be overflowing with misinformation on the subject and people who do have the knowledge don't really seem all that keen on sharing it. I'm always sending you to Wikipedia to start your searches into new topics but this is one time when the article could be improved upon drastically.

Let's get one thing out of the way: we're not just talking about ninja stars.

Shuriken can be translated as "sword hidden in the hand" or "hand hidden blade" and really this shouldn't just be limited to thrown weapons but is more generally any blade which is hidden in your hand. "Shu-Ri" --> "hidden in the hand" and "Ken" ---> "blade".

You can get a lot of history but the general motif seems to be that even the most mundane items can be effective weapons. Coins, washers, needles, nails, knifes or even flat pieces of metal are potential weapons.

There are two basic forms that shuriken tend to take.

Bo shuriken are long spike-like throwing weapons. One can imagine that there will always be improvisational Bo Shuriken around: chopsticks, hair pins, nails or even screwdrivers.

The second type are shaken. While bo shurkien were straight and dart-like, shaken have some shape. Shaken can be further divided into two class. Hira shuriken are the most familiar: they are the throwing stars from the 1990's ninja craze- the ninja stars I mentioned earlier. Hira shuriken can have any number of arms. As far as I can tell roppo shaken has six arms, juji shaken have only 4 and enbangata shaken are washer-like disks that have no arms but just a sharpened circumfrence. Then finally there are senban shaken that are more like lozenge shaped (i.e. diamond shaped). Both hira and senban shaken tend to have holes in their centers which apparently improves aerodynamics and can be used to string a bunch of shaken together.

To recap:

Bo Shuriken --- long spikes

Hira Shaken --- stars

                 Roppo --- 6 armed shaken 

                 Juji --- 4 armed shaken 

                 Enbangata --- washer

Senban Shaken --- diamonds

I ordered a set of five bo shuriken from Flying Steel. Flying Steel seems like a reputable manufacturer but at a fairly reasonable cost. There were a couple of other suppliers (other than the multitudes and multitudes of junk sites around) but just like it is hard to find trustworthy information on shurikenjutsu, it's hard to find trustworthy sellers(if you are aware of any other worthwhile suppliers let me know). That being said Flying Steel seems very professional.

Now I just have to figure out what I'll do for a target before they arrive and I start practicing.

Gotham Knights Online

Locked out of Gotham Knights Online! What does this mean? I read that blog everyday.

Here I am praying that more people will follow my Batman training so that I have a larger pool of potential experts and these guys are turning people away. Weird.

Oikiryu Jiu Jitsu

I asked my sensei what school of Jiu Jitsu I'm studying today at class and found out that it is Oikiryu that I have become a pupil of.

So what do I do after class? I come home to look it up and write a detailed description of it for you my faithful readers. But what do I find out from my trusty search engine? Nothing.

Nothing at all. In the age of the internet how can that be?

So I start to get a little more creative. Maybe it's aikiryu... no, nope. If it is so young and so western then I wouldn't expect a confusion over the spelling.

So what's going on here? Did I misunderstand my sensei? Is my spelling wrong? Is it uncommon? As always if anyone has anymore information than I do please speak up. Leave me a comment.

PS. Last week we were introduced to methods for deflecting attackers armed with knives and this week we started point combat. Holy shit, Batman! Did I ever feel like a cat in water! I've never punch or kicked before this and I'm being thrown in the ring and asked to just do it! It was crazy but by the end I was starting to get the hang of it. Although, I was told I have to loosen up.

Batman's Last Fermi Problem

Diamonds are just carbon all bound together. Each carbon is bonded to 4 other carbons. If you think about that a bit you will see that means there are TWO bonds for every atom (imagine/draw a fairly large grid - count the number of nodes/intersections and count the number of connecting lines. If this ratio isn't exactly half it's because the edges of the grid might cause trouble [if you draw it smarter or bigger it will get closer to 2]). That means that there is 3eV of energy available for every atom. Let's assume Mr. Freeze's gun can access all that energy.

