This thread is a follow up to the geometry article in the latest edition of Timber Framing. I had meant to post it a little while back, but just now got to it.

It is difficult to fully explain the processes involved through written media, and I am sure that some of you might have some questions about it. The purpose of this thread is to answer any questions you all might have, clarify anything that isn't perfectly clear, and in addition to introduce some more complicated techniques that could not be covered in the basic introduction, and maybe eventually to show some other methods of using these principles.

So for starters, this is open to your questions. What would you all like to know about?

DLB

It would be nice to see a contemporary draft of the outcome. I can't "see" the structure described within the geometry.

Thank you for the article, DL. Could you please suggest references for those who wish to read about the system?

I also have a problem with seeing the structure clearly. I assume the perimeter lines on plan views and elevation are arris but I am uncertain about the interior members, are the interior members center or side referenced? I assume the purpose of the schematic is to set up all the ratios of length and the location of members on a gird, but I find a conflict in having both conditions simultaneously. The problem rests in having posts with width and beams with depth represented with lines which can only represent length. For instance, when drawing is fleshed out, in order for the braces to maintain the indicated length, the braces must shift position laterally with the width of the posts and vertically with the depth of the beams. If the braces are fixed in the grid, the brace length will vary with the width and depth of the posts and beams, also the brace length to post length ratios will vary from the scheme.

Brook, I'm workin on it. I'll try (try) to have it up tomorrow if I find the time

Roger,
These things are all matters that have to be taken into account when making the design, and there is a certain matter that needs to be addressed regarding how the lines represent 3d timbers.

I use a system of alignment that requires a certain understanding of how the timber frame will go together. The system is different depending on the type of frame it is designing.
Certain frames will be aligned directly to the lines, wit the lines marking an edge. If I were framing a building with bents, I would start the layout from one end and work toward the other when aligning timbers, thus all bent would be marked with the line on perhaps their east end, or what have you.

For a German-style frame, I would have the geometry lines mark the outer edges of the corner posts, and the centers of other posts.

Due to the nature of wood joinery, in certain cases the geometry lines will not give you the exact locations of certain framing members, but instead serve as a reference line for establishing the final locations, braces are an example. The actual locations of the braces on the frame will be offset from the geometry lines by factors based on timber sizes, type of joint used, etc. so the brace itself may be 4" or so off from the geometry line. This is no different from the fact that wood trusses by the nature of how they are put together differ in some ways from the 'ideal' engineering schematic. The trick in geometry is knowing how joinery and load forces actually work, and taking this into account on your final layout.

Also, the braces will never maintain the length indicated on the layout, the lines shown will never be the actual lengths of any timbers, rather they are reference lines. This system is by necessity a scribe system, and so final lengths of timbers are established by scribing them to each other when aligned to the geometry.

When using German style long braces, the lines depicted on my drawings are only there to remind me where the braces go and what direction they slope, their actual positioning is dependent wholly on the positioning of the posts.

The entire purpose of the geometry is to establish a layout to use for a scribe system. The final layout is really no different that the building layouts used to this day by the French Carpenters, for example; it is merely arrived at by different means.

It would be possible, I suppose, to develop the geometry so that it could be used with a square rule system, but this would require you to work down the geometry to the point where you have representations shown on your drawings of the ideal sized timbers. This system you need only to work the geometry down to the alignment lines. With a square rule drawing, you would have to take special care to measure the dimensions yielded and transfer them over to the real world.

as for references, my primary reference has been the book, Canterbury Cathedral, Aspects of its Sacramental Geometry, be Colin Joseph Dudley. It has a thorough introduction to the basics of simple geometric constructions, and a thorough treatment on the complex geometry of a Medieval Cathedral, its windows, facades, and pavement, as well as the symbolic importance of Geometry in the Middle Ages and in ancient times (it deals with Pythagoras, Euclid, Plato, Augustine, etc.)

I want to make a mention of one thing, and that is the purported exactness of Geometry.

When I develop my designs, there is always going to be a certain amount of inexactness. This is because I am dealing with imperfect tools on an imperfect medium, with imperfect vision. Even my 20/15 vision is subject to minute discrepancies now and then. The result is that lines will inevitably get 'off' at some time or another. If you study any of my drawing very closely you will find this.

