So, remember the proper hand washing techniques:
- Use hot water and soap.
- Scrub hands for 20 seconds.
- Clean under fingernails.
- Rinse thoroughly.
- Turn faucet off with paper towel.
Got it? We got a course on hand-washing at a University! I still can’t believe it. Of course nobody obeys it, especially the last point. What I believe we should tell people is that they should dry their hands with those paper towels instead of using electric hand dryers if they really want to clean them. The air flow of the hand dryer does remove the water, yes. But drying your hands with a towel is some sort of mechanical cleaning, so it will remove the water and whatever else is on top of your skin.
Just for taking a picture, I really turned off the faucet with a towel. And I even opened the door with a towel:
The Smithsonian Institution abolished paper towels in an effort to help the environment. Since I know about that I wanted to do the following calculation:
Recently I found some numbers on carbon dioxide emissions of power plants. I ended up calculating with about 700g CO2/kWh. Most hand dryers heat up the air instead of simply accelerating it. They use about 2kW of energy for about 45 seconds which is 0.025 kWh or about 18g of CO2 emissions. This results from wasting about 5g of carbon. That should be roughly the worst case for an electric hand dryer.
According to Wikipedia tissue paper has a weight of about 20g/m2. The surface is not even and there are usually two layers, so let’s calculate with 50 g/m2. I believe that I use about 0.05 m^2 of paper towel for drying my hands, so that’s about 2.5g. Not all of that is carbon, but I still believe that with the additional CO2 expenses during production and transportation, paper towels are probably worse than electric hand dryers. Especially than those hand dryers that just use a strong air flow instead of heating it.
(However, paper towels are made from sustainable resources. That might change my mind again.)
Our group will eventually have to leave from the room which I’m in right now. Well, this plan exists since … dunno, a long time ago. In fact, in June 2008 Susi sent me a mail saying that they would have to move “soon”. And in December I also believed that we would be relocated, but the processes at the UDel are sometimes very slow (and we don’t really want to give up this room, so we don’t speed things up).
Now things are slowly starting. There was a granite plate in our lab, with an estimated weight between 2,000 and 5,000 pounds. Some very friendly workers build a small crane in our lab, and finally lifted this granite plate:
That was amazing! :-)
Last week the heating system in our lab was finally fixed (if anyone at the University of Delaware reads this and also has problems with the heating, simply call 1141). At this event we learned about how our heating works:
The air system supplies us air at a constant temperature of 60°F (which is 15.5°C). It’s always the same, summer and winter. In winter, this air is obviously preheated, and in summer it is a/c’d down. Then there is a steam network, probably running somewhere between 200°F and 300°F, but this is just a guess. So how does our room get warm? The incoming air (60°F) can be detoured through a heat exchanger in our room which is fed by the steam network. A thermostat controls how much air goes through the heat exchanger, and how much air directly comes to our room. It’s always interesting how people find ways of wasting energy!
In the previous years the pneumatic actuation of our thermostat was broken, leaving the valve open so that the air was constantly heated to a room temperature of 80-90°F which I can hardly stand (27-32°C). So this system doesn’t just waste energy, it’s also unreliable. Unfortunately I didn’t take any pictures of myself sitting topless at my desk and sweating anyway.
Next week (from Sunday to Sunday) they’ll shut the campus-wide steam network off. They do this once a year to clean things. That means: No hot water in our buildings, and no re-heating of the pre-cooled air. That means that our lab will be cooled down to about 60°F for one week, and there is no way to control this temperature. Luckily I’ll be in St. Louis most of the time.
I’m currently changing some citations in my thesis. Originally I planned to cite some Wikipedia articles such the one about Differentiation of inverse functions. They have a section about higher derivatives of those inverses, and those were really useful for my work! Unfortunately I can’t find a normal textbook which also presents these formulas, so that’s why I wanted to cite Wikipedia.
Mascha was the first one who tried to convince me that citing Wikipedia is not a good idea. I didn’t listen to her. Alex was the second one, and I did listen to him (sorry Mascha!). Without any quotable source I had to add an appendix page in my thesis just for showing the derivation of these formulas. Okay, that Wikipedia citation is gone. Unfortunately there are still a few others left.
While I searched the formula in different textbooks, I found this the 1968 “Schaum’s Mathematical Handbook of Formulas and Tables” by Murray R. Spiegel. It claims to be printed both in the United States and in Korea. Sounds like good teamwork, eh?
Hey, I told you that Andi didn’t join us on our trip to the Delicate Arch? He had other plans. There are many roads in the Arches National Park that are for four-wheel-driven cars only. Now, we had an AWD Jeep. So far so good. Andi only needed a place to go. The golden rule from old video games is: whenever you see a closed door, you have to open it. There will be something interesting behind it. Guess what Andi did?
His plan was to reach one of the hills on the following picture, and things were really looking good for him! There were a few trails were other people had driven before, so Andi knew that things were safe.
