Diameter * sin(180 degrees / 7 sections). Sin(180/7) = 0.43388. Just make sure you're doing degrees and not radians. (if radians, you'd take sin(pi/7)). To convert .9051 to 32nds, just multiply .9051 by 32 and round to the nearest whole number. Everyone's phone has a calculator. In 32nds, it comes out to 3 and 28.9585/32nds; slightly less than 29/32 which may be why 3 and 29/32 made it slightly too long
Why not use a decimal rule? Saves the conversion step, and the loss of accuracy. If you have a digital caliper, you already have one, and it is more accurate than a tape measure. What possible reason is there to use fractions?
@@TensquaremetreworkshopFractions, decimals - different ways to express values. Or are they? The sine of an angle really isn’t a number, it’s the proportion of the side opposite an angle to the length of the hypotenuse of a right triangle including that angle (or the angle’s compliment). Trig values like sine, cosines, and tangent are ratios, not really simple values. Just sayin’, it’s hard to get away from fractions and ratios in this world.
@@johnnyragadoo2414 Yes, fractions and decimals are different ways to express values. But if the value is already a decimal (as, clearly, in this case) why convert it to a fraction? There will often be a loss of accuracy, and it is a step not needed. A ratio IS a number. What else could it be? It is a dimensionless number, but still a number. And your calculator will give it to you as a decimal. Not hard to get away from fractions at all. Especially if the calculation gives you a decimal number to start with. When people talk of fractions, they usually are referring to binary fractions (where the divisor is a power of 2). As values get smaller (or more accurate) it gets unwieldy- not met anyone who works in 128ths, never mind 256ths. Machinists move to thou and tenths. So, decimal. And they are often mixed with fractional dimensions. Errors waiting to happen. Why not use divisors that are a power of 10? (i.e. decimal...) I repeat my question- What possible reason is there to use fractions for this task?
I’m 85 years old, love working in my shop building anything. I don’t know what I enjoy more the math for calculating angles, dividing circles, like what you did, or trying to figure out spacing for a box joint/dove tail project. Then building the jigs and fixtures to make what ever it is the old brain comes up with this week. Still have’nt figures out what is more fun, the morning bowel movement, a cup of coffee or doing the math and solving building problems. Excellent video, thank you for taking the time. From. Missouri.
You don't need an online conversion. Just measure a circle in metric measure for the circle diameter; Diameter * Table number = Product/number of sections in same metric units as the metric measure of the circle's diameter. Example; if you wanted 45 sections and your diameter was 2.000000 m, the chord would be 3.1022 cm, (or one degree would be a chord of about 3.87775 mm). [Please check my calculations.]
@@bcase5328 You missed the point. We don't use metric measurements in the United States and that is the audience he is speaking to, we who use the Imperial system measurements of inches and fractions of an inch.
Well Herrick, it seems that I'm about the only one that would want Your system as they all have a "better one" ? So ,at least one simple soul has benefitted from Your kind video .Thank You.
You can do this without any calculations, charts, measurement numbers or fancy technical terms like "chord" that don't even come up with the correct solution. Just set your compass to what you think it might be and walk it around the circle. Re-set your compass by about 1/7 of the "gap" and try again. You will have it spot on in a few tries.
Using the chord length is a perfect solution. Literally. It's the lack of precision of the chart and rounding to whole units that cause the error. But the old old school method is to estimate and adjust until you get it close enough.
Estimate and adjust is OK for a low number of sectors but it gets really messy and laborious if you need say 30 sectors. lots of rubbing out and re-doing. I'll stick to calculators thanks.
Calculation is the best way to find the cord length .After that fine adjustments , are probably necessary to make it work out exactly. Listen to the man in the video . He knows what he is doing . If you don't know how to do the calculation , use the table. Either way , you can't go wrong with what is done in the video . For a small circle , it may be better to draw a large circle with the same center as the small circle . Divide the large circle into the desired number of equal cords . Then draw lines from the center of the circle to the outer circle divisions. The intersections of these lines with the smaller circle will divide the small circle exactly . @@franklunt8975
Instead of stepping around the circle in one direction only, go halfway from the starting point in one direction, then go back to the starting point and fill in the remaining half going in the opposite direction. Particularly when the segment count is on the higher side. This will reduce the accumulation of error should your compass be spaced too wide or too narrow. As effectively noted already by another commenter, using the trigonometric formula is superior in that it obviates the need to have the table of factors at hand. It's always worthwhile to understand the mathematical underpinnings, which facilitates the derivation of solutions for other problems. By the way, it's chord, not cord. 😉
Great video, man. Here's a possible cheat I've used. I bought a digital caliper with fractional conversion built in. I set it to 3.9051, locked it in place, and mark the points. Again, Great video.
For decimal equivalents, I use the Decimal Equivalents table from the Grainger catalog. It shows both fractions of inches and metric units. Select the table and print to .PDF. Transfer the .PDF to your phone (somewhere you can easily find it), and download a .PDF viewer.
Thanks for keeping in the video the adjustments made. So many of these videos edit those parts out, leaving the guys out in the real world wondering what they're doing wrong.
When counting off 32nds, sometimes it's easier to go backwards. So instead of counting 29 of them from the 3" mark, count back 3/32 from the 4" mark. (That works because 32/32 is a full inch.) Also, you don't always have to count from an inch mark. For instance, you can find, say, 3 19/32 by counting up 3/32 from 3 1/2" since 1/2"=16/32".
@@Tensquaremetreworkshop You're going to be throwing away that resolution anyway as soon as you use a ruler or tap measure. Thinking 8 digits of resolution means anything in woodworking is ludicrous.
@@TedHopp I am not suggesting that. If a calculator uses fractions, what divisor does it choose? Sets the accuracy. With decimal you take the number of significant digits you want- you choose.
A simpler method I've used is to divide the 360 degree circle by number of segments wanted to get the angle of each segment. Mark a line from ctr. to o.d.. Using a protractor set to this angle, mark a second line from ctr. to o.d.. You can then set a compass across these intersecting points. Mark the other points with compass.
That's the way I learned as a sheetmetal worker apprentice. It doesn't matter the size of the circle. Just divide the segments into 360° to get your angle from center. Then for accuracy walk it off on the circumference with dividers or compas
This video is not about dividing a circle in segments, it’s mainly about converting decimals to fractions to deal with imperial units. The cord of any angle is r*2*sin(180/n) No tables, no websites, just one formula.
Interesting, thanks; but the secret is the prepared table so not so much a trick as having the data. By the way, inches × inches gives you inches² rather than inches; so the 0.4339 has to be simply a multiplier rather than a length in inches. I've not tried it but I suspect it doesn't matter which measuring system you use as long as you are consistent, so no conversion needed. Edit: Having now read other comments I see the above point has already been made. Ah well, I took the time to write it, so I'm leaving it 😉
That's right, it's a truly dimensionless quantity - cord length divided by diameter. Measure both in cm, inches, atomic radii or astronomical units and it will just work.
Retired carpenter (76). Great explanation. Mostly remodeled. Learned many “tricks of the trade” from other carpenters including my Dad. Hated running into the occasional hack “can’t see it from my house types (fired a few in my time). Thanks for the presentation. You were “flexible, but not limp” as my Dad used to say. 😂
I don't care what any one else has said, this is really helpful! If it doesn't quite turn out right, make an adjustment, just like he did. Gang, work in thge real world, MAKE it work!
You should be able to find that chart in the Machinery Handbook as well. This method is great on a flat plane surface where you can use dividers but not so easy with a part that has a bore and can't establish a center point. But this is a keeper piece of information and appreciated.
Good video, but just wanted to point out that when you convert .9051 to 32ths you have to round up to get 29/32 the actual number is something like 28.9 something and so that leads to that discrepancy , you have to take that rounding error into account
I love that compass that you are using . I have tried to do this circle dividing operation , and I can tell you that you definitely need a compass with that fine an adjustment . You will struggle otherwise . Even if you are only dividing by 5 . The higher the number of equal sections , the more difficult it will become --- I am pretty sure .
The multiplier at step 2 is not a number of inches, it is simply a number. If you multiply four inches by the number three, you get twelve inches, i.e. a length. If you multiply four inches by three inches you get twelve square inches, i.e an area. Because the multiplier is simply a number, it will work equally well if you are working in inches, feet, metres, or any other unit of length.
You want to know the fraction conversion to a decimal value, just multiply the decimal by the smallest marks on your ruler. .9051 inches in 16ths of an inch is .9051×16=14.4816 The result is the number of sixteenths of an inch. Rounded up to 14.5 sixteens, you got 7/8 +
The same chart is found in Machinerie's handbook used by machinists for laying out bolt circles the old fashioned way. As opposed to letting a CNC machine do it with coordinates. I never go around the circle in one direction. I go from both sides around so the error is smaller. Using Vernier calipers helps too so I don't have to convert to fractions.
@@tonymiller8826 That was my point- 'Verniers' HAVE to be decimal to work. But it is the decimal part that is important. Because the manufacturer wanted to add a Vernier feature, he was forced to use decimal, and you now have a decimal scale. They should also be available in other measuring devices, and are in most of the world. 95% of it.
Your video caught my eye. Another method without "look up table". Bisect one segment to create right triangle. Use trig to calculate side opposite. Multiply that by two to find chord length.
0.4339 is just a coefficient with no unit if it was in inches you would end up with square inches after calculating the length. It's not very important but just to say when doing the same in metric use the same coeff don't convert it to cm.
This technique is demonstrated here on a relatively small circle, which could be easily "stepped off" using an estimated cord distance on dividers, then readjusted a few times to get it right on. But it gets more complicated and time consuming with a larger circle and/or more sections. With that in mind, the simple math equation and multiplier number chart shown in this video will save you time getting the needed cord length. You may still need to adjust your caliper (or beam compass for larger circles) to get it right on in your "real world" application, but any adjustment should be minimal and much less frustrating. I appreciate all the comments here from people who are much smarter than me. 👍
How about someone dumber than you? Am I allowed to comment? BTW: Out in a field, you can do a rope for the radius of the circle, peg in the ground and another rope for the cord distance and two people. You can quite quickly mark out a large circle this way. This is handy if your town needs some tourism because you can make a "crop circle" with a funny pattern to get some reporters to come see.
When I was still working as a sheet metal worker, part of my job was dividing circles into any number of sections. But I used a different method without mathematics or tables that one of my teachers had shown me. All that was needed was a compass and a ruler. That was a very long time ago and I doubt I could now recall how it was done. But after a lifetime in engineering I'd anyway solve the problem instead with a bit of trigonometry and a calculator. BTW, I found metric for these kinds of problems easier to use than inches, no conversion from decimal to fractions needed.
No need in Imperial either- just use decimal. Machinists work in thou- which are decimal. If you have a measuring caliper, it should offer decimal operation.
@@Tensquaremetreworkshop True. I've never understood why carpenters use fractions of inches. It was the same for me when I was doing my sheet metal worker apprenticeship.
Doing anything in fractions is simply not as simple as doing it in a decimal system. And NASA has lost a million $ satellite because at one point somebody botched up the conversion from decimal to fractions. Just look at a set of drills. In decimal you can sort 20 sizes with .5 mm real quick. Just call out the first 20 sizes in fractions once. And then convert to decimal!
@@mikethespike7579 It works for "carpentry" because precision beyond 1/16" is rarely required. That said, I wish we had just gone metric back in the 1070s. Life would be easier and cheaper (one set of drills, sockets, etc.)! But it is what it is.
if you don't have the book with the pre-calculated table of values use the 'law of cosines' for the general case (wikipedia has a good article on that).
