Floatation calculations, or what will it take to float your boat ?

[mikezohsix]

I needed to figure out how much floatation to put into my Grumman I/O that I?ve been redoing. I read the USCG rules, but found that the answer wasn?t there, at least in a way that helped me when I was standing in the insulation aisle at HD.

So I did some math, that I thought I?d share with others, that is pretty practical.
May seem like one of those math quizzes, but it does work?

Fresh water weighs 62.4 pounds per cubic ft, so one cubic foot of foam will float 62.4 pounds. (I?m not going to consider the weight of the foam in these calculations because it would have a minimal impact.)

So, if I want to know how much foam I need to float my 3.0 OMC I/O setup, the first thing I need to know is how much the drive train weighs. I asked here, and a got a couple of different answers, but the average estimate seems to be about 650 pounds.

How many cu ft of foam would I need? 650/62.4 = 10.4 cubic feet.

What do you do with the 10.4 cubic feet?

A 2? thick x 24? wide x 8? (96?) long foam board is 4608 cu in.
Divide cu in by 1728 to get cubic feet.
4608/1728 = 2.7 cubic feet per board.
To get to the needed 10.4 cubic feet, you need 10.4/2.7, or 3.9, which rounds up to four 2? boards

So, 4 two inch boards will float by drive train.

I guessed that the rest of the aluminum boat weighs in at 400 pounds.
To float 400 pounds I need 400/62.4 = 6.4 cubic feet of foam
6.4/2.7 = 2.3, so I need another two and a third 2? boards, for a total of 6.3, to float the whole boat.

Now 2? foam won?t fit everywhere, so here?s the numbers for the other foam boards at HD.

2? thick is 2.7 cu ft per board
1.5 inch thick is 2.0 cu ft per board
1 inch thick is 1.3 cu ft per board
? inch thick is 1.0 cu ft per board.

That all sounds good on paper, so what did I fit in my boat?

I put absolutely every bit of foam I could in the back of the boat to try to level float it if things ever went that bad. I had a bellows rip on another boat one time and man the water comes in fast. I can?t think of another thing that would put that much water in the boat except tearing the bottom out of it.

In total I got four 2? boards, one 1.5 inch board, and four ? inch boards, for a total of (4*2.7)+(1*2.0)+(4*1.0) = 16.8 cu ft, which will float (16.8x62.4) = 1048 pounds

With 650 pounds for the drive train, plus 400 pounds for the boat, brings my guess for the total weight to 1050 pounds. Pure luck, but it looks like I?m right on the line.

The USCG goes into a discussion about things that float in the boat, that if tied to the boat will keep it from going to the bottom, like seats, trapped air in fuel tanks, trapped life preservers, and some help from things that also help like the wood (decks etc) in the boat.

An empty 10 gallon tank is 1.3 cu fit, which will float 1.3*62.4 = 83 pounds
Guessing a seat would displace about 10 gallons, having 4 bigish seats probably more, that?s 330 pounds, which puts me comfortably over sinking (assuming my weight estimates are decent).

Now for the money part of it?.

The pink foam at HD cost about $5.18 per cubic foot ($14 for a 2? sheet)
The blue buoyancy billets cost about $11.5 per cubic foot at the local lumber yard ($89 for a 7? x 20? x 8? piece).
Poured in place foam is $13.25 per cubic foot, based on a 8 cu ft kit for $105

I replaced the transom in my boat because of the original poured foam trapping water against it. The poured foam also trapped water in small pockets against the deck, and prevented the water from moving freely in the bilge to the pump. The slow moving water didn't clean the stuff out from between the ribs etc, making it trap even more water, adding to making the decks soft. All strikes against pouring again (at least in my opinion). The money part is obvious.

The moral of the story, based on my boat, get every bit of foam board you can in the boat and you?ll float the boat in a worst case situation, for way less than half the price of poured foam, with none of the poured foam issues.

 

[ezmobee]

Re: Floatation calculations, or what will it take to float your boat ?

Cool thread. Got any pics of the foam installed?

 

[Bob_VT]

Re: Floatation calculations, or what will it take to float your boat ?

Your boat....... the flotation was already figured in when it passed the USCG test. It becomes almost a no brainer by duplicating the cubic inches or feet of flotation that once was ...... you should be okay.

I love your line of thinking and the cost per cu ft will help out MANY people in the future. I am sure we will refer to this thread quite a bit.