Now that we know how much energy we can get from each atom we need to guess how many atoms are in a diamond. To do that we need the mass of the diamonds. When jewelers talk about carats their really just talking about mass --- 1carat = 0.2g. Maybe you know what the carats of some famous diamonds are? 100 carats is a BIG diamond so let's say 30 carats or in grams: 30 carats * (0.2g / 1carat)= 6g.

How many atoms are in 6g's of diamond? Well what's the atomic weight of carbon? If you don't know, can you imagine where carbon is on the periodic scale? It's near the beginning but not first and it's nowhere near the end. So say between 1 and 100. You could then say 10g / mol. OR you could have memorized your periodic table and remembered the value is actually 12 g/mol but really what's the difference?

So now we know the number of atoms in the diamond is about 6g * (mol/12g) * (6*10^{23}atoms/mol) = (36/12)*10^{23}atoms = 3*10^{23}atoms. And since we guessed about 3eV is released from each of those which means the energy is (3eV/atom) * 3*10^{23}atoms * 1.6\times10^{-19}J/eV = 9* 1.5 *10^4J = 13.5 * 10^4J = 10^5J.

Is that alot? We said in previous questions that a person uses 3.5*10^3J every day and the energy of a subway train is 10^7J. The energy Mr. Freeze can get from a diamond is somewhere in between.

And here ends the Fermi Problems part of my Batman training - at least on the blog. But if you have any superhero Fermi problems that you think I should do on Building Batman just leave a comment and I'll give them a whirl.

Batman's May Be Chemist But I'm Not Yet

Whoa!

Don't I have any chemists reading Building Batman? No? No chemists training to become Batman? Oh, well...

I was thinking about the Final Fermi Problem and it occurs to me that I made a bad estimate:
I said that each carbon is bound to 8 others because of the crystal structure. That's not true.

Carbon is tetravalent which means it will always have the equivalent of 4 four bounds, no matter the crystal structure.

Now you and I know that when estimating that factor of two isn't a big deal but I thought I'd better tell you in case you're you're doing this last Fermi question or in case a chemist stumbles past Building Batman.

PS If you are a chemist, you might get a kick out of this periodic table

Fermi Freeze - Batman Training's Last Fermi Problem

I like that fact that every reaction releases about 1.5eV of energy so let's make our last superheroic Fermi Problem one that uses that fact and then move on with the Batman Training.

What's the energy Mr. Freeze get's from diamonds (assuming it's a chemical process and not nuclear)?Diamonds are just carbon all bound together. Each carbon is bonded to 8 other carbons. (As always I'm just putting the simplest way of thinking about this together: Diamond is a crystal structure made of two fcc lattices).

Great Comment

I know that not everybody who reads a blog takes the time to read the comments but M.C. Elroy left a really great note on my jiu jitsu post and I wanted to point it out to you.

Flash Forward a Billion Years

So we are going to guess how much oxygen the Flash uses each day.

As a few reminders:
   (1)The hydrocarbons in our food get split up and carbons are oxidized into C0_2 meaning we really do burn the food we eat.

   (2)Typically,there is an energy release of about 1.5eV when one atom exchanges an electron with another. The units eV are related to joules by 1eV = 1.6 * 10^{-19}J = 2* 10^{-19}J.

   (2)Food is mainly composed of long chains of CH_2. When it is decomposed to get the energy it holds the carbon binds to two oxygen and the two hydrogens bind to a single oxygen meaning there are TWO reactions for every CH_2 which need THREE oxygens.

We already found that the Flash uses 5 * 10^9J per day. How many reactions is that? Turn joules into electron volts and divide by 1.5eV for every reaction:

5 * 10^9J * (1.5eV / 1.6 * 10^{-19}J) = 5  * (1.5/1.6) * 10^{28} = 5* 10^{28} reactions.

