It's that time of year again. So I've gathered some more nasty questions to make another April Fools' Column. But first I have to get serious about something for a moment.
Death in the Family: I knew Frank Goodenough for over 30 years, and worked with him for over 12 years. I've sent him many notes in the last eight years—a big envelope every week, as long we have been doing this column. Such a pleasant, enthusiastic guy. I was sure Frank would be around forever. But cancer got him on Friday the 13th of February.
We all need to take good care of ourselves. The next time you men take your annual physical exam, ask your doctor to run the PSA (Prostate Specific Antigen test), to make sure prostate cancer does not sneak up on you. Frank will be remembered fondly by everyone who had the good fortune of meeting him.
Puzzler 1: Four guys named Ari, Ben, Cal, and Don have to cross a bridge. But the bridge is only strong enough to hold two men at a time. It's dark outside, and they have only one flashlight. If two guys cross using the flashlight, one guy will have to come back carrying the flashlight. (They cannot throw the flashlight across the bridge.) Ari takes one minute to cross; Ben is slower at two minutes; Cal is slower at five minutes; and Don is very slow at 10 minutes. They all have to make it across in 17 minutes.
This problem is given to Earl and Fran. Earl soon figures out that the best answer is 19 minutes. Fran says she knows the way to get everybody across in 17 minutes. How is that possible? The answer will be published here in two weeks.
Puzzler 2: A couple of my readers pointed out a new "invention" that is supposed to get much higher efficiency from an incandescent light bulb. This invention was recently published in one of the popular electronics magazines.
Sure, if you use an SCR circuit to chop the 115-V ac power going into a little 30-V 50-W light bulb, you can set a very-narrow-pulse duty cycle. You also can establish an average voltage of perhaps 12.3 V (as measured by a dc voltmeter) across the bulb, and an average current of 0.6 A (as measured by a dc ammeter). And the light is as bright as an ordinary 100-W bulb!
Because 12.3 V x 0.6 A is only 7.4 W, the author claims that his circuit provides a factor of 10 or 12 more efficiency than ordinary dumb incandescent light bulbs. Why isn't everybody doing this? What's the problem? Check the end of this column for the answer.
Puzzler 3: You folks who have Internet accounts may have read about the "new" ice-water-and-pizza diet. Simply, if one drinks a lot of very cold water, the amount of calories to warm that water up to body temperatures (at the rate of 1 calorie per gram x °C) is almost as great as the calories in the pizza. Did you know that? See my comments at the end of the column for the details on this diet.
Puzzler 4: A couple readers pointed out that a spokesman for Sandia National Labs said that they had designed a long gear train which increased the POWER output from a nano motor, by a factor of over a million (Electronic Design, Jan 26, p. 35). How did they do that?
Puzzler 5: As long as we are tweaking government laboratories, let's not forget the NASA engineer who claims he can get more bandwidth from an amplifier. Leonard Kleinberg has applied for a patent for the invention of connecting a small capacitor across the summing point of an op amp— from the negative input to the positive input. How does this work?
Puzzler 6: The data from my GPS receiver was really not useful in Nepal. It did provide one fun fact, which I figured out when I got home. I had three maps of the Annapurna area. One was grey, drab, and crude, by Mandala. One was very colorful (publisher not identified). And one was German, very crisp and meticulous. When I got back from Nepal, I compared the GPS readings I took at each campsite. When I got to the village of Jagat, the GPS said I was 1.2 mi. east, and 1.3 mi. south of the town—per the map. Did that mean that we were camped outside of town? Or that the GPS readings were WRONG? After all, the grey map did agree with the crisp map.
Puzzler 7: Everybody knows why man-hole covers are round. (You DO know that, don't you?) But where can you find man-hole covers that are NOT round?
Solution to Puzzler 1: Wait 'til the next issue.
Solution to Puzzler 2: How about that 50-W bulb that puts out as much light as a 100-W bulb, with hardly 8 W of input power? Well, the average voltage across the bulb may be 12.3 V, and the average current may be 0.6 A, but the average power is NOT 7.4 W. In fact, the average power must be determined by the time integral (over one cycle) of the instantaneous V x I, not by just multiplying (average volts) x (average amperes).
When the duty cycle of a pulsed waveform is very small, the error is huge, if you were to just multiply the dc readings together. This measurement error has been so well documented and debunked that you can look it up on Don Lancaster's web site: http://www.tinaja.com/muse112.pdf.
This is not a new mistake, but a very old mistake. The inventor multiplies the average dc voltage by the average dc current, and insists he has measured the average power.
When I asked why commercial wattmeters say the bulb is actually using 70 W instead of 7.4 W, he said they are just prejudiced against him, and the power company's wattmeters are in error. He says he can say anything he wants, no matter what I think because it's a freedom-of-speech issue. Well, if he can say anything he wants—so can I. Especially if I am right...
