estimation
rallain | August 26, 2010Might as well jump. Jump. Go ahead, jump. - Van Halen
Suppose everyone in the world got together and jumped. Would the Earth move? Yes. Would it be noticeable? Time for a calculation. Note: I am almost certain that I have done this before, but I can't find where.
Starting assumptions.
7 billion people.
Average weight: 50 kg (you know, kids and stuff)
Average vertical jump (center of mass): 0.3 meters - and I think that is generous.
Mass of the Earth: 6 x 1024 kg
Gravitational field near the surface of the Earth is constant with a magnitude of 9.8 N/kg
Ignore the interaction with the Sun and…
rallain | August 25, 2010You know I wander around the intertubes, right? Who doesn't? Anyway, I saw this collection of strange google Earth images. Yeah, it is kind of dumb, but this one made me think:
That article said the image was from TechEBlog, so there is that.
I have no idea what this thing is, but it is clearly tall. How tall? Instead of searching online for info about this structure (that wouldn't be any fun), I figured I could do a quick analysis of the shadow. Here we go. First, I need to make some measurements. It turns out that Tracker Video tool for analysis is also quite excellent to use for…
rallain | August 9, 2010Here is a quick one. One of the big news stories recently was this regarding WikiLeaks and the release of the Afghan War Diary. There could be tons of things to discuss regarding this - but I am not going to do that. The first thing that struck my mind was "over 91,000 documents". That seems like a lot.
If each one of these documents were printed on one page, how big would the stack of paper be?
I could just estimate this - fermi-problem style. But instead, I thought would use a stack of paper. Here is a pack of 500 sheets of paper.
Opening it, I can measure the thickness:
How thick…
rallain | August 3, 2010You thought I was going to talk about a problem that math teachers could use, didn't you? Well, maybe math teachers can use this. (note: when I say "teachers" I really mean "learning facilitators")
It all started when I read this valedictorian speech from Erica Goldson. Here is part of it:
"I am now accomplishing that goal. I am graduating. I should look at this as a positive experience, especially being at the top of my class. However, in retrospect, I cannot say that I am any more intelligent than my peers. I can attest that I am only the best at doing what I am told and working the…
rallain | July 30, 2010The Lord of the Rings trilogy came on TV again recently. My wife and I can't help but to watch this even though we have it on DVD. Anyway, I was thinking about the part where Gondor sends a signal to Rohan asking them for military aid. Since this was before the invention of email, they had to do it with a signal fire. Hopefully this clip won't be a spoiler for you, but this is from the movie. Actually, all of the clips available have embedding disabled. So this is just a picture of that clip. If you want to see it, go to the youtube version.
One other spoiler: Sauron is really Frodo's…
rallain | July 26, 2010Here is part of a picture some of my friends posted from a recent high school reunion.
It may be hard to tell, but this is part of a picture of 7 females all wearing black. I just wanted to show you that they were indeed wearing black without giving away anymore details. If you are one of these people and you want your whole picture included, I will be happy to make that change and include your face.
Anyway, my first comment was: "Wow, everyone is wearing black. Was this a planned event or was black part of the dress code?" The response was that it was just pure chance that all the women…
rallain | June 21, 2010Of course I am talking about Arnold Schwarzenegger. After looking at how many bullets he carries in Commando, I remembered this scene (also from Commando) (warning: maybe some not great language and some killing. You have been warned)
If you don't want to watch that clip, here is a shot (sorry for the quality).
Clearly Arnold is strong, but there is more than strength involved here. Oh, don't bring your "he did it with wire stuff". I am not buying that. Also, I am talking about THE Arnold - he is real. I am not talking about the character in the movie (not real). Now for some physics…
rallain | June 16, 2010Somewhere on the internet, I came across this Cracked.com article on movie myths about guns. The article wasn't too bad, but I really liked this video they included from Arnold's movie Commando.
The myth for this particular clip was that guns never run out of ammo in the movies. Right away, I thought: I wonder how many bullets he shot? BRING IT ON.
First, I am going to find the fire rate of Arnold's weapon. Oh, I know I could look it up on Wikipedia or something - but I am not going to do that. I am going to determine the fire rate from the clip.
After capturing an audio segment where…
rallain | June 11, 2010Back to the discussion about hiding an electric motor in a pro racing cycle. Before, I looked at a video of Fabian Cancellara to see how his speed and acceleration compare to other bikers. The claim on the internet is that he pulls away so fast that he must have a motor hidden in his bike.
Just to be completely clear, I don't think he is cheating. Then why bother? If you ask that then this must be the first time you reading this blog. I welcome you. No, but really, this is what scientists do. How hard would it be to cheat?
From my analysis, it seems that a person could ride like he…
rallain | May 15, 2010I was going to just leave the oil spill in the gulf topic alone. Not because it isn't important, obviously it is. Rather, I wasn't going to do anything because I didn't really have anything to add to the topic. After a couple of readers requested it, I think I do have something to add. How exactly do you estimate the amount of oil flowing into the gulf?
What do I have to start with? A video. Here is a video of the undersea oil leak.
