The Golden Mean

S

shane justice

Joined
May 12, 2003
Messages
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Does anybody use this mathematical idea when it comes to designing knives?

I have tried to use it when it comes to handle length vs. blade length...it always seems to have the proper look...

But how does it then apply to a three dimensional object?

For instance...does the width of the blade make an impact on height...visually...and then also for things such as balance (weight)?

Also...for something like selection of guard material...would the guard thickness need to be in realtion to the width of the ricasso?

Is the Golden mean a constant or are their variables to the equation?

Shane
 
For aesthetics, it will make an object more visually pleasing, but in knives, the form is more dependent on function than appearance.
If appearance and function are both there, this is a plus.
The golden mean phi is derived with an equation, from what I've read, and may be found here.
 
The golden mean is a good thing in designing rooms,houses,and art work.It is not particularly of use in knives.Knives ,being basically cylindrical,are already out of the mean.The main use of the mean is in length to width ratio.If a 10" bowie was to apply the golden mean it would have a 6" wide blade and handle.
 
I think it was Steve Sando who did a nice presentation of how this can apply to knife design. Somehow, most knives that look right end up having proportions very close to those of the Golden Mean - at least in terms of blade/handle length. The guard/ricasso proportion is a good thought, follow up on that please! I'm not sure how it would apply to the "thickness" of a knife but that's worth investigating too.

I tried to find Steve's original post but can't remember his user name accurately enough to do a search. It's been quite some time but would be worth looking up.
 
Sando, Dave.
Quillion daggers and Bowies are ones that first come to mind when thinking of the proportions of the ricasso/guard, blade/handle sizes.
 
If I can remember a few ideas about human proportion...

The most "attractive" people are found to have certain proportions that roughly equal a ratio of 1 to 1.6....now bear with me cause I could have it wrong...

If you look at a knfe handle that is 4.5 inches long...that would make the blade 7.2 inches long. That ain't too bad.

OK so if we design a knife with a 1/4 inch guard...the ricasso would have to be .4 inches...Too small visually right? But then add some spacers or one of those ferrules that are so popular...and you might be up to 5/8...which would put the ricasso to around one inch and we get the proportion for all of the pretty knives that look right to us.

Does this make any sense?

I have been using this as a rough guide for design....It seems to work well until the blade gets under four inches or over about 9 inches.

4" handle produces a 6.4" blade
4.25" handle = 6.8 blade
4.5 handle = 7.2 " blade
5" handle = 8 inch blade
5.5" blade= 8.8" blade

Can we apply this equation of proportion to some other dimensions...

Such as weight...to suggest the best balace between handle/ guard materials and blade?

Shane
 
You guys have hit upon one of my favorite subjects. PHI, the Divine Ratio, Golden ratio, etc.,

Noah's arc was built using the Golden Ratio, so was the arc of the covenant, and the curtains surrounding the arc. (colors, IIRC). The dimensions were given down by God in cubits, the length of a man's forearm.

The Egyptian pyramids were designed using the golden ratio. If the base is the square, the height is the radius of the circle.

All nature and the universe were designed with the ratio, including the human DNA spiral, plants, and flowers.

And some say we're here only by accident?? PHI proves that all nature was purposely designed by somebody or something. :) PHI, 1.618, is an illogical number, meaning it never comes out even, like PI, 3.1416, no matter how far you take the numbers, they go on to infinity.

Research PHI, as suggested above, then read "The DaVinci Code".

I'm glad to see that so many on this forum know about PHI. Very few people do.


:rolleyes:
 
I try to use the golden mean in everything. It gives strength and balance through the tapers. It makes the profile pleasing to the eye. Like Don said it is in all of nature. If it works for mother nature it will work for knives, and anything else for that matter.

Larry
 
Me and Leonardo...we both like Pie! :D

I had the priviledge of teaching a small bunch of kids about Leonardo and his inventions. Doing the research for the class, I learned more about the DaVinci code...and that is where a lot of my design ideas come from....

He had some pretty neat thoughts...

The forearm measurement as it relates to the body proportion really touched home. (The japanese use the forearm to measure the right length for a tanto, don't they) Seems like the idea of proportions is Universal.

just cruising through the WWW...I found a good site "goldennumber.net"(Sorry still don't know how to post a link.)
Talks about the human hand...and Fibonacci...

Way neat stuff guys!

There's a bunch more to this...

Shane
 
For fun I designed a knife trying to use the 'golden mean' for everything I could. Came up with this:

birdn2.jpg


I used it for pin placement
Handle to blade length
The drop of the point to the blade width
Distance of pins from the spine vs. the width at that point.
Stuff like that.

All calculator done.

I agree that artists naturally produce that ratio, frequently. Some of us use a calculator.

Steve
 
I didn't do a good job of searching this subject for back threads...my bad.

But, I noticed on the two blades presented...the lovelss...and the lovely blade by Sando...(neat one BTW) ( I really like the detail)both turned the ratrio around so the blade had the smaller measure...1...and the handle used the 1.6 ...neat variation...I was doing it the other way around...doh!

I use it as a rough guide...dang criculator is pretty fancy thinking...

how did you determine blade width...and thickness...how did you apply the ratios...and where did you combine them to work in harmony?

SHane
 
Whenever I have applied it to blade lengths and handle lengths the knife doesn't look appealing to my eye, I guess an awful lot is in the eye of the beholder. What I have found that it applies to really well is determining guard length. I have found the when working with a flat oval guard, like on a bowie, if you apply those proportions from the width of the blade (not the ricasso, but the blade just before the coil) to the width of the guard, It will look good just about every time. Sometimes it can be hard to determine the exact width for a guard- is it too small or does it stick out too much on the top and the bottom? You can eyeball and second guess it for some time, so a ration like this can make life easier.
 
Ever look at a tree..... Starting at ground level the tree extends upward following the golden mean. The roots follow in the same way. Natures way to combine balance and strength. I use this ratio in the same way..... Starting at the guard the blade length follows forward. Guard follows it above and below. Handle follows it back. Usually ends up looking good. Balance feels natural.
 
Then Old Phi looks to be pretty handy....

But I agree...the eye does take the final measure

I really enjoyed the example of the tree.

How would the ratio apply if we were to look at max blade width...compared to the max handle width?

Shane
 
shane justice said:
Then Old Phi looks to be pretty handy....

But I agree...the eye does take the final measure

I really enjoyed the example of the tree.

How would the ratio apply if we were to look at max blade width...compared to the max handle width?

Shane
Click to expand...


Easier to explain it in person but here goes. Draw a + on a piece of paper. You got the idea of blade and handle length....extend horisontal line forward for blade length and back for handle. This is the streangth line. For the width remember the thickness on top of the spine is greater than at the blade edge so to keep balance the mass of thicker steel at the top should be the same as the thinner steel on the bottom.....Thicker steel does not go as far above the strength line as the tapered thinner does below. Same with the handle but remember the handle can be shorter since, like the roots of the tree, it is thicker for more distance, the mass is balanced in a shorter length. Pin placement and other astetics look good when they follow the natural mean also.
 
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