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How to “Quarter in an Arc” | Simple Geometry for Radius Concrete Forms
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- Опубликовано: 5 май 2023
- You won't need this construction math method very often, but have it ready in your tool kit anyway! You'll be a hero! More math - The Golden Spiral - • 3 Blacksmith Efficienc...
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Awesome book that gives you step-by-step photos ruclips.net/user/postUgkxTNB_zFBSnTo_O1PqfVUwgi7ityw0JlKt and directions to make every day project. I can see myself making a few of these projects and giving them as housewarming and holiday gifts!
Scott, you showed me into a world I had never seen with your early videos on carpentry pro tips with saws, squares and the like when I found this channel 5 or 6 years ago. You made me want to become a carpenter, specifically a rough carpenter. I’ve been around the western United States learning things from people in construction and agricultural trades since you showed me how wonderful the world of productivity can be when I was 18- not yet out of high school! I count you as the single most influential mentor in my short career span, which I hope to one day have been a long and successful career like you have showcased on this channel. These days I work for myself, usually by myself, in my own little carpentry business. I still come to your channel weekly, if not daily, for knowledge and inspiration. Thank you, keep up the good work.
Bravo!
when i was a teenager i was showed this as a drafting class hadnt used it in years since highschool i dont know if they teach this anymore in math class but when i was teenager they did we talking early 90's to mid 90's and that is why geometry is so important especially when you do carpentry or if you use stuff like autocad or any cad program when i bought a 3d printer and started using it i was felt like i knew the information already but just forgot becuase of not using it in so many years so i had to rememorize everything again when i saw the video it all came back to me , and i am a carpenter , good for you got your own business i hope you are very successful i wish you the best !
@Jack Thomas...I'm sure Scott has many more "tricks" he can share with you if you can't figure it out by yourself. As you get more experience some things you'll be able to visualize and make a plan ahead of time. You're going to be okay!....glad to see a younger generation entering the business of construction. Good luck!!!
If you have questions, don't be afraid to ask. You may inspire a video.
Well said
These are the kind of videos I love to watch on RUclips thank you
I ran into a situation today where I needed this, and because of this video I knew exactly what to do and how. Worked perfectly, thanks.
Rarely do I watch a video twice. This one gets a second view as I am just in need of this solution or a boat building project. Thanks 🇨🇦
Very informative knowledge. Once you know it, no one can take it from you. Thanks!
Excellent piece. The storytelling really pulls it together as a meaningful short film. Great drone shots make it all easy to visualize. Masterful.
I actually figured this out as an appraiser years ago when I was attempting to calculate the area of a structure with curves. Makes perfect sense when applied to laying out an area. It doesn't come up often, but when it does, it is a most useful tool.
Age is catching up with you my favourite craftmen,you have passed alot of knowledge worldwide.
I hope that stuck somewhere in my head, but I appreciate the fact you clean that paint tip after every mark! You are a professional in every aspect and a joy to watch. Keep it up!
This is fascinating. We ended up "backing into" this process when we needed to layout a radius for a railroad track we were laying that passed right next to a building on the inside of the arc. Essentially, given a known tangent length between two points you could use a specific offset to get the tangent that makes the curve of radius that you needed from the start and end points of the total arc.
Rip Dennis Bunker. Your name lives on through the men you taught.
Great demonstration. I almost used this trick one time to layout a curved section of glued boards (like a glulam).
it's always a good day when you learn something useful. Thank you!
Thank you for teaching this.
You could use this same technique in reverse to find the center of a circle(bisect a circle).
My younger brother taught me that, a trick ive used a lot in machining.
WOW
I love math! When it's applied it's even better!
Just goes to show - there is always something to learn - thank you. Both the term and the method are new to me. I doubt I will ever utilize it, but having it in my toolbox will mean I will still have the solution if the question ever arises..
Thanks I don't know when I will ever use this ,if ever, but thanks watched it 3 times!
I can see this being useful when objects in the way prevent you from finding the center of a circle from which to string a radius line, in this case about 133 feet long. You could even put two centers with a long string between the two to trace out an ellipse. The other issue is how hard it is to manage such a long string without stretching or catching on ground debris.
Looking forward to the pour that goes with this.
