I hope I can explain my dilemma clearly enough to have someone lend a hand.
I would like to have 8 drawers in a jewelry box which are all progressively different in face height. The upper drawer (MIN ht) is 1-9/16″ in height. The lowest drawer (MAX ht) is 2-9/16″. The remaining six drawer faces in between, should get progressively taller from top to bottom. IOWs, the remaining drawers should (going from top to bottom) begin larger the the MIN ht, but never exceeding the MAX ht.
The entire height that these drawer faces will occupy is 13-1/8″. Adding the upper and lower drawer heights, we get 2-18/16″, or 3-1/8″, which leaves us 10-inches to fit the remaining six drawers into.
This is a linear mathematical problem, of that I am certain, but my method ends up consuming more than 10-inches.
Any suggestions would be greatly appreciated.
Replies
Phillip,
I think you are going to be disappointed in the proportions. One straightforward solution follows:
Lets say we want these six drawers each the same delta larger than the next smaller drawer. So, the first of these is one delta bigger than the 1 9/16" drawer. The next is two delta bigger than that, and so on. If you add all these up, you get siz times the 1 9/16" plus 21 deltas. Since that has to equal 10", then delta has to be 0.0298" (to the nearest 10 thousandth). The second largest drawer is then less than 1 3/4", which is quite a bit smaller than your largest drawer.
But, that solution will work (though measuring to that kind of accuracy is tough!)
Bob
Bob,Thanks for your insight. Your thinking was nearly parallel to my own and you are spot on about the delta part.The real issue (as I see it anyway) is that I have thrown a wrench into the works by having both MAX and MIN sized drawers that I want to have the inner drawers blend nicely between. Most arithmetic progressions begin with the smaller drawer then generate the remainder of the drawers progressively to fill the drawer cavity.I seem to vaguely remember a way using a straight edge to generate variable sized points to do something such as this. For certain, it is a snap to do just that to create equally spaced areas, but this is just the opposite of what I want. It will probably come to me at 3 A.M.I appreciate the help and the math you did.
space between drawer?
Have you looked at
http://www.woodbin.com/calcs/index.htm
?
BB
Your link to the WoodBin may be the ticket.This is such a silly mathematical problem that I should have been able to figure it out. However, a few of WoodBin's internal links are just what I've been looking for: Arithmetic Progress, Geometric Progression, ... Thanks for the help. I really appreciate it.
If I understand... (I know it's a big IF)
Total height = 13 1/8 or 13.125
Smallest drawer= 1 9/16 or 1.5625
Largest drawer = 2 9/16 or 2.5625
2.5625 + 1.5625 = 4.125
13.125 - 4.125 = 9
6 drawers left so the MOST they could be is 1.5 or SMALLER than your smallest drawer
Something isn't right.....
Scott W.
Scott,You have a very good eye. And, your math is impeccable as well.I did in fact note 13-1/8 inches. I should have noted 14-1/8 inches. Thanks for pointing that out.Phillip
I don't think your going to get there easily.Here is it is just adding 1/16 to each drawer after the first which goes over your total size by 1/81.5625
1.625
1.6875
1.75
1.8125
1.875
1.9375
2
------
14.25If you go down to just 1/32 it is:1.5625
1.59375
1.625
1.65625
1.6875
1.71875
1.75
1.78125
-------
13.375If you make the first two the same, second two the same etc. adding 1/8 per pair you can get:1.5625
1.5625
1.6875
1.6875
1.8125
1.8125
1.9375
1.9375
--------
14Still 1/8 short but you could just add 1/16 to each of the last two & it would be difficult to detect.Your best bet, and easiest to do IMHO :-)Scott
Scott,I truly appreciate all the math you've done on my behalf. I think that your last set may be the solution and here is why I think that. First of all, since these dimensions represent the height of the drawer faces, we both know that there must be some separation between each drawer if it is to function properly. Having said that, the missing 1/8" from this set could easily account for this required space between the upper and lower edges of each drawer. In addition, my original plan was to have the upper two drawers equal in height because they will be partitioned into 9 equal quadrants for rings or whatever the owner will find appropriate to store in them. So, if we have 'progressive pairs' of drawers cascading from top to bottom, this will work out just as well.In truth, when I was at this point in my thinking, the idea of progressively different drawer heights was born. Having been fortunate in selling some of my work, not a single buyer has ever questioned me as to why I did this or why I did that. Point being, this piece's owner may be no different. This may turn out to be a very difficult piece, but IMHO, if it's not worth doing why bother in the first place? Anyway, these are some of the gremlin's that all craftsmen and craftswomen have banging about in their heads when designing a piece, which I have no doubt you know quite well.I babbled on long enough. Again, I sincerely appreciate all the time you spent with your detailed posts. When done, I will post the finished piece.Warm Regards,
Phillip
See if this helps.
http://www.taunton.com/finewoodworking/SkillsAndTechniques/SkillsAndTechniquesPDF.aspx?id=2636
Edited 10/1/2008 2:19 pm ET by nboucher
Thanks for the link. I have that issue and did take a look at that article.I appreciate your post and time.
I can never make them come out right by math. Draw the cabinet face full size, draw a curved line, bottom right to top, mark 6 even spaces on the line and draw parallel horizontal lines across the face on these marks. Try several different slants and curves untill you like the proportions. Malcolm Granberry
Malcom,You've hit the nail on the head. The 'Malcom Methodology' is great Idea!! I've been working on this mathematically and hope to have a solution soon. Since most of us wear many hats during the day, this will take a day or two as we all know.What I have attempted to do is to put your words into a graph or picture. Please see attached image.The way that I think I would go about this is to use one of those flexible curves that are commonly used to draw arc's in woodworking. Lee Valley has these in 24" and 36" lengths. These are not marked in length, but after the curve is drawn, the utilized curve length used could be measured to determine its length. This length could then be divided by the number of drawers required. Once this increment is determined, it could me marked on the flexible curve then this segment could be matched against the actual curve and marked. Horizontal lines from these marks to the vertical edge of the cavity would then represent the drawer heights. And, as you said, the flexible curve could be steepened or flattened to obtain the required affect in drawer heights. A person could adjust and tweak to their hearts content.I hope I have correctly interpreted your methodology. I appreciate your help.Phillip
Take a look at Hambridge progressions or do some digging into Fibornacci. No need to reinvent the wheel!
T.Z.
Good idea save for the fact that most folks would probably think that the Fibonacci Sequence was some sort of spicy Italian dish. Keeping it simple, in this case, may be the prudent way to go.
I can never make them come out right by math. Draw the cabinet face full size, draw a curved line, bottom right to top, mark 8 even spaces on the line and draw parallel horizontal lines across the face on these marks. Try several different slants and curves untill you like the proportions. Malcolm Granberry
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