This is an interesting technique and useful for very large circles (ie greater than 12"). Here is a technique that is dead accurate but needs a computer and printer. Open any spread sheet program. Type the same number (any number) in a column of cells. (eg Type "7" for seven segments in seven cells). Highlight the cells and click to create a flat pie chart. Now remove all the "fancy" colors and details you don't need. Highlight the pie chart, size it as big as you need it, and click "Print". Done, and very accurate. Takes much longer to describe than to actually do. In my application, I am only interested in the angles, not the finished size.
I usually draw a line through the center of the circle . It gives me two starting points. This works great for cutting the error in half as long as I am not building a watch! LOL!
Thank you for sharing. There is a multitude of good ideas that arrive at the same conclusion, or nearly. To multiply the diameter by Pi and divide the result by the number of segments required will give an accurate distance. As an example a circle of 1 metre diameter will have a chord length of 20.9 millimetres for 150 segments. My phone has given me a figure up to 14 decimal places. For anyone that doesn't have a compass they can measure from one point of the circle to the next point at which the measurement on the ruler indicates and then repeat.
Easy. Use the compass to mark points on each leg of the angle that are equi-distance from the vertex; draw a straight line between those two points, set the compass points to a visually estimated one third of that distance; begin iteratively stepping off those thirds along the line, making small adjustments each time until reaching that "just right" spacing. (If the angle in question is >180, do it for the reciprocal sector (pie shape) of a circle, and the back azimuths will then be the trisecting lines you seek.) (If exactly 180 degrees, draw a circle with origin "O" at the vertex, and inscribe a hexagon in that circle. ...almost a trivial matter since each side* of such a hexagon = the radius of the circle.) * - 60 degrees for a hexagon, i.e. a trisected 180 degrees. While that may not pass the most rigorous mathematical scrutiny, it should suffice for most practical purposes.
An excellent vid' but I do have a couple of minor points. Firstly: It doesn't matter what system of measurement you use; imperial , metric, cubits or matchsticks; the numbers remain the same. Just don't mix the units. Secondly: Marking out from the start point and marking to the halfway point, then working in the opposite direction from the start point to the halfway point, minimises any error. Finally: Dividing 360 by the number of segments will give the subtended angle in degrees, between segments. Using this angle, the radius of the circle and any web Chord Calculator will give the length of chord. It can also be calculated using the formula :- Length of Chord = 2*Radius*Sin(Subtended Angle/2). Mind you! Having said that, tables are a much the easier way. 🤓👍
@@johnmcdonald9977 Metric has the added advantage that the fourth step is completely unnecessary. Only the imperial/ customary unit system works with fractions as a definitive measurement, most of the time. there are rulers that have inches divided in tenths and hundredths, but these are specialty items.
It would be a lot quicker to guess the cord length and just adjust the compass ( as you did ) until you get 7 equal segments or whatever number you are aiming for.
If the object of the exercise is to divide a pizza into 7 sections for a group of 7, proceed as follows: Cut it in half. Cut each half into quarters and then cut each quarter into eighths. Eat one section and rearrange the remaining parts evenly spaced on the plate and serve. (Nobody will notice the missing bit and you might even get praise for how fairly you've cut it.)
Wow, this is such an incredible faff! It’s time America moved to metric, you won’t believe how much simpler it is. I grew up in England using imperial measurements but we changed when I left school!
Well at nearly 90 a tenth of "thou" is easier for me to use than decimal points for Metric .It was once remarked that the metric system was devised as being easier to use by the majority of Romans because they had 10 fingers .
I started my trade apprenticeship in Imperial then later moved to a country that uses the Metric System. I find being fluent with both is a huge benefit. I have another problem solving tool and approach the Metric only guys don't have. In most cases the Metric system is easier but not in all. Being able to use fractions and 10ths makes solving a lot of layout problem that demands accurate division of spaces so much easier or demands numbers results than aren't fractions of mm. But then again you wouldn't have a clue about what I'm talking about since you can't add, subtract, multiply or divide using inches,, what shame you criticize a language you know nothing about,, 😢😢
What would be interesting is how to get the multiplier if you don't have access to the chart in the Fine Woodworking. In other words, what is the mathematics involved to get those numbers?
The book has an error: the 7th chord is actually '0.4305' - the book says '0.4339'. That gives a final fraction of 28/32. Very subtle difference! Anyway, thanks for the video. Interesting technique.
I don’t think that is correct. I believe the calculation for the chord length is “sin(pi/7)” which equals .43388. Not sure what formula you are using to get .4305?
The (. .4339 ) isn't inches. That same .43 39 is just a multiplier. So that wii work for metric also. It is just the multiplier for 7 equal parts of a circle . I also prefer inches . But it works without conversation of the multiplier because that is just a given % of a circles conformance.
The decimal inches to fractional inches could also be worked out via ratios. (0.9051 is actually 9051/1000, so set up your equation with the desired denominator, eighth, sixteenth , thirty second, etc, as follows 9051/1000= X/32, then solve for X; 0.9051 = X/32; 0.9051 x 32 =X; X = 28.9632 or 29/32nds)
OMG! "I'm an American, I'm working in inches", Thank you SO much!! Nothing at all wrong with Metric. But, if I want to know, I'll look it up. I wish all American RUclipsrs would just follow this philosophy. When I watch European videos, I don't expect them to use Imperial. And when I care enough, I do the conversions. And it usually means more to me then, I remember it better. Sorry, I just had to rant. This was a cool video, great explanation and well done. Thank you for sharing!
For a German (77) it‘s always very entertaining to watch you struggle with fractions. Especially when you have to use decimals in between! Like thousands of an inch when it has to be any more precise than a RHPHW.
Thank you very much, Mr.Kimbal. Actually, I was trying to figure out how to divide a circle into 4 equal sections to build a paper pyramid with a slant angle of 76.345 grades. How do you find the slant angle of a paper pyramid? You know, Is interesting how I ask (myself) a question about a circle divided in parts to find the perfect slant angle and just your video showed up. My intention is to build a pyramid of a 6 1/2 feet with an angle slant of 76.345 eventually. You got a kind intention, people who are synch with the same intention will resonate with your kindness. Again, thank you.
RUclips is evidently listening to you (or reading your mind). 😳 I have no insights for getting that precise slant angle. Best wishes with your project. 👍
Not sure whether the 6.5 feet is height or width but either way the calculations are straightforward if the apex is directly over the centre of the base. Your height is one side of a right angle triangle and your base is at 90 degrees to that. So you have a right angle triangle with a known side and a known angle. Trigonometry will then give you the other dimensions and the rule that internal angles in a triangle add up to 180 degrees gives you the third angle.
Let's say that you want to change the diameter of the circle to 8 inches. You already have the circle divided, so just use the same paper and set your compasses to a four inch radius, draw the circle and it's already divided into seven sections. Works for any size smaller than nine inches.
Its all so much easier in metric. This whole exercise relies on having the book that most people don't have so its mostly a wasted exercise. However, simple maths solves the problem i.e. the chord length is 2 r Sin(a/2), where r is the radius and a is the segment angle, it could also be written as d x Sin(a/2), where d is the circle diameter. With modern scientific calculators it will be much quicker to use the formula than to look up the chord factor and then punch in the relevant info to come up with the answer. I can't see how this determination would be useful to most Architects as they will use a CAD program, where by pressing a button or pointing a scribe a circle is instantly divided into segments, gone are the days of drawing boards and tee squares.
The one assumption that you've made in your calculations is that you knew where the center of the circle was. Without the center of the circle, you would have trouble coming up with the pie chart configuration, even though you would be able to divide the circumference of the circle into equal parts. On paper this could be simplified, however in the real world such as you suggested in a landscaping situation, or in a large round piece of wood, this (not knowing where the center of the circle ) would be a problem.
With a suitable sized right angle square it's not difficult to find a centre. Even for a very large circle a little trial & error with a tape measure should find it. After all, how perfect does the landscaping need to be to not be spotted as being slightly out ?
If the circle was drawn with a compass then you would know where the centre was. If not:- Put the tang of your tape measure on a fixed point on the circle and rotate the tape about that point to find the maximum dimension across the circle and draw a line along the tape. Do the same thing at about 90 degrees and the centre is where the lines cross. The more times it's done from different points on the circle, the greater the accuracy.
It's difficult to draw a true circle without knowing where the center is. In landscaping, you can employ a cord and pegs to lay it out exactly. Stonehenge was likely laid out this way.
A chord of a circle can be bisected which will intersect the center of the circle. A 2nd chord on the same circle can also be bisected, this will intersect the first bisection at the center point of the circle. I’m sure there is a RUclips video that explains this technique. Cheers!
No need to actually find the center. You only need 3 points along the circumference of the circle to be able to complete the circle. Create a triangle from the 3 points. Pick one point to be the apex of the triangle and extend the legs from it so each leg is longer than the distance between the other 2 points. Slide the triangle so the legs are always touching the non-apex points. The apex of the triangle will always trace the arc along the circumference of the circle between the 2 points without needing to find its center. Need to continue the arc? Place your apex on one point and another point of your triangle on the existing arc. The remaining point of your triangle will be on the circumference of the same circle. Mark that point and continue as above.
At 78, and English, I was brought up with Imperial measures. However, I now use metric far more simply because it is more accurate from the beginning. Loved the video, as geometry eas akways my favourite part of maths.
metric is not more accurate. objectively speaking neither is more accurate for they are both capable of measuring to whatever degree of accuracy you require. so you are probably talking about 'subjective accuracy' or 'the accuracy I get when I use' and that's a different thing. For the common person that probably means measuring to the nearest mm instead of the nearest inch. Much more accurate. Or to the decimetre rather than inch. For the dyi person it might mean measuring to the nearest mm instead of the nearest quarter. Much more accurate. Or the nearest eighth. Still more accurate. Or the nearest sixteenth. Still more accurate. Or the tradesman maybe to the nearest 1/32. Nope. Not more accurate. 1/32 of an inch is less than 0.8 mm. It is smaller in the order of 4/5. Hence more accurate. 32nd of an inch are or were routinely marked on measures, even school rulers. The question is: why did people not use them? Why did the different people use 1/16 or 1/8 or 1/4 etc.. ? And the answer is plainly that they used according to the level of accuracy they want. Nowadays it is assumed that 90% of people and tasks require only 1mm. This is not true. It is an assumption. The same as the assumption that metric is 'more accurate' . In fact I have a vernier caliper with scales in both metric and imperial. It measures to 1/1000 of an inch imperial and 1/50 millimetre in metric. 1/50 of a mil is greater precision than 1/1000 inch. The question is why does it do this? How does it do this? And must it do this? Is it something inherent in the two scales? Nope. Not at all. They did it by using two different verniers. The imperial scale divides 25thou divisions by 25 to give 1000. The metric scale uses 50 division of 1 mil. to give 1/50 mil. But the imperial scale could just as easily have used 50 division itself, to give a half thou precision. It is all question of choice, for purpose, for person.
There are two types of countries in the world: those that use metric, and those that have put men on the moon. I think proper inches are just as accurate as sillymeters, if you measure accurately. My mill and lathe are both in inches. Thousandths, actually, with a full turn of the wheel on my mill table being exactly 1/16". You realize of course that your body contains several proper units of measure, when quickness is more important than absolute accuracy and there are no official rulers or yardsticks handy, right? Spread your arms. That is a fathom. Six feet for you landlubbers. Once you calibrate your personal fathom and your personal great stride for a yard, you got that nailed. Mash your thumb on something and mark to either side. One inch. You can calibrate that too, by how hard you mash and flatten your thumb. Standard units of measurement have real world equivilants. whereas metric used to be sort of based on something something something but is now just arbitrary and meaningless. If your measuring and marking are accurate, then inches are just as accurate as french units. One advantage of metric is if you can count decimal places, even if you can't do math, you can sort of do math. Metric was invented for the mathematically challenged, which is why it was invented in France. I am sort of surprised the Italians didn't dream it up, for building their infamously out of plumb towers and stuff.