Thanks Scott for all those nuggets of knowledge you drop on us. I'm 33 so maybe a little old for being your grandson but you are my internet grandpa, I learned so much of my practical knowledge from you !
And thanks Denis !
Thanks Scott and thanks Dennis for another useful construction trick in my tool box. Keep up the good work
This is incredible 👏 thanks Dennis
I used to do something just like this kinda intuitively when I was building berm turns for my dirtbike when I was a kid. I didn’t square it, just kinda eyeballed, but still, this is wicked cool!
I love watching your videos! There all so nolagable and supreme thank you for sharing your time!🙂🤘
That little drone operator did a great job😊
Thanks for showing me something that will stick in the back of my mind. One day, right after I've poured a new curved concrete slab I will remember this method. I've been a fan of your videos and for a long time. Nate and Scott, you are both great teachers not only in skill and methods, but in being a man! KEEP UP THE GOOD WORK!!!
Useful knowledge that leaves in the mind is priceless. Thanks Denis Bunker.
Thats awesome scott, it may take a few revisits for me to understand it completely, but when i do watch out! Keep up the good work!
Thanks for the awesome content and great videos!!
Thank you scot as always never miss a video
My primary occupation is stair building. We get called on to design on the fly and I might be able to apply this technique. Thanks for the tip.
Hi Scott, I saw a workman trying to solve one of these problems on a house I was having “rehabilitated.” I asked what he was doing and he said he was trying to establish the arc based on the distance from a straight line, (what was actually a chord), It took me a few minutes to solve a geometry problem and I showed him how to get the arc….of course I wasn’t surprised that he had serious difficulty believing me with the obligatory rolling of the eyes, etc. - I am, after all, just “a civilian” and not in the business….the answer I gave him worked and I handed him the formula to use if he ever had a requirement to do something similar….I have no doubt, he tossed the paper….
Anyway here’s the way I would have done this. We have the length of the chord, 190’ We have the greatest distance from the chord, 40’ (which is a point on an imaginary circle). You build your perpendicular from the 40’ point, passed the chord and continue for another few feet. The length is unimportant, the extension is just give you a line to follow. What we want is just the radius of the imaginary circle. If you have the radius, you don’t have to do all the other measurements. So here goes:
C is the chord length, 190’.
A is the perpendicular distance from the chord to the point on the circle, 40’.
R is the radius of the circle to be calculated
R = C²/8A + A/2
= (190*190)/8*40 + 40/2
= 132.8’, the radius.
So now just run a line from the 40’ mark along the perpendicular for 133’ That;'s the center of the circle.Just run a taught line from that point with a spray can along the arc…..
I've had to use this a few times over the years....I never remember the formula, so I have to re-figure it. - as I've gotten older, it;s taken longer to do the problem.....I'll be 78 in a few weeks and it only took me 20 minutes this time around...up from 5 when I was 40....hmmmm....
Cool. I use this in woodwork sometimes. I kinda thought I was the only one that knew how ( that I've ever come across) so pretty cool to see you put out the video.
This is a great tool for when you know the chord, and the offset ( or loft ) of the curve, but not the radius as such, or when the centre of the circle is inside a building, or in the neighbours yard, or whatever.
I use it laying out circular curves on beams, where the radius isn't important, just the length and loft. Layout is quick, and pretty magical. And the the bendy piece of wood people... sometimes you just don't want a catenary curve.
Awesome knowledge thank u
Another great use of Pythagorean Theorem.
Outstanding
Thank you so much Scott for making this video. I learned a new method today for finding the arc of any radius. Most of the time as an engineer I use calculus to solve problems like this one. I can do it much faster with more accuracy with calculus than I Can if I solved it with geometric methods. However I love your very practical expose of the geometric method as well. Keep up the making of these awesome videos with educational and informative content.
interesting, your right I will probably never need to use it at my age. 70 plus but it is always good to learn, it keeps me young.
Love your work 👍
Thank you so much! So many tricks of the trade die with the men that hold them that it’s scary to think where we would be without guys who share them.
I'll remember it, and pass it on. Thanks, EC.
As always impressive
that's an incredible trick!!
