OK, so I have often browsed through the old Daisy Wheel Topic and read what is there a few times already. I thought about posting to that topic, but it hasn't been active for quite some time. Beyond that, I have a specific point to make so I decided just to start a new thread.

I want to describe to you all how I use the daisy wheel (well I guess I have used it like twice) to lay out a building. This is the result of a lot of reading and studying, and most importantly experimenting. That last step is the most important, we will never know how valid our ideas are until we try to put them to use. And when we try to use a system like this, certain things only become obvious once we try.

When I first studied the daisy wheel, I looked at these circles and reasoned that the intersection of the various circles was the key to everything. This is of course true, but it is incomplete and very limited. If your building lines rely solely on the intersections of circles, then there are but a few practical structures that can be built.
What is needed are straight lines. I drew a diagram of 7 circles, then took a ruler and connected every point on those circles. What you end up with is an interesting assortment of triangles, rectangles, and useful angles. Of interest is the fact that once all points are connected, the lines form 12 equilateral triangles of equal size within the central circle that all combine to form the "star of David" figure (All 3 angles on an equilateral triangle are, by the way, 60 degrees)

There is also the prevalent rectangle repeated over and over which has a ration of 1:2 between its short side and its diagonal (the long side would be an irrational figure somewhere close to 1.73 times the short side) The daisy wheel also provides a means to divide this rectangles into perfect thirds along its long side -which would be impossible mathematically since the long side is irrational. The figure produced by this was apparently used frequently in medieval windows.

Now when I am laying out a building I can use any intersection as a line of reference, intersections between circles, between lines, and even between a line and a circle. This allows me, with just 7 circles, to create a large number of different building layouts. The best thing is that they all have very excellent and attractive proportions.

Now I like to try to make my designs at least somewhat transferable to standardized measurements -this helps me to get a picture in my mind of just how big a structure will be, and also helps a lot when calculating materials and so on. To do this, I set my dividers to 4 inches, or sometimes 3 inches. Having the radius of your circle equal to a standard imperial measurement will result in a lot of your dimensions easily reflected with feet and inches. I have yet to investigate, but I would feel pretty safe to say it is easier to convert to the imperial system from the daisy wheel than it is to the base 10 metric system, due to the prominence of 12 and of fractals on the daisy wheel itself, and the fact that the imperial system is based around the number twelve, and the inch is broken down into fractals (coincidence? perhaps not...)

I promise you all that I will put up some pictures. I am actually needing to make a new layout for a building I am working on, so I can just take pictures of all of the steps in creating this layout.

Now when I am laying out a building, I lay out every single principle framing member according to my "daisy lines" The most important pieces -the walls, roof line, ties, etc. I lay out using the lines from the daisy wheel itself. But once I have created the basic outline of the structure, I suddenly have a whole new set of lines, angles, and intersections that I can use to lay out the rest of the fame. For example, on one structure I have a double sloped roof, to calculate the slope of the shallower, lower portion I drew a line from where the main pitch intersected one of the daisy wheel's lines to some other point on the chart. Basically if you look hard enough, any basic design will tell you how to lay it out further. I think of it like this: Lay out the basic outline of the building, and then let it lay itself out from there. Just follow its instructions and you will be pleased with the results

Pictures to come, I promise!

Here are some pics, with explanations of what's going on. Hopefully this will help clear up any confusion.



If you look really closely, you can just make out the circles scratched onto the paper. I use steel dividers, not a pencil compass, because I don't trust the accuracy of a pencil lead. If I am drawing a scaled down version of a building, then I ought to be sure and be extremely accurate.



I then connect every single circle intersection with every other intersection. This results in a whole bunch of lines. If you study the shapes created very closely, you can learn a lot. I think I could spend all day just studying the wheel at this point. Notice the 12-sided shape, formed by 12 identical triangles, in the center see also the 2 star of David designs. Each comprising of 12 identical equilateral triangles. I could go on and on talking about all of the things I see in the graph if I really wanted to



Look closely and you can see some pencil lines. This is the start of a building layout. Some lines rely on the intersection lines of the graph, other 'secondary' lines rely on the primary building lines. Notice that the Daisy wheel was kind enough to supply me with a method to divide the main rectangle into exact thirds. (You'll just have to take my word for it, the curvature of the camera lens distorts proportions and lines a bit)



Here the layout lines are colored so they stand out. Red lines rely solely on the graph itself, yellow lines rely at least partially on the red lines

Rafter Layout:

So one might ask, how do you lay out rafter cuts when you are using the Daisy Wheel? Some have suggested that you might scribe rafter pairs together to get them to match, but I can think of a much easier way. Triangles. If you look at the roof layout in my previous post, you can observe that the roof peak is divided exactly down the center into 2 equal right triangles.

