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# Inverse xs area proportional drill bit set population

Pre-emptively rectify bit size distribution imbalance
 (+18) [vote for, against]

Drill bits break.

How easily they break is proportional to how strong they are.

How strong they are is proportional to the cross sectional area.

Finally, how often they break is proportional to how easily they break *and* how often you use them.

As a result, when you buy a set of general purpose wood and masonry bits, you break all of the thin useful bits and are left with a load of fat useless bits. You then buy another set and start the whole process again, accumulating yet another family of fat useless bits.

If they sold sets of bits where the number of each size of bit in the set was inversely proportional to the square of the diameter and proportional to their usefulness, then you would get through them all at a roughly similar rate.

I imagine a quick survey of "usefulness" would find 2mm wood bits for pilot holes, 6mm wood bits for screw holes and 6mm/8mm masonry bits for red and brown plugs would be the most used and therefore require perhaps three times as many.

Here is a quick calculation of how many should be in a set based on this formula:

WOOD
Size....Qty
13mm.....1
12mm.....1
11mm.....1
10mm.....2
9mm......2
8mm......3
7mm......3
6mm.....14
5mm......7
4mm.....11
3mm.....19
2mm....127
1mm....169

METAL
Size....Qty
13mm.....1
12mm.....1
11mm.....1
10mm.....2
9mm......2
8mm......8
7mm......3
6mm.....14
5mm......7
4mm.....11
3mm.....19
2mm.....42
1mm....169

This must be a sensible distribution, because the maths says so.

 — wagster, Oct 07 2008

(?) Brazil nut effect http://findarticles..._20_160/ai_80747803
[hippo, Oct 13 2008]

Yes, or the stores could stock replacement packs in a range of sizes to suit the curve. For example, the next pack down doesn't have a 13mm bit - but it does have a few extra 1mm and 2mm bits. The next has no 12mm, but extra 1/2/3/4mm ... etc. Each pack would have the same weight of metal in it.
 — BunsenHoneydew, Oct 07 2008

Good idea - I have a set with two 1mm bits but one of everything else, so manufacturers have at least started to think along these lines, but it's not that great.
 — hippo, Oct 07 2008

 Size....chance of.....per .........breaking.....blue ......................moon 13mm.....169/169......1 12mm.....169/140......1.2 11mm.....169/121......1.4 10mm.....169/100......1.7 9mm......169/81.......2.1 8mm......169/64.......2.6 7mm......169/49.......3.4 6mm......169/36.......4.7 5mm......169/25.......6.8 4mm......169/16......10.6 3mm......169/9.......18.8 2mm......169/4.......42.3 1mm......169/1......169.0

Quite so sir
 — BunsenHoneydew, Oct 07 2008

 // accumulating yet another family of fat useless bits. //

 Very like General Elections, then ?

Good idea by the way - for hobbyists. But machine shops tend to buy drill bits by the box of 100, all the same size ....
 — 8th of 7, Oct 07 2008

 Someone, somewhere, has done this calculation on the bit/attachment set I bought with my cordless Dremel. Will count it out later.

Also...mighty close to a "fibonacci tree" on those estimates. Well done!
 — 4whom, Oct 07 2008

Good One, I feel your pain, Bro'.
While we are at it can we have a couble of spare 13mm sockets in a socket set please?
And an extra 8mm or two. Thanks Muchly!
 — gnomethang, Oct 07 2008

Absolutely!. But when I need a drill it is for piddly, fiddly little things stuck on air ducts etc. These are the ones more likely to break.
 — gnomethang, Oct 07 2008

I have a piece of Black and Decker sh*t that comes with two soft driver bits that won't go in the standard bit holder, and a fool attached to the other end.
 — wagster, Oct 07 2008

I like the idea, although there are sources out there that sell individual bits, even to residential/hobby users.
 — MechE, Oct 08 2008

Some guys I work with were complaining about just this today. The set should have extras of the more commonly used sizes as well (1/4" etc.).
 — sninctown, Oct 08 2008

I love the Quickbits idea - have to find some of them.
 — wagster, Oct 08 2008

I think I should invent the erectile drill bit, then. One size fits all, in a while.
 — Ian Tindale, Oct 08 2008

[UB], it's possible to get professional quality hex-shank bits, and they're VERY good - but not exactly inexpensive.
 — 8th of 7, Oct 08 2008

driller thriller +
 — xenzag, Oct 08 2008

I have a cheap set (30 quid from Maplins of all places) that has, if I remember vaguely, a couple of 13mm bits, increasing to about twenty 1mm bits. Not really used it much yet.
 — david_scothern, Oct 08 2008

[+], although I find I blunt 10mm drills as often as I snap 3mm ones.
 — Srimech, Oct 08 2008

If the bits were stored all together in a hopper, proportionally mixed, and sold by weight, it would work out the same in the long run
 — BunsenHoneydew, Oct 13 2008

I thought the cereal box effect was where some other bastard fishes the freebie out first.
 — Ian Tindale, Oct 13 2008

No, that's the "democracy" effect.
 — 8th of 7, Oct 13 2008

[UB] That's more commonly called the "Brazil nut effect" (link)
 — hippo, Oct 13 2008

Contents may settle in another country.
 — Ian Tindale, Oct 13 2008

 Coincidentally, I am tight (edit:right) now eating a bag of chocolate coated peanuts, raisins and brazil nuts. All the excellent brazil nuts are getting eaten first, having risen to the top, leaving only the second-class peanuts and raisins.

Damn the brazil nut effect!
 — wagster, Oct 13 2008

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