Saved for future study and use
Hello Mr Wadsworth, I would just like to say that I appreciate your videos so much. Many years ago, I looked up how to properly use a ladder, and your video on that subject was about 6 months old at the time. I've been hooked ever since. I could listen to you talk about anything. Cheers from Australia 🇦🇺 ps, I wish you would do another narration. I've listened to The Blacksmiths Boy so much that my wife even knows the story 😂
I think if I had to do this I would maybe do a 3-4-5 square to split the main arc but after that I feel like I could throw a lot of stakes in the ground quickly to get a very accurate arc by making an estimate on perpendicular without doing a 3-4-5 check. Just keep halving the distance and quartering the arc! Thanks for the tips!
Nice! Back when I was a college student, my summer job was doing construction layout. We frequently had to lay out curves for road bends. We used a theodolite and a chord/deflection procedure. It required trig calculations to be done beforehand, a royal pain since this was pre-calculator days and a slide rule didn't have the needed precision.
Yes! I use Pythagoras all the time. Cool video!
Good to know. A total station layout insrument is what would be used now. This can be used to transfer your 138'-9-15/16" radius to a 8 ft piece of plywood to cut 3-1/2" strips to use as top and bottom plates of form walls. It works the same way, construction Master calculator helps
I’m gonna have to watch this a couple more times…
Very interesting.
It was brilliant! My favorite thing to. Take the drawing board to the field. Spray painting dirt.
I just did it on an A4. Saved me half a day in the paddock...
Danke!
Making a spectacle of one's self is life's learning curve!
Also, I have wondered who's music accompanies your videos
👍👍👍Thank you.
Maths was never a subject that I ever passed in primary or secondary school.
But this even made sense to a dumbarse like me 😂
Nicely presented, thank you 😊
Thanks Dennis. I'll use this technique when I'm making my crop circles.😂
If you do have room behind the chord to find a center-point and run a string to scribe the arc, here's a simple formula for figuring what the radius of a section of arc (like shown in video) is from the chord length and center sagitta height. ((Height divide by 2), plus, (Width squared divide by 8x height ) = radius.) or, H/2+ WxW/8xH= r.= string length. Cheers.
Thanks, Dennis! ;)
Good episode
Thank you Sir my head hurts right now.😅 I myself would not be doing this. I did see the marking on the floor of the arc. This makes sense.
Such a cool video ❤ reminds me of Art Attack 😂
Needs title and thumb, never been so early the editing hadn't finished up 😂
Got your steps in on that one.
simply: Thank you.
This technique is a common approach used in computer graphics where it's known as "subdivision surfaces"
In math we call the 3,4,5 triangle he's using a "pythagorean triple"
Could you do a follow up video on a smaller scale or white board, you lost me somewhere in the field
What is the official geometric curve of that arc? Or is it just connecting the widest point to the ends?
pretty sure its just connecting the widest point to the ends, fitting the spaces available on site.
Each new triangle added to a straight run between stakes more closely approximates the circular arc that intersect the original three points (the endpoints and the first perpendicular). So, if you need a true circular arc between two points, coming out to a certain midpoint distance from the straight line between them, this will allow you to do it without having to find the center of the circle (which may not be a reachable location) and pivot around it.
Kinda similar to how I figure out the capping on half round or eyebrow windows. I never really learned it I just kinda figured it out on my own
There’s an ms concert in cedar city .. wonder if it’s a remnant of the ms out of Vegas you speak of
I like the title and thumb
"what is this?" It's rock music!
You seem to like a good guitar riff. Here's one you should check out, whether you share it with us or not: Jerky Dirt - "Forklift Truck" Not as crazy a this one, but the same vibe is there. Jerky Dirt is one guy in Nottingham, UK, pumping out album after album of amazing "fuzz" rock.
Watched this twice and still confused but will remember this video if I ever need to lay stone/tile curved.
thanks.
To lay out an interior archway, use the 'Long Compass', using 3 finish nails and two sticks, and a pencil.
Or run one query in a GIS app to render a curve and then just walk around with your phone to draw the line. AGPS is accurate to
That was pretty cool though
I wanted to put in a block wall next to my curving property line that has property corner stakes but nothing indicating the 112' arc section on a 42' section. I could not run an arc due to sloping terrain and physical obstructions. I ended up using the county satellite images and using the built in measuring tool to take measurements. My neighbor agreed with my layout and i built the wall 6" back from the line. How would you measure the curve with obstructions and sloping ground?