But this doesn't worry me, because it is not important for these drawings to be perfect. The development drawings are never going to be used to establish the final measurements of anything.
If conditions permit, I prefer to recreate the geometry at full scale -actually use the same methods to make the full scale layout that the timbers will be aligned to for scribing. But if this doesn't suit then I make a large layout on a sheet of 4x8 plywood. It should be noted here that my geometry is developed so that a full scale plan can be made without needing much more space than the building or wall or whatever will actually occupy. it is a 'confined' geometry. These final geometries are done on a very large scale, because as such they will not be subject to much of a degree of error -the higher the scale the less margin there is for error. A drawing done on a sheet of paper will always contain error, I don't care how good you are. This is because a pen line is not 1 dimensional, and a sheet of paper is not a flat surface and a number of other factors.

DLB

I don't see an issue with brace lengths. As DL points out the building will be scribed. The top outside edge of the brace, where it contacts the post/sill/tie, can extent to the outside edge of post, continuing at the given angle. The the shoulder of the brace is then scribed and the length is then known. Some of these lines could be placed anywhere upon the member, a datum line, and then referenced to the full scale lofting lines on the floor.

I suspect if the first floor of the building was constructed the following framing members could them be laid out full scale on the now constructed floor. I think I would board the floor over extending the boarding a foot beyond to the edges just for the extra room. Maybe set up a derrick to handle the timber.

I suspect once the scribing is started DL will switch from using the compass to using dividers.

sorry for not getting the drawings up yet, I have been terribly busy over the last week or so.

DLB

I haven't gotten back on this for a while, because I have been working on a new development. I feel that I have finally come up with a system that meets all of my requirements, and it is simpley this:

With this figure, I have everything I need to make almost any structure. The construction of this figure is astonishingly simple, and on it there are a great many useful geometric ratios. This figure, based on a single measurement for your building, is the key to achieving the proper geometric proportions without having to go through a great many operations.

I will let you all ponder this a while before I show you how it's used -so let's get to thinkin here folks!

Here is how it is done, there are a few steps that could be bypassed (mostly at the beginning) but they are important to establish the figure as based on a single measurement to yield proper proportions.

We start with a distance x which is equal to some important measurement on the building. For example on a German Frame x~3', 3' being the spacing between common posts.

We than draw a line and mark out a segment with 4 sections equal to X, line DB in the drawing, with its center at C

With its center at C, we draw an arc that intersects line DB at points D and B, the radius of this arc is equal to 2X

With the same radius, we draw 2 more arcs that intersect the circle with center C and line DB, one with its center at D and the other with its center at B

We then draw 5 lines FG, FC, FB, GC, and GD to form our basic figure.


Point H is formed by the intersections of lines DG and BF. Line HC is perpendicular to line DB.

There are many other lines that can be drawn, but this is the basic figure.

By using this figure, I am able to accomplish a completely self contained geometry, that is the geometric layout is contained entirely within the building lines, a must when working in confined spaces. Furthermore, this figure is just as easily made with rope and string (full scale ground layout) as it is with a compass and straightedge, which was one of my major goals.

The secret to this figure is using it as a 'key' from which all of a buildings measurements and proportions are taken and transferred to where they are needed. It is a figure of Ad Triangulum Geometry, and is somewhat a variation on the Daisy Wheel -it could be called the 'half wheel'. Taken beyond its simplest execution, the daisy wheel could also be used in a similar way, but this figure yields the same results with less effort.

DLB

Alright, now for those of you who have been following this, here is how this figure is used to design a building.

The first step, a shown, is to choose a master measurement. In all forms of Geometry this is a necessary first step and here it is of course no different. For this figure, this measurement should be something fairly small. In many of my geometries the master measurement that everything is based on is something important like the width of the gable ends. In this system, it must be something small. Rather than choosing a measurement such as the width of some portion, or the spacing between bents, etc. it may be easiest to instead choose a small measurement that is a fraction of one of these. For example, if your bent spacing is twelve feet you might make your master measurement a fraction of this at 3 feet. Somewhere in the 3 to 4 foot range is the best.

This 'master measurement' does not necessarily have to be the same for each portion of the frame, we will see later how that works.

Let's say we start with the floor plan. The length of the building is to be a multiple of 3 so we make our master measurement 3 feet. We then make the figure as described earlier.

My preferred procedure is to make the figure along one of the principle lines of the drawing, such as one of the walls, and then the perpendicular line yielded is a useful reference point, acting as an axis.

From this point on whenever I need a distance measured out and marked, such as the width of the plan or the spacing of floor joists, I set my compass to the length of one of the lines on the figure, and measure out a line of this length or a multiple thereof. In this way, I am not performing a geometric operation for every line yielded, but rather I am measuring out distances with a compass .

