Hi Allen,

Thanks for running those numbers, and the info on pin-hole alignment. Since my halyards are 7/16", then a hardwood pin that "looks" right ought to be sufficiently strong. Splicing too small a pin on a thick line just looks silly, and puts a tighter radius on the splice. And even my biggest toggle pins (or my wooden belaying pins, for that matter) are still much lighter than a SS shackle. I might try a bronze toggle pin where I have high-load HM lines (running backstay), but for lesser things I think the wood will be all right.

I agree, wood looks like a good choice. I think the numbers I ran are for white oak. Teak would be about the same and may have some advantages.

The thing I have not done is run some numbers on how large a diameter toggle we should use. That would be an interesting exercise but would depend on the size of the hole in the headboard so may be a little hard to generalize.

I am going to show my work as I am unsure of it. Perhaps someone can verify what I have done or correct it.

The question is, how large a toggle do you need to hold the halyard per the technique shown HERE and discussed above. I am going to solve this for 5/32 Amsteel which is 4000 pounds breaking strength and assume that I want to be able to hold that load at breaking strength. Finding halyard load is not easy. The chart in the back of Brion's book (page 372) for a 35 foot boat says 800 pounds. That would be a 5:1 safety factor, which sounds fine so I went with that.

The way the line is led is not exactly a knot but it does offer some stress relief to the toggle. I tested that around a very smooth post which for sure would be worst case compared to the friction of a head board. It took only 4 pounds to hold a 22 pound test weight. Thus the 4000 pound load could be held with 727 pounds on the toggle.

I assume a .75 inch opening in the headboard and 727 pounds gives a bending moment of 51 inch pounds per this formula ( w * l^2 ) / 8 .

Using a pin of radius r the load on the outer most point r from the center of the pin is 51 * r / J where J is the moment of inertia of a circle which is ( pi * r^4 ) / 2

Combining these the maximum stress as 32 / r^3. Aluminum is 35,000 psi which says r minimum is .097. That is a diameter of .194.

Oak is 7440psi so r is .16 and diameter is .325 or just over 5/16. Being wood, perhaps an additional safety factor would be appropriate and a 3/8 to 1/2 inch toggle would give that. Wood has the additional issue that the surface might crush and I did not analyze that.

I would love for someone to verify these numbers and I would encourage nobody to use them or rely on them until that happens.

Allen rocks!
 

I've always loved smart people. I asked a physicist once to work out a the measurements of a gaff sail of 300 sq ft following the ratios in the Gaff Rig Handbook. I expected him to take a week or so......he did it right there on a torn-off sheet of notebook paper using equations he had memorized. I kept the paper for a souvenir, I was so impressed. Sounds like Allen could of done it in his head.
Anyhow, my 7/16" regatta braid halyards are nowhere near strong enough, it seems, to break a 1/2" wooden toggle, and the toggles I'm turning are a little fatter than that. Also they're Rosewood and Cocobolo, so they're lots denser and harder than oak or teak. I'll probably go with some 5/8" bronze rod pieces I have left from another project for really heavy-duty loads, but it seems that for my halyards wood'll be fine. Easier to undo a toggle on an icy dark line with gloves on than most shackles.
Love to hear more about the math of it and testing.
Ben

Just be sure to remember that a lot of the strength comes from the way the line is arranged, the semi-knot. Not sure of your setup but I know that I could not get 7/16 line to pull the loop through the hole in a headboard. It is even difficult with my 5/32 Amsteel because I did both a brummel and a lock stitch and the lock stitch is too far away from the toggle and tends to interfere with the loop. I will probably cut it all off and move the lock stitch to the inch or so closest to the eye.