@@growleym504 You are correct that Metric and Imperial are equally 'accurate'. I believe the post was confusing Metric and decimal. And here we have the actual issue. Mixing fractions and decimal gives problems. You say your mill table is 1/16 full turn, and is calibrated how? All machinists work (small scale) in decimal- for the US that would be thou. And tenths(!) If you want to do that on your mill, there must be a discontinuity on the scale, because 1000/16 is 62.5. That means you cannot rely on the scale if the movement goes past that discontinuity- you have to do some sums. Plus, you may want to work in decimal (thou) but your drills and cutters are fractional. Oops! With letter and number drills to fill in some of the gaps. No such problem in Metric- they are all decimal. Simples. Metric units, to be specific SI units, have the advantage of eliminating almost all of the tedious conversion factors that plague Imperial calculation. There are 1000 liters to the cubic metre, and a litre of water weights a Kilogram. A Watt is one joule per second. A joule is one Newton metre. A tonne is 1000 Kg. Get the idea? [ A horsepower is 746W (approx) or 33000 ft lbs per minute. But then you know that.] BTW two errors. Neither Liberia or Myanmar have put men on the moon (the other countries that use imperial)- not even with the help of German rocket scientists... And the US went officially Metric in the mid-seventies. Just have not managed to do it yet...
@@Tensquaremetreworkshop You are correct there is a discontinuity. The units are in thousandths. A full turn is about 62.5 divisions. Sixteen turns is an inch so you can easily reset zero there, or actually anywhere. For a lot of parts that I end up having to make, quarter turns are well within tolerances. For fine stuff I stick to decimal. It's a great system. If you crank your handwheel for 8" or 10", the feed screw and gears will give you enough slop to require re-zeroing anyway, on these cheap Chinese machines. I can do math, so conversion is no obstacle.
@@growleym504 I love it when people attempt to defend a flaw. If moving to a number of features, re-zeroing at each one introduces an error. Not zeroing means you have to keep track of the halves. Yes, one can deal with it- but you do not have to. Operating in decimal is simpler and less error prone. Which is why DROs work that way.
Or just work it out via ratios (A is to B as C is to D, or A/B = C/D): (remember, 0.9051 is actually 9051/1000) - set up your equation with the desired denominator, eighth, sixteenth , thirty second, etc, as follows (I’m gonna use thirty seconds) 9051/1000 = X/32, then solve for X; 0.9051 = X/32; 0.9051 x 32 =X; X = 28.9632 or 29/32nds)
wonderful information, I had a 7 foot diameter steel frame that needed 8 sections laid out.... sure wish I knew this Chord method.....cheers from Florida, Paul
Of course it does depend on the degree of accuracy needed but if you mark out from your first point working anti clockwise to half way around the circle and from your first point clockwise for the other half, it minimises any minor inaccuracy in the cord length. Although this is an excellent instructional vid', I was disappointed to find that your method required tables and mathematics. I have geometric methods for dividing a circle into many number of segments but in all my years I have never found a geometric solution for five. If anyone has a method of setting out five segments using only straight edge and compasses, I would be very grateful to hear it.
As others have noted, the discrepancy comes from the 29/32 fraction not being exact - it doesn't matter how you propagate your points, seven times that angle will always be a little too much! As for your construction, try looking up how to construct a pentagon. This is the same thing as dividing a circle into five segments, but mathematicians usually refer to the polygon name rather than the circle. There's even a very neat method that just involves knotting a piece of paper. Take care though - not all polygons can be constructed with compass and straight edge! So, 7, 9, 11 and 13 and infinitely many others cannot be constructed that way.
The more sections dividing the circle, the more errors accumulate- like the width of one line "off" from perfect width of the compass multiplied by the number of sections adds up to the quarter inch off.
I CAN do it without ANY chart! No TRIG! NO MATH CALCULATIONS! 1. Determine the circumference with a piece of paper (or similar material) . 2. Divide circumfrence "paper" into however many sections you want - transfer back to circle. NO breaking it down into 32nths or whatever! EXACT measurements. Don't need to know center of circle!
Odd - Even does not matter. Don't no where you got the idea of even number of sections. I got it out of an old "Machinist Handbook" to cut an ELEVEN TOOTH GEAR.@@herrickkimball
@@herrickkimballI’m not crazy about his solution but he could use a separate carpentry trick my dad (a carpenter) taught me on how to divide any linear measurement into a chosen number of equal sections. Use a ruler laid diagonally across that paper with 0” on one edge at the beginning of the paper and your chosen number on the opposite side and end of the paper (lets say six sections, so the 6” mark on the ruler touches the opposite side at the end of the paper. 0 through 5 = 6 sections) Mark each measurement mark, 1” through 5” on the paper. Each mark makes the divisions. Doesn’t matter if you use metric or imperial, still works as long as the numbers are divisible by your chosen number of sections. For metric you could use any cm measurement that is divisible by 6 and fits diagonally from end to end. So say 18cm. 18 divided by 6 is 3, so increments of 3. Mark every third number 3, 6, 9 … through 18. No fractions: easy.
A good Old craftman tip : Instead of going round the same way, go in both directions, reduce the times you should move the tool from the point,and the error should be reduced, am i right 😊or what
A little like this example:The times i would move a 2 m level is 2-3 times unless total accuracy is of no importance, the accumulated error is just too big, ☺️👍🏻
Engineer, here, born and raised in Merica. Let’s not make excuses for English unit of measure. They suck. Even the English got rid of shillings, pence, and so on, in their money. (For all practical purposes we’ve gotten rid of Pence, too.). You’ve done a great job of explaining this, and I am going to use this knowledge. You did a great job explaining how to convert the fraction of an inch from decimal to 32nd’s. Thank again! Thanks for sharing your knowledge! I’ll use this. And just for grins I’m going to make a chord length table jus like the one you shared.
Technically, it is not the unit that is English, but the size of it. For example, the French also uses feet and inches- they were just a different size (their King was a different size). Many measures can be traced back to Roman ones, perhaps they should get the blame... Interesting that some people want to keep measures that are based on the size of (someone's) human body. And claim they are 'natural'.
You have an accumulated error by moving the tape measure twice, 1/64 off when marking the three inch mark and 1/64 off when marking the 29/32 mark. Off course the error could go either way, if the error goes the same direction for both marks, then 1/64 + 1/64 = 1/32 and 1/32 x 7 = 0.21875" or close to the 1/4 inch that you are off. My guess is that the diameter is slightly off along with the sharpness of the lead on the compass and the pencil thus introducing three more errors. Once when instructing my students (I was an applied physics, math and CAD/CAM instructor) we took three different tape measures (different brands) and aligned them next to each other to check the accuracy, two were real close, but not perfect, the third tape measure was off about .010" to .015". Another way to do it is by using a CAD program to give you the exact measurement quickly and there are a few free CAD programs out there. Just my two cents worth...Good video, especially for those with limited math skills!
That doesn't give you the straight line computation (3.9051" chord as it is used here). Instead, it gives the arc length as if you were wrapping a string around the circle 4.0392"
Nice technique, thanks. Really no conversion necessary for metric. Indeed, even the conversion to a fraction could just refer to “units”; the measuring system is completely irrelevant to the process.
I cannot recommend this method. What if your original circle isn't exactly 9"? Now all the measurements will be off. What if the web site that converts to fractions isn't precise enough? What if you don't have internet access? What if after a hard day in the sun you're prone to math errors? The old timers would get calipers, estimate the distance, and walk the calipers around the circle. After 7 steps (in this case), you're either short, on, or long. If short or long, make the appropriate change to the calipers and walk around again. Repeat until you're "close enough". Then walk both ways, counterclockwise and clockwise, and mark between the paired lines. This step averages out the error.
Exactly. I use that divider/caliper trick to find the center of boards. In the real world "precision" is an ideal. You work to "close enough" instead. My dad was a sheet metal worker and used 22/7 as an approximation for pi so long, that he forgot the decimal version. You want to scale your working definition of "precision" to the size of the project, and remember that each decimal place is ten times smaller than the previous one. Then employ tactics that minimize cumulative error between the approximation you are working to, and the ideal you are aiming for. The video example is frustrating because .9051 has no common factors with any power of 10 except 1, so converting it to a common fraction is never going to be exact, expressed in any useful common fraction. In fact, it is an instance where using the metric system might be superior.
@@theeddorian No, the _decimal_ system is superior. The arbitrary length of a meter and all its meaningless subdivisions don't matter. American Machinists have been using decimal inches for 100 or more years.
@@tonyennis1787 Read what I wrote again, and take your personal biases out of the internal text in your head. No carpenter or woodworker, or landscaper works to the tolerances a mechanical engineer uses. For wood working, either system works quite as well as the other. And arguably, a system that uses common fractions will be superior for woodworking, especially if you use hand tools. They are easier to calculate with in your head, as long as you aren't using any measure finer grained than a 64th of an inch, which is slightly more than 0.39 mm. And that is entirely reliant on IF you employ any kind of universal measurement system at all. You can do very high quality work and never employ a measurement in either inches or millimeters. One of my neighbors has a table I built for her, which is scaled to her size. The only measurement I took was three pencil marks on a stick. One was the height of the top of her thigh when seated on one of her cut down chairs, and the others were the length and width of the leftover counter top piece she wanted to use as a top. It is square, level, supports my weight, and lets her work at it seated in a modified chair that allows her feet to touch the ground. I never did measure it.
@@tonyennis1787 I understand, and I think I mentioned this. Engineers work to tolerances most of the rest of the world doesn't appreciate. I don't agree that tenths of an inch is superior to any other system, or that any particular system is even useful in a wood shop. I personally do prefer common fractions when I am measuring things in the shop. The arithmetic is easier for me. You might want to look at "BY Hand and Eye" by George Walker and Jim Tolpin. You really do not need a ruler in a small shop unless a client walks in with a list of dimensions.
Easely divide …. And you have to use a chart, calculator, online app, … Read 16th’s as 2 32’s … Line out, use the compass, … and then eyeball a correction. Yeah, that’s a piece of cake, .. LOL ;) It does not help that when you determine a chord with a little error, … you will add that error every time on every part. I would: Divide 360 degrees into the number of parts. That would give me 51,4285… degrees. Times two: 102,857 degrees. (*) Draw that angle within the circel. Now where the angle touches the circle, I mark the dots. With the help of my compass I can easely determine the middel between those two marks … so i have determined the chord for one part. Needed: compass, simple calculator for a division and a multiplication and a protractor. And no need to deal with imperial of metric measuring. (*) by multiplying by 2, you use a greater angle, thus making the error you get when rounding up, smaller. It’s easy to measure an exact middle between two points with a ruler, without having to fear to make a round-up error. Also, i’m from a part in the world where we use metric … so no need to deal with 16th’s or 29/32….. Just my 2 cts
A trick in carpenter's eyes - or a simple calculation an elementary schoolboy's eyes (a student, who pays attention to the calculus classes and remembers what the sin function is for). And, @3:30, the ratio is dimensionless, i.e not in inches. Later, the required conversion is the "benefit" of the imperial system but again, you can do that conversion almost as quickly with a calculator or on a scrap of paper, no need for the internet thingy, as long as you know the elementary calculus. Ya, the formula for the "magic" table you so kindly allow viewers to printscreen is sin(180°/n), there you go, no need to thank me, it's beyond elementary.