When I move from the ground plan to another drawing, such as the gable elevation, I need to create another figure for this drawing. If the width of the building was yielded by a measurement from the figure than it may not be a multiple of the master measurement, and so you have to establish a new base for the figure. The simplest way to do this is to use whatever measurement from the figure that you used to get this distance, or perhaps a multiple of it if it is too small. This way you ensure the buildings geometric relationship to itself, without having to adhere to a strict numerical relationship in your measurements (like everything is a multiple of 3)

I hope this explains the process a little bit...

DLB

I was asked to help a client with a queen post barn design. He gave me some ideas he wanted and let me make up some designs to show him.

He told me he wanted a 24x36’ barn with either a 3’ or 4’ knee wall. And either an 8/12 roof or a 10/12 roof. As far as the roof pitch went, he told me “whatever looks right.”

He wanted to make sure that the top of the tie beam was at least 10’ over the height of the first floor, and that any beam on the second floor met code of 7’ 6” head height clearance.

I made up some drawings, had a meeting with him and he selected this gable end view for his barn.



Just for fun and as a learning experience I decided to try applying your “half wheel” system to this design to see what it may tell me.

I started out by applying the half wheel to the base line. Like this:



This showed me that I had placed the queen posts at the right location. And I was happy with that.

It also seemed to show me that the top of the tie was just a little too low. And that I thought it should be even with line F-G.

Next I made a copy of the half wheel at the top of the tie to see what that would/could/might show me.
Like this:



I didn’t really see anything that jumped off the page to me.

After that I made a copy at the top of the plate to see what that would/could/might show me.

Like this:



If we look at your point “H” as the apex of the roof, which I am not sure it is meant to be, we see that the roof line would be at a 30 degree angle.
So just for fun and a learning experience, I moved the tie up to the top of line F-G as shown here:



Next I applied the half wheel to the top of the new tie:



I didn’t see anything here.

After that I applied the half wheel to the top of the plate, again.

Like this:



Again just for fun, I changed the roof line to make the apex of the roof the point “H” to see what that would look like.

As shown here:



In order to maintain a clearance of 7’ 6” below a spreader beam between the two purlin plates, I had to move the rafters up and this created a taller knee wall.



I am curious to see what you think of what I have done.

I am awaiting your comments.

Jim Rogers

Jim, have you tried applying a full daisy wheel to the 3rd version, where nothing jumps off the page? It looks like the tie could raise a foot or so and the ground floor would be the the line connecting the 2 lower petals. With a 2nd wheel laid on top, where the orientation is rotated(north south vs east west) the center peak petal would dictate the peak.

Without pictures this stuff gets foggy.

I am working right now on a rendering of Jim's building using the half wheel method. Thanks Jim for giving me a good example to use to show my methods.

What A little while guys...

DLB

Tim:
I did understand what you meant.

I created this one:



It shows the roof to be an 8/12. If I did it right.

Jim Rogers

Ok here it is. I have developed a close copy of Jim's building using geometry methods. It is not exactly the same, but should be very close.


We start out with the figure as normal. Here X is 6 feet, since the width of the elevation is 24 feet.


Next we define the width of the building and the height of the first story based on the measurements of the half wheel.


Next, we define the height of the knee wall. This is arrived at by taking a measurement from the figures with the compass that suits our needs, here highlighted in red. Using the compass, we transfer that measurement to the wall height, again shown in red.

Next the roof height is defined by taking another measurement from the figure and transferring it to where it is needed. Again highlighted in red. Except reviewing the drawing now, my highlight of the line stopped to soon. it should extend all the way to the lower left hand corner of the figure. Also the roof height line should extend to the cross-tie line, not the knee-wall line. oops

The brace lines are drawn, again by taking a measurement from the figure and transferring it to where it is needed.

And finally we draw in lines to represent the timbers to show bent configuration.

Compare our geometry-yielded figure to Jim's numerically yielded design:


The measurements are very very similar, I will try and get approximations up soon.

Keep in mind, the measurements will not be exactly the same. One drawing is made with pure geometry, the other I assume was made with numbers. Jim's drawing comes out to nice measurements of inches and feet, and a common roof pitch, mine will not but rather will yield a bunch of numbers with geometric ratios, not equal to whole inches or even convenient fractions of an inch. Which reminds us, Geometry is a scribe system not a numeric layout system

Hope this clarifies things for you...

DLB

I appreciate your drawings but some of them the lines are light and I can't see the red.

Are you saying to extend line D-G to the wall to determine the plate height?

And I do understand that this is scribe but I wanted things to look proportional.

Jim

You said:
"Next the roof height is defined by taking another measurement from the figure and transferring it to where it is needed."

Where is this measurement taken from?

And I can't see where you placed it?

Can you explain this more?

Jim

I will post direct links to the pictures so you can look at them in higher resolution...

http://i538.photobucket.com/albums/ff345/HiddenOrder/Geometria/GEO%20Article/scan0008.jpg
http://i538.photobucket.com/albums/ff345/HiddenOrder/Geometria/GEO%20Article/scan0009.jpg
http://i538.photobucket.com/albums/ff345/HiddenOrder/Geometria/GEO%20Article/scan0010-a.jpg
http://i538.photobucket.com/albums/ff345/HiddenOrder/Geometria/GEO%20Article/scan0011-a.jpg
http://i538.photobucket.com/albums/ff345/HiddenOrder/Geometria/GEO%20Article/scan0012-a.jpg
http://i538.photobucket.com/albums/ff345/HiddenOrder/Geometria/GEO%20Article/scan0013.jpg

The line for the roof height is one of the long diagonals on the figure, line DH. With the compass, this measurement is transferred to define the roof height. It extends along an extended line CH upward from the intersection of line FG, which also marks the top of the Tie Beam in this layout.

The plate height is simple line FG extended in either direction



for comparison, here is your layout superimposed over mine. I could do a little bit of tweaking to make mine match yours a little closer, but considering how quick I did it I am quite surprised at how close they actually are.

http://i538.photobucket.com/albums/ff345/HiddenOrder/a-gableendview-start1-1.jpg

Let me know if you have any other questions

DLB

As far as differences go, My tie is slightly higher, and as such so are the braces, and my knee wall is slightly shorter. The overall wall height ends up being just about the same, as are the locations of the queen posts and the center post. My roof pitch is ever so slightly steeper.

Thanks for explaining the measurement D-H. And how you applied it. That was the one I was missing.

I think I understand your layout now. It was a very interesting exercise.

The comparison is truly amazing. And I guess it shows that my proportions weren't that far off.

Thanks again.

Jim Rogers

Jim,
In all honesty, a building designed with geometry and one designed with feet and inches are often times going to be very similar, sometimes the difference may only be a tiny fraction of an inch. My belief however is that the geometry allows us to arrive at sound relationships and profiles quicker than we would through mathematics, and is a lot more enjoyable.

My interest in geometry arises out of historic curiosity, but after experimenting with it I have discovered the tremendous rigor of its methods, and its incredible ability to yield beautiful figures that are also wonderful structurally.

Of course the more I think about this, the more questions I seem to have.
One is why did you pick this distance shown in red on scan11-A as the distance to use to figure the roof height above the tie beam? or distance D-H.

Jim,

My drawing are semi-measured. Meaning I measure what the figures come out to in inches so I know the general area of what they will measure out to. It is a useful reference to have.

So here, the choice of dimensions used was similar perhaps to your choice for your original measurements. Why did you choose 10 feet for the tie beam? why did you choose 4 feet for the knee wall?

I chose my measurements largely because those are the ones that closest matched yours, and also are the ones that made the most sense to me at the time.

Hope that helps

DLB

Tim, I can tell you what the results will be because of the fairly straightforward proportions of this building. With the two 'petals' aligned with the tie beam, the other will line up with the queen posts. That is simple, because the queen posts are located at the 1/4 and 3/4 locations relative to the width, which is where the petals would also be.

The daisy wheel always divides a given space into fourths.

The question, however, is what happens with the daisy wheel when you draw in the hexagram...

I should explain something about my figures and the trend of my geometries.

My geometries have been trending away from arcs and circles and more toward a series of lines to create geometric figures, and there is a very valid reason for this.

If I am performing the geometry at full scale to create the scribing layout itself, I may not always be doing so on nice smooth-troweled concrete. I may be doing it on uneven ground, possibly complete with grass and other obstructions. As such, there is no good way to accurately draw arcs and circles.

And it is important to note, when performing geometry the smaller scale it is done on, the more prone to error it is. A small drawing the size of drafting paper can often times have noticeable and measurable errors that arise simply as a consequence of the thickness of pen lines or one minute misplacement of a compass point. For this reason, I am insistent that geometries should be totally redone at full scale to ensure things come out as intended. The shop drawings serve their purpose, but it is not to be used to get any final measurements for anything.

This figure was designed so that it can be easily done with a length of rope on the ground to determine the points. It is not necessary to actually mark a single arc. It is the culmination of all of my efforts, but was arrived at largely by accident. I made it on one of my drawings while trying to arrive at a certain proportion (which it yielded). After studying what I had just done I discovered it was exactly what I had been trying to develop all along. With a few minor modifications and perhaps a little increase in its complexity, it can give you just about any proportion you could want. In its simplest form as shown here it is more than sufficient for most applications.

One important thing to consider is that it is often helpful to actually make this figure multiple times, as for different parts of your structure you may want to use a different base number. For example, I designed a building with it where the gable walls use a figure with a slightly larger base number than that used to design the side walls and floor plan. But the number for the gable walls is ultimately derived from the figure used to design the side walls and floor plan. Thus they are all still related by the geometry and are proportionate to each other.

It may even be useful for complex frames to have a number of figures derived from each other. But any one part of the frame should be limited to the use of a single figure to keep it from becoming too arbitrary.

Now I would like to see more people do like Jim, and try their hand at applying these techniques to their own projects.

I am working on a frame right now designed with this system. As soon as I can figure out how to get up good pictures of my large shop drawings (the lines dont show up well on my camera and they are too big to scan) I will try to post some up for demonstration. IT may be some time before the plans are totally finished however.

DLB

In reply to Tim's request for rotating the wheel.

I can and did but I can't login to photobucket right now. Something is wrong with their site, I think.

Why did you want me to show that?

Jim

Ok, well I stated why I used the dimensions I used; as they were the requests of the client.

The reason why I asked you why you used the lines you used, was I was trying to understand and learn your system so that I can use it to design other width frames.

If you had a reason why, such as "this is how they used to do it." Then it would make sense to me. If you are inventing or establishing a "new system" based on what you know of the old way of doing things. That's fine too, I'm just trying to understand.

You said you just picked one that somewhat matched my design. That was good and I now understand that. But what I'm looking for is a system that we could use every time we want to design a frame that "looks right."

If line D-H is the line to use every time, that's also good, I'll do that. But I thought you were trying to teach a system to use over and over to do it every time.

I'm willing to learn, and I wanted to understand the reason or the basis for using a line length for determining other building proportions.

Jim Rogers

Jim,

My procedure is to choose lines that are of a dimension in the area of what I want. If I want a height of 8 feet for example I will choose a line that approximates 8 feet on the diagram. This means I do I have scale for my drawings and I do check the lengths of certain lines with a ruler to see if they fit my requirements.

I chose line DH, for example, because it would result in a roof pitch close to what I wanted.

In the case of your design, your dimensions were based on customer specifications. In the case of my version of it my dimensions were based on your specifications.

We can design buildings using geometry to meet our preconceived specifications just as we can with inches and feet. It's just our measurements will end up relating to each other in slightly different ways.

We don't always have to use line DH as I used it. In fact on my shop design that I am working on my roof pitch is arrived at by much different means, as there is no dropped tie to base the roof height off of as I did here. I simply chose a starting point and a measure from the half wheel that would place the peak in the right spot.

For this it is necessary to have a building's general design already in mind. You need to know how high your walls are going to be, what you want fora roof pitch, where you want your braces, etc. Then you simply choose dimensions off of the figure that will yield the proper dimensions. It is no different than how we do things with a ruler. We know about where we want things to lay, so we force them to adhere to our standards of measured because we have to. Here we instead force them to conform to the measures yielded by geometry.

If we instead want to design a building that flows totally out of geometric forms, this is not the method to do it. We must instead apply the complexities of the Ad Quadratum and Ad Triangulum systems. But if we know what we want, and just require a means of arriving at exact locations and dimensions than this is the system. This geometry is a replacement for the measuring tape, to be used by an architect who already has a good idea of what he wants his building to look like.

Hope this helps

DLB

The problem with the daisy wheel as most people use it is that it is overly demanding. Its simplicity often times robs us of the ability to make frames as we want them to be. It is a great tool if you want to make a simple frame that follows its limited geometries, but it falls short when freedom of design is required. If your client does not want one of the few simple 'daisy wheel frames' then you need another tool -either to complicate the wheel to get what you need or a freer geometry from the start. That is the reason I have this 'half wheel'.

Simply put, the purpose of the half wheel is to provide a geometry that can be used like a measuring tape, a means of meeting out dimensions.

That said, I am not anti-daisy wheel. I like it. I use it. Sometimes I scratch it into a board here and there when thinking (or bored). It has its uses, but there are times when we need another tool.

My geometries arise out of an attempt to discover how man might have created buildings to suit his needs, to fit specific situations, etc. when he didn't have a standardized measurement, a square, and when the Daisy Wheel just wouldn't do. This is an attempt to explore how we might create things without measuring tapes. Take it for what it is worth, you may decide just to stick to your measuring tapes and that is fine.

Geometry should not be viewed as a science. It is not a set of rules like 'you must use line AB for such and such, line CD is to be used for this... etc. Rather it is a free art. You use the lines of geometry to fit your vision, or in a business setting to meet the demands of your clients. For my shop design I needed a plan approximately 14x24 feet with walls about 8 feet high. SO I set out to get dimensions close to that from my geometry. With a base 3 half wheel, I was able to achieve those exact measurements. I didn't get them because geometry made me do it. But rather I got them because, trough the geometry, I could.

Interestingly enough, the inspiration for the creation of my 'free geometry' concept where you transfer measurements instead of performing increasingly complex geometries came from a fiddle...

DLB

Tim:
I was able to login today.

Here is the drawing you wanted me to post.

Jim

DB:
Thanks for your explanation of your system.

Jim

Your welcome.

But I can't help but feel that a lot is left unclear here. I find it is very hard to actually explain things like this in such a setting. It's one of those things that's best done face to face, where you can talk with people and do things right in front of them.

If you all have any other questions (not just Jim!) fire away. And if you have any challenges for me (specifications of a building for me to try my hand at) then fire away on that too!

DLB

DL:
I don't think that I'm unclear on your system. As of right now I don't have any further questions.

The whole reason why I tried it was to see if it could help me to design the correct roof pitch for this client's barn.

I have another one or two projects in the wind that may come about in a while. And if they do I may try your system to see how it will produce a frame design that "looks right."

Jim

My hope is to develop a system that can work well in conjunction with standardized measurement, meaning that we can create designs with it that are hybrid geometry and numeric. For this I can see a number of advantages. I hope that this system will accomplish this goal, which is part of why I'd like some more opportunities to test it.

One reason for this idea is that it sometimes makes sense for us to lay out the walls of our buildings using numbers. That way we easily can make a footprint of exact specifications. But when it comes to roof structures, particularly trusses, I believe geometry is the way to go. We can have numerical floor plans with geometric roofs. A big reason for this is the inherent beauty of geometric order. Another big advantage is the engineering value inherent in true geometric ratios.

And of course, there is the also the case of the fully geometric structure. The question always remains, what is its true value? Is geometry in this sense merely a novelty, or an advertising scheme? Or does it hold REAL value (other than, 'it looks neat')? These are important questions that we need to continually ask ourselves.

To me, the biggest advantage of geometric design combined with scribe layout is the total lack of numbers, and the resulting total lack of mathematical calculations. I like the idea of being able to pick up a compass and draw out figures that I would have to otherwise use complex trigonometry to get. And this is why I am a proponent of geometry for roofing. Design it with geometry, measure your drawings to fairly tight tolerance and let your computer figure out the numbers needed to please the engineer. The result is you do no math.

And I am not necessarily saying you are very unclear, it is just that there is a lot more to my systems than I am able to explain in this way. It is impossible to teach something thoroughly without actually being there. I think you have a good grasp of the system, but there are a number of complexities, and there is a certain art to it that can't be explained that can only be learned by seeing and doing.

DLB

It is common in Timber framing for the location of certain members such as braces to be related to other members by geometric ratios, such as 1/3. Normally this is come at by dividing the measurements to get the right number. That stinks. That is especially annoying when the measurement is not easily divided. The third is an especially troublesome fraction, since inches cannot be easily divided into true thirds mathematically.

Geometry gives us some easy methods for getting at these simple ratios without having to strain our brains. Indeed, once we are used to the simple steps involved it is like second nature.

The major advantage of designing a frame from the outset with geometry is that, as a result, these fractions are often already found for us.

Which brings me to this, on my rendering of Jim's building I made a mistake. For the brace length I took a length off of the figure that 'looked right' when in fact I should have used my compass to divide the post length to get a stronger brace to post ratio. A simple error, made by forgetting the principles of the system I was using. Oops.

I won't hold that against you.....