To make the plumb cut at the top of the rafter, one must simply transfer this triangle onto the end of each rafter. To do this, the hypotenuse is aligned along what will be the top edge of the rafter, with the short leg of the triangle oriented toward what would be the center of the structure, or the end of the rafter as it were. The short leg of this triangle supplies you with your exact plumb cut. More accurate than a framing square I would guess. It is important that the vertex where the hypotenuse and the short leg meet be positioned exactly where you want the peak of the roof to come out on the rafter, this way you can be assured that each rafter will come out to the exact right length. Any such angle cut anywhere on the structure can be made in a similar way, all you have to do is transpose the triangles from the daisy wheel onto the timbers. One easy way to do this is to make 3 lengths of some material such as good stout string (that won't stretch too much) each equal to lengths of the triangle, only scaled up a bit (by way of dividers) then orient them until all three points match up. Then you have a perfect triangle.

Now I should also mention how I transfer the lines from the daisy wheel into the reel world. The answer: Dividers

The building shown previously was drawn with a 4" radius circle. If you observe, the height of the walls to the first cross member is equal to radius of the circle. SO if I want the walls to be 8 feet high, then I assume the entire graph to be drawn in a scale of 4" = 8', or expressed rationally 1:24 So that means that I find all real world measurements by setting the dividers to the length of any given building layout line on the graph, and step it off 24 times in a nice straight line. It's very important to have good straight lines or else all of your measurements will end up a little off. If you do this, you can then create a ground layout that allows you to do a french scribe method or some other such method. If you want to do square or mill rule, then you will have to do a little bit of math and measuring to find out how your timbers will actually set up to these lines.

It should be noted that All of my building lines are drawn along lines that stretch from one intersection point to another. These points do not have to be matching points or anything like that, just any two points anywhere on the graph. As I said earlier, these points are formed by the intersection of any two marks, whether they be circles, connecting lines, or even the building lines themselves. The points connected to form the building lines often lie well outside of the building's bounds, and sometimes it takes a bit of looking to find a line that does what you want it to do, especially for roof lines. It seems you can really make just about any roof pitch you want. The building in the picture was designed to have a half-hipped roof, hence the horizontal line near the peak.

I really just ought to make a video, or write a book with lots of pictures! I feel like I am doing a lousy job of illustrating how I use the daisy wheel.

I would also be interested in learning how others use this fascinating bit of ancient technology.

And I have a question. Are there any known examples of the daisy wheel's appearance outside of Britain? Is this figure ever found carved onto buildings in France or Central Europe?

As for transferring the design into the real world, I.E. making an actual building with the proportions represented in the drawings, there is some degree of difficulty.

The lines on the graph are 1 dimensional. They have only length, and as such they cannot account for the other 2 dimensions of actual wooden timbers. The lines merely mark centers and intersections, they do not really tell where a timber 'is'. We run into the greatest difficulty at joints where timbers do not join at the same height, for example in an English tying joint, or certain rafter joints. In such instances, you have to come up with a way to account for this variance.

To convert your building from the 1 dimensional lines of the graph to 3 dimensional reality, I can think of 2 methods. The most obvious method is the French Scribe method. Here we simply take of design and enlarge it, creating a full-scale version of it right on the ground, using strings stretched across or some such method to represent the lines off of the design. Then we are free to align our timbers with these building lines and scribe our joints onto each other. Observe, however, that these lines usually represent outer edges and not necessarily center lines running down the middle of timbers. For example, the lines for the walls should be taken as representing the outside of the posts, and a horizontal line should represent the bottom of ties and joists. The main reason to do this as I see it is so that, assuming you set your dividers so that standard measurements would result in the final building, predetermined distances such as building width and interior ceiling height will still retain their imperial measurements (or metric, if you absolutely must) For example, on my building I set the dividers at 4" so that I could have a ceiling height of 8 feet, and a total length of 24 feet. If I do the layout as described then My building's length should measure exactly 24 feet from end to end, measuring from outside corner to outside corner, and my wall height should measure exactly 8 feet from top of floor joist to bottom of ceiling joist. Note that should you decide that you would rather have your wall lines mark the inside edge of your posts, then you are going to run into a lot of trouble once you start running your rafters.
Another reason to do it this way is that it allows you to use irregularly sized timbers. In other words, all of my timbers do not have to be exactly 6 inches wide (I use rectangular, rather than square, timbers, so they might be as narrow as 4 inches at times, with a depth of 9 inches or more)

Now I was just thinking about 2 story buildings. In this case you may want to make an exception to the rule of layout lines marking an edge rather than a center. If you don't line up the first floor joists with the line marking the center, then the second story is going to be several inches shorter than the first. If you do, then both stories are going to be a little bit shorter than the ideal size. So It's a matter of choice, would you rather have A nine foot first floor and an 8 foot second floor (which would result if you laid out your building to have 9 foot ceilings, aligned the bottom of you joists to the line, and use 12 inch joists) or 2 8'6" stories (same layout for wall height, only the 12" joists are aligned with the line marking their center)

Really the only rules that I would set in stone are that: Building lines mark the OUTSIDE of posts, and roof lines mark the BOTTOM of rafters. It might be beneficial to actually have one or two lines here and there be a center line, with others marking edges.