Im not good at math. Just like your last step, I guesstimate circumference sections and adjust compass in tiny movements till I hit the starting mark . Takes about as long as it took to write these two sentences. Asked a cabinet maker once how he laid out an oval table top, said he had no formula ,just used his father's full size templates.There is a mathematical way to do it also. Again, hopeless for me. I drove two nails for length of oval , and used a piece of string tied in a circle to allow for width at centre of oval and used a pencil to pull string in an oval around the two nails. Close enough to perfect and took less than a min. The maths for it was baffling to me.
You took a very easy math problem and complicated it by requiring table lookups and online web calculators... Also, because of the way you put your compass flat on the paper when setting the distance, you introduced some error into its set length. You should have had it with the point stuck into your starting point and then kept adjusting the screw until it produced a mark exactly over the distance you have measured. Also, my starting in one direction and continuing in that direction all the way around the circle, you allowed for more error to creep into your marks. If you had marked both ways from the starting point and then did the same from those two points, your introduced error would have been half of what it was. An even better solution would be to use a compass with points on both ends so that you could pivot from one end to the next as you moved around the circle. This would have removed the accumulated error that was caused by where in the pencil lead width mark you were placing the sharpened point of the compass.
@@Tensquaremetreworkshop -- Not for those of us in the US who are competent working in fractions... It would be completely idiotic if you told everyone that the way to do this was to first go buy a new measuring device because what you've always worked with isn't good enough... Personally, I would have done the video different, showing the simple math involved (without tables and such) with the result in a decimal inch AND THEN show how to convert from the decimal inches to fractional inches if the viewer did not have a decimal inch measure. This could be structured to work with either the US Customary Units OR the metric system since the calculations are basically unitless...
@@CurmudgeonExtraordinaire As I have said several times, I agree that the base unit is not important. In this type of case. Being forced to do a conversion because the only scale available is in vulgar fractions is, for me, not acceptable. It severely, and unnecessarily, reduces the accuracy involved. An extra step that makes things worse? How can that be a good idea. A Vernier caliper, which is a fairly cheap and useful tool, will be in decimal. Cast off your hair shirt, and embrace accuracy.
@@Tensquaremetreworkshop -- From a math standpoint, fractions are usually more accurate... With decimals, you are only stating a value to a certain number of significant digits... If you say "1/2", then it means EXACTLY that value... If you state "0.5", then it is "0.45
@@CurmudgeonExtraordinaire Wow, talk about shooting blind! I actually have a degree level math qualification... Saying 0.5 means a tolerance spread of .05? Since when? Quote a source. Tolerances are usually expressed separately, as they vary. It may be '0.5 [+0,-0.005]' for example. Try expressing that as a fraction. From a math standpoint, 0.5 is 0.5 in the same way that 1 is 1. Indeed, there is an explicit way of expressing tolerance, in engineering, via a convention- if you write 0.500 you are defining the value to three significant figures, so it can only vary by +- 0.0005. (there has to be trailing zeros for this convention to apply). Try doing that with fractions. And in the real world there is always a tolerance- exact is a platonic ideal. More accurate? There are more decimal numbers than fractions, so how can fractions be more accurate? Above, you specified the error in the weight of a Kilo of water- as a decimal. Care to do it as a fraction- to the same accuracy? But at least you used Celsius - well done.
@americo2958 Medicine delivered in cubic centimetres, engine sizes in litres, photographic lenses in millimetres, food information labels in kilo calories...the list goes on. Question, what does two and a half pints of water weight? In metric two and a half litres of water has a weight (mass) of 2.5 kg...easy :-). Join us ASAP.
As the saying goes, "there are nations who use the metric system, and there are nations who put man on the Moon". P.S. I'm also in the metric system camp. 😅
I noticed that for 100 sections, the multiplier is 0.0314. Hmmm. That is suspiciously similar to pi divided by 100. If you don't have a chart to look up the multiplier, could one not divide pi (3.14 by the number of sections (pie slices) you want. It is not exact on all of them but it might be due to the difference in the number of places of pi you use. Just guessing about that but I calculated a few of them and they came to within three decimal places. I don't know if this is a direct correlation or simply a quirk of the close relationship between the arc length and the chord length of a particular section. I did notice on some of the odd-numbered sections that they were a fraction larger than listed in the chart. There may be a rule to compensate for certain numbers of desired sections but it is late and my brain is too tired to investigate further tonight. Maybe someone with more knowledge about these things than myself (which is almost nothing) can enlighten us all.
If the number of sections does not equally divide into 360 (360°), than some rounding is going to need to take place. 7 sections, shown in the video was a particularly bad number to use as an example because the division into 360 goes on infinitely. The number shown on the chart will likely work good enough for most projects but it will never be exact. Fun fact: Internal combustion engines always have a number of cylinders that will equally divide 360° to keep a consistent circular rotation of the crankshaft, without the slightest hiccup.
Dividing by pi only "works" for a large number of sections/pie slices. It does not work for smaller numbers. Reason: dividing by pi gives the exact distance around the curve, however when you mark out the distance, it is a straight line distance you want, not around the curve. For lots of sections these two are close, never exact, but otherwise they are quite different.
@@psidvicious Always? There are five cylinder engines, and currently 3 cylinders are popular- more efficient, apparently. Even numbers were used to simplify crankshaft machining- the bearings are in one plane. Not an issue with modern machining.
@@psidvicious You do understand that the choice of the number of degrees in a circle is arbitrary, and comes from the use of base 60 by the Babylonians? Another way (and very common) to divide a circle is into radians. And, in that case, no number of cylinders divide into equal radians. You seem to think the division requires a whole number of this arbitrary measure, the degree? Further to this, radial engines are very common in 7 cylinders!
Would you say you provide a (partly) digital way here? Any multipliers of some demanding number would be easy in many cases, like if i have 7 equal sections i divide them by 4 to get 28 equal parts. Carl Friedrich Gauss (en.wikipedia.org/wiki/Carl_Friedrich_Gauss ) was so proud of having found a way to divide a circle into 17 (equal) parts (as in en.wikipedia.org/wiki/Heptadecagon ), "claiming" this to be his greatest discovery in the year 1801 as far as it's told, so he might used calculus, but this must have been a rather/mostly analog(ue) way.
8:30 the math world and real world didnt correspond because you use a lot of approximations in multiple steps. Thats why we in the math world will use pi/2 instead of 1.5708 until we get to the very end and use the approximation
Excellent idea. I looked up the ideal number of pie slices from a 9" pie pan and the internet told me 6 to 8. Well, that would be 7 and that's why I chose 7 for this video. It occurred to me that pie pans could be made with slight indents in the perimeter at the 7-slice dimensions as a guide for precise slices. For pizza slices I can see the same idea. This could be a really big money-making idea for someone! 👍😁
It's easy to use a protractor, and you won't have to rub out and try again - you'll get very close, first time. Divide 360 degrees by the number of segments you need, then use a circular protractor to get the right answer first time. Let's say you want 11 segments. 360/11 = 32.72727 - you can't measure such tiny divisions of a degree on the protractor, but as close as you can get is 3/4 of the way from 32 to 33 degrees. Then, on you calculator, press "+", "=". That will add 32.727 to the 32.727 you already had, to give 65.45454. press "=" several more times to get 98.181818, 130.90909, 163.63636, 196.363636, 229.0909, 261.818, 294.54545, 327.2727, 360 - and we have done the entire circle. Place your protractor and without moving it again, mark out all the angles, then draw lines from your centre to each mark.
Why bother with the chord lengths at all? 360 divided by 7 is 51.4286 degrees. so just set a mitre guide or angle setter to that, draw any radius and mark off the other radii. A tiny adjustment may be necessary, as in your case, to correct inaccuracy in setting the instrument, but you could get to the same place much more easily. Think 7 equal angles, not chords.
1) It is NOT .4339" - the factor is dimensionless, so no ". 2) Why convert from the decimal number to fractions? Use a decimal measure. If you are a machinist, you already have one (you will be used to working in 'thou'- i.e. decimal). If not buy one- using fractions is limiting and without justification. You are also losing accuracy by approximating. 3) Those in the Metric world (95% of the world) do NOT need to 'convert'- it is you who are converting. By definition the inch is 25.4mm. BTW the USA became officially Metric in the mid-70s.
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Diameter * sin(180 degrees / 7 sections). Sin(180/7) = 0.43388. Just make sure you're doing degrees and not radians. (if radians, you'd take sin(pi/7)). To convert .9051 to 32nds, just multiply .9051 by 32 and round to the nearest whole number. Everyone's phone has a calculator. In 32nds, it comes out to 3 and 28.9585/32nds; slightly less than 29/32 which may be why 3 and 29/32 made it slightly too long
Brilliant info - thanks! 👍🇬🇧
Why not use a decimal rule? Saves the conversion step, and the loss of accuracy. If you have a digital caliper, you already have one, and it is more accurate than a tape measure.
What possible reason is there to use fractions?
@@TensquaremetreworkshopFractions, decimals - different ways to express values.
Or are they? The sine of an angle really isn’t a number, it’s the proportion of the side opposite an angle to the length of the hypotenuse of a right triangle including that angle (or the angle’s compliment). Trig values like sine, cosines, and tangent are ratios, not really simple values. Just sayin’, it’s hard to get away from fractions and ratios in this world.
@@johnnyragadoo2414 Yes, fractions and decimals are different ways to express values. But if the value is already a decimal (as, clearly, in this case) why convert it to a fraction? There will often be a loss of accuracy, and it is a step not needed.
A ratio IS a number. What else could it be? It is a dimensionless number, but still a number. And your calculator will give it to you as a decimal.
Not hard to get away from fractions at all. Especially if the calculation gives you a decimal number to start with.
When people talk of fractions, they usually are referring to binary fractions (where the divisor is a power of 2). As values get smaller (or more accurate) it gets unwieldy- not met anyone who works in 128ths, never mind 256ths. Machinists move to thou and tenths. So, decimal. And they are often mixed with fractional dimensions. Errors waiting to happen.
Why not use divisors that are a power of 10? (i.e. decimal...)
I repeat my question- What possible reason is there to use fractions for this task?
Huh maybe you get that
I’m 85 years old, love working in my shop building anything. I don’t know what I enjoy more the math for calculating angles, dividing circles, like what you did, or trying to figure out spacing for a box joint/dove tail project. Then building the jigs and fixtures to make what ever it is the old brain comes up with this week. Still have’nt figures out what is more fun, the morning bowel movement, a cup of coffee or doing the math and solving building problems. Excellent video, thank you for taking the time. From. Missouri.
😂
4:48 You don't need an online conversion. Just multiply 0.9051 by 32. 0.9051 x 32 = 28.96 = 29, your measurement is 29/32.
Ummm mm really
You don't need an online conversion. Just measure a circle in metric measure for the circle diameter; Diameter * Table number = Product/number of sections in same metric units as the metric measure of the circle's diameter.
Example; if you wanted 45 sections and your diameter was 2.000000 m, the chord would be 3.1022 cm, (or one degree would be a chord of about 3.87775 mm). [Please check my calculations.]
@@bcase5328 You missed the point. We don't use metric measurements in the United States and that is the audience he is speaking to, we who use the Imperial system measurements of inches and fractions of an inch.
Yea if you did it this way you would have known 29 was rounded up so like a smidgen less than your perfect 29/32 mark you made the first time.