And we said 3 oxygens for every 2 reactions means we need 5 * 10^{28} * 3/2 = 7 *10^{28}$ oxygens per day.

That sounds like a lot but is it really? There's 6 * 10^{23} atoms in every mole and oxygen is eighth on the periodic table which means 1 mole weighs 8 grams. So then the Flash goes through 7 * 10^{28}  *  (1/6 * 10^{23}) * 8g = 8 * 10^5 g = 800 kg of oxygen each day. WOW but wait a minute...

In the last question we found that there's about 10^{18} kg of oxygen in the atmosphere. Which means it would take the Flash 10^{15} days or 3*10^{12} years or 3000 billion years.

Jiu Jitsu

On Tuesday was my first Jiu Jitsu class. It was great! I think I'm going to enjoy this component of my Batman training more than I had expected.

So before I get started I should clear up a few things. When I mentioned that my quest to become Batman would soon include martial arts training, I posted a link to Jiu Jitsu. Jiu Jitsu is a Brazilian variant that is descended from Judo. This IS NOT what my dojo teaches. The class that I'm attending teaches Jujutsu; however, they spell it Jiu Jitsu. As I understand it, Jiu Jitsu is a more archaic term and Jujutsu is the more accepted term.

Out of respect for my dojo, I'll refer to the tradition as Jiu Jitsu, ok?

To get an idea of the spirit of Jiu Jitsu, let me give you a brief historical tour of it's development. In feudal Japan, the combination of heavy armor and a highly tuned offensive techniques made samurai warriors the ultimate tank of the era. If one were to meet such an opponent unarmed and unarmored, one would need specialized techniques to be victorious. Striking an armored opponent wouldn't do the trick and allowing them the room to utilize a katana or yari would be a very bad idea. Jiu Jitsu is martial art for neutralizing enemies through grappling, throwing, locks and chokeholds. In this regard, it is far more akin to western wrestling than other eastern martial arts; however, there is a substantial difference: whereas wrestling seeks to pit strengths, Jiu Jitsu is literally the "art of softness" or the "way of yielding". Wikipedia says it quite well: "These techniques were developed around the principle of using an attacker's energy against him, rather than directly opposing it."

We began with exercises and stretches. These weren't so bad except for the squats. Those are muscles that I have not invested in and they were stiff until this morning. We were then introduced to falling techniques. Since Jiu Jitsu is a grappling art, absorbing the impact of falls is crucial.

We then learned three locks and two chokes. Although I've been practicing them every day I won't try to explain them to you yet. Don't worry though. I will as soon as I feel more comfortable with them and have found a reasonable body of resources on the internet to point you to.

PS If anybody does know of good resources that I should be familiar with please leave me a comment.

Fermi's Big Gulp

So we already guessed how much the Flash would have to eat but what about breathing? He needs air to turn all that food into energy. Would he use up the entire atmosphere?




Ok. Some backup science info. Energy release is controlled by mitochondria and the production of ATP through the Krebs cycle. It seems fairly complicated to me but in essence the most important thing for accessing all the stored chemical energy in the food is the oxygen intake and the carbon dioxide output. The hydrocarbons in our food get split up and carbons are oxidized into C0_2 and a bunch of water reactions are also needed to make this happen BUT the point is we really do basically burn the hydrocarbons that we eat.

Chemical reactions are all about exchanging electrons. Remembering that we are estimating: typically, when one electron is exchanged between two atoms there is an energy release of about 1.5eV. The units eV stand for electron volts and their just a convenient unit for \textbf{energy} when electrons are involved. To convert to everyday joules just know 1eV = 1.6 * 10^{-19}J = 2 * 10^{-19}J.

And one last thing: Most everyday hydrocarbons are just long chains of CH_2.