Now, I am not the first to estimate the oil flow rate (NPR on Purdue Prof's estimation and here a commenter make a quick calculation). Like I said, I am…
rallain | March 26, 2010Time for another Fermi problem. There was a recent story in Science News that talked about the effects of the Chilean quakes on the Earth's rotation. The basic idea is that some ginmourmous amounts of rock moved closer to the Earth's center. Since the angular momentum of the Earth is conserved, the angular rotation rate would increase. The estimated change of the day was by about 1.26 microseconds.
Could all the cars in the USA be used to change the rotation of the Earth?
Well, I shouldn't have phrased the question that way. Of course 1 car technically is all you need to change the…
rallain | March 13, 2010The most basic explanation of Pi is that it is the ratio of the circumference to the diameter for a circle. That seems simple enough, but it turns out that Pi is an irrational number - so you can't just write it down. Oh, I know that you are an uber-geek and you could recite the first 80 digits of Pi. But the question is - how many digits are enough?
In this post, I am going to assume that we don't know the true value of Pi (which is essentially true). I can then use propagation of error techniques to see how dependent different calculations are on the value of Pi.
Super Brief Intro to…
rallain | March 8, 2010I know many readers like the fermi questions (like how much would it cost to review all youtube submissions). Well, you are in luck - Diary of Numbers is having an estimation contest. Here is the question:
Mario has appeared in over 200 video games as Nintendo's main mascot. He has starred in TV shows, comic books, and feature films, but anyone who's played one of his games knows it's not all fun and games for the lovable plumber. He is constantly falling down bottomless pits, getting eaten by giant mutant mushrooms, and otherwise killing himself all while trying to save a princess who is…
rallain | March 1, 2010There was a Buzz Out Loud episode in the not-to-distant past where the discussion of youtube came up. I can't remember the exact details, but the main point was that it would be impossible for google (the owners of youtube) to review all of the videos that were submitted.
And here is my calculation. How much would it cost google a year to do this? First, I need to pick some variables (and I will first do this symbolically - then you can put in your own values if it makes you happy).
Submission Rate (s): This is how many minutes of video are submitted each minute (so the units would be…
rallain | February 2, 2010This one has been on my mind for quite some time. What kind of power source would you need to run a lightsaber? I was actually worried recently about this post when I saw the Discovery Channel show "Sci Fi Science". In that particular episode Michio Kaku talks about how you would actually build a lightsaber. The episode was a little silly, but the science wasn't too bad. In end Michio decides to build a type of hand held plasma torch. Doing this, he estimated that the lightsaber would need a power source on the order of mega-watts.
He didn't do what I was thinking. I am thinking about…
rallain | January 31, 2010This is really random, but quick. I was channel surfing and saw the end of the movie: Fantastic 4 - Rise of the Silver Surfer. SPOILER: At the end someone really big explodes in space. There, that wasn't too much of a spoiler, was it? (unless you read the title)
I know I am a loser. I initially thought: wow, that seemed pretty fast for that scale. I wonder if that exploding stuff was going faster than the speed of light. OH! I know, I will use Tracker to measure it. It is video that is set for analysis since it has the Earth in there - and I am pretty sure I know how big that is.…
rallain | January 22, 2010Since my previous post on R2-D2 flying was so popular, I thought I would follow it up. I was going to add these two points in the comments, but a separate post seems to make more sense.
Point 1 - R2 flies at a constant speed
Well, he obviously doesn't always have to fly at a constant speed. However, in the clip I was looking at there are two important things in the analysis. What angle is R2's thrusters at? Is R2 flying at a constant speed? I found a much better quality version of the flying R2 from Billy Brook's site. That helped out a lot. So, on to Tracker Video Analysis (I always…
rallain | January 21, 2010You know I can't help but like Star Wars. Even with the new stuff, I watch it. Recently, I was watching the Clone Wars cartoon and noticed something odd about the way R2-D2 flies. I know what you are saying...."the odd thing is that he flies at all. Why didn't he fly in episodes 4-6?" Who knows. Here is the best image I could get of R2-D2 flying (from wookieepedia).
What is wrong? Well, maybe you can't tell from the image I posted. Here is a diagram of flying R2-D2.
If R2 (I can call him that because we are good friends) was flying like that, why would that be a problem? That would…
rallain | December 29, 2009I saw this post about Panasonic's home battery. The claim is that this will lead a battery that can power a house for a week. I wonder if I can estimate how big this battery would be.
First - to estimate the energy a house consumes. My first approximation is that you could probably run a house off of a 5000 Watt generator, but this probably isn't the average power use for a house. It is probably lower. I am going to go with an estimate of 2000 Watts as the average power over 1 day. How much energy would this be for 1 week?
The article above claims that it is a lithium ion battery.…
rallain | December 25, 2009So, analysis of the movie Up is pretty popular in the blogosphere. Figure I might as well surf the popularity wave. So, I have a couple more questions.
The most important thing to estimate is the mass of the house. I am going to completely ignore the buoyancy of the house. I figure this will be insignificant next to the buoyancy needed. Anyway, let me go ahead and recap what has already been done on this in the blogosphere.
Wired Science - How Pixar's Up House Could Really Fly - from that post:
First, they calculated (seemingly correct) that the buoyancy of helium is 0.067 pounds per…