Now here is where you can get creative. You learned where the water "sits" and causes problems...... when you install foam be sure to leave adequate drain passages. Another place to add more flotation in under the gunwales and you can also improve things by running your cables and electric through conduit.

Thanks for all the math references You have a PM

 

[erikgreen]

Re: Floatation calculations, or what will it take to float your boat ?

Something you may not have considered is that for all that foam to do its job it has to be submerged in water... IE your boat will have to flood. If your boat floods, then at least part of it is under water. So you can actually subtract from the amount of foam you need the weight of the part of your boat that's actually submerged. If you want, assume the entire hull is just barely submerged.

It's counter intuitive. Think of it like this - a 1x1x1 meter cube of steel weighs about 7850kg in air.

1 cubic meter of pure water weighs 1000kg (by design). If you put the steel cube in water it displaces 1000kg of water. Since 1000kg < 7850kg (negative buoyancy), it sinks.

So if you attach to the steel cube a float that provides 6855kg of floatation (less than the weight of the cube) and drop it in pure water, it floats just below the surface of the water, which is almost good enough for someone to get on it and keep warm (the extra weight of someone getting on would make it sink up to their neutrally buoyant depth, or usually their neck).

Your boat metal won't provide a lot of buoyancy compared to the foam, but it will provide some. A nearly empty gas tank would provide some, so would gas (some, not a lot).

Another note about your numbers.. $13.25 per cubic foot is high. If you get 2 lb foam from US Composites (my favorite place), it's about $7.25 per cubic foot in 8 foot kits. Less per cf if you buy more. You can even pour it into a shape like a plank, then fit it into the boat by trimming.

Keep in mind that whatever foam you use, it's flammable, so cover it where it's exposed to heat or near wiring.

There's a reason why only small boats have foam as you're finding out. It's hard enough when you have a boat like yours... 1000lbs or so. For a 30 foot FRP boat that has a weight of eg 9000 lbs, you need to find somewhere to put 144 cubic feet of foam. A 30 footer feels big, but not that big, especially when you have to fit in fuel tanks, engines, water tanks, etc under decks. For reference, that's a block of foam 5ft x 5 ft x almost 6 feet tall.

The best way I've seen so far in a boat to do floatation is collared boats like SAFE boats or RBBs. You put the floatation on low gunwales just above the waterline so it actually makes the hull wider and more stable at rest, the gunwales, hull and supporting structures are smaller and lighter than they would be without the collar which saves fuel, the foam can't flood so the boat is nearly unsinkable, on plane the foam is out of the water so it doesn't cause drag... perfect place for it to be. The design isn't useful for every purpose, unfortunately.


Erik

 

[jspano]

Re: Floatation calculations, or what will it take to float your boat ?

i'm having a hard time finding extruded foam(closed cell) here in fl.
i might have to use reg foam expanded. any thoughts to using a 2 part system and trying to use forms so the foam can be made and then installed so the ribs will not be blocked or all the other bad results from poured in foam????

joe

 

[kciv]

Re: Floatation calculations, or what will it take to float your boat ?

What the boat weights divided by 62.4 equals cubic feet of foam has a large safety factor. What you are really looking for is buoyancy (what the boat weights in water). The problem is coming up with the average density of the boat.

If everything was made of aluminum (169/ft^3).

1000 lb boat x (169 - 62) lb/ft^3
----------------------------------- = 10.2 ft^3 of foam
169 lb/ft^3 x 62 lb/ft^3

Any students of Archimedes out there with a practical way of determining boat density?

 

[mikezohsix]

Re: Floatation calculations, or what will it take to float your boat ?

Cool thread. Got any pics of the foam installed?

sure...

I started with putting pieces down between the ribs, with plenty of room for water to get to the bottom of the bilge...

I then laid in lengthwise pieces from 2" down to 3/4 to fill the area. I used a straight edge across the stringers to keep them from being in the way of the deck.

I also filled the two bow areas

I filled the area on either side of the engine, this is where the bulk of the four sheets of 2" went

with foam

before foam - so you get an idea of the area

 

[mikezohsix]

Re: Floatation calculations, or what will it take to float your boat ?