Breathing Room

Last night I attended my very first Jiu Jitsu class and so have raised my Batman training to the next level. I'll tell you all about it tomorrow. But tonight, let's answer yesterday's non- Superhero Fermi Problem (we'll use this answer for the next, and second from last Fermi problem).

The atmosphere pushes down on you (you might not have the weight of the world on your shoulders but you definately have the heavens weighing down on you). That pressure is measured in atmospheres (atm). The pressure of the atmosphere is normally 1atm (duh). In useful units 1 atm = 10^5 N/m^2. Where's that pressure come from? All the air molecules over head weigh down on you. Since the pressure is force per area, above every 1 meter squared there is a force (or weight) of 10^5N and remembering Force=Weight=mg where we round gravity to 10m/s^2. So the mass of the particles above 1 meter squared is 10^4kg.

We already used the area of the earth in the buses Fermi question and we use it again here: surface area of earth =5*10^{14} m^2. We know the mass of atmosphere above every square meter AND we know the total number of square meters that make up the surface of the planet. Therefore, we estimate the total mass of the atmoshere to be 10^4 kg/m^2 *   5*10^{14} m^2 = 5 * 10^{18}kg of air in the atmosphere!

BUT

Air isn't pure oxygen, O_2. The percent of the atmosphere that is O_2 definitely isn't 100%and it's not 1%. So we could guess 10% but I think that it's fairly common knowledge that air is 20% O_2 so let's use that number.

5 * 10^{18}kg * 20/100 = 10^{18}kg of oxygen. That's alot of elephants - or subway trains for that matter of oxygen. Wikipedia says that the atmosphere is really 5 quadrillion tons. A ton is 1000 kg and a quadrillion is 10^15 so we were only off by a factor of 5. Once again, we're pretty darn close.

Cause's He's Batman (and has a new game out)

Ctrl+Alt+Del
To answer his question: No. Throwing a razor sharp boomerang knife is not a good way to incapacitate someone. However, from my boomerang throwing experience I think that a normal, non-knife-like boomerang could do the job. Batman would then need a separate shuriken weapon for quick cutting but nonlethal pain.
Building Batman will be training with shuriken next month. ' Can't wait.

Penny Arcade

P.S. Disney bought Marvel this morning (assuming the investors ok the 4 billion dollar deal).

Fermi Question: What is the mass of the Atmosphere

What's the total mass of all the oxygen in the atmosphere?

Useful unit conversion: 1atm = 10^5  N/m^2.

Would the Real Superman Please Standup

The mass of the train should be the same (recap: car of a train is heavier than a truck [we've heard the term oneton-truck so let's say a truck weighs 1 ton]. It's probably more than 10 trucks but less than 100 so we say 30 tons. And there are 6 cars so about 2 * 10^5kg.

In the Spider-man question we said the train was going about 30km/hr. But this is Metropolis, the city of tomorrow! So let's say the city has levitating Shinkansen which can travel upto 600km/hr. Since it probably didn't have time to reach it's fastest speed in the city we'll say the train has a velocity of 100km/hr = 100km/hr *  1000m/km * 1hr/3600s = 100/3.6 m/s = 30m/s when it comes flying of the tracks.

Just like before we can find it's original kinetic energy (KE = 0.5 * m * v^2 = 0.5 * 2 * 10^5kg * (30m/s)^2 =10^8J). That's an order of magnitude larger than the train Spidey stopped.

But here's the second kicker: whereas Spider-man took 10 blocks to stop the train Supes has only half a block if this train isn't going to crash into a crowded skyscraper. So remember there's 10 blocks in every kilometer - so half a block is about 50m.

So the force is F=W/d = 10^8J  / 50m = 5 * 10^6N.

That implies Superman is about 500 times stronger than Spider-man. If that's not a 'super' Fermi problem, I don't know what is.

All this talk about Superman is a good excuse for me to put up this link to a Comedy.com post

Metropolis' Marvel - Stronger than a Locomotive

This superhero Fermi problem is just like the last Spider-man one so we'll use it as warm up.