Well Herrick, it seems that I'm about the only one that would want Your system as they all have a "better one" ? So ,at least one simple soul has benefitted from Your kind video .Thank You.
I agree with you . There is nothing wrong with Herrick's method .
You can do this without any calculations, charts, measurement numbers or fancy technical terms like "chord" that don't even come up with the correct solution. Just set your compass to what you think it might be and walk it around the circle. Re-set your compass by about 1/7 of the "gap" and try again. You will have it spot on in a few tries.
Using the chord length is a perfect solution. Literally. It's the lack of precision of the chart and rounding to whole units that cause the error. But the old old school method is to estimate and adjust until you get it close enough.
Estimate and adjust is OK for a low number of sectors but it gets really messy and laborious if you need say 30 sectors. lots of rubbing out and re-doing. I'll stick to calculators thanks.
Calculation is the best way to find the cord length .After that fine adjustments , are probably necessary to make it work out exactly. Listen to the man in the video . He knows what he is doing . If you don't know how to do the calculation , use the table. Either way , you can't go wrong with what is done in the video . For a small circle , it may be better to draw a large circle with the same center as the small circle . Divide the large circle into the desired number of equal cords . Then draw lines from the center of the circle to the outer circle divisions. The intersections of these lines with the smaller circle will divide the small circle exactly . @@franklunt8975
I like it your way, Bill!
Instead of stepping around the circle in one direction only, go halfway from the starting point in one direction, then go back to the starting point and fill in the remaining half going in the opposite direction. Particularly when the segment count is on the higher side. This will reduce the accumulation of error should your compass be spaced too wide or too narrow.
As effectively noted already by another commenter, using the trigonometric formula is superior in that it obviates the need to have the table of factors at hand. It's always worthwhile to understand the mathematical underpinnings, which facilitates the derivation of solutions for other problems.
By the way, it's chord, not cord. 😉
Great video, man. Here's a possible cheat I've used. I bought a digital caliper with fractional conversion built in. I set it to 3.9051, locked it in place, and mark the points. Again, Great video.
For decimal equivalents, I use the Decimal Equivalents table from the Grainger catalog. It shows both fractions of inches and metric units. Select the table and print to .PDF. Transfer the .PDF to your phone (somewhere you can easily find it), and download a .PDF viewer.
Thanks for keeping in the video the adjustments made. So many of these videos edit those parts out, leaving the guys out in the real world wondering what they're doing wrong.
When counting off 32nds, sometimes it's easier to go backwards. So instead of counting 29 of them from the 3" mark, count back 3/32 from the 4" mark. (That works because 32/32 is a full inch.)
Also, you don't always have to count from an inch mark. For instance, you can find, say, 3 19/32 by counting up 3/32 from 3 1/2" since 1/2"=16/32".
counting off 32nds is definitely going backwards. The calculator gives decimal- measure in decimal.
@@Tensquaremetreworkshop Some calculators can display results in fractions.
@@TedHopp Yep, what a misuse of technology… Most calculators work to 8 significant figures, but let us just throw away that precision.
@@Tensquaremetreworkshop You're going to be throwing away that resolution anyway as soon as you use a ruler or tap measure. Thinking 8 digits of resolution means anything in woodworking is ludicrous.
@@TedHopp I am not suggesting that. If a calculator uses fractions, what divisor does it choose? Sets the accuracy. With decimal you take the number of significant digits you want- you choose.
A simpler method I've used is to divide the 360 degree circle by number of segments wanted to get the angle of each segment. Mark a line from ctr. to o.d.. Using a protractor set to this angle, mark a second line from ctr. to o.d.. You can then set a compass across these intersecting points. Mark the other points with compass.
That's a good alternative. Thanks!
That is just what I was thinking. I've laid out building foundations using this method. You don't need tables or charts to refer to.
I agree.
That's the way I learned as a sheetmetal worker apprentice. It doesn't matter the size of the circle. Just divide the segments into 360° to get your angle from center. Then for accuracy walk it off on the circumference with dividers or compas
This video is not about dividing a circle in segments, it’s mainly about converting decimals to fractions to deal with imperial units.
The cord of any angle is r*2*sin(180/n)
No tables, no websites, just one formula.
Interesting, thanks; but the secret is the prepared table so not so much a trick as having the data. By the way, inches × inches gives you inches² rather than inches; so the 0.4339 has to be simply a multiplier rather than a length in inches. I've not tried it but I suspect it doesn't matter which measuring system you use as long as you are consistent, so no conversion needed.
Edit: Having now read other comments I see the above point has already been made. Ah well, I took the time to write it, so I'm leaving it 😉
I guess technically the unit of the conversion factor is "per chord" since the calculation gives the length per chord as the answer.
That's right, it's a truly dimensionless quantity - cord length divided by diameter. Measure both in cm, inches, atomic radii or astronomical units and it will just work.
Retired carpenter (76). Great explanation. Mostly remodeled. Learned many “tricks of the trade” from other carpenters including my Dad. Hated running into the occasional hack “can’t see it from my house types (fired a few in my time). Thanks for the presentation. You were “flexible, but not limp” as my Dad used to say. 😂
I don't care what any one else has said, this is really helpful! If it doesn't quite turn out right, make an adjustment, just like he did. Gang, work in thge real world, MAKE it work!
You should be able to find that chart in the Machinery Handbook as well. This method is great on a flat plane surface where you can use dividers but not so easy with a part that has a bore and can't establish a center point. But this is a keeper piece of information and appreciated.
What do you mean? This method does not require you to locate the centre.
the chords lengths are also in the Machinery's handbook pocket companion as well as in the spiral bound machinist's ready reference book.
Good video, but just wanted to point out that when you convert .9051 to 32ths you have to round up to get 29/32 the actual number is something like 28.9 something and so that leads to that discrepancy , you have to take that rounding error into account
I love that compass that you are using . I have tried to do this circle dividing operation , and I can tell you that you definitely need a compass with that fine an adjustment . You will struggle otherwise . Even if you are only dividing by 5 . The higher the number of equal sections , the more difficult it will become --- I am pretty sure .
The multiplier at step 2 is not a number of inches, it is simply a number. If you multiply four inches by the number three, you get twelve inches, i.e. a length. If you multiply four inches by three inches you get twelve square inches, i.e an area. Because the multiplier is simply a number, it will work equally well if you are working in inches, feet, metres, or any other unit of length.
Very decent that you mentioned your source. You mother raised you right!
Great trick. I froze the video at 3:15, went to full screen and took a screen shot. Now I have it printed out and also saved in my 'Repairs' file.
Great presentation. Thank you.
Thank god I use metric.
I love your unspoken rule of thumb. “Try maths and if that doesn’t work, just guess”.
It is decimal that makes it easier. Works just as easily in Imperial decimal. Converting to fractions was entirely unnecessary.
yeah....sit back and have a piece of pi.
You want to know the fraction conversion to a decimal value, just multiply the decimal by the smallest marks on your ruler.
.9051 inches in 16ths of an inch is
.9051×16=14.4816
The result is the number of sixteenths of an inch. Rounded up to 14.5 sixteens, you got 7/8 +
The same chart is found in Machinerie's handbook used by machinists for laying out bolt circles the old fashioned way. As opposed to letting a CNC machine do it with coordinates. I never go around the circle in one direction. I go from both sides around so the error is smaller. Using Vernier calipers helps too so I don't have to convert to fractions.
It is not the Vernier that avoids the fractions, it is using decimals. Which Vernier measurement requires. Why on Earth do people use fractions?
My Vernier calipers don’t read in fractions. I have several, they all read in .001” or .02 mm. So yes it is the Verniers.
@@tonymiller8826 That was my point- 'Verniers' HAVE to be decimal to work. But it is the decimal part that is important. Because the manufacturer wanted to add a Vernier feature, he was forced to use decimal, and you now have a decimal scale. They should also be available in other measuring devices, and are in most of the world. 95% of it.
@@Tensquaremetreworkshop Whatever, you comment like an AI bot.
@@tonymiller8826 I am guessing that is an attempt at an insult- but my algorithms cannot resolve that.
Why not diameter x Pi for circumference then divide by number of sections desired?
Seems easier that needing internet to look up charts.....
Your video caught my eye. Another method without "look up table". Bisect one segment to create right triangle. Use trig to calculate side opposite. Multiply that by two to find chord length.
That's how the measurement chart was created.
That's most likely how the measurement chart was created.
0.4339 is just a coefficient with no unit if it was in inches you would end up with square inches after calculating the length. It's not very important but just to say when doing the same in metric use the same coeff don't convert it to cm.
This technique is demonstrated here on a relatively small circle, which could be easily "stepped off" using an estimated cord distance on dividers, then readjusted a few times to get it right on. But it gets more complicated and time consuming with a larger circle and/or more sections. With that in mind, the simple math equation and multiplier number chart shown in this video will save you time getting the needed cord length. You may still need to adjust your caliper (or beam compass for larger circles) to get it right on in your "real world" application, but any adjustment should be minimal and much less frustrating. I appreciate all the comments here from people who are much smarter than me. 👍
How about someone dumber than you? Am I allowed to comment?
BTW: Out in a field, you can do a rope for the radius of the circle, peg in the ground and another rope for the cord distance and two people. You can quite quickly mark out a large circle this way. This is handy if your town needs some tourism because you can make a "crop circle" with a funny pattern to get some reporters to come see.
When I was still working as a sheet metal worker, part of my job was dividing circles into any number of sections. But I used a different method without mathematics or tables that one of my teachers had shown me. All that was needed was a compass and a ruler. That was a very long time ago and I doubt I could now recall how it was done. But after a lifetime in engineering I'd anyway solve the problem instead with a bit of trigonometry and a calculator. BTW, I found metric for these kinds of problems easier to use than inches, no conversion from decimal to fractions needed.
No need in Imperial either- just use decimal. Machinists work in thou- which are decimal. If you have a measuring caliper, it should offer decimal operation.
@@Tensquaremetreworkshop True. I've never understood why carpenters use fractions of inches. It was the same for me when I was doing my sheet metal worker apprenticeship.
@@mikethespike7579 Even worse is that drills and cutters are in fractional sizes. In Imperial, that is. Metric is, of course, decimal.
Doing anything in fractions is simply not as simple as doing it in a decimal system. And NASA has lost a million $ satellite because at one point somebody botched up the conversion from decimal to fractions. Just look at a set of drills. In decimal you can sort 20 sizes with .5 mm real quick. Just call out the first 20 sizes in fractions once. And then convert to decimal!
@@mikethespike7579 It works for "carpentry" because precision beyond 1/16" is rarely required. That said, I wish we had just gone metric back in the 1070s. Life would be easier and cheaper (one set of drills, sockets, etc.)! But it is what it is.
if you don't have the book with the pre-calculated table of values use the 'law of cosines' for the general case (wikipedia has a good article on that).
Simple and common sense, taken one step at a time! Thank you for this service! Ive bookmarked this for future use!
This is an interesting technique and useful for very large circles (ie greater than 12"). Here is a technique that is dead accurate but needs a computer and printer. Open any spread sheet program. Type the same number (any number) in a column of cells. (eg Type "7" for seven segments in seven cells). Highlight the cells and click to create a flat pie chart. Now remove all the "fancy" colors and details you don't need. Highlight the pie chart, size it as big as you need it, and click "Print". Done, and very accurate. Takes much longer to describe than to actually do. In my application, I am only interested in the angles, not the finished size.
I usually draw a line through the center of the circle . It gives me two starting points. This works great for cutting the error in half as long as I am not building a watch! LOL!
