Designing Furniture

I was thinking about the design process the other day, while I was designing a vanity for my daughter.  I was sketching away when the mail came in and I found an article in one of the woodworking magazines I get.  I read the article and started to scratch my head not understanding it all.  I am not always the brightest light bulb in the box.  

They were talking about "The Golden Section", "Fibonacci Numbers", and "Arithmetic Progression".  Have you ever heard of them?  I had not until I read the article.  So I asked my daughter about them. She is into the arts so I thought maybe that she had heard of them.  Well the only one she had heard of is the "Fibonacci Numbers".  The others she had not heard of.  So I am still looking at this with a big question mark over my head.  I decided to write this article, because sometimes, I understand things better when I rewrite things on paper.  Lets see if it will work this time.  If I get something wrong in this article please let me know so I can correct it right away!!!

Lets start with some basics about proportion.  Proportion is an important part of the design process. It is what makes a piece look right within its environment and within its self.  Understand?  Kinda like taking a full size table and placing half size chairs around it.  It just don't look right! Either the chairs need to be bigger or the table needs to be smaller.  By the same token, if you have a chair that is built to normal size but the seat area is only half the size it is suppose to be (width wise), again it is not going to look right.  So proportion is an integral part of the design process.  But how do we get the proportion right?  For some, just looking at a drawing is enough to tell if the proportions are correct. For those of us without that gift, we can use the principles I listed above ("The Golden Section, Fibonacci Numbers, and Arithmetic Progression".)  

Golden Section History

The "Golden Section", sometimes referred to as the Divine Proportion, Golden Ratio, or the Golden Mean, was discovered by the Greek mathematician Pythagoras.  He started and headed a philosophical and religious school in Southern Italy called the Pythagorean's Brotherhood and used the pentagram to represent their group.  Later Phidias, a Athenian architect using the Golden Section came up with Phi.  You remember that from math class don't you? The number 1.61803333333? It drove me crazy in math class.  I started having nightmares about my math teacher after reading that darn article.  Later on Leonardo of Pisa came along and took things to the next step.  Fibonacci, as Leonardo called himself, published a book around 1202 called "Liber Abaci".  In it he introduced a math problem where a pair of rabbits were placed in a field, they can not escape or die.  At the age of 1 month the female gives birth to 2 new rabbits (1 male, 1 female), the female rabbit does this each month for 1 year.  How many rabbits would there be at the end of the year?  The answer to this question contains a series of numbers (1, 1, 2, 3, 5, 8, 13, 21, 34, 55.....).  This series of numbers is called the Fibonacci Numbers or the Fibonacci Series.  If one looks at the ratio that occurs after the number 3, it is 1:618, which is known as the Golden Ratio today.  There are those who say that this ratio is found in nature, art, the population growth, architecture, in music, the human face and other items as well. 

Using It

Here is the basic idea, as I understand it. Lets say you have a table top that you want 20" deep.  To make it into a Golden Rectangle multiply 20 by 1.618 (20x1.618=32.36).  Now you can take the 32.36 and round it off.  I would change it to 32.5, you now have a Golden rectangle that is 20" x 32.5"  that should be pleasing to the eye.  An interesting fact is if you draw a square within your Golden Rectangle, the remaining rectangle will also be a Golden Rectangle.  When trying to figure out the size of the legs and such on a table, or any other piece, use the same principle. You can scale all the other elements by again using  the Golden Section or you can use the Fibonacci Numbers.

If you use the Fibonacci Numbers this is how, as I understand it.   The numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. (Each number is the sum of the previous two.) If you have a cabinet that you are building and you want the total height to be 84", and you are looking for the size of the feet you would divide 84 by one of the Fibonacci Number.  Figuring out which number will come with time and making educated guesses.  Lets say that we divide our number by the number 13. 84 divided by 13 equals 6.46"  which you can round to 6.5 (6 1/2")  you would make your leg/foot 6 1/2" tall.  To find out how wide the leg/foot is going to be, turn it into a golden rectangle by multiplying by 1.618 (6.5x1.618=10.51 or 10 1/2")  

Arithmetic Progression

The last thing I am going to look at is Arithmetic Progression.  If I can get you to think about a chest of drawers, you will realize (if you haven't already) that the drawers are usually different sizes, with the largest being on the bottom.  Now how do they do that and get it to look good?  They use this technique.  Each drawer is in proportion to the others.  The easiest way to do this is to add your drawer divider to the previous drawer size.  so lets say your first drawer is 6" and your space between drawers is 1".  6 + 1 = 7, so the next drawer face would be 7".  Using the same method, the next drawer size would be 7 + 1 = 8".  

If you use all the things we have talked about, you will end up with a very eye-pleasing piece of furniture.  Keep in mind however, that your eye should rule over the Golden Section, The Golden Rectangle, Fabonacci Numbers, or Arithmetic Progression. What you build should please YOU.

Some Final Thoughts

Here are some final thoughts about designing tables.  Please keep in mind that these are only rules of thumb.  Your table height should almost always be between 28 1/2" and 32".  The most common height is 30”.  

The height of the Apron (from the bottom edge of it to the floor) should be no less than 24".  Whoever is sitting at the table should have at least 24" of room.  For example, if your table height is 30", the table top is made of 1" (true) stock, that would mean that your apron should be no larger than 5".

The overhang, or the distance from the front edge of your apron to the edge of your table can vary greatly.  The average is any where from 10" - 18".

To figure out the elbow room around the table use a figure between 23" - 30" per person.  23" will provide a fair amount of room but may feel cramped for a large individual, such as myself.  

The standard table top width is between 30 and 34" for rectangular tables, 40" x 40" for a square table.  To make a rectangular table that will seat 6 people comfortably, make it about 60 x 30".  For a circular top, make it about 44” to seat 4 people, or 54" to seat 6 people. 

To taper the legs of your table, you should start about 1" below the apron and taper it so that it is half its width at the bottom.  For example if the leg is 2" wide you would want to taper it to 1", and if the height from the floor to the bottom of the apron is 25" you would start the taper at the 24" mark.

Other Sources

"Popular Woodworking", December 2003 Issue #138

"Illustrated Cabinetmaking", by Bill Hylton, Reader's Digest, Pleasantville , N.Y.

"Measure Twice, Cut Once", by Jim Tolpin, Popular Woodworking Books, Cincinnati .

"Encyclopedia of Furniture Making", by Ernest Joyce, Sterling Publishing Co. Inc., New York .

"Cabinetmaking and Millwork", by John L. Feirer, Bennett Publishing Co., Peoria , Il .

I hope you Enjoyed this "article" or should I say book report. Writing it was as much a learning experience for me as I hope it was for you.  If you would like to see an article on a specific subject please drop me a line and I will see what I can do.