Surveyor
Scott
I was a little suspicious about the factor of 1/4 of the previous Sagitta as a dimension to use. Arcs and angles never seem to work out in whole numbers. It's close, but I got 26.0195% as a number. Hopefully someone will check me out on this. Still, I was a fun exercise. Mr Slingshot.
You are correct, quartering the middle ordinate does not make the arc perfect but it's closer than the eye can tell, especially on something with some size to it like this. Your ratio is bang-on. Multiply the previous middle ordinate (saggita) by 0.260195 to get the next one!
Stand by, I did it wrong, that ratio only works once. Let me find the correct formulae and I'll rearrange it so it's useable/useful
@@Richardbomgardner I found out it only works once also so I suspect with each new cord the difference will become smaller. I’ll be interested in what you find. As a tool and die maker for over 40 years I solved these kinds of problems daily.
Heck yeahI still solve them daily and love it! I'm a licensed professional land survey and a structural concrete contractor.
So digging into the math, the long chord to sagita ratio is not fixed but it stays dang close to 25%.
To absolutely nail this, you need to calculate each middle ordinate (sagita) for each reduction.
2*(M/LC)=tan(I/4)
M is middle ordinate length
LC is long chord length
I is the angle of the arc.
Use the first LC and M to calculate the I, then use the half the LC and the M to calculate the 2nd LC using Pythagoras. The use the formula above to calculate the 2nd M, but using half the original angle.
His middle ordinates in a perfect world would be:
40
10.4078
2.62795
0.65862
0.16475
You'll notice ratio changes slightly each time but stays close to 25%
Fun problem!
@@Richardbomgardner Good job. If I needed this often I would make an Excel spread sheet where I could enter the variables and and the number of times to calculate. I learned something new because I had never heard of this layout problem before.
Or carry a laptop with an app on it. LOL. But it was fun seeing how it use to be done. Still dont think I could do that after watching just once. I'll have to google it for a written explanation.
... and then you still have to do the lay-out.
@@bgtyhnmju7 If it's a job that HAS to be done with high accuracy it will probably be a public works project in which case it will be done by specialists . . .
Have you seen the Public Works guys at work?? Anyways, your argument is high accuracy work needs high accuracy - sure. And then there's less demanding layout, where strings and spray paint will do.
You can also always multiply 345 each by any number. 6 8 10 works, 9 12 15, 12 16 20, ect.
Trying to find a mathematical explanation of this, having no luck. It seems the sagitta lengths reducing by 1/4 each time is dependent on the particulars of this layout.
Was it more easy to understand on Spanish, but I appreciate all of your videos.👍
I'm always a little befuddled when people's go-to square triangle is 3:4:5. It confines you to weird measurements and juggling 3 numbers and 3 multiplications in your head. *It's much easier to just remember 1.41.* (Or sqrt(2) if you want to be fancy). Take any matching square sides, the hyp is always 1.41x that length. I.E. A right angle isosceles triangle. 10 feet for both the horizontal and vertical, the diagonal is 14 feet. 5 feet, the diagonal is 7 feet, etc. Just any measurement mirrored on both horizontal/vertical, and all you do is multiple by 1.41 to get the diagonal. Any length at all, no picking special numbers or ratios. Walk down any side of anything that you want to be a square side, take any number you want, 1.41 that is the diagonal. That's way less math than trying to figure out what the closest thing to a 3/4/5 you can muster with your current space and then keeping track of all 3 and what you're multiplying.
That's irrational.
you lost me, i think i'll stick to 3:4:5 :D
@@xyzct It works, just not as easy or quickly until today with your phone calculator. 30 years ago it was easier to 3,4,5
@MattsAwesomeStuff...You're wrong about your factor. You need to carry it to a minimum of 4 decimal points or more (for your example, 1.4142) for a more accurate calculation. After you've made ALL FINAL CALAULATIONS, then you can reduce that number/answer to the nearest 32nd or .01.
Your factor number is just a general rough estimate and us in the detailed construction business build to a much higher degree of accuracy....i.e., we want our 4" plumbing vent pipe (4.625" o.d.) that is at the end of that 150' long 5 1/2" wide wall to actually be in the center of the wall because it will only have 7/16" of wood on each side of the pipe!!!!.....and/or the bolt holes in the end of our 75' "I" beam supporting our concrete bridge to be accurately drilled because the beam has a close tolerence that is engineered into it). The diagonal of a 150' X 150' building is actually 212.13195' or 212' 1 9/16"+. Your 1.41 factor gives the diagonal of 211.5' or 211' 6"., a discrepancy/error of 7.584 inches (7 9/16"+). That's not good enough!
