## Friday, June 15, 2012

### Flies walk on the ceiling

A tricky feat for sticky feet?
Flies walk on the ceiling. I can’t. But don’t think it’s for lack of trying!
People naturally assume that flies have this super-human ability – that their feet have some extra-special sticky stuff that enables them to perform this incredible feat. They don’t.
Consider the relative sizes of the fly and the human. I will take a rough estimate of the fly’s length to be 1 cm (musca domesticas[1]), and a human’s length to be 2 m. Humans are roughly 200 times as long as flies.
How about the weight? All else being equal, weight is proportional to volume, and volume is proportional to the cube of the size (length times width times height). Based on that, if a fly weighs one flyweight, then a person weighs 200X200X200 =  eight million flyweights.
Now consider the relationship between the sticky pads a fly uses and those which I might attempt to use. I might requisition pads which are 20 cm in diameter in order to walk on the ceiling. A similarly proportioned fly would have pads about 1 mm in diameter.
Here it starts to get interesting. The sticky force between the sticky pad and the ceiling is proportional to the amount of sticky stuff in contact with the ceiling, which is to say, proportional to the area of the sticky pads. All else being equal, my sticky pads would hold a weight which is 200X200 = 40 thousand times the weight of the fly’s sticky pads.
If the glue on the fly’s feet is capable of tacking ten flyweights to the ceiling (we’ll design in a little safety margin, since flies generally work without a net) then the same glue covering my sticky pads should be capable of holding 400,000 flyweights. But, I weigh in at 8 Mega-flyweights.
When I step out onto the ceiling after carefully collecting the glue from the feet of 40,000 flies, the glue doesn’t hold. I come crashing to the floor, breaking my neck. (Well actually, I only broke my neck in four of the ten trials.) It is all a question of size, not of how good the glue is.
Termination by terminal velocity
This brings me to the second point. If, for some reason, a daredevil fly were to let go of the ceiling and free-fall to the floor, would it get hurt? To determine this, I have carefully performed pteraectomies (wing removal surgery) on flies. (Animal rights activists, remember: This is all in
the name of science. It was performed under anesthesia. I had about eight beers before I got started.) After removing the wings, I dropped the flies from a height of eight feet onto a concrete floor. Those flies which the cat did not eat survived, and actually appeared to enjoy the experiment. (I am thinking of opening a bungee jump for flies. Anyone interested in investing?)
How can this be explained? Am I a wimp compared to these Rambo-esque moscids? Well, probably. But there is another explanation which is more soothing to my ego. Again, it has to do with surface area and volume.
The wind resistance one experiences in free fall is roughly proportional to the surface area which is presented to the air. This is why, if you should happen to inadvertently debark from a plane somewhere over Kansas City without a parachute, you should remember to fall lying parallel to the ground rather than toes pointed earthward. Remembering this at the right time could add milliseconds onto your life!
The same effect of size applies here. The force of the wind resistance on the fly compared to its weight is significantly larger than it is for me. As a result, the terminal velocity[2] of a fly is much less than my (really) terminal velocity.
Even if the fly were to hit the cement at the same speed as myself, much less damage would be done to the fly. This has to do with some really technical stuff like the mass to structural strength ratio, which is too complex to get into here. (That’s just my way of saying that I really don’t
understand it.)
Summarizing, flies can walk on the ceiling and I can’t. If they fall from the ceiling, they don’t get hurt, but I do. Flies are certainly coming out ahead in this comparison, but read on...
Splish, splash
Since its getting into summer, I took a bath this morning. As expected, I climbed out of the tub with no particular difficulty. But as I stepped out, I happened to glance down into the water, and discovered that I had been sharing my morning ablutions with a fly. (Needless to say, the fly was quite disgusted when he realized that he was in the same water as a human being!)
As I toweled myself dry, I happened to notice that he was actually a bit more than disgusted. He was in a state of distress. The fly was hopelessly trapped in the water, a hapless victim of surface tension.
I had a sudden rush of power as I realized that, for me, the surface tension of water meant having to dry myself with a towel. For him, surface tension is a matter of life and death.
Newton, the fly
What if Isaac Newton had been born as a fly? I’m sure that the reader is aware that there has been a movement promulgating the notion that Isaac Newton was indeed a fly, but the movement has yet to gain much of a foothold in conservative states like Wisconsin.
If Newton was a fly, I doubt that gravity would have attracted his attention. We have seen that gravity just does not have the same gravity for a fly as for a human. To take a wild guess, I would say that Flysaac Newton would probably have discovered the laws of surface tension instead.
The point is, physics is an entirely different animal for entirely different animals. When we make big changes in scale, the rules of physics change entirely. The intuition which we have keenly honed for one set of circumstances may no longer apply.
A pressing discussion
I had occasion at work one day to be discussing how wide ink spreads as it passes through the nip point in rollers on a printing press. The first engineer stated that ink is pretty thick, so he would not expect it to spread very much. The second engineer argued that the viscosity of ink goes down as it is worked between the rollers. A third engineer pointed out that ink is not between the rollers for long enough to spread very far at all. The fourth engineer countered that the pressure between the rollers is quite large, so the spread should be large.
I asked the ink spread question of one pressman whose intuition said that ink spreads “gobs and bunches” in the rollers. He related to me an incident where a sparrow thought that it should be on the cover of Newsweek. I mean literally on the cover of Newsweek.
This poor sparrow flew into the rollers of a press, and very quickly experienced the transformation from a three dimensional being to a two dimensional object. In the transformation, there was a significant increase in two of the dimensions, to make up for the sharp decrease in the thickness dimension. Hence, sparrows spread between the rollers of a press, and the implication is that ink does as well.
Contrary to the celebrated sparrow experiment, we have performed direct experiments of the spread of ink in between rollers and concluded that the amount of spread[3] is very small, less than one centimeter. So much for intuition.The moral of this story is that intuition is only valid under the circumstances that the intuition was formed. When venturing into new ground, it is best to test assumptions.

[1] My father taught me to use fancy scientific names when I don’t know what I am