How to calculate chain locker volume

[P69]

I'm redesiging the anchor chain storage in the bow to keep it lower and a bit farther aft.

I've removed the forward water tank and will place a parition about 18" aft of the current chainlocker/vberth bulkhead.

I'm trying to calculate the volume of that triangular area to see if the 18" is too far aft or not far enough aft for the 200' of 5/16" chain and a hundred or so feet of line.

The problem I am running into is that I can't find a formula to account for the narrowing of the area towards the bow and narrowing down. I found formulae for trapezoids, spheres, triangles, cones, but none account for narrowing in x and z axes.

I don't need the exact volume of this compartment because I know the chain and line will not fill it evenly, but I'd like to get it pretty close so I don't make a huge mistake either way (too large or too small).

I found a formula to calculate the volume that a given length of chain will take, well, actually two formulae, so I know what volume I need to create

((Fathoms * D^2)/2 )*1.7 
        OR
  V = 0.85*L*D^2

  Where  D = Diameter of chain in inches (i.e. 5/16")
              L = Total length of chain in fathoms
Both give same answer

Interestingly, I have a barrel of 550' of 5/16" chain and the calculated volume of that barrel is only 4.417 cuft and it contains 550'. Formula calibrated to barrel volume:  V = 0.4935*L*D^2

The above formulae result in 7.61 cuft for same length of chain. Possible that the formula accounts for non-compact storage or uneven distribution in the locker?

Depending on the formula I use (the one with 1.7 factor or the one calibrated to the barrel of chain) I will need betwen 1.48 cuft or 2.74 cuft for 200' chain. Then I need to add some volume for 5/8" three strand at the bottom of that pile (rode will be 200' chain, then 100' 5/8" 3 strand)

Does anyone know the way to calculate or closely estimate the volume of a given triangular locker that tapers in two of the three axes?

I've attached a diagram (chainlockerdimensions.pdf, not to scale) with measurements. This pdf includes an overlay of the diagram on a photo of the locker in an effort to add clarity.

Also attached is  a broader picture of the vberth area showing the proposed location of the partition (LookingForward.jpg)

[SVJourney]

I'm sure that Pete will be on here with an app soon.

In the mean time, you can integrate by steps for a fairly accurate volume.  Treat it as a triangle and measure height (h) and width (w) where you think your wall will be, then move forward, say 2 inches and do it again.  and again and again until you are all the way forward.  Then integrate:
1/2h times w times 2 + (your next measurement) + (your next measurement) + (your next measurement) and so on.

This will give you volume in cubic inches.

[SVJourney]

My concern is that you chain will not stack well , or perhaps at all in that location by just sliding down the hull.  I've seen people cure this by using ABS pipe from the exit of their windlass to desired pile point to have the chain drop into the well at the top of the space. 

[P69]

Thank you for the advice on estimating the volume of that compartment; it worked.

This method shows me that I have about 3.2 cuft with new partition at 18" aft.  Now I have some data to work with and can modify my spreadsheet to adjust the position of the new partition to ensure enough room for the chain.

Regarding the concern of getting the chain into that compartment, I'm still working on that. Haven't ironed that one out yet. I need to work out the issue of having enough slope in any angled parts of the chain path (if any) so the chain doesn't stop and make sure I have at least the 18" of fall form the windlass so it has no issues self-tailing (Maxwell VWC 1500). My objective is to get the chain as far aft as I can and still have it completely self-stowing. I realize that much of the space will be unusable by the chain because of the way chain self-stores and the shape of the compartment, but this gives me an idea of where to go.

I'll eventually muscle the 250' (or whatever length I decide to use) of chain to the boat and do a test, but I'm not ready to cut my 550' length from the barrel for a test because I 'm not certain  I want to use 250' (maybe 200 or maybe 300').  This gives me a starting point.

Thanks again

[SVJourney]

Completely understood. 
Just for giggles (NOT an anchoring expert!) let me tell you what we did, and learned after 18k NM and crossing the Pacific. (deep anchorages and LOTS of coral bommies).

Almost nobody had more than 300' of chain.  And it worked for everyone we talked to.  Nobody found established anchorages that they needed more.  I doubt many people's windlasses would lift more if anchored that deep.
300 ft of 5/16HT is 360 lbs.  Our Pearsons were not designed for that much weight forward but removing the water tank compensates for that much chain forward.

On Journey, we had 200ft 5/16HT chain and 200 feet of 5/8 3-strand.  The 3 strand was coiled up and stowed high on the anchor locker held up by velcro.  If needed for extra scope (storm conditions) we could deploy it.  Not once in 5 years did we need to even in anchorages up to 70 feet deep. Our Rocna was fine at 3:1 scope.  One advantage is that the line did not fill the chain space.  The other advantage is that line , while still spliced to the chain, was still brand new at the end of the trip as it wasn't sitting under 200' of wet chain, moldering and weakened. 

There were times I wished for more chain (70 ft deep anchorage) so 300 ft seems okay.  Would still have 100 ft of line attached at the end for shock absorption during storm conditions though.

Just my 2 cents....

Wayne

[P69]

Wayne, thank you for the insight that you found to be typical use in that area.

The direction of my redesign is to provide for adequate chain and line stowage (it's an organization I have  ) . Chain down low, line up high, 200' chain (+/- 50'), then 100 (+/- 50') attached to the bitter end of the chain.  I'll have plenty of room in the upper areas of the original chain locker and the upper, outboard reaches of  the new anchor locker for several 50' and 100' chunks of line. Most of this planning is for storage of ground tackle needed to tying up for hurricanes, rather than for routine use.

We usually get 1 or 2 near misses every year here in the Southeast US.  Because the dock is exposed to the SW - NW (fetch varies from 4 miles to 1/2 mile in those directions), I move the boat when predicted winds exceed 45kts.  I usually set out 4 to 5 anchors ( 35 - 55 lbs, 8:1 scope) 4 to 5 shore lines up in the bend of a local bayou, which only 10' deep. Typically, I swap out the long chains for 25' and 50' lengths and add line for the rest of the scope, that way everything is nice an stretchy; bottom is mud, so no issues there.  All my cleats are on top of the toe rail,  no issue with chafe; no line touches the gunwale or chocks, which I removed when I put the 12" cleats up on the toe rail.  Chafe on the trees is eliminate by wrapping chain 2 turns around each tree, then shackling both chain ends to the 3-strand leading back to the boat.


Somewhat off-topic, but what do you tie your bitter end to in the bow locker?