However, just before he reached the top of his hill, he got stuck. There was no chance of getting any further. He even had to put the doormats under his wheels to get enough grip for getting of the hill again…
In the end, Andi was really satisfied. Driving on those dirt roads is just so much fun. And he had successfully put enough dirt onto the car to make us wash it later that day…
You know what this story reminds me of? A very small calculation. It shows that the maximal steepness which a car can climb is quite limited. Let’s assume a non-interlocking connection between your wheels and the ground, and static friction. You want to drive up a hill with a steepness of α. α=0 would be a level surface, while α=π/2 would be orthogonal to the ground. Your car’s gravity force is m·g, but the normal component (which presses you to the ground) is just N=m·g·cos(α). The other fraction of the gravity force is tangential to the road, so it will try to pull you off the hill: m·g·sin(α). The only force that stops you from going downhill is the static ground friction. Its maximum value can be estimated as Ff=µ·N. Putting it all together we have m·g·sin(α)=µ·m·g·cos(α), or α=arctan(µ).
The coefficient of friction µ is roughly 0.4 on normal soil, 0.6 on tarmac and 0.8 if you drive a track vehicle (such as a tank). Now, from the formula I presented above you can easily calculate the maximum steepness α.
For µ=0.4 it is α=22°, for µ=0.6 you get α=31° and the tank will go uphill with at most 39° of steepness. That should explain why Andi couldn’t make that hill…
The numbers above do of course assume that it’s dry. Once things get wet you’ll end up with a coefficient of friction in the order of µ=0.2. That is 11° of steepness. If things get icy, then µ can become virtually 0. And if you don’t have an all-wheel-driven car, than approximately half your car’s normal force will go to non-actuated wheels. That basically means that you can divide all these values by two…
Oh, I forgot to give the good news: The calculation I presented describes only a static case. If you can get enough momentum by taking a run-up, there are no such limits :-).
Steffi has sent me a link to a great YouTube video which gives a really intuitive understanding of what “spacetime” is. It all starts with the question of why you’re aging slower when you’re traveling at high velocities. Please consider this as a must-watch:
This video is linked on bestofyoutube.com.
If you had fun watching this, you might also want to read the “Basic Concepts” chapter about spacetime on Wikipedia. It introduces a simple characterization of what “distance” is in spacetime. Don’t worry about mathematical prerequisites, it only talks about a very simple formula:
Once you understood the terms “Time-like interval” and “Space-like interval”, you will be able to calculate the time that passes between two events, assuming that you travel from one to the other without being accelerated: Suppose you’re going from Magdeburg to Stuttgart. You start in Magdeburg at 3pm and you arrive in Stuttgart at 8pm. How long have you traveled?
Damn, I thought I could save some more time this way ;-).
A young Ph.D. student in our group is working on the simulation model of a multi-bar-linkage since a few weeks. She was already working on this problem before I went to Las Vegas, and that was in March. Actually it’s really a simple system, but our adviser wants her to use some strange method which is … well, strange. Now, I spent the last few hours on setting up the dynamic equations with the standard Lagrange formalism and some holonomic constraints which I could directly put into the Lagrangian. Well, to sum things up, my simulation model was written down after a few hours and it worked immediately.
Well… if things were so simple, then I wouldn’t write about it on this blog. The bars in this linkage system had roughly a length of l=10m. The gravity constant is g=9.81m/s2, and a linearization yields T=sqrt(l/g). I’ve therefore concluded that the time constants in this system are at roughly 1s. I think this fits with what you see in the simulation plots. I thought that a simulation step size of 0.1s would be sufficient to get acceptable results, so I set the MaxStep bound of ode45 to 0.1s. The left-hand side figure shows my first simulation result (the plotted values are angles in radians). On the second plot you can see the overall system energy.
I wasn’t adding any energy to the system, so I decided that the total energy was fluctuating a bit to much in the simulation. Maybe taking a maximum step size of 0.05s would be better?
See the difference? The pink link doesn’t infinitely turn around now, but instead it oscillates from a little less than -π to a little more than 0. Everybody knows that pendulums are chaotic systems, where a small change in a parameter or an initial condition can yield a complete change in the overall system behavior. Now, apparently the numerical errors due to the finite step size can cause the same effect.
To get better results, I’ve reduced the step size to 0.01s, with this disappointing outcome:
Instead of decreasing the fluctuations in the total energy I’ve increased them. I hate chaotic systems. And unstable systems. And especially systems which are both unstable and chaotic. Still, I’m already much further than our poor Ph.D. student, so I’ll send her the results and go home. It’s already 10:40pm. I shouldn’t spend so much time in the lab.
Edit: Just before I left I realized that I had to chose different initial conditions to address her problem. I chose my step size at about 0.02s, and I like the results. The animation however doesn’t really look physical, so I might still have screwed something up. It’s 11:54pm now. I’ll be leaving tomorrow. FML.