Use Scott's knowledge and you'll be where you're supposed to be.
A nifty trick that works great on paper to solve a pre-existing geometry.👍 That doesn't pay-off in the field with a measure in hand. Who does 1.41 multiplication in their head? Who needs to pull out a calculator when measure and mark is faster? As far as finding square, if you can't mark out 3x,4x,5x and remember one number (the 5x) you're wasting time. There's also a simple formula, that does need math, for figuring what the radius of a section of arc (like shown in video) is from the chord length and center sagitta height. ((Height divide by 2), plus, (Width squared divide by 8x height ) = radius.) H/2+ WxW/8xH= R. Those are often the only dimensions given in an architectural plan, and the builder has to figure out the radius. Works in reverse also, from a radius and one of the other two dimensions.
Yep. Watched it 5 times. I think I got it but as in a previous comment, was the 190, 40 part of the desired layout?
ye, i think the 40 was just the distance out on site, also a handy number to start quartering in the demo, 40/10/2.5 etc
i noticed I you started with 190ft and a 40ft sagitta. were those just the initial constraints for this demonstration as one might find on a site?
Yes
My mathematician father will love this technique no doubt. 😂
👍from me.... is there a place where I can buy radius PATTERNS?? I want to use such to see which one fits the outside of my trees best because I want to build a good fitting box around them to build off of
That field is so large one could use a centre of circle reference... 😁
I agree that when your radius is over the length of a tape measusre this is a good, albeit time consuming, method.
I recently learned that A×A=B×C. One would have to look it up, but when you understand this formula, you can find the radius, height, or width (given 2 of the 3) for any arch. Changed my carpentry game.
Not that I would use that as I am 71 but I got confused with a×a=b×c would you explain for an old man
@Roger Lein you'd have to see a picture of a circle with all this but ill try. 'A' can be any half of a cross section, anywhere on a circle. The other "a" is the other half. B and c are the perpendicular sections of that same circle. If you know the width of an arch, you know "a" and "a". Half of width is "a". Knowing a×a=b×c, and Also Knowing the Intended height of arch (B), you can solve for c . That will be the diameter. Now divide by 2, and you have the radius. Know that line B and c intersect a and a in the center, forming a cross of some sort. I tried.
Denis Bunker 💪🏻
👍🏻👍🏻👍🏻👍🏻
Why, after you spray a mark on the ground, do you spray over your shoulder?
Cleaning the tip
PgD is right, but didn't mention that turning the can upright is part of it. Marking paint is used with the can inverted. When you flip it upright and spray a tiny shot, that shot is nothing but propellant. With a regular spray paint can meant to be used upright, you flip the can upside-down.
I do sheet metal lay out and I tried to follow but I’m lost. It no compute.
Sagitta is Italian for arrowhead, so I figured it was something close to that 😉
As the old axiom goes "Layout is king"
Why did you choose 40ft for your first sagitta?
Arbitrary. It's the amount of curve he (or the plans) wanted.
😊
The thing that has me confused is that it seems like you flip the 345 triangle calculation on the second sagitta and i dont know why. The first sagitta was 40 (the 4 of 345) then 30 on the cord and 50 for the hypotenuse... But the second sagitta you measure 10 (120 the 3 for the 345) the go 160 (the 4 for the 345) on the new chord and 200 for the hypotenuse. Why flip the 3 and 4 side for the second sagitta? I thought it would be 10 feet (one quarter of 40 the original sagitta lengh) by 7.4 (one quarter of 30) with a 12.5 foot hypotenuse...
The first arc height was 40’ (480”) 1 chord
The second arc height was 10’ (120”) 2 chords
The third was was 2’-6” (30”) 4 chords
The fourth was 0’-7½” (7.5”) 8 chords
The fifth would be 0’-1⅞” (1.875”) 16 chords
The sixth would be 0’-15/32” (.46875”) 32 chords
Each chord is one half of the previous chord.
Each arc height is one quarter of the previous arc height.
The chord quantity is doubled each time from the previous quantity.