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Thread: Mathmatics and Cataraft Capacities ?!

  1. #1
    Member BluNosDav's Avatar
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    Default Mathmatics and Cataraft Capacities ?!

    I was working with one of my kids on math problems the other night. We were calculating the volumes of various geometric shapes: cubes, spheres, cylinders, etc. Then I got the idea to use the same math formulas to approximate the load carrying capacities of catarafts. I've always been perplexed by how different raft manufacturers can advertise vastly different "load capacity" numbers for tubes that are almost exactly the same shape, diameter, and length??? With watercraft of all types, load capacity is actually the "displacement" (volume) of the water supporting the "weight" of the vessel, and cataraft tubes are just about the simplest hull shape in the boating world.

    Cataraft tubes are basically cylinders, with cones at each end. So I used the following formulas:
    Volume of a cylinder = Pi (3.14) multiplied by the tube's radius squared (r2), multiplied by the length of the tube (h), or = 3.14 r2 h.
    Volume of a cone = one-third of same formula for a cylinder, or = 1/3 (3.14) r2 h.

    In order to keep all of the numbers managable, I converted all of the dimensions into feet (cubic feet),
    and then multiplied the volumes by 62.4 lbs, which is the weight of one cubic foot (ft3) of fresh water.

    I wanted to get an "apples-to-apples" comparison, so I used measurements provided by the same manufacturer, and since I'm thinking about buying a big Aire cataraft, I did calculations for all of their 18-foot models. I also had to use some standard for where the full sized tubes (cylinders) ended, and where the tapered ends (cones) began. I decided to use Aire's advertized "waterline lengths". I don't think Aire would favor any one of their own models over another, and so the comparisons should be useful. And I know that the tapered ends of catarafts kick up, instead of pointing straight back like on some sportboats. But, for comparisons of similar tubes, from the same manufacturer, the formulas should be pretty accurate.

    All are the same 18 feet in length, and the dimensions used for each are:

    Leopard: 10ft waterline / 1.1ft radius (26.5" tubes) / 4ft cones
    