A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: recommendation for slide rule ?
From: Paul Hirose
Date: 2009 May 17, 15:25 -0700
From: Paul Hirose
Date: 2009 May 17, 15:25 -0700
Other than a few beginner or specialized models, just about all slide rules have a full set of trig scales: S, T, and ST (also called SRT). Some basic models combine S and ST into one scale, cutting accuracy in half. Don't expect results as accurate as sight reduction tables, at least from an ordinary 10 inch rule. Take a look at the trig scales in some good close up photos (I'll supply some links later) and see if the graduations are fine enough to meet your needs. Of course if you're just doing this for fun, who cares? Sines, arc sines, cosines, and arc cosines are found with scale S. One scale suffices for all due to symmetry, e.g., sin 30° = cos 60°. All that's required is double numbering for the graduations. Scale T takes care of tangent, arc tangent, cotangent, and arc cotangent. This scale goes up to 45°. Tangents of larger angles are obtained by symmetry. E.g., tan 60° = 1 / tan 30°. So, to multiply by tan 60°, you manipulate the slide rule as if dividing by tan 30°. As on the S scale, T scale graduations are double numbered to make this easier. It's still a little confusing, at least at first. A few slide rules provide the luxury of a double T scale so you don't have to invert your thinking for angles over 45°. The computational power is no greater, but your mental workload is reduced. Scale ST or SRT handles small angles, less than about 5.7°. In this range sine and tangent are practically identical, so a single scale suffices for both. With these scales you can find any trig function to about 1 part in 1000 accuracy with a 10 inch rule. That's true for any angle, though a little knowledge of trig identities may be required. For example, how do you get the tangent of 89°, when the T scale goes no higher than 84.3°? The solution is to realize that tan 89° = cot 1° = 1 / tan 1°. So use ST to find tan 1°, then take the reciprocal. Another dodge will find the sine or tangent of arbitrarily small angles. For example, to find the sine of .5° (off scale on ST), get the sine of 5° and mentally divide by 10. It works because the sine or tangent of a small angle is practically proportional to the angle. That kind of knowledge is far more important than owning a fancy slide rule. For sight reduction you don't need features like double length root scales, log log scales, and the like. K+E's 4080 family are classic science and engineering rules, though overkill for navigation. On the other hand, they are plentiful and affordable on eBay. The company published a nice hardbound manual, and these also come up for auction frequently. There are several variants, denoted by model number. The second digit is 0 if plastic covered mahogany, 1 if solid plastic ("Ivorite"). The fourth digit is 0 if trig scales are sexagesimal, 1 if decimal ("Decitrig"). That last is something to keep in mind for celestial use. A dash number gives the length: -1 = 5", -3 = 10", -5 = 20". Over the years K+E made several changes to the scale set. I think the last was the addition of the DI scale in the 1950s. One notorious problem with K+E rules of a certain age is deterioration of the plastic in the top and bottom cursor bars. It's known as KERCS (K+E rotting cursor syndrome). A material change around 1940 eliminated that problem. I have a 50 year old 4181-3 which has much signs of use but no trace of plastic breakdown. Wood can have problems too. In some pictures I've seen online, the uneven gap between the slide and body indicates something has warped slightly. Most of these were really old rules from the early 1900s, though. This site has information on K+E slide rules: http://www.mccoys-kecatalogs.com/index.htm Incidentally, the top two contestants in the 2009 World Champion Slide Rule Competition used rules from the K+E 4080 family. Back in the day, Pickett marketed a "Texas Speed Rule" designed for this competition. Nowadays these fetch high prices on eBay, but ordinary Picketts are inexpensive. The cheap models are plastic, but most are aluminum. According to the company, the slide is supposed to be lubricated with petroleum jelly. I think that's messy. A few years ago I sprayed mine with gun cleaning solvent (after removing the plastic cursors), lubed with Break-Free, then wiped everything dry, including the sliding surfaces. This treatment didn't affect the markings at all, and the rules still work fine. Others use silicone lube. Or you could just run the rule unlubricated. I've handled some beat-up student Picketts which clearly had never been given any care at all. Their action was surprisingly good, enough to make me wonder if lubrication was worth the bother. Sterling is another make you see a lot on eBay. These are inexpensive plastic rules. I still use the 9-scale Sterling Precision rule given to me as a kid. Those are the brands I have owned and used much. There are many more. Dietzgen and Post are both well known. From Japan there are Ricoh and Hemmi , both with extensive lines of bamboo rules. I've never handled one, but bamboo is said to be dimensionally stable and self lubricating, excellent for slide rules. From Germany you have the Aristo brand, common on eBay. Note that European slide rules often (but not always) put the trig scales on the body, not the slide. I can't help thinking this would make something like cos b cos c cos A awkward. Then there are the British Thornton rules with their unique "differential trig" scales. Some informative sites: http://www.oughtred.org/ http://tech.groups.yahoo.com/group/sliderule/ http://www.sliderulemuseum.com/ http://www.geocities.com/usra482b/index.html http://www.quadibloc.com/math/slrint.htm http://home.att.net/~ross3/HemmiCat.htm http://www.sliderule.ca/index.shtml http://www.sliderules.info/ The cheapest, widest selection of slide rules is on eBay, but if you'd rather pay a higher price to avoid the "item is sold as-is", try these vendors: http://home.att.net/~ross1/SRTC/SRTC.htm http://www.sphere.bc.ca/test/sruniverse.html Online slide rule simulator: http://www.antiquark.com/sliderule/sim/index.html -- I filter out messages with attachments or HTML. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavListemail@example.com -~----------~----~----~----~------~----~------~--~---