In Matt Wagner's Trinity, Superman catches an out-of-control train (with say 6 cars again) that comes off it's tracks as it rounds a corner. He brings it to a stop before it can hit any buildings.

How much force did the Man of Steel use to do this?

How to Replace Batman's Bottom Bracket

I mentioned that I have running, swimming and biking each about twice a week throughout the
summer.

It turns out that all of that biking isn't just hard on me – It's hard on my bike too. My bike developed a grinding sound if I accelerated at all. Repairs needed to be done. But I figured that this could be a worthwhile exercise too. The Batman doesn't depend on anyone. Readers from the very beginning may remember that I suggested I don't really buy into the whole “Batman's the goddamn Batman. He built his bat-mobile from scratch, he personally programmed the bat-computer. All while staying out every night fighting crime and singlehandedly running a multinational corporation.” I tend to prefer the incarnations where Barbara handles all things computers, The Outsiders act as crack-squad, Harold (and later Hiro) takes care of equipment, Alfred manages Bruce Waynes' personally life and Mr. Lucius Fox runs the family business – rather than versions where Batman does everything himself. Not only is it more realistic it's also far more interesting.

BUT that being said, I have no doubts that Bruce is handy with mechanics and all things technical so I decided to fix my bike myself rather than bring it in to a shop.

I didn't know what I was getting into. First off, it would have been far cheaper to bring it into a shop since I had to buy a bunch of specialized tools and second I ended up doing way more repairs than I had expected to.

The funny sound came from my bottom bracket. Mine is a Cartridge bearing which just means that the bearings and the axle are housed in a sealed tube. The bracket is fitted to the frame of the bicycle by a square taper. This thing sucks. I had to buy an adaptor and the adaptor is a real pain.

So to change your bottom bracket you need to take it out before you buy a replacement (unless of course you work on your bike a lot and if that's the case why are you reading an introduction to replacing your bottom bracket?) To take it out you first remove your crankset (if your unlucky like me that requires a specialized tool called a crank extractor). This isn't difficult but just be careful when you screw the extractor into the crank – they are pretty fine threads. It's a clockwise turn to get the crankarms off.

Before doing anything else you have to measure the length of axle you are replacing and the width of the frame where it sits in. This is important. You then ask the boys at your local bike shop for a bottom bracket of those dimensions (the guy didn't believe me so I had to hull my bike all the way to the shop – I guess it's an uncommon size).

To remove the old bottom bracket you start on the non-drive side (i.e. the left hand side when you look down while sitting on you bike – the side without the chain). Using the stupid adaptor turn COUNTER-CLOCKWISE. Other side next (drive side). This time turn CLOCKWISE. Did I ever have a hell of a time getting these out. They were really seized in (I guess with rust). I had to buy a larger wrench to get more torque.

Inserting the bottom bracket is pretty simple since it's just two pieces and you just took it out. The only thing to remember is to grease the tapers! This is so that the bracket doesn't seize to the frame like it did for me.

While I was doing all of this I realized how warped my chainring was. Those are the big gears at the front. Since the bike was all apart I got a new one. In fact, the bike shop sold me my bottom bracket and the crankset as a single package. I guess that's pretty common.

I also decided to replace the hub gear. You have to know that my bike is a single speed and so doesn't have all those cassettes. It's just a single cogged freewheel like on a BMX. To remove this I needed another specialized adaptor. The trick to getting this off is to not use a wrench. PLEASE do yourself a favor and put the adaptor in a vice, set the wheel on top of it and then just turn the wheel (or maybe this is better but whatever). You get so much more torque and it is perfectly balanced.

Since I had this off I took out all the bearings, cleaned them and put them back in a ton of disgusting heavy grease. I also did this for my pedals.

This took a long time but it's finally done. In the spirit of Batman, I did it myself and I'm ready to be back on the road training.