You could use a protractor and just measure angles: 360 / n, where n is the number of divisions.
Love the tutorial. helpful like the links to decimal chart. Get er done, Larry the cable guy. Their are so many solutions to derive same objective.
Thank you for sharing. There is a multitude of good ideas that arrive at the same conclusion, or nearly. To multiply the diameter by Pi and divide the result by the number of segments required will give an accurate distance. As an example a circle of 1 metre diameter will have a chord length of 20.9 millimetres for 150 segments. My phone has given me a figure up to 14 decimal places. For anyone that doesn't have a compass they can measure from one point of the circle to the next point at which the measurement on the ruler indicates and then repeat.
Interesting Herrick. For your next challenge, come up with a system that will trisect any angle using a compass and straightedge.
Ha ha. Yes indeed - and don't forget to collect your Nobel Prize in mathematics when you're finished.
Easy. Use the compass to mark points on each leg of the angle that are equi-distance from the vertex; draw a straight line between those two points, set the compass points to a visually estimated one third of that distance; begin iteratively stepping off those thirds along the line, making small adjustments each time until reaching that "just right" spacing.
(If the angle in question is >180, do it for the reciprocal sector (pie shape) of a circle, and the back azimuths will then be the trisecting lines you seek.)
(If exactly 180 degrees, draw a circle with origin "O" at the vertex, and inscribe a hexagon in that circle. ...almost a trivial matter since each side* of such a hexagon = the radius of the circle.)
* - 60 degrees for a hexagon, i.e. a trisected 180 degrees.
While that may not pass the most rigorous mathematical scrutiny, it should suffice for most practical purposes.
An excellent vid' but I do have a couple of minor points.
Firstly: It doesn't matter what system of measurement you use; imperial , metric, cubits or matchsticks; the numbers remain the same. Just don't mix the units.
Secondly: Marking out from the start point and marking to the halfway point, then working in the opposite direction from the start point to the halfway point, minimises any error.
Finally: Dividing 360 by the number of segments will give the subtended angle in degrees, between segments. Using this angle, the radius of the circle and any web Chord Calculator will give the length of chord. It can also be calculated using the formula :- Length of Chord = 2*Radius*Sin(Subtended Angle/2).
Mind you! Having said that, tables are a much the easier way. 🤓👍
It's only easy if you have that table!
@@nickwhite2996 Very true!
My, oh, my! Ok, I give in! It doesn't matter which system you use. My preference is metric, No offence intended to anyone!
@@johnmcdonald9977 Metric has the added advantage that the fourth step is completely unnecessary. Only the imperial/ customary unit system works with fractions as a definitive measurement, most of the time. there are rulers that have inches divided in tenths and hundredths, but these are specialty items.
In geometry and other math, it’s a chord, not a cord. This is, of course, also true for music.
but you need a bit of cord to measure the length of the chord.
It would be a lot quicker to guess the cord length and just adjust the compass ( as you did ) until you get 7 equal segments or whatever number you are aiming for.
If the object of the exercise is to divide a pizza into 7 sections for a group of 7, proceed as follows: Cut it in half. Cut each half into quarters and then cut each quarter into eighths. Eat one section and rearrange the remaining parts evenly spaced on the plate and serve. (Nobody will notice the missing bit and you might even get praise for how fairly you've cut it.)
Wow, this is such an incredible faff! It’s time America moved to metric, you won’t believe how much simpler it is. I grew up in England using imperial measurements but we changed when I left school!
Well at nearly 90 a tenth of "thou" is easier for me to use than decimal points for Metric .It was once remarked that the metric system was devised as being easier to use by the majority of Romans because they had 10 fingers .
I started my trade apprenticeship in Imperial then later moved to a country that uses the Metric System. I find being fluent with both is a huge benefit. I have another problem solving tool and approach the Metric only guys don't have. In most cases the Metric system is easier but not in all. Being able to use fractions and 10ths makes solving a lot of layout problem that demands accurate division of spaces so much easier or demands numbers results than aren't fractions of mm. But then again you wouldn't have a clue about what I'm talking about since you can't add, subtract, multiply or divide using inches,, what shame you criticize a language you know nothing about,, 😢😢
Durn chief! So many geniuses! Thank YOU for taking the time to make this simple and easy for everyone.
What would be interesting is how to get the multiplier if you don't have access to the chart in the Fine Woodworking.
In other words, what is the mathematics involved to get those numbers?
SIN(180 / # Sections ) x Diameter = Chord Length
Many thanks for the math.@@wyldanimal2
I hate math and you made it easy, thank you!
The book has an error: the 7th chord is actually '0.4305' - the book says '0.4339'. That gives a final fraction of 28/32. Very subtle difference!
Anyway, thanks for the video. Interesting technique.
I don’t think that is correct. I believe the calculation for the chord length is “sin(pi/7)” which equals .43388. Not sure what formula you are using to get .4305?
This is a good place to use a caliper and skip the decimal to fraction conversion.
The (. .4339 ) isn't inches. That same .43 39 is just a multiplier. So that wii work for metric also. It is just the multiplier for 7 equal parts of a circle . I also prefer inches . But it works without conversation of the multiplier because that is just a given % of a circles conformance.
if the circle conforms, why need all those decimals?
@@seanmahoney1077 cause pie is analog not digital
The decimal inches to fractional inches could also be worked out via ratios. (0.9051 is actually 9051/1000, so set up your equation with the desired denominator, eighth, sixteenth , thirty second, etc, as follows 9051/1000= X/32, then solve for X;
0.9051 = X/32;
0.9051 x 32 =X;
X = 28.9632 or 29/32nds)
OMG! "I'm an American, I'm working in inches", Thank you SO much!! Nothing at all wrong with Metric. But, if I want to know, I'll look it up. I wish all American RUclipsrs would just follow this philosophy. When I watch European videos, I don't expect them to use Imperial. And when I care enough, I do the conversions. And it usually means more to me then, I remember it better.
Sorry, I just had to rant. This was a cool video, great explanation and well done. Thank you for sharing!
That comment cracked me up. That is such… uh… an American comment 😂
Always something interesting every time I visit your channel. Thank you very much!
For a German (77) it‘s always very entertaining to watch you struggle with fractions. Especially when you have to use decimals in between! Like thousands of an inch when it has to be any more precise than a RHPHW.
and just as much fun to find exactly 1/3 when using decimals
Thank you very much, Mr.Kimbal. Actually, I was trying to figure out how to divide a circle into 4 equal sections to build a paper pyramid with a slant angle of 76.345 grades. How do you find the slant angle of a paper pyramid? You know, Is interesting how I ask (myself) a question about a circle divided in parts to find the perfect slant angle and just your video showed up. My intention is to build a pyramid of a 6 1/2 feet with an angle slant of 76.345 eventually. You got a kind intention, people who are synch with the same intention will resonate with your kindness. Again, thank you.
RUclips is evidently listening to you (or reading your mind). 😳 I have no insights for getting that precise slant angle. Best wishes with your project. 👍
Not sure whether the 6.5 feet is height or width but either way the calculations are straightforward if the apex is directly over the centre of the base. Your height is one side of a right angle triangle and your base is at 90 degrees to that. So you have a right angle triangle with a known side and a known angle. Trigonometry will then give you the other dimensions and the rule that internal angles in a triangle add up to 180 degrees gives you the third angle.
Let's say that you want to change the diameter of the circle to 8 inches. You already have the circle divided, so just use the same paper and set your compasses to a four inch radius, draw the circle and it's already divided into seven sections. Works for any size smaller than nine inches.
You could enlarge it also.
Its all so much easier in metric. This whole exercise relies on having the book that most people don't have so its mostly a wasted exercise. However, simple maths solves the problem i.e. the chord length is 2 r Sin(a/2), where r is the radius and a is the segment angle, it could also be written as d x Sin(a/2), where d is the circle diameter. With modern scientific calculators it will be much quicker to use the formula than to look up the chord factor and then punch in the relevant info to come up with the answer.
I can't see how this determination would be useful to most Architects as they will use a CAD program, where by pressing a button or pointing a scribe a circle is instantly divided into segments, gone are the days of drawing boards and tee squares.
The one assumption that you've made in your calculations is that you knew where the center of the circle was.
Without the center of the circle, you would have trouble coming up with the pie chart configuration, even though you would be able to divide the circumference of the circle into equal parts. On paper this could be simplified, however in the real world such as you suggested in a landscaping situation, or in a large round piece of wood, this (not knowing where the center of the circle ) would be a problem.
With a suitable sized right angle square it's not difficult to find a centre. Even for a very large circle a little trial & error with a tape measure should find it. After all, how perfect does the landscaping need to be to not be spotted as being slightly out ?
If the circle was drawn with a compass then you would know where the centre was.
If not:-
Put the tang of your tape measure on a fixed point on the circle and rotate the tape about that point to find the maximum dimension across the circle and draw a line along the tape. Do the same thing at about 90 degrees and the centre is where the lines cross. The more times it's done from different points on the circle, the greater the accuracy.
It's difficult to draw a true circle without knowing where the center is. In landscaping, you can employ a cord and pegs to lay it out exactly. Stonehenge was likely laid out this way.
A chord of a circle can be bisected which will intersect the center of the circle. A 2nd chord on the same circle can also be bisected, this will intersect the first bisection at the center point of the circle. I’m sure there is a RUclips video that explains this technique. Cheers!
No need to actually find the center. You only need 3 points along the circumference of the circle to be able to complete the circle. Create a triangle from the 3 points. Pick one point to be the apex of the triangle and extend the legs from it so each leg is longer than the distance between the other 2 points. Slide the triangle so the legs are always touching the non-apex points. The apex of the triangle will always trace the arc along the circumference of the circle between the 2 points without needing to find its center.
Need to continue the arc? Place your apex on one point and another point of your triangle on the existing arc. The remaining point of your triangle will be on the circumference of the same circle. Mark that point and continue as above.
What would be the angle on the end of a 2x4 chord, for that matter, any size lumber? Don't know much about trigonometry! 🤔
At 78, and English, I was brought up with Imperial measures. However, I now use metric far more simply because it is more accurate from the beginning. Loved the video, as geometry eas akways my favourite part of maths.
metric is not more accurate. objectively speaking neither is more accurate for they are both capable of measuring to whatever degree of accuracy you require.
so you are probably talking about 'subjective accuracy' or 'the accuracy I get when I use' and that's a different thing.
For the common person that probably means measuring to the nearest mm instead of the nearest inch. Much more accurate. Or to the decimetre rather than inch.
For the dyi person it might mean measuring to the nearest mm instead of the nearest quarter. Much more accurate.
Or the nearest eighth. Still more accurate.
Or the nearest sixteenth. Still more accurate.
Or the tradesman maybe to the nearest 1/32. Nope. Not more accurate.
1/32 of an inch is less than 0.8 mm. It is smaller in the order of 4/5.
Hence more accurate.
32nd of an inch are or were routinely marked on measures, even school rulers.
The question is: why did people not use them?
Why did the different people use 1/16 or 1/8 or 1/4 etc.. ?
And the answer is plainly that they used according to the level of accuracy they want.
Nowadays it is assumed that 90% of people and tasks require only 1mm.
This is not true. It is an assumption.
The same as the assumption that metric is 'more accurate' .
In fact I have a vernier caliper with scales in both metric and imperial.
It measures to 1/1000 of an inch imperial and 1/50 millimetre in metric.
1/50 of a mil is greater precision than 1/1000 inch.
The question is why does it do this?
How does it do this?
And must it do this?
Is it something inherent in the two scales?
Nope. Not at all.
