To List; A few have expressed surprise at my dependance on and faith in calculations. They apparently do not need math in their profession.
The engineering profession relies on math. We could not do our work without it. A bridge designer needs math to ensure his bridge won't fall down. Airplanes are rarely tested in wind tunnels - it is too expensive, and sometimes they can't test what we need to know. They are designed on computers using math models. When you get on a plane, you are betting your life the equations are correct. They are. We rely on math to predict the performance of something. We create mathematical models on a computer, and stress them until they break. Then we see what we can do to improve the performance without adding cost or weight. Sometimes we find we have overdesigned a part, and it is not subject to as much stress as we thought. We can change it and make it less expensive to build. When we build something, we measure every parameter we can and compare the results to the model. They must agree to within a very small error. Afterwards, the engineer is measured by his peers on how close his predictions come to the actual result. Everyone benefits when an engineer does a good job. People may die when he fails. So our math must be correct, and other engineers must agree with the calculations before anything is built. It is sometimes difficult to spot mistakes in other people's work. But, yes, we rely on our calculations. I try to add a crosscheck in every calculation I do. This provides a sanity check in case I multiplied instead of dividing, or I picked the wrong root of a polynomial equation. I have tried to use Microsoft's Excel, but find myself wasting more time getting the fonts to display properly than doing a calculation. Another problem is when I want to reverse a calculation and want Excel to tell me the initial parameters. I have to rewrite the equations. This is a good source of mistakes, and it is difficult to cross-check the answer. I found a solution. For those of you who don't mind running DOS, there is an excellent program called Mercury that will allow you to do just that. It is available at http://archives.math.utk.edu/software/msdos/calculus/mrcry209/.html (Yes, the url is strange, but it is legal and works.) This program is unlike any others you may have seen. Basically, you tell it the relation between parameters, and give it one or more unknowns. If the equations are correct, it sets up a matrix and figures out how to solve the equations. Here's a simple example. We know Ohms law states E = I * R So we enter the equation: E = I * R Now, it's easy to calculate E since it is in the format Excel needs. But if you already know the voltage, and need to find the current, you have to rewrite the equation to look like this: I = E / R This is sometimes not easy, and you may forget to add or subtract a parameter on either side. This type of error is difficult to find. With Mercury, you don't have to rewrite the equation. You just give it the information you have, and it rewrites the equation for you. In the above example, you simply enter the following relationship: E = I * R and tell it that you know the voltage and resistance: E = 3 R = 10 Hah, it says. You know E and R, therefore you must be looking for I. Before you can take your finger off the key, it gives the following solution: E = 3.000000000 I = 0.300000000 R = 10.00000000 So the current is 0.3 Ampere. Neat! The calculations we need in making cs are quite simple. But the unit conversions are tricky and can make life difficult. With Mercury, you only need to enter the conversions once, and it figures out where they are needed and what form to use. For example, we know 1 ppm is 1 milligram of silver per litre. How many ounces of silver are needed to give 21.5 ppm in 2 gallons? We tell Mercury the relationship between the variables: ppm = mg / litre ; ppm = milligrams per litre litre = 3.785411784 * gal ; how many litres in a gallon (US) mg = 1000 * gram ; how many milligrams per gram goz = 0.03527396 * gram ; how many ounces in a gram lb = 8.3454 * gal ; how many pounds in a gallon soz = 16 * lb * ppm * 1e-6 ; sanity check The last entry is the sanity check. It calculates the number of ounces from the weight in gallons, and should give the same result as the goz variable. Now we test it with known quantities. We set the number of gallons to give 1 litre: ppm = 1 gal = 1 / 3.785411784 It reports the following: Solution ppm = +1.0000000000000000 mg = 1000*gram = +1.00000000000000 litre = +1.00000000000000 gal = +0.2641720523581484 gram = +0.00100000000000000 goz = 0.03527396*gram = +3.52739600000000E-05 lb = +2.20462144574969 soz = +3.52739431319951E-05 Checking the results, we see the ppm calculation is correct, the lb calculation is correct, and the two ounce calculations agree for the first six digits. This is encouraging. Now we try to solve the original problem - How many ounces of silver are needed to give 21.5 ppm in 2 gallons? We enter the new information: ppm = 21.5 gal = 2 We tell it to solve the equations and Viola - it reports the following: Solution ppm = +21.5000000000000 mg = 1000*gram = +162.772706712000 litre = +7.57082356800000 gal = +2.00000000000000 gram = +0.16277270671200 goz = 0.03527396*gram = +0.00574163794565 lb = +16.6908000000000 soz = +0.00574163520000 Again, the goz and soz numbers agree to six digits, and both have increased. So we may have the correct algorithm, and look for someone else to check it. Once we are certain the conversions are correct, we no longer need to go through this again, and can use it for future work. A proven algorithm is worth it's weight in gold. Of course, we can work backwards and give it any result, then have it tell us what parameters are needed to produce that result. A truly marvellous piece of software. I believe Excel Solver might do something similar, but I'm not really sure how it works. I know it is very slow. There are other programs that work the same as Mercury, but run in Windows instead of DOS. They are called "equation solvers". They are much better than the old slide rules I used to use:) Best Regards, Mike Monett -- The silver-list is a moderated forum for discussion of colloidal silver. Instructions for unsubscribing may be found at: http://silverlist.org To post, address your message to: [email protected] Silver-list archive: http://escribe.com/health/thesilverlist/index.html List maintainer: Mike Devour <[email protected]>
