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