If you want to see the original foam, check out the pics in my "restoration", nice way of saying repair, thread...

http://forums.iboats.com/showthread.php?t=362705&highlight=grumman

 

[BobsGlasstream]

Re: Floatation calculations, or what will it take to float your boat ?

mikezohsix,
Very well done. I like the way you showed your train of thought and the math to support it. Several folks have also brought up some good points too.
You can build cheap molds and pour the foam in any shape you want.
Just remember you are looking for a free rise density when pouring foam. The moment you try to contain it you are creating pack density which will be higher then free rise.
In simple words don't put a lid on it, or make sure excess has a easy means to escape.
Once again, very well stated.
Have a great Day.

Bob

 

[erikgreen]

Re: Floatation calculations, or what will it take to float your boat ?

The other thing about the two part pourable foam is that it has to be poured in a warm (80s F) room to get full expansion. In 60s you'll be losing maybe a third of the volume you could get.

The most accurate way to determine the buoyancy of a boat when filled with water is to fill it with water and stick it on a scale. If you do this, take lots of pictures and post here

Other than that my only suggestion is to weigh the boat, then assume that the weight is 100 percent aluminum or fiberglass (minus big parts like the engine) then use the weight of that much fiberglass or aluminum in water to figure out its buoyancy.

My own fiberglass boat is about 3500 lbs, minus the engine and drive about 2500, but we'll assume for this discussion that the 3500 is all glass. According to the Glen-l site a cubic meter of solid fiberglass weighs 4061 lbs (interesting... less glass in my boat than a cubic meter). 4061 lbs is about 1842 kg.. so fiberglass is about 1.8x the density of pure water(from my above post, 1 cubic meter of water is 1000kg or 1 metric tonne). We can subtract the weight of an equal volume of water to find buoyancy. 1842kg - 1000kg gives us 842kg negative buoyancy for the fiberglass cube in pure water.

So far so good. Using the numbers above we can figure out that for each 1842kg cubic meter of glass, we only have to add buoyancy for 842kg, since the rest of the weight is already supported.

We can represent this fraction as 842/1842, or about .457 decimal. Since it's a ratio the units don't matter... we can multiply the weight of my boat, 3500 lbs (again, we're assuming that's all glass when it's not) times .457 to find out how much weight we need to add buoyancy for... about 1600lbs, or 25 cubic feet of foam to have neutral buoyancy. On top of that I'd add in about 500lbs of buoyancy in order to make sure it floats at the top of the water column (the surface) and has enough buoyancy to let me climb on it and stay partly out of the water.

FYI, a cubic meter of aluminum weighs about 2020.75kg. If you subtract the weight of your drive system and gas, cargo, etc you should have a number not too far off from the weight of the hull. So the ratio we figured out above (which, by the way, is the inverse of the specific gravity for a material) is about .506. For a 400 lb aluminum boat, that means you need 202 lbs of buoyancy for neutral buoyancy of just the hull. For a boat that small probably it would be a good idea to add a couple hundred pounds above the neutral minimum to ensure you can climb on, but more is better, so the rough calculation Mike is using is probably good.

Isn't math fun?

FYI, I'd never put foam back in my boat except in very limited circumstances. It's really a safety measure for lake boaters or calm water boaters, a way to give them something to hang onto until help comes. That doesn't outweigh the problems it causes for me in a partly wooden boat, not to mention the space it takes up.

Where I boat I'm planning on bringing a life raft if I can, plus survival suits... the water temp most of the year is about the same as the Bering sea, so unless you have the suits being able to cling to your partly floating boat won't help... you'll have a heart attack in 10 minutes or so unless you can get most of your body and those of your passengers out of the water. All foam would do (unless I had a huge amount) is keep the boat near the surface....


Erik

 

[noworries79]

Re: Floatation calculations, or what will it take to float your boat ?

Great thread! Thanks for the info!

 

[BWR1953]

Re: Floatation calculations, or what will it take to float your boat ?

Thread bookmarked!

 

[Bob_VT]

Re: Floatation calculations, or what will it take to float your boat ?

Thread bookmarked!

I included this in the How to section http://forums.iboats.com/showthread.php?t=288451

Remember Mythbuster's raised a boat from the bottom using ping pong balls

 

[mikezohsix]

Re: Floatation calculations, or what will it take to float your boat ?

Commander Green -

I did consider the difference in the specific gravity of the boat materials and water, and if that would make a big difference in how much floatation would be required. Since in my boat, way more than 50% of the weight of the boat is in cast iron, and ci is around 450 #/ft3, vs water at 62 3/ft3, over 7 times more dense, I just left it out of the discussion and considered it to be part of the factor of safety.

