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Be very, very careful what you put into that head, because you will never, ever get it out. Thomas Cardinal Wolsey (1471-1530) |
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Bad Rain FAQ | |
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Click on the symbol for its explanation. |
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Preamble
This FAQ (Frequently Asked Questions) is written by Alistair B. Fraser. It is in response to questions posed over the years by readers of the Bad Meteorology pages. If you have arived on this page without having read those pages or the other Bad Science pages, then what follows, will probably make little sense.Issues discussed below (arising out of the Bad Rain page)
Although the questions presented here are often ones asked by a specific person, each is chosen to characterize a group of similar questions which have been asked about the topic.
Questions arising out of Bad Rain:What is the evidence?
What is the evidence?
Who does one trust? My teachers say one thing about the shape of raindrops; you say another. What is the evidence for either position?
Who should you trust, your teachers or me? The answer is neither of us. To just accept what either says reduces science to dogma; information to be accepted on the basis of an authority rather than on the basis of evidence. However, you then raised the really important issue when you asked: what is the evidence. I don’t know how your teachers would answer the question about the evidence for the teardrop shape of raindrops, because as far as I know there is no such evidence (only myth). Maybe they would just slough off your question with the dismissive remark, "Oh everybody knows that!" Well, if it were so that everybody knows this, alas, everybody would be wrong.
But, what is the evidence to support the spherical cum hamburger shape? It comes in many forms, some direct, some indirect, but all consistently supportive.
Photography: All photographs of raindrops as they fall support the position that the shape of small drops is spherical and large drops become increasingly squashed in the vertical. Such photographs do not reveal any teardrops. Curiously, while the taking of such photographs is moderately technically demanding, there is a way to demonstrate the spherical shape of the small drops in a laboratory or museum for everyone to see. A continuous stream of water is provided from a small opening (such as a syringe). The water breaks up into a stream of equally sized and equally spaced drops, the size of which is determined by the flow rate. Now, if this is examined with a stroboscopic light in which the frequency of the flashes can be adjusted, the drops can be made to appear to hang in space (for each new flash, a new drop has moved into the place of the previous one). Then a simple magnifying glass enables one to examine the drops, which although falling, seem apparently to hang in space. The drops have to be examined well away from the syringe itself so as to allow drop oscillations resulting from the abrupt formation to die down.
Theory: Modeling of the raindrop using the equations of fluid dynamics applied to the circulation in the drop, the air flow around it and the drag reveals the same shapes: sphere changing into a hamburger. So, theory revealing the same shapes serves to explain why the raindrops appear as the do.
Rainbows: One of the most important insights a teacher of science can provide is that ideas are linked. The behavior of one thing is not independent of the behavior of another. In this case, if raindrops were really teardrops, then the rainbow, as we know it, could not be seen! Every observation of the rainbow you have ever made is evidence for the spherical shape of raindrops. Now it is certainly true that a teardrop can have a circular cross section in the horizontal and so could produce tiny vertical sections of the rainbow. However, that is all it could do; the great bow which one sees rising on one side, arching across the sky and descending on the other side could not form from teardrops. Curiously enough, the rainbow even contains observational evidence for the squashing of the raindrops as they get larger, but while easily seen, the linkage between the observation and the drop shape is a tad subtle. So, rainbows as we all enjoy them are possible only with the spherical cum hamburger-shaped raindrops.
Radar: The fact that small drops are spherical and larger drops become squashed in the vertical is sufficiently well known in the scientific community that weather radars are constructed to extract information about the drop-size distribution of the rainfall using these shapes. Such radars rely on two polarized signals, for which the returned signal from the rain depends upon aspect ratio of the raindrop and so reveals information about the size of the drops. Extracting such information from the radar gives a greatly improved estimate of the rainfall rate --- an important piece of information for estimating everything from available water supply for agriculture to flood potential. While such radar sets are not yet common, this rainfall estimation ability using polarization radars to distinguish the degree of squashing of raindrops is sufficiently established that the U.S. National Weather Service plans to add dual polarization ability to all its radars.
Reading your explanation as to the nature of raindrops I could not ignore the following sentence: “With increasing size, the fall velocity increases...” I would like to point out that according to Newtonian physics size and mass do not affect the speed of a falling object.
I am always fascinated when someone sends me a message such as this (sometimes Galileo is credited, sometime Newton, sometimes others), because it represents a triumph of poorly understood theory over observations.
Forget theory for a moment. Take observations. The fact of the matter is that big drops fall faster than small ones! This is verified by every observation (and there are thousands of them) that have ever been made on raindrops. Indeed, it is a simple thing to check yourself the next time there is drizzle. Then compare their fall speeds with those of rain. Sigh..., that is just the way it is, independent of the way you apply (actually misapply) Newtonian physics.
But, how are the observations reconciled with the theory? Fairly easily actually. There are (at least) two forces involved (not one) and the behavior of a drop depends upon both. After all, Newton’s law says that a NET force results in a change of momentum (F = ma is just a special case).
The force of gravity is proportional to the mass of the drop and thus approximately proportional to the radius cubed. The drag on the drop (it is falling through air after all) is approximately proportional to the surface area and thus radius squared. Thus as the radius increases the significance of gravity increases relative to drag. The result is that the terminal velocity of the drop increases with drop size. (Caveat for those who already understand the behavior of drag: yes, I know that as the drop gets larger, the drag does not continue to increase as the radius squared).
Newtonian physics does not say that size and mass have no influence on the speed of a falling object (as you claim) unless, the object is falling through a vacuum so that the only force on it is that of gravity.
Rain does not fall through a vacuum.
I didn’t know that the shapes of falling raindrops are so different from what we see illustrated on the weather-maps. But frankly, I think we should let the symbols stay as they are (a raindrop like a parachute or like a hamburger would lead to confusion).
I have no more problem with the representation of a raindrop as a teardrop in art than I do with the presentation of the works of Picasso or El Greco (with their anatomically incorrect people). Yet, I would make a distinction between the scientific rendering of things and the artistic rendering. Would it not bother you if the works of Picasso were used as a serious representation of human anatomy in the teaching of surgeons in an a medical school?
In an supposedly scientific presentation such as a weather forecast in which the presenter apparently wishes us to believe in his understanding of the behavior of the natural world, I have considerable difficulty in believing he strengthens his claim to this understanding by presenting the world as it is not.
