Two More Ways (Of 4!) to Draw Arcs

Here are 2 more ways to draw arcs that are accurate and that will fit a predetermined dimension. One of these methods allows you to use a predetermined arc radius.
#arcs #drawingarcs #designdrawings #arches
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Arcs are very common in home construction, furniture design, sign making, and architecture. Usually, the arc needs to fit in a space of predetermined width or height. Sometimes, but not as often, the radius of the arc needs to be determined or used. If a large radius is used, it becomes awkward to actually use the radius due to the amount of room needed. In these cases, it’s better to use (somewhat) simple algebraic formulas to determine the layout.
This episode will show methods 3 and 4 for drawing an arc of a predetermined height and width. These dimensions are more commonly known than the radius of the arc, or the size of the circle that the arc is being “sliced” off of.
You can view Episode One where DirtFarmerJay shows you how to draw a fair arc using a flexible piece of material and nails for one method, and nails and a tapered board for the second method.
See Episode One - Two (of 4) Easy Ways to Draw Perfect Arcs - here: • Two (of 4!) Easy Ways ...
Method 3 can be used when you know both the height of the arc, as well as the baseline width. Using paper, 5 nails, 2 wooden yardsticks/lath pieces, and a pencil, you can easily draw a fair arc.
Method 4 is used when you know only two of the three dimensions of an arc: 1.) the width (baseline) of the arc, 2.) the highest point of the arc from the center of baseline (known properly as the sagitta), and 3.) the radius of the arc. In all fairness, this is a “somewhat” simple way. It takes calculating, using an algebraic formula.
Frankly, this DirtFarmer ain’t smart enough to figure these things out on his own. I reached out to www.freemathhelp.com and asked about how to figure this out. Dr. Peterson responded almost immediately with authoritative information and the link provided below. Thanks, Dr. Peterson, for pointing me (and ultimately our viewers) in the right direction. YOU ROCK.
The link Dr. Peterson supplied offers three different formulae, the one you choose depends on what dimension you are missing.
For instance, if you know the height (sagitta) of your arc, as well as the baseline, but want to determine the radius, one method will work. So it goes for each calculation. If you know two dimensions, but are missing the third, you can calculate it with the appropriate formula.
To access the formulae, visit: en.wikipedia.o...)
Watch for future episodes where we’ll show you methods for drawing true whole and partial ellipses (ovals).
Drawing arcs beautifully is a great skill you’ll use over and over again as a maker, and you can JUST DO IT YOURSELF!
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[@richardsextro1627]

Thanks for putting this together. The first method you show (on the previous KZbin), using a flexible strip, like a metal ruler doesn't, in fact, make a true arc portion of a circle, so in some sense, it is not equivalent to the other three methods you discuss. It may be "close enough" in some uses, but I think the viewers should be cautioned that at large sagitta, it will be obviously different than a true circle arc. I think its a parabola, but I haven't worked out the math

[@AnthonyDeGallery-lz2fq]

Very helpful tips. Thank you so much! And I appreciate the fact that you are very well spoken and speak very clearly in detail as well as the process is simplified !

[@DirtFarmerJay]

Glad to be a help.

[@ericstreff5810]

Really helped me out on a portico job I’m doing with an arched ceiling

[@DirtFarmerJay]

Excellent! Glad to be of help. Best, DFJ

[@robertpenoyer9998]

If running the two straightedges along each pair of nails strikes a circular arc, then using only 3 nails--the end points of the baseline and the top of the sagitta--to construct the straightedges will also strike a circular arc. Once the straightedges are built, remove the nail on the sagitta and simply run the straightedges along the end points to strike the arc.

[@richardsextro1627]

A quick additional note - I used the method described by John Thompson in his comment below for drawing an arc for the profile of some stretchers for a table I am making. And it works great and is very simple. It's essentially the same as the third method you demonstrate. All you need are two nails at the beginning and end of the chord and the height of the arc at the mid-point of the chord. The layout is two straight 'sticks' - one running from the top of the sagitta to one end of the chord and the other stick from the top to the other chord end. I drilled a hole through the stick where they overlapped and used a flat-head 1/4-20 bolt as the pivot. Once that angle is fixed by tightening the bolt, then you slide the assembly along the nails with a pencil at the point where the two sticks cross. A perfect arc segment of a circle. And now I have an adjustable 'arc maker' I can use for other projects.

[@DirtFarmerJay]

Richard, I really like the idea of an adjustable jig and the way you did it. Simple and effective. I'll give that a shot myself. Thanks for taking time to detail your approach. Best Regards, DFJ

[@squigglyverm]

This is very helpful thank you! :D

[@DirtFarmerJay]

Glad it was helpful! Keep watching squiggl. Best to you, DFJ

[@johnthompson1266]

An old master Carpenter taught me a slightly better way. Make the base line and mid point. Mark the height up from the mid point. Then with the two board against the end nails and cross at the midpoint secure the cross angle. Now the arc is trace with a pencil at the intersection. Just a little bit easier.

[@dicksargent3582]

I agree as a blacksmith I've used this method often for arches over gates and window grills. It's very similar to drawing circles with a framing square.

[@parkavenue6970]

What do I think? I am astounded! It is beautiful and amazing that such an effect, can be accomplished with training. Thank-you!

[@DirtFarmerJay]

You're very welcome. Best, DFJ

[@TNtoolman]

Slick... Segment could be titled "The Arc of the Dirt Farmer"

[@DirtFarmerJay]

Love it. It would sound more classic that way... Best, DFJ

[@warrior4christ777]

The radius of you arc would be 24.14 inches if you to draw the whole circle risesq +1/4 arc sq ÷2× rise =24.14

[@Robertoayon]

👏👏👏👏

[@DirtFarmerJay]

Glad to be of help!

[@doughambright9712]

I love what you did. Great geometry, but the term "tangent" does not belong in this discussion because a tangent is a line, in the same plane as a circle, which intersects the circle in only one place.

[@DirtFarmerJay]

Thanks, Doug. Preciseness matters. Thanks for the assist. Best, DFJ