They did it by using two different verniers. The imperial scale divides 25thou divisions by 25 to give 1000.
The metric scale uses 50 division of 1 mil. to give 1/50 mil.
But the imperial scale could just as easily have used 50 division itself, to give a half thou precision.
It is all question of choice, for purpose, for person.
There are two types of countries in the world: those that use metric, and those that have put men on the moon. I think proper inches are just as accurate as sillymeters, if you measure accurately. My mill and lathe are both in inches. Thousandths, actually, with a full turn of the wheel on my mill table being exactly 1/16". You realize of course that your body contains several proper units of measure, when quickness is more important than absolute accuracy and there are no official rulers or yardsticks handy, right? Spread your arms. That is a fathom. Six feet for you landlubbers. Once you calibrate your personal fathom and your personal great stride for a yard, you got that nailed. Mash your thumb on something and mark to either side. One inch. You can calibrate that too, by how hard you mash and flatten your thumb. Standard units of measurement have real world equivilants. whereas metric used to be sort of based on something something something but is now just arbitrary and meaningless.
If your measuring and marking are accurate, then inches are just as accurate as french units.
One advantage of metric is if you can count decimal places, even if you can't do math, you can sort of do math. Metric was invented for the mathematically challenged, which is why it was invented in France. I am sort of surprised the Italians didn't dream it up, for building their infamously out of plumb towers and stuff.
@@growleym504 You are correct that Metric and Imperial are equally 'accurate'. I believe the post was confusing Metric and decimal. And here we have the actual issue. Mixing fractions and decimal gives problems. You say your mill table is 1/16 full turn, and is calibrated how? All machinists work (small scale) in decimal- for the US that would be thou. And tenths(!) If you want to do that on your mill, there must be a discontinuity on the scale, because 1000/16 is 62.5. That means you cannot rely on the scale if the movement goes past that discontinuity- you have to do some sums. Plus, you may want to work in decimal (thou) but your drills and cutters are fractional. Oops! With letter and number drills to fill in some of the gaps. No such problem in Metric- they are all decimal. Simples.
Metric units, to be specific SI units, have the advantage of eliminating almost all of the tedious conversion factors that plague Imperial calculation. There are 1000 liters to the cubic metre, and a litre of water weights a Kilogram. A Watt is one joule per second. A joule is one Newton metre. A tonne is 1000 Kg. Get the idea? [ A horsepower is 746W (approx) or 33000 ft lbs per minute. But then you know that.]
BTW two errors. Neither Liberia or Myanmar have put men on the moon (the other countries that use imperial)- not even with the help of German rocket scientists...
And the US went officially Metric in the mid-seventies. Just have not managed to do it yet...
@@Tensquaremetreworkshop You are correct there is a discontinuity. The units are in thousandths. A full turn is about 62.5 divisions. Sixteen turns is an inch so you can easily reset zero there, or actually anywhere. For a lot of parts that I end up having to make, quarter turns are well within tolerances. For fine stuff I stick to decimal. It's a great system. If you crank your handwheel for 8" or 10", the feed screw and gears will give you enough slop to require re-zeroing anyway, on these cheap Chinese machines. I can do math, so conversion is no obstacle.
@@growleym504 I love it when people attempt to defend a flaw. If moving to a number of features, re-zeroing at each one introduces an error. Not zeroing means you have to keep track of the halves. Yes, one can deal with it- but you do not have to. Operating in decimal is simpler and less error prone. Which is why DROs work that way.
I looked for the fraction calculator, but I did not find it. What is its url?
www.inchcalculator.com/inch-fraction-calculator/
Or just work it out via ratios (A is to B as C is to D, or A/B = C/D):
(remember, 0.9051 is actually 9051/1000) -
set up your equation with the desired denominator, eighth, sixteenth , thirty second, etc, as follows (I’m gonna use thirty seconds)
9051/1000 = X/32, then solve for X;
0.9051 = X/32;
0.9051 x 32 =X;
X = 28.9632 or 29/32nds)
wonderful information, I had a 7 foot diameter steel frame that needed 8 sections laid out....
sure wish I knew this Chord method.....cheers from Florida, Paul
Maybe hold your compass, the set point not the pencil, to perpendicular to the paper for better results?
Of course it does depend on the degree of accuracy needed but if you mark out from your first point working anti clockwise to half way around the circle and from your first point clockwise for the other half, it minimises any minor inaccuracy in the cord length.
Although this is an excellent instructional vid', I was disappointed to find that your method required tables and mathematics. I have geometric methods for dividing a circle into many number of segments but in all my years I have never found a geometric solution for five. If anyone has a method of setting out five segments using only straight edge and compasses, I would be very grateful to hear it.
As others have noted, the discrepancy comes from the 29/32 fraction not being exact - it doesn't matter how you propagate your points, seven times that angle will always be a little too much!
As for your construction, try looking up how to construct a pentagon. This is the same thing as dividing a circle into five segments, but mathematicians usually refer to the polygon name rather than the circle. There's even a very neat method that just involves knotting a piece of paper. Take care though - not all polygons can be constructed with compass and straight edge! So, 7, 9, 11 and 13 and infinitely many others cannot be constructed that way.
Always easier to use a ruler/scale with 10’ths inch. You can then avoid silly fractions like 29/32’s.
The more sections dividing the circle, the more errors accumulate- like the width of one line "off" from perfect width of the compass multiplied by the number of sections adds up to the quarter inch off.
I CAN do it without ANY chart! No TRIG! NO MATH CALCULATIONS!
1. Determine the circumference with a piece of paper (or similar material) .
2. Divide circumfrence "paper" into however many sections you want - transfer back to circle.
NO breaking it down into 32nths or whatever! EXACT measurements. Don't need to know center of circle!
Good idea but will it work with an odd number of sections? How would you fold the circle into 7 equal sections?
Odd - Even does not matter. Don't no where you got the idea of even number of sections. I got it out of an old "Machinist Handbook" to cut an ELEVEN TOOTH GEAR.@@herrickkimball
@@herrickkimballI’m not crazy about his solution but he could use a separate carpentry trick my dad (a carpenter) taught me on how to divide any linear measurement into a chosen number of equal sections.
Use a ruler laid diagonally across that paper with 0” on one edge at the beginning of the paper and your chosen number on the opposite side and end of the paper (lets say six sections, so the 6” mark on the ruler touches the opposite side at the end of the paper. 0 through 5 = 6 sections)
Mark each measurement mark, 1” through 5” on the paper. Each mark makes the divisions. Doesn’t matter if you use metric or imperial, still works as long as the numbers are divisible by your chosen number of sections. For metric you could use any cm measurement that is divisible by 6 and fits diagonally from end to end. So say 18cm. 18 divided by 6 is 3, so increments of 3. Mark every third number 3, 6, 9 … through 18. No fractions: easy.
How about doing a 8 section circle ? For example, doing a 24’ Navajo Hogan with door opening towards east….
For example if mesurement of the circle is fraction do also turn that into a decimal b4 u multiply it?
A good Old craftman tip : Instead of going round the same way, go in both directions, reduce the times you should move the tool from the point,and the error should be reduced, am i right 😊or what
Sounds like it might work. 👍
A little like this example:The times i would move a 2 m level is 2-3 times unless total accuracy is of no importance, the accumulated error is just too big, ☺️👍🏻
Engineer, here, born and raised in Merica.
Let’s not make excuses for English unit of measure. They suck. Even the English got rid of shillings, pence, and so on, in their money. (For all practical purposes we’ve gotten rid of Pence, too.).
You’ve done a great job of explaining this, and I am going to use this knowledge. You did a great job explaining how to convert the fraction of an inch from decimal to 32nd’s.
Thank again! Thanks for sharing your knowledge! I’ll use this. And just for grins I’m going to make a chord length table jus like the one you shared.
Technically, it is not the unit that is English, but the size of it. For example, the French also uses feet and inches- they were just a different size (their King was a different size). Many measures can be traced back to Roman ones, perhaps they should get the blame...
Interesting that some people want to keep measures that are based on the size of (someone's) human body. And claim they are 'natural'.
You have an accumulated error by moving the tape measure twice, 1/64 off when marking the three inch mark and 1/64 off when marking the 29/32 mark. Off course the error could go either way, if the error goes the same direction for both marks, then 1/64 + 1/64 = 1/32 and 1/32 x 7 = 0.21875" or close to the 1/4 inch that you are off. My guess is that the diameter is slightly off along with the sharpness of the lead on the compass and the pencil thus introducing three more errors. Once when instructing my students (I was an applied physics, math and CAD/CAM instructor) we took three different tape measures (different brands) and aligned them next to each other to check the accuracy, two were real close, but not perfect, the third tape measure was off about .010" to .015". Another way to do it is by using a CAD program to give you the exact measurement quickly and there are a few free CAD programs out there. Just my two cents worth...Good video, especially for those with limited math skills!
Compute the circumference (2 · π · r) and divide by 7
That doesn't give you the straight line computation (3.9051" chord as it is used here). Instead, it gives the arc length as if you were wrapping a string around the circle 4.0392"
To skip the decimal to inch conversion: get metric altogether🤗
Nice technique, thanks.
Really no conversion necessary for metric. Indeed, even the conversion to a fraction could just refer to “units”; the measuring system is completely irrelevant to the process.
Not to be too pedantic, but your number in step 2 is unit-less, not inches.
I cannot recommend this method. What if your original circle isn't exactly 9"? Now all the measurements will be off. What if the web site that converts to fractions isn't precise enough? What if you don't have internet access? What if after a hard day in the sun you're prone to math errors? The old timers would get calipers, estimate the distance, and walk the calipers around the circle. After 7 steps (in this case), you're either short, on, or long. If short or long, make the appropriate change to the calipers and walk around again. Repeat until you're "close enough". Then walk both ways, counterclockwise and clockwise, and mark between the paired lines. This step averages out the error.
Exactly. I use that divider/caliper trick to find the center of boards. In the real world "precision" is an ideal. You work to "close enough" instead. My dad was a sheet metal worker and used 22/7 as an approximation for pi so long, that he forgot the decimal version. You want to scale your working definition of "precision" to the size of the project, and remember that each decimal place is ten times smaller than the previous one. Then employ tactics that minimize cumulative error between the approximation you are working to, and the ideal you are aiming for. The video example is frustrating because .9051 has no common factors with any power of 10 except 1, so converting it to a common fraction is never going to be exact, expressed in any useful common fraction. In fact, it is an instance where using the metric system might be superior.
@@theeddorian No, the _decimal_ system is superior. The arbitrary length of a meter and all its meaningless subdivisions don't matter. American Machinists have been using decimal inches for 100 or more years.
@@tonyennis1787 Read what I wrote again, and take your personal biases out of the internal text in your head. No carpenter or woodworker, or landscaper works to the tolerances a mechanical engineer uses. For wood working, either system works quite as well as the other. And arguably, a system that uses common fractions will be superior for woodworking, especially if you use hand tools. They are easier to calculate with in your head, as long as you aren't using any measure finer grained than a 64th of an inch, which is slightly more than 0.39 mm. And that is entirely reliant on IF you employ any kind of universal measurement system at all. You can do very high quality work and never employ a measurement in either inches or millimeters.
One of my neighbors has a table I built for her, which is scaled to her size. The only measurement I took was three pencil marks on a stick. One was the height of the top of her thigh when seated on one of her cut down chairs, and the others were the length and width of the leftover counter top piece she wanted to use as a top. It is square, level, supports my weight, and lets her work at it seated in a modified chair that allows her feet to touch the ground. I never did measure it.
@@theeddorianSo many words.