That discussion is part of the USCG calculations, which are too complicated for anyone less than the OEM, or someone who really likes to figure that stuff out. Since most of us don't know the actual weight of the different materials that make up the boat, the USCG calculations become nothing more than best guesses.

If you get to the best guess point, is it worth considering the fact that (in my case) the engine displaces 1.5 ft3 of water, or about 90 pounds?

It's a fun exercise and discussion. What shocked me was that I ended up with enough floatation to be pretty close to floating my boat by accident. The little bits here and there, like fuel tanks, displaced water, and on some level, seats, makes me pretty confident that if I left my boat for two weeks in the water (which I do), and something bad happened, it would still be there, not on the bottom.

mk

 

[mikezohsix]

Re: Floatation calculations, or what will it take to float your boat ?

Any students of Archimedes out there with a practical way of determining boat density?

The hard part of that one is practical.
Weigh the boat, sink it in a big graduated cylinder, and see how much water it displaces. You'd get pounds per cubic foot for the whole thing.

Now, if i only could find a big enough cylinder....

 

[BWR1953]

Re: Floatation calculations, or what will it take to float your boat ?

I included this in the How to section http://forums.iboats.com/showthread.php?t=288451

Remember Mythbuster's raised a boat from the bottom using ping pong balls

Yeah, that mythbusters episode was way cool.

 

[coolguy147]

Re: Floatation calculations, or what will it take to float your boat ?

about the air trapped in the gas tank wouldnt most it go out the vent?

try the match what you had before then put anything extra you want for peace of mind. probably much simpler then your idea but heck good post

 

[coolguy147]

Re: Floatation calculations, or what will it take to float your boat ?

Yeah, that mythbusters episode was way cool.

thread highjacker watch out ^:

 

[erikgreen]

Re: Floatation calculations, or what will it take to float your boat ?

Commander Green -


That discussion is part of the USCG calculations, which are too complicated for anyone less than the OEM, or someone who really likes to figure that stuff out. Since most of us don't know the actual weight of the different materials that make up the boat, the USCG calculations become nothing more than best guesses.

At some point, everything we "know" about boat construction is a best guess unless we're doing the in-depth analysis to figure the numbers out.

But there's value in buoyancy calculations regardless of whether we're exact or not... for a smaller boat like yours the rough calculations are fine. For a boat a bit larger or made of different materials the difference can be worth determining... learning you can use 10 cubic feet of foam instead of 15 can leave you a lot of space free.

If you get to the best guess point, is it worth considering the fact that (in my case) the engine displaces 1.5 ft3 of water, or about 90 pounds?

You, as the owner of the boat, are the only person who can answer that. When the difference between the amount of foam needed to float the weight of the whole boat and the amount needed for positive buoyancy when the hull is filled with water is less than the average weight of one person, then it doesn't matter too much.

But when you're talking about a difference several times that amount, it's worth figuring things out as closely as you can. Otherwise you handicap your use of the boat by taking up too much space for foam, or you give yourself a false sense of security by not having enough.

It's a fun exercise and discussion. What shocked me was that I ended up with enough floatation to be pretty close to floating my boat by accident. The little bits here and there, like fuel tanks, displaced water, and on some level, seats, makes me pretty confident that if I left my boat for two weeks in the water (which I do), and something bad happened, it would still be there, not on the bottom.

For your boat, having it filled with water and off the bottom would be good enough... aluminum hulls don't tend to rot. For those of us with larger fiberglass boats, it wouldn't be much consolation

Erik

 

[timfives]

Re: Floatation calculations, or what will it take to float your boat ?

I needed to figure out how much floatation to put into my Grumman I/O that I?ve been redoing. I read the USCG rules, but found that the answer wasn?t there, at least in a way that helped me when I was standing in the insulation aisle at HD.

So I did some math, that I thought I?d share with others, that is pretty practical.
May seem like one of those math quizzes, but it does work?

Fresh water weighs 62.4 pounds per cubic ft, so one cubic foot of foam will float 62.4 pounds. (I?m not going to consider the weight of the foam in these calculations because it would have a minimal impact.)

Good calculations, just a question on where you found the flotation factor for the foam of 62.4 lbs/ft?

Nice work

T