There is another way to do it that doesn't require creating a full scale layout, so that you can cut all of your joinery in a smaller area like a cluttered shop or a crowded city lot. I thought of this one day while taking a shower -I doubt I am the originator of this idea, it's probably a way that someone used hundreds of years ago, but I had never heard of it that I remember.

Basically the idea is this: Take a given framing member, let's say it's a post. This post s stepped off for length, the length being set to the full distance between the two lines it is bounded by on the drawing. Note that the space between the bounding lines is not the same as the actual length of the post. Add a little extra yet for good measure.

Then any other timbers that join this post should be matched up and scribed and so forth. Let's say there is a plate running along the top, and on top of that is a tie beam. All three of these timbers need to be scribed together right now, aligning the bottom of the tie with the mark on the post for total ceiling height. Here you will glad you left some extra on the post, because it may tenon into the tie just a little bit, in which case the post would actually be longer than the distance between bounding lines. It will also need to tenon into the sill below, in which case even more additional length is added, assuming that the top of the sill is aligned to the bottom bounding line of the structure (to maintain interior wall height)

To do it this way, you'd have to have a lot more faith in your ability to step thing off correctly, because you don't have a nice big layout to constantly reassure you that everything is right.

Hi D.L

This forum is an ideal place to pose questions for the timber framing community to try to help you by providing answers or opinions that might help fill gaps in your own knowledge base and of course that of others.

It is becoming obvious that you are approaching a point where you really should consider writing articles for publication that could be better supported with photos, illustrations and of course appropriate references.

Some of the aspects that you raise above are in the process of being researched by others (Laurie Smith) with some articles having already been published in "Timber Framing", "Mortice and Tenon" and "Vernacular Architecture" journals.

I would like to encourage you to reach a wider sudience where the content of your topic could be subjected to peer review in order to help establish reliable outcomes.

Your message is important and is in danger of being lost if simply confined to this forum.

Regards

Ken Hume

And, by all means your contribution here on the forum is welcome.

The daisy wheel, in my opinion, is a underused tool. Somewhere here on the forum a short term poster posted an older barn for sale, it used curved brace stock and a close bent system, both appearing to fit the same circle. When I have more time I will look for it or someone else may link to it.

I know of one small building that is daisy wheel constructed, I think it was moved out west. Built by a group directed by Laurie Smith just last fall. I added onto my existing house this winter using a two circle lay out. I have not compiled all the "how I did it" in a why clear enough way for the forum. I did wander a bit and used a healthy bit if fudge in getting from paper to reality. I should at least post a photo of the lay out on paper.

I didn't go all out with connecting as many points as you suggest, I think I went in the opposite direction and used just a minimum of points. There was already some dictated points, as I had previously constructed the foundation, so I was working with in a set of givens. Excuse my vagueness I will see if I can put up a picture, I have been meaning too.

Tim

Hear hear! Contact me for advice and encouragement regarding publication of your work.

Ken,

I wanted to post this here for 2 reasons, 1: to show my methods to others so that they could learn and hopefully improve upon them, and 2: to set up my methods for critical review -to let others pick through and see where I may be wrong or doing things the hard way when there is a better way.

What I have presented here is the result of a lot of research, reading what little material is available, or at least that I could find, on the subject. Although I am certainly open to the idea of publishing these things for the benefit and review of a wider audience.

Tim, the connection of points has been a major question for me. It is hard to decide how far to go on connecting things. Should you only connect the points within and along the central circle? This limits you, and does not allow you to cut the circle into quarters for example. Should you connect all opposing points, i.e. those points that are reflected across the center of the diagram? My opinion is that any way you come up with will work, but the Daisy Wheel will reveal a whole lot more to you (in my opinion) when you connect everything. When I draw the last line, everything falls into place and some interesting geometric figures pop out at me. I believe it is also important to note that the same ratios are to be found in the complex diagram as can be found in its simplest form, just in greater number. The biggest benefit I see is that when you do connect everything, the building truly does begin to lay itself out in front of you. After you draw the first couple of lines, establishing the most basic outline of a structure, everything else becomes incredibly obvious. It's really quite remarkable.

I also try to work with a set of givens whenever I can, because that makes real world work so much easier. The daisy wheel does seem to let you force things on it if you must, although it will be a little more difficult.

Joel- certainly! If you think that is the way to go.

Now I asked this question once before, but no one seems to have answered it.
Are there any known examples of the Daisy Wheel being inscribed on timbers or masonry anywhere in continental Europe? IS there evidence that this was a universal Medieval technology, or was it confined to England? Have any medieval German or French or other buildings been shown to reflect daisy wheel dimensions, as Mr. Smith has shown many English buildings to do?

HI DL,

This symbol is widespread across Europe and elsewhere.

Regards

Ken Hume