Although Matlab is the toy of choice for control engineers, we sometimes have to use Maple or some other symbolic manipulation program. Now, there is one thing about Maple which I absolutely don’t like: If I define a time-dependent variable such as x(t), I cannot directly use Maples symbolic differentiation tool for differentiating w.r.t. x(t):
diff( sin(x(t)), x(t) ); Error, invalid input: diff received x(t), which is not valid for its 2nd argument
Today I found a really neat solution on mapleprimes.com. They are simply defining a new function sdiff which basically does what I also did a lot of times, substituting x(t)=x and differentiating w.r.t. x:
sdiff := proc(expr, sym) local t; subs(t=sym, diff( subs(sym=t,expr), t) ); end:
It is called like this:
sdiff( sin(x(t)), x(t)); cos(x(t))
Maybe you want a lot of ice. Maybe you want no ice. Maybe you want your top securely fastened, or maybe you want to go topless. Hmmm? Maybe you want to mix Coke and Sprite? Maybe you want to let your cup runneth over (we wish you wouldn’t). Whatever you do, make sure to have things your way.
This is what the Burger King soda cups say, and actually I chose to have a lot of ice. Enough ice in fact to do a little experiment.
A Pepsi bottle says that a serving of 240ml contains 28g sugar which accounts for 9% of my daily needs of carbohydrates. Wikipedia says that these 28g sugar contain about 106 to 109 kcal, while Pepsi says that there are only 100kcal in a 240ml serving. But in this experiment I didn’t care about energy at all, so this doesn’t matter.
I wanted to play around with the densities of different fluids and their effect on buoyancy. Everybody knows that the hardly preventable melting of the arctic ice will not raise the sea water level since the arctic ice swims, but the similarly unpreventable melting of the antarctic will. Ok, some of the ice on Antarctica is also floating, and there is so much ice that melting it will really take a long time. Now, I wanted to find out the effects of ice swimming not on fresh water, but on a water-based solution. Salt water for example, or sugar water. Since I wanted to drink the outcome of my experiment, I chose the sugar water.
So let’s start. I took two plastic cups, both 17.5g of weight. I added about 143g of ice each and then filled them up to the brim with water and Pepsi:
As expected the Pepsi glass weights more since the sugar increases the fluid density. Let’s assume that I filled both cups to the same level and that there are no more hidden air bubbles inside. Then 152g of water have the same volume as 166g of Pepsi, resulting in a Pepsi density of roughly ϱPepsi=1090kg/m3. Please don’t give to much on this number, it’s not very accurate. All I want to say is that the density of Pepsi is higher than the density of tap water.
Well, since Pepsi has a higher density, a swimming cube of ice needs to displace less Pepsi than water for generating the same buoyancy force. Now, since the underwater volume of my ice cubes is smaller for the ice swimming in the Pepsi than for the ice swimming in the water, we can expect to have higher icebergs sticking out of the Pepsi cup. And indeed, the theory works:
Now an interesting question comes up: Would the Titanic have seen the icebergs earlier if the ocean was made of Pepsi instead of seawater? You might argue that seawater is also just a solution of water and salt which renders seawater to be pretty much the same as Pepsi or Coke. However, the density of seawater is roughly ϱSeawater=1030kg/m3. That means that Pepsi has a much higher density than seawater and the Titanic might have made it! Congress, I recommend a law to fill the oceans with Pepsi or Coke, for safety reasons. Maybe Pepsi for the Pacific and Coca-Cola for the Atlantic?
My experiment however was about melting the ice, not ramming ships into it. Therefore I had to wait. The following pictures were taken 5, 10, 15, 32, 40, 71, 86 and 111 minutes after starting the experiment.
About 140 minutes after the experiment started the last few ice cubes melted. I wanted to take a picture, but just in that moment something strange happened. All of the sudden most Pepsi evaporated!
I don’t know why the water stayed where it was.
Anyway, what have we learned from this experiment?
- Pepsi weights more than water.
- The water level in Pepsi doesn’t change at all when the ice melts.
- A cup full of ice and Pepsi needs about 2.5 hours to completely melt away.
Still, there is an unanswered question:
- What if the melted ice wouldn’t have mixed with the Coke?
I believe that the cup would have “runneth over” in that case. Maybe I’ll set up an experiment to verify this. Ice has a density of 917 kg/m3, so I’ll have to find a cheap fluid substance which doesn’t mix with water but which still has a higher density than ice. Cooking oil probably won’t do… Any suggestions?
(I though about putting the ice cubes into little watertight rubber balloons instead. That would also prevent the two substances from mixing, but I’m afraid there would still be air inside my ballons.)
In the last days I was teasing Andi a bit because he claims that California would be the golden state with sunshine all around the clock. Now, the weather in Newark is much better than the weather in Palo Alto right now.
But to be honest: I hate this weather! It’s much too hot, I can’t stand the humidity and I already got a sunburn today (it’s still April!). Summer really sucks. Maybe this is the reason why I’m afraid of global warming.
You might now propose to go into some building. Right, most American buildings have aircon. The problem is that our administration at the University of Delaware just doesn’t get a plumber to fix our heating / aircon system. Yes, the controller itself is working. Yes, the shown temperature matches the room temperature. So I conclude that some valve must be stuck or something: