Designing a Box - Part 2...

It has been a busy week or so, but I’m finally getting back to this box design.

To reestablish the premise in this exercise, I want to improve my furniture design skills and to do that, I’m going back to the basics. I am attempting to design a basic box that has no specific purpose, researching the rules of furniture design and testing them as I go along.

In the past post I discussed the Golden Rule of Ratio, or Phi, and tested the concept using some simple outlines drawn to scale. The result was respect for the rule while not committing to using it exclusively. Testing it in this application, it didn’t allow me to focus in on one dimension, but it did allow me to narrow down the choices.

Now that I have a few basic sizes to work with, I need to determine what to add to the design and what effect those additions will have on the results. There are two additions that must be considered; where the lid meets the body of the box and a base for it all to rest on.

I have seen some very well constructed boxes but never one with an invisible joint where that lid meets the body. Even in the finest of cabinetry, a well-hidden joint like this becomes distorted over time and it becomes noticeable. Where that line appears affects the proportions of the piece and its placement must be considered in the original design of the box. That much I know. Where that placement should be is something I have to determine.

If there is a rule regarding whether or not a piece should have a base, I can’t find it. I do know that I like the look of bases on just about everything. To me, a base gives “grounding”, especially when it is a little wider than the piece itself. How much wider is something that has to be decided but most important to me at this point is the height. Is there a rule that works that will tell me how high the base for my box should be? Let’s find out.

The Fibonacci Sequence

Researching this rule I discovered that it is a process of “creating a series of dimensions that are related by the Golden Ratio”. Hopefully, I will have more exacting results from it than I had with the Golden Ratio itself.

The Fibonacci Sequence first become known in 1202 in a math book titled, Liber Abaci which has been translated into either, The Book of the Abacus or, The Book of Calculation. Do you ever wonder about the authenticity of something like this when the translators can’t even agree on what the title means? On top of there not being a consensus on what the title of this publication means, it turns out that the author, a Mr. Fibonacci, worked under a number of aliases, being; Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci and Leonardo Fibonacci. Hey, I trust him already, don’t you?

The basis of this rule, while complicated to understand, is quite simple to execute. From my previous test I have come up with two different proportions that I have decided to work with; 14” x 8.5”, the one closest to the Golden Ratio, and 14” x 10 1/4”, the one I think best represents an emotion, in this case power.

For the first one, the Fibonacci Sequence would be as follows:

8.5, 14, 22.5, 36.5, 59, 95.5

This may appear to be a random listing of numbers but it is derived from adding 8.5 to 14, which equals 22.5. You then add 22.5 to 14 and come up with 36.5. The 36.5 is added to the number that came before it, which is 22.5, which gives you a total of 59. Add that number to the number that came before it and you get 95.5. Clear as mud, eh?

For my other choice the series would be:

10.25, 14, 24.25, 38.25, 62.5, 100.75

These numbers can be applied to a design in a number of different ways, even using them as the numerator in a fraction to develop a series of measurements based on one of the overall measurements of the piece.

So now that I have these numbers, what am I supposed to do with them?

The answer, in this particular case, is nothing. In this example only the ratios are relevant as the only dimension that we can use is the actual height of the box.

For these calculations we need to start with a consecutive sequence of three Fibonacci numbers as we are looking to divide the height by 3 for the three sections of the box; the base, the body and the lid.

Using the base three numbers of 2, 3 and 5, I come up with a value of 10, or (2 +3) + 5 = 10.

Dividing the height of the box, 8.5” by this value,10, gives me a decimal value of .85.

Now I have to multiply this value by the first value in the sequence and you end up with a value of .85 x 2 = 1.7”. This is to be the height of the lid.

Now, multiplying that same value (.85) by the second number in the sequence, and I get - .85 x 3 = 2.55”. This is the height of the body of the box.

One more time, I multiply the same value by the third value in the sequence and I get -  .85 x 5 = 4.25.

If this works, the three values should add up to the height I started with. 1.7 + 2.55 + 4.25 = 8.5. Son-of-a-gun – it totals correctly.

So what these calculations tell me is that the lid should be 1.7” high while the base should be 4.25” high.

That same set of calculations for my box that has a height of 10 1/4 works out as follows:

Dividing this height of 10.25 by the same sum used previously (10) and I get 1.025

Multiplying 1.025 by 2 gives a value of 2.05. When multiplied by 3 I end up with 3.075 and multiplying it by  5 results in 5.125.

Checking my math, 2.05 + 3.075 + 5.125 totals 10.25, so my math is correct.

These calculations tell me that for this higher box, the lid should be 2.05” high while the base is a whopping 5.125” high.

I don’t know about you, but I don’t hold up much hope for this rule resulting in a pleasing display in this particular application, but lets see.

I think I can safely say that if your building a chest of drawers, Mr. Fibonacci’s trip into mathematical hell might be worth the adventure, but for my little box, I believe it is only partially right. The proportions for the lid line work very well for me, but on both there is just too much base to give the box a balance.

For this experiment, I’ll give the Fibonacci Sequence 50% out of a possible 100%.

Shaker Influence

As I cannot find a specific rule that is purported to be the “Golden” one for determining the height for a base on a box, I’ll have to turn to accepted examples from the past and figure the ratios they used to base my calculations on.

I don’t know anyone interested in furniture design that isn’t impressed by a piece of Shaker. The craftsmen of this style truly knew a thing or two about proportion and design so searching the web I came up with this example.

This particular pine painted blanket box, circa 1820, is a dovetailed example that was probably made in New York. It has a hinged breadboard lid and stands on a finely dovetailed bracket base. It is 24 1/4” high, with a width of 45 3/8”.

I chose this example because its dimensions do not conform to the Golden Ration. If created using that rule, at this height it would be just shy of 40”. Obviously, the designer of this piece made it considerably longer than he should have.

In the hopes that this particular image wasn’t distorted in any way, I brought it into AutoCAD to take some measurements from it. Using the known height, I scaled the traced image to gain other measurement, the main measurement I was after, of course, being the height of the base. Achieving that I could calculate how that height value relates as a percentage of the overall height of the piece. I recorded a height of 7 1/4” for its base, and based on the known overall height of 24 1/4”, I calculated that the base is 30% of the total height of the piece.

In the case of my box designs, using that value of 30%, the 10.25” high box would have a base roughly 3” high, while the golden rule example, being 81/2” high would have one 2.55” high. Lets see how those figures work out.

In both of these I left the lid line where the calculations of the Fibonacci Sequence told me to as I do like those proportions.

In this case, the Shakers knew what they were talking about. The base is in complete agreement with both the golden ratio developed proportion and the one that exceeds it.

The Golden Thirds

The base of this box is 30% of its overall height, which is relatively close to being one third of that overall height.

There is actually a rule out there called “The Golden Thirds”, or “The Golden Mean” which states that if you must divide up a plain, divide it into thirds, both horizontally and vertically. If you are going to place something on that plane, place it at least on one of the lines of that grid, preferably where the gridlines intersect, but if not at those four points, then at least on the lines.

So lets see what happens when we start to analyze what my Shaker friend did when he was calculating the dimensions of this blanket box.

As stated, according to the Golden Ratio, this blanket box should have a width of 39 1/4”, the result of multiplying its overall height of 24 1/4” by 1.618.

The designer, instead, gave it a length of 45 3/8”, or, in other words, he extended its length by approximately 15%.

Now going by the Golden Thirds, the base should be 33% of its overall height, or just a hair over 8”. The designer, however, only made it 7 1/4” high. This means that not only  is the box 15% longer than the first rule calls for it to be, but the base is actually 10% lower than the second rule says it should be. Did the cabinetmaker that made this box not understand these rules, or did he ignore them for a reason? Lets find out.

In these four illustrations, the bottom two have used the rules covered to set the height of the lid as well as the height of the base. The two in the top row have used the rule to set the heights of their lids, but the bases are set according to my Shaker friend’s calculations.

Tough call, isn’t it. I can see a distinct difference in the proportions of the bases, especially in the box with the exaggerated proportions.

Starting with the obvious one, the one at the lower right, I believe the base is way out of proportion for the height of the box. The lid is fine, but the base, which is set by the Golden Mean, is just too much.

The one to its left, with its overall proportions calculated using the Golden Ratio and its base height set by the Golden Thirds, has a better balance between the two and tends to support the rules.

The two at the top, however, whether Golden Rule proportioned or my exaggerated proportions, have a better balance between their overall dimensions and the dimension of the base than the other two, their bases being calculated from the Shaker value.

The result of this is that I think I have developed a new rule here – “The Tin Rule”. This new rule states that a base should have a height that is 30% of the piece’s overall height. Let’s see if that one holds up for a number of centuries like the others have.

Summary

Thus ends this part of the experiment. I have learned some more interesting things about design and rules.

1. The Fibonacci Sequence works well when there are a fair number of divisions in a piece, but when there are few, like on my box, it is not that helpful
2. Having used this rule to determine the height of the lid, however, I have to acknowledge that it can be of some use, but only when used with caution
3. The Golden Mean Rule works reasonably well in applications like this, but again, I’m not sure I would rely on it completely
4. Good design is not finding one rule and sticking to it, but combining different rules to achieve balanced proportions
5. Finally, my Shaker friend taught me that if you are going to distort one rule of proportions, you had better be prepared to distort the others

One other thing I have learned researching the in’s and out’s of furniture design -  designing furniture is really no different than any other type of artwork. All these rules that I have come across researching this topic are the same ones that all graphic designers, architects and artists get drilled into their heads their first year of learning their crafts.

So it is back to researching the next phase of this experiment – shapes. Catch ya’ next time.

Peace,

Mitchell

Designing a Box - Part 1...

Given that the weather here is a constant -2˚C (around 28˚F) and we haven't seen the sun in weeks, it is not conducive to working in my shop, which, in case you were unaware, is currently located on the balcony of my apartment. Thankfully, we are moving into a new residence and I will be able to return to sawing, chiseling, and in general, whacking away on wood by the end of next month.

As I currently cannot spend time being intimate with a hand tool, I had to figure out something to keep my brain functioning and keep myself moving forward in my quest to master the art of putting two pieces of wood together so they stay that way. I could; of course, while away my hours cruising the web looking for more technical information, but the creative juices are humming so I must find a “fix”.

Before I get carried away in this writing and forget, did you see the latest video WoodTrek.com has posted? I don’t know anyone who isn’t fascinated by carving, whether actually doing it, or just looking at it. Keith’s latest video documentary has Brad Ramsay, of Irion Company, showing us more of his magic with a gouge, this time explaining how to hold it, motivate it and direct it. Definitely an informative filled 4 1/2 minutes.

All right, back to what I plan on doing with my next month.

Creating furniture, whether on a small scale like me, or pumping out whacking big armoires, all require an understanding of design. I have spent a lifetime in design, in one form or another; either in photography, graphic design, architecture and interior design, and have spent a lifetime studying the basis to ensure those designs have been commercially successful. The one thing I have never done, though, is put any formal thought into the in’s and out’s of designing furniture. This abundance of arrogance or lack of understanding has been proven time and again as I have never been completely happy with any particular piece of furniture design I have come up with. While I have never been completely happy with any piece of design I have done, I have noticed that I’m even less enthralled with my furniture pieces. Thinking about it, I feel this is because I have never taken the time to properly understand the design principles that furniture design is based on. I am not alone and I am sure this phenomenon of never being happy exists in all endeavors. I really don’t know any designer who is ever happy with what he or she has produced. This, I think, is a good thing. When you complete a design of something or other and you can find no fault in it, nor find a way to improve it - sell your pencils, your done. That second guessing of yourself and that pushing for something better is what keeps a designer motivated and striving for something a bit more “perfect”.

So here is what I have come up with as a way to challenge myself over the next month and improve my furniture design skills at the same time - I’m going to design a box. That’s it. A box. You can call it a Tea Caddy, or a Jewellery Box or even a Keepsake Box, but the bottom line is that it is just a box. I plan on using this simple object as a test to see where formal knowledge about design will take you. As I complete one element of design theory I’m going to take what I learned and apply it to this simple six-sided object to see if the theory works or not. Where will it take me, I have no idea, but I expect to have a hell of a time with it and enjoy the journey. So let’s get started.

The first “rule” is one that anyone who has even glanced at a woodworking article about design will recognize - “The Golden Ratio Rule”. Now there is a whole mathematical equation behind this basic rule and even a special name for it - “Phi”. Now I have never been one to get lost in the technical side of things, and given I have a difficult time balancing my chequebook, this is definitely not the one I’m not going to start getting technical with, so let me simplify it for you.

The Golden Ratio Rule, simplified, means; to give something a pleasing balance to the eye, its height should be 60% of its total width, or visa versa. (For those that appreciate the exact, this is a “rounded off’ value. If you must, the full value is 1.6180339887498948482)

Sounds simple, doesn’t it? So lets see if it works in practice.

Below are eight shapes, all based on one dimension – 10”  (I told you I wasn’t good at math). Two employ the Golden Ratio Rule. Click on it to enlarge it and remove the distractions and see if you spot which ones employ this rule.

When you read my answers, the first calculation is always the width and the second, the height.