@@tonyennis1787 I understand, and I think I mentioned this. Engineers work to tolerances most of the rest of the world doesn't appreciate. I don't agree that tenths of an inch is superior to any other system, or that any particular system is even useful in a wood shop. I personally do prefer common fractions when I am measuring things in the shop. The arithmetic is easier for me. You might want to look at "BY Hand and Eye" by George Walker and Jim Tolpin. You really do not need a ruler in a small shop unless a client walks in with a list of dimensions.
Easely divide …. And you have to use a chart, calculator, online app, …
Read 16th’s as 2 32’s …
Line out, use the compass, … and then eyeball a correction.
Yeah, that’s a piece of cake, .. LOL ;)
It does not help that when you determine a chord with a little error, … you will add that error every time on every part.
I would:
Divide 360 degrees into the number of parts. That would give me 51,4285… degrees.
Times two: 102,857 degrees. (*)
Draw that angle within the circel. Now where the angle touches the circle, I mark the dots.
With the help of my compass I can easely determine the middel between those two marks … so i have determined the chord for one part.
Needed: compass, simple calculator for a division and a multiplication and a protractor.
And no need to deal with imperial of metric measuring.
(*) by multiplying by 2, you use a greater angle, thus making the error you get when rounding up, smaller.
It’s easy to measure an exact middle between two points with a ruler, without having to fear to make a round-up error.
Also, i’m from a part in the world where we use metric … so no need to deal with 16th’s or 29/32…..
Just my 2 cts
You are working in inches, and the chart is based on one inch. How would you convert to feet? Example, a 9' circle into 16 pieces?
A trick in carpenter's eyes - or a simple calculation an elementary schoolboy's eyes (a student, who pays attention to the calculus classes and remembers what the sin function is for). And, @3:30, the ratio is dimensionless, i.e not in inches. Later, the required conversion is the "benefit" of the imperial system but again, you can do that conversion almost as quickly with a calculator or on a scrap of paper, no need for the internet thingy, as long as you know the elementary calculus.
Ya, the formula for the "magic" table you so kindly allow viewers to printscreen is sin(180°/n), there you go, no need to thank me, it's beyond elementary.
You can get decimal sae measuring tapes. They are used for the aircraft industry. Suoer nice.
Im not good at math.
Just like your last step, I guesstimate circumference sections and adjust compass in tiny movements till I hit the starting mark . Takes about as long as it took to write these two sentences.
Asked a cabinet maker once how he laid out an oval table top, said he had no formula ,just used his father's full size templates.There is a mathematical way to do it also. Again, hopeless for me. I drove two nails for length of oval , and used a piece of string tied in a circle to allow for width at centre of oval and used a pencil to pull string in an oval around the two nails. Close enough to perfect and took less than a min. The maths for it was baffling to me.
Awesome and extremely helpful. Thank you kindly!
Thanks for sharing great job!
Works exactly the same with the same chart for cm's. Plus no converting to fractions at the end.
What issue is that proven shop tip ?
You took a very easy math problem and complicated it by requiring table lookups and online web calculators...
Also, because of the way you put your compass flat on the paper when setting the distance, you introduced some error into its set length. You should have had it with the point stuck into your starting point and then kept adjusting the screw until it produced a mark exactly over the distance you have measured. Also, my starting in one direction and continuing in that direction all the way around the circle, you allowed for more error to creep into your marks. If you had marked both ways from the starting point and then did the same from those two points, your introduced error would have been half of what it was. An even better solution would be to use a compass with points on both ends so that you could pivot from one end to the next as you moved around the circle. This would have removed the accumulated error that was caused by where in the pencil lead width mark you were placing the sharpened point of the compass.
He further complicated it by converting the decimal number obtained into a fraction.
@@Tensquaremetreworkshop -- Not for those of us in the US who are competent working in fractions... It would be completely idiotic if you told everyone that the way to do this was to first go buy a new measuring device because what you've always worked with isn't good enough...
Personally, I would have done the video different, showing the simple math involved (without tables and such) with the result in a decimal inch AND THEN show how to convert from the decimal inches to fractional inches if the viewer did not have a decimal inch measure. This could be structured to work with either the US Customary Units OR the metric system since the calculations are basically unitless...
@@CurmudgeonExtraordinaire As I have said several times, I agree that the base unit is not important. In this type of case. Being forced to do a conversion because the only scale available is in vulgar fractions is, for me, not acceptable. It severely, and unnecessarily, reduces the accuracy involved. An extra step that makes things worse? How can that be a good idea. A Vernier caliper, which is a fairly cheap and useful tool, will be in decimal. Cast off your hair shirt, and embrace accuracy.
@@Tensquaremetreworkshop -- From a math standpoint, fractions are usually more accurate... With decimals, you are only stating a value to a certain number of significant digits... If you say "1/2", then it means EXACTLY that value... If you state "0.5", then it is "0.45
@@CurmudgeonExtraordinaire Wow, talk about shooting blind! I actually have a degree level math qualification...
Saying 0.5 means a tolerance spread of .05? Since when? Quote a source. Tolerances are usually expressed separately, as they vary. It may be '0.5 [+0,-0.005]' for example. Try expressing that as a fraction. From a math standpoint, 0.5 is 0.5 in the same way that 1 is 1.
Indeed, there is an explicit way of expressing tolerance, in engineering, via a convention- if you write 0.500 you are defining the value to three significant figures, so it can only vary by +- 0.0005. (there has to be trailing zeros for this convention to apply). Try doing that with fractions. And in the real world there is always a tolerance- exact is a platonic ideal.
More accurate? There are more decimal numbers than fractions, so how can fractions be more accurate?
Above, you specified the error in the weight of a Kilo of water- as a decimal. Care to do it as a fraction- to the same accuracy? But at least you used Celsius - well done.
You can go in opposite directions and then take the average (halfway point) rather than adjust your compass.
Fun and useful. Thank you.
A call to all Americans, convert fully to metric, you are half way there as it is. Regards from Dublin 🇮🇪 .
I wish we would, it would solve a lot of problems
@americo2958 Medicine delivered in cubic centimetres, engine sizes in litres, photographic lenses in millimetres, food information labels in kilo calories...the list goes on. Question, what does two and a half pints of water weight? In metric two and a half litres of water has a weight (mass) of 2.5 kg...easy :-). Join us ASAP.
As the saying goes, "there are nations who use the metric system, and there are nations who put man on the Moon".
P.S. I'm also in the metric system camp. 😅
Thank you for sharing! 👍✌️🇬🇧
I noticed that for 100 sections, the multiplier is 0.0314. Hmmm. That is suspiciously similar to pi divided by 100. If you don't have a chart to look up the multiplier, could one not divide pi (3.14 by the number of sections (pie slices) you want. It is not exact on all of them but it might be due to the difference in the number of places of pi you use. Just guessing about that but I calculated a few of them and they came to within three decimal places. I don't know if this is a direct correlation or simply a quirk of the close relationship between the arc length and the chord length of a particular section. I did notice on some of the odd-numbered sections that they were a fraction larger than listed in the chart. There may be a rule to compensate for certain numbers of desired sections but it is late and my brain is too tired to investigate further tonight. Maybe someone with more knowledge about these things than myself (which is almost nothing) can enlighten us all.
If the number of sections does not equally divide into 360 (360°), than some rounding is going to need to take place. 7 sections, shown in the video was a particularly bad number to use as an example because the division into 360 goes on infinitely. The number shown on the chart will likely work good enough for most projects but it will never be exact.
Fun fact: Internal combustion engines always have a number of cylinders that will equally divide 360° to keep a consistent circular rotation of the crankshaft, without the slightest hiccup.
Dividing by pi only "works" for a large number of sections/pie slices. It does not work for smaller numbers. Reason: dividing by pi gives the exact distance around the curve, however when you mark out the distance, it is a straight line distance you want, not around the curve. For lots of sections these two are close, never exact, but otherwise they are quite different.
@@psidvicious Always? There are five cylinder engines, and currently 3 cylinders are popular- more efficient, apparently. Even numbers were used to simplify crankshaft machining- the bearings are in one plane. Not an issue with modern machining.
@@Tensquaremetreworkshop 3 and 5 cylinders work fine because they both divide into 360 equally. 7 or 11 cylinders are pretty much non-exsistent.
@@psidvicious You do understand that the choice of the number of degrees in a circle is arbitrary, and comes from the use of base 60 by the Babylonians? Another way (and very common) to divide a circle is into radians. And, in that case, no number of cylinders divide into equal radians. You seem to think the division requires a whole number of this arbitrary measure, the degree?
Further to this, radial engines are very common in 7 cylinders!
Would you say you provide a (partly) digital way here? Any multipliers of some demanding number would be easy in many cases, like if i have 7 equal sections i divide them by 4 to get 28 equal parts.
Carl Friedrich Gauss (en.wikipedia.org/wiki/Carl_Friedrich_Gauss ) was so proud of having found a way to divide a circle into 17 (equal) parts (as in en.wikipedia.org/wiki/Heptadecagon ), "claiming" this to be his greatest discovery in the year 1801 as far as it's told, so he might used calculus, but this must have been a rather/mostly analog(ue) way.
8:30 the math world and real world didnt correspond because you use a lot of approximations in multiple steps. Thats why we in the math world will use pi/2 instead of 1.5708 until we get to the very end and use the approximation
Thank you Herrick.
At last! A fool proof method of avoiding fights over who's pizza slice is biggest!
Excellent idea. I looked up the ideal number of pie slices from a 9" pie pan and the internet told me 6 to 8. Well, that would be 7 and that's why I chose 7 for this video. It occurred to me that pie pans could be made with slight indents in the perimeter at the 7-slice dimensions as a guide for precise slices. For pizza slices I can see the same idea. This could be a really big money-making idea for someone! 👍😁
The true meaning of PI
What an absolutely archaic measuring system you have, 11.71875 Barleycorn. America really needs to join the 21st century.
All you're doing is finding one side of an inscribed polygon. So just do the trig. No book required. Much simpler.
It's easy to use a protractor, and you won't have to rub out and try again - you'll get very close, first time.
Divide 360 degrees by the number of segments you need, then use a circular protractor to get the right answer first time. Let's say you want 11 segments. 360/11 = 32.72727 - you can't measure such tiny divisions of a degree on the protractor, but as close as you can get is 3/4 of the way from 32 to 33 degrees. Then, on you calculator, press "+", "=". That will add 32.727 to the 32.727 you already had, to give 65.45454. press "=" several more times to get 98.181818, 130.90909, 163.63636, 196.363636, 229.0909, 261.818,
294.54545, 327.2727, 360 - and we have done the entire circle. Place your protractor and without moving it again, mark out all the angles, then draw lines from your centre to each mark.
Why bother with the chord lengths at all? 360 divided by 7 is 51.4286 degrees. so just set a mitre guide or angle setter to that, draw any radius and mark off the other radii. A tiny adjustment may be necessary, as in your case, to correct inaccuracy in setting the instrument, but you could get to the same place much more easily. Think 7 equal angles, not chords.
1) It is NOT .4339" - the factor is dimensionless, so no ".
2) Why convert from the decimal number to fractions? Use a decimal measure. If you are a machinist, you already have one (you will be used to working in 'thou'- i.e. decimal). If not buy one- using fractions is limiting and without justification. You are also losing accuracy by approximating.
3) Those in the Metric world (95% of the world) do NOT need to 'convert'- it is you who are converting. By definition the inch is 25.4mm. BTW the USA became officially Metric in the mid-70s.
Nice compass. Osborne, I think. Almost as valuable the Starrett 92.