Wonder why your dovetails joints don't fit?
Denis Ch�nard, Orl�ans, Ont.
>You've labored to get a through dovetail joint together, measuring, marking, sawing, chopping and trimming. You then put the joint together only to find that there are a few gaps here and there. AARRRGGGGHHH! You kick yourself in the rear end at your ineptitude and ask aloud "why can't I make a tight dovetail joint?!!?!?!?!??!"
The answer is easy. It's because the odds are stacked way against you...
WARNING: some math ahead
Let's take a joint with n tails. Each of the pins and the tails need two cuts to define the shape, which gives us 4n as the number of cuts. Then there's the issue of cutting/chopping the baseline in each socket. There are 2n+1 of these (draw one joint to help visualize the whole thing).
Now, each and everyone of these operations can go wrong. Therefore the expectation of the number of bad cuts is equal to:
(6n + 1) * "error rate"
So for a joint with three tails, that gives 19 operations, and if you miss once every 10 cutting or paring operations, you can expect on average to have two nearly bad cuts per joint, and a probablilty of 13.5% of nailing the joint perfectly.
With six tails, the expectation of failed cuts jumps to 3.7 per joint, and the probability of nailing the joint goes down to 2.0%.
I've been working recently on a carcasse that had nine tails at each corner, in this case expectation comes to 5.5 failed cuts and the probablilty of a perfect joint falls to 0.3%.
So if you cut your dovetails without measuring, minimal marking, no trimming and no test-fitting, like Frank Klausz does, give yourself a rousing round of applause if you can put a gap-free joint together!
Take heart, this was the worst case scenario...
In practice, the second part of joint is fitted to the first, and you can mark your joints, test whether the cuts are straight and fix (pare) them if they're not, to make the first part of the joint perfect (which we'll assume here). The number of cuts then falls to (n still being the number of tails in one joint) (4n + 1) (2n + 2n + 1, as I'm still allowing mistakes at the baseline) instead of 6n + 1.
Under this scenario a three tail joint would have 1.3 bad cuts on average and a 25.4% probability of a perfect joint, a six tail joint would rate at 2.5 bad cuts and 7.2% chance of success, and a nine tail joint would be 3.7 misses and 2.0% of nailing it.
With practice you get better at cutting and paring the joints. Let's say that you've progressed to the point where you screw up one cutting or paring operation out of every hundred attempts. Then for three tail you would get a 87.8% probability of a perfect joint, 77.8% for the six tail joint and 68.9% for the nine tails.
Then there's a few "cheats" one can use. Glue will swell up the pins and tails a bit and help hide small gaps. If one leaves the second part of the joint a bit fat, the mating parts will compress together and help hide more gaps (but there's a risk of splitting one of the boards). I don't have a figure for this, but this will help boost the success rate.
BTW, the results are the same whether one does through or half-blind dovetails.
Morale of this story:
- No wonder there are gazillions of dovetail jigs on the market
- Don't be too hard on yourself if a dovetail joint isn't immaculate...
- Practice makes perfect
I believe the math to be accurate, if I screwed up somewhere please let me know...
DC