1. 100% x 100%, or 10” x 10”
2. 100% x 75%, or 10” x 7.5”
3. 100% x 60%, or 10” x 6” (The Golden Ratio)
4. 100% x 35%, or 10” x 3.5”
5. 35% x 100%, or 3.5” x 10”
6. 60% x 100%, or 6” x 10” (The Golden Ratio)
7. 75% x 100%, or 7.5” x 10”
8. 100% x 100%, or 10” x 10”

Analyzing each shape, here are my observations.

Numbers 1 and 8 definitely do not work for me and I will admit that my opinion is tainted in this case from experience gleaned from other design applications. Squares, while used often in modern design, have no sense of line or balance on their own. They are just, well - there. To work, a square must rely on its surroundings to give the shape proportion. As this is a box all on its own, my opinion is that a square one just won’t work.

Number 2 is one I could live with, although it appears to me to be a bit bulky. If these dimensions were to work, there would have to be some accoutrements added to force it to appear, for lack of a better word, sleeker. Staring at it, I did have to acknowledge that its height is out of proportion with its width, yet it does project a certain power, which is what I like about it.

Number 3 does work, so the rule does have teeth. The balance between its height and width is right on the money. The one thing that struck me about it, however, is that it did not evoke any feeling in me. There was no jumping up and down, screaming, “That’s the one, that’s the one!” The dimensions do not offend the eye, but they didn’t tantalize it either.

Number 4 appears too squat for me, like there is something missing. Its squat appearance, to me, is less than gratifying. It just does not draw my eye to it, and when my eye does pass over it, it keeps on going, as the shape holds no interest.

Number 5, with the same dimensions as number 4, but standing on end, looks like it will fall over in the slightest wind. At these dimension ratios, there is no stability horizontally. This shape, for me, defines the reason why I have never seen a pretty telephone pole – too skinny – too tall. You could modify this shape to improve it, like give it a prominent and wider base, and that is something to be considered.

Number 6, another sized to the Golden Ratio, but this time vertically, works, but to me, it is a toss-up between it and number 7. Number 6 is well proportioned, but it does seem to me to be slightly narrow, and therefore, a tinge unstable. It is not near as unstable as number 5, but not as stable as number 7. Again a wider base would be a huge asset to it.

Number 7, the same dimensions as number 2, works for me vertically, but has only borderline acceptance horizontally. While it is wider than the one that employs the Golden Ratio, to me it has more “presence”, more “power”. Proof of this is in the viewing. When your eye wanders from one to another within the vertical samples, it keeps coming back to this one and is held there longer than with the others. Unlike numbers 5 and 6, it does not need anything added to it to give it stability; its dimensions give that all on their own.

Another thing I noticed while viewing these shapes is that many can be categorized as “masculine” or “feminine”, especially the vertical ones. Numbers 1, 2 and 8 are seriously masculine. There is power in their dimensions, and they do not require any further additions to project that feeling of power. Number 4, with its low dimension ratio, appears to me to be very feminine. It projects a “softer” connotation than the others. You could also add number 5 to the feminine category, but really, it is just too damned skinny to be anything but a bad choice. What I find a bit fascinating, though, is that the Golden Ratio ones, numbers 3 and 6, are neither masculine nor feminine in stature. Could this be one of the reasons the Golden Ratio has been a rule of thumb these last two thousand years?

So there it is. The first “test’ of a rule. With these simple forms, all based on one similar dimension, I have convinced myself that the Golden Ratio Rule should always be considered. As with any “rule”, however, you have to know it to know when to break it. From this simple test of it, I have learned a couple of things about it.

1. While there is strong evidence this ratio works in the vertical, it does not seem to me to stand-alone when it is rotated horizontally.

2. A shape conforming to the Golden Ratio is gender neutral. While some may think this observation is a bit of a stretch, the reality is, there is gender in shapes, and proportions go a long way in defining them. Applying this observation to my simple box is going to cause a quandary because the essence of this exercise is to produce just a simple box that is pleasing to the eye yet has no defined purpose. If this box were to be a man’s Jewellery box, a higher ratio might not be a bad idea. If it were to be a woman’s, however, a lesser ratio might be in the cards. This means that, to properly determine the ratio, the final usage of the item and the gender to which this item is meant for, must be determined first.

The final conclusion that I came to is that the Golden Ratio must be considered in the design as it does have a great deal of merit. I just won’t be chiseling it in stone anywhere soon.

Peace,

Mitchell