That little light bulb is actually running not at 8 W, but around 70 W. The efficiency of the bulb IS actually a little higher than that of the ordinary store-bought 100-W bulb that runs on 115 V ac. You can always get an incandescent bulb to run with higher efficiency (lumens per watt) by running it too hot, with too much V and I. But then the life of the bulb drops off rapidly, typically with the inverse of the seventh power of the voltage. So, if you need a bulb with high efficiency, go ahead and run it hot. But be prepared to replace it often.
That reminds me: These days, many flashlights do run their bulbs very "hot." This gives you higher efficiency, and more light, for a specified amount of battery drain. But the bulb life is LOUSY. These flashlights have a designed bulb life of only five hours, which is not mentioned at all. So be sure to take one or two spare bulbs on a long trip. I have no objection to the trade-off (improved efficiency vs. poor bulb life). But I consider it unconscionable, that the flashlight makers never warn you about the need to bring spare bulbs.
If you really want to get me on a rant, I'll explain about the Taguchi expert (Phillip Ross) who tells us, in his book Taguchi Techniques for Quality Engineering, to beware of flashlights where the bulb burns out too fast—because the manufacturers of batteries make them with such poor quality and tolerance, that the high battery voltage burns out the bulb too fast. Don't look now, but flashlight batteries are all made with the same chemistry—zinc and carbon.
Even alkaline batteries have the same voltage, 1.5 to 1.59 V, when new. There is no such problem as "bad quality causing too high voltage on flashlight batteries." But the Taguchi expert wanted us to believe that HE cares more about quality than we do, because he wants to browbeat the battery manufacturers into using higher quality. He didn't even understand that the flashlight bulbs burn out early because they are rated to operate at 2.2 V, but are operated at 2.7 or 2.8 V, for higher efficiency!
Solution of Puzzler 3: About that ice-water diet: Yes, it takes a certain number of calories to warm up the ice water you drink. But this diet relies on the confusion between a "calorie" and a "Calorie," which is actually a kilocalorie. (The calorie, which is short for "gramcalorie," is the amount of energy required to heat 1 g of water 1 °C.) A Calorie, by which all food energy is rated, is the amount of energy required to heat 1 Kilogram of water 1 °C). When we talk about the energy in food, we are likely to use the term calorie, even though we always mean kilocalorie or Calorie. The amount of energy required to warm up a glass of ice water is correctly computed in calories—and thus is 1000 times too small to make much difference in your Calorie intake. If you see this hoax in print, debunk it.
Solution for Puzzler 4: Of course, even though the Sandia guy said that a gear train could increase the output POWER, the editors at Electronic Design shouldn't have printed that statement. Maybe the useful TORQUE or FORCE could have been increased by a factor of 100 or 1000, but surely not the power. And it will be interesting to see what actual output force or torque multiplication can be achieved, allowing for friction, and allowing for the finite strength of a tiny nano-etched silicon gear, before it breaks or binds up.
Solution for Puzzler 5: The NASA engineer, Mr. Kleinberg claims to be able to get more bandwidth, by connecting a small capacitor across the inputs of an op amp. How does this work? Poorly. He applied for a patent on this because nobody else had tried to do that before. In MOST cases, people avoid adding in such capacitance, because it causes peaking, ringing, and extra output noise. It is not literally untrue that one can cause the 3-dB bandwidth to increase a little—it is just not useful in most cases. If you are going to install a capacitor, you can get increased useful bandwidth by installing it across an input resistor.
Solution for Puzzler 6: At Jagat, the GPS readings said that I was 1.2 miles east of town, and 1.3 miles south of the town. Did that mean that I was camped outside of town? Or that the GPS readings were WRONG? No, just because two maps agree, does NOT mean they are right. In this case, the colorful map was (nominally) correct. It agreed with the GPS. It said that Jagat was 40% of the way up from Sange to Chamje. The other maps agreed on 65% of the way. So in Nepal, as elsewhere in the world, maps are not necessarily correct, even if two maps agree!
In a couple years, Nepal will have maps as good as USGS maps, but the good maps have not yet been completed as far west as Annapurna. If you want to see all 22 of our campsites' locations (allowing for ±100 or 200 meters of uncertainty) you can look them up on my web site. NOTE: Even if there is some disagreement with the map, two hikers with GPS receivers should be able to find the same place with better accuracy! If you want to know how to buy the right map, even if it does not have any publisher listed, look in the Trip Report.
Solution for Puzzler 7: Of course, if a manhole cover is round, it cannot fall into the hole. However, in Nashua, N.H. there are still manhole covers that are triangular.
All for now. / Comments invited!
RAP / Robert A. Pease / Engineer
Mail Stop D2597A
P.O. Box 58090
Santa Clara, CA 95052-8090
Circle 550 if you think the answer to Puzzler 1 is 17 minutes.
Circle 551 if you arrive at 5 minutes.
Circle 552 if you took less than 17 minutes to arrive at your answer.