Unfortunately, it's been pouring for hours.

The Dark Knight Returns

I registered and payed for my beginner-level Jiu-Jitsu yesterday. It feels like I've been wait forever to start. The first class is on Sept. 2nd. Classes occur once a week and go for 10 weeks. I'll post what I learn each week.
P.S. I'll post all the other Fermi problems this weekend and then we'll be done with them.

For Those Who Don't Read AppleGeeks

Sticky Situation

This one's stolen from Guesstimation.

In the second Spider-man movie Spidey stops a six car subway train by attaching his webs to it and pulling it to a stop in 10 or 20 blocks.

How much force does he need to do this?

Food for Thought

Let's answer this in three parts. How much energy does the average American consume, how much does that cost, how much does each calorie cost and how much energy would the Flash need.

There's a number of ways we could estimate how much one person spends per month for food. You could say that you eat out every meal (3 times a day) at some fast food joint for $10 a meal. That kind of life style has a monthly bill of 30 * 3 * 10=$1000 per month. I think that's high at $30 per day. What about $1 per day? At that price food would only cost you $365 each year. Ya right. So the easy numbers between $1 and $30 are about $10 per day or $3 per day. Let's be nice to Wally and say $3 per day or about $100 per month.

So we've guessed it can costs about $3 a day to eat (I know it seems low). Now we must guess how many calories you consume a day and so find the cost of every calorie.

How many calories do you eat per day? Maybe you know this maybe you don't. If not, maybe you know how many calories are in a McDonald's Value Meal (1167 cal) or in a can of coke (200 cal) or in a steak (500 cal). Therefore, you eat more than 1000 cal and probably not 10,000 cal. So then we guess the geometric mean which is 10^{7/2} = 3000 cal per day. So let's convert from calories to Joules (there's 4200 Joules in every calorie). 3000 cal/day * 4000 J/cal = 12 * 10^6 J/day. A physicist like Ray Plamer or Reed Richards would be happier if we turned this to Watts. Watts are Joules per second. So as a side note the power usage of a human being is 12 * 10^6 J/day * day/24hr * hr/60min * min/60sec = 150 W. Oh good - more power than a lightbulb.

So anyway that was a sidequest. The important thing is that a person consumes 3000 cal or 10^7 J everyday. Plus spends $3 a day for that food. That means that $1 will buy you 1000 cal or 4 * 10^6 J.

Next we have to estimate how much energy the Flash needs. Let's guess that most of his energy goes to running (that way if our answer is small compared to a normal person we can add the energy of a normal person to it or if our answer is big compared to a normal person we know that it is insignificant). The energy of him running is kinetic. We already used the equation for kinetic energy KE = 0.5 * m * v^2. If we allow for fictitious elimination of frictitous forces then if we can guess his speed, we will know the energy needed to get him to that speed. He needs that much energy every time he runs to that speed. Remember we are guessing for an average day, not at his fastest nor his slowest.

The speed of light (3 * 10^6m/s)?. %1 the speed of light? The speed of sound (300 m/s)? The speed of thought (only about 100m/s since it depends transport mechanisms of ions crossing membranes)?

Let's guess that he goes 10 times the speed of sound for an average run. The energy he needs to reach that speed is KE = 0.5 *m * v^2 = 0.5 * 100kg * (10 * 300m/s)^2= 0.5 * 100 * 9 * 10^6J=5 * 10^8J.

Since he needs that much energy every time he gets to those speeds we need to ask how often does he go that fast? We are talking about a cocky jock with a fairly large rogue gallery. So let's say he goes more and once a day but less than 100 times a day. The geometric mean: 10 times.

Then the energy the Flash needs for running in a day is 5 * 10^9J. At a price of $1 for every 4 * 10^6 J, the Flash must spend 5 * 10^9J / (4 * 10^6 J/$1) = $10^3 = $1000 more per day than muggles.

We said that a single person could eat for $100 per month and based on that the Flash's monthly grocery bill is $30,000. That's more than some of use make in a year! Notice that if we had said that Wally ate out for every meal his bill would be 10 times greater. A bright supervillain interested in discovering the Scarlet Speedster's secret identity might begin by looking for abnormally large grocery bills.

Like a Bat Out of Hell

I happened to be in the western part of Canada this weekend and thought it would be really cool to do some bouldering in the rockies. I'm here for a really quick trip and so climbing was just going to be something I squeezed in as I drove into the eastern part of the mountains. I packed my shoes and everything seemed to be going really well. The guy I was going with was excited, the people I'm travelling with didn't care if we stopped for a bit and the weather was beautiful. Near the town of Coalman we spotted what looked like a great face. We pulled over, changed and started hiking. We just arrived at the site when suddenly a huge dark cloud lumbered over the mountain. It didn't waste anytime looming. It came fast and hard. We got stuck in a hail storm and didn't get any climbing done. The rain didn't let up until we were out of the mountains again. It was too bad. I don't know when I'll be back there.

The Cost of Being Super

How big is the Flash's grocery bill?

For this superheroic Fermi Question you'd might like to know that every Calorie that you eat has about 4200 Joules of energy. Also guessing how fast he goes is tough. Consider average days for the Flash and think to yourself that he's much faster than the speed of sound but not any where near as fast as the speed of light. (Just an average day. That's all I'm saying.)

Skeletal

How heavy is he without his skeleton? I'm about 70 kg. Logan's pretty buff. Maybe say 100 kg.

How much of that is bone? 1%? Nah. 100%? 30%? 10%? Ya, 10% seems like the best answer. 10% of 100kg is 10kg. So that's 10 kg of bone and 90 kg of other stuff in your body.

Well, let's guess that bone and muscle and everything inside of us is all the same density. This is really not so bad of a guess because nothing inside of us is as heavy as rocks or as light as air. We pretty much have the same density as water.

The density of water is 1 kg/L = 1000 kg/m^3. So then 10kg of bone has a volume of about 10 kg / 1000 kg/m^3 = 10^{-2} m^3.

If that normal skeleton is removed and replaced with an adamantium one. If we can guess the density of adamantium then we can multiply it to the volume of a skeleton that we just found and we will know the mass which we can then ad to the 90 kg of left over non-skeletal stuff.

What's the density of adamantium? Well it's got to be heavier than water. 100 times heavier? No way. 10 times heavier seems like a good guess which says it has a density of 10 * 1000 kg/m^3 = 10^4 kg/m^3. Another way we could find this is we could look up the densities of some metals and notice that tungsten is pretty heavy at 19.25 g/cm^3 and that iron and silver and all of those are all pretty close at 7.9 or 10.5 g/cm^3 which are both 10 g/cm^3 = 10^4 kg/m^3 as far as we are concerned.

So using this density we find that the mass of an adamantium skeleton is about 10^{-2} m^3 * 10^4 kg/m^3 = 100 kg. So now with his new shiny skeleton Dark Claw or Wolverine weighs 100 kg + 90 kg = 200 kg or about twice as much. This isn't a shockingly high value. A person had an adamantium skeleton wouldn't sink in and leave foot prints in concrete or be too heavy to use the elevator.

Dark Claw's Adamantium Skeleton

In the 1990's DC and Marvel did a cross over event and mashed their characters together into "amalgams". The character they combine with Batman was Wolverine to create: Dark Claw.

At that time Wolverine had an adamantium skeleton which was one of the things that helped make him invincible (Batman often suffers from the same problem: invincibility by popularity). I can imagine some side effects to having a metal skeleton. Is weight one of them?

How heavy is Wolverine/Dark Claw with his adamantium skeleton?

Tons of Kryptonite

Let's assume that the entire planet of Krypton is made of Kryptonite. With the wide variety of kryptonite this doesn't even feel like such a stretch of the imagination.

So the planet explodes causing the mass that was the planet to shoot outwards and expand as a shell of debre. If we can figure out the fraction of that shell to hit the earth than we know the amount of kryptonite to hit earth (if we know the original mass of the planet krypton. Let's go with the 10 times greater than earth that Mohitparikh guessed instead of my 25 times (although for estimating it doesn't really matter!)).

We need to know the area of the shell. That depends on how far it's expanded. So we have to ask ourselves: How far is Krypton from Earth?

Well, how long did it take Kal-El to get to Earth? The fastest his rocket (it's usually a rocket) could possibly travel is the speed of light. You don't have to know the speed of light to know that a light-year is a unit of distance. It is the distance that light can travel in 1 year. So if Kal-El was put in the rocket (that goes the speed of light) as a new born and he arrived on earth as a yearling then Krypton is 1 light-year away. If he arrives as a 10 year old then Krypton is 10 light-years away. Here's a fact: No solar system is as close as 1 light-year away from us. Usually Kal-El is not 10 years old when the Kents find him so let's take the geometric mean and say that he was a toddler of 3 when he crashed on Earth and therefore Krypton is 3 light-years away.

Some more facts: Proxima Centauri is 4.2 light-years from us. Sirius A and B are 8.6 light-years. Vega is 25 light-years. So by guessing 3 light-years we are saying that Krypton was one of Earth's closest neighbors in a really big neighborhood.

Let's find out what 3 light-years are in useful units. Everyone rememembers the speed of light? It's 3 * 10^8 m/s. Here's the coolest trick I learnt from the Guesstimation book: You can either to all the slow multiplying of 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, 365 days in a year --- OR --- you can memorize that there are pi * 10^7 s in every year. It's a really good estimate. It's easy to remember that pi is about 3.14 and there are 3.15 * 10^7 sec / year. Cool, eh?

Anyway, how many meters to Krypton? 3 light-years times 3 * 10^8 m/s * pi * 10^7 s/year equals 27 * 10^{15} m (cuz pi=3, remember?). Which we round to 3 * 10^{16} m.

So what is the area of the shell of the exploded Krypton when it reaches earth? Well, we just found the radius of the shell (3 * 10^{16} m) and the total area of a shell is A=4 * pi * R^2. Which means the area is 4 * 3 * (3 * 10^{16})^2 = 4 * 3 * 9 * 10^{32} = 100 * 10^{32} = 10^{34} m^2.

We only need one more piece of information: How much of that hits earth?

All the Kryptonite is kind of evenly spread over the sphere so the density is d = M / A = 6* 10^{25}kg / 10^{34} m^2 = 6 * 10^{-9} kg/m^2. Now we know how many kg pre square meter and all we need is the area of the Earth that this hits. It's really the silhouette area or the cross sectional area A = pi * r^2. To do this you need to know or guess the radius of the Earth. I happen to know that it is r = 6000 km = 6 * 10^6 m.

That means that the cross section of earth is A = 3 * (6 * 10^6 m)^2 = 3 * 6 * 6 * 10^{12} = 100 * 10^{12} = 10^{14} m^2. When we multiply the area by the density we will have the mass of Kryptonite that hit the Earth. 6 * 10^{-9} kg/m^2 * 10^{14} m^2 = 6 * 10^5 kg. Holy Rao, Superman. That's 600 tons! But if you think about spread over the entire earth most of it would be dust and really we never made any guess about what fraction of the mass on Krypton was Kryptonite.

Notice, the Wikipedia page on Krypton says that Superman's home planet is 50 light-years away. If we ignore what this would mean about how fast Kal-El's rocket would travel (not to mention the Kryptonite rocks themselves) and redo the calculation then there's only 2 tons of Kryptonite on Earth. BUT even if it moved at 10% of the speed of light, it would take the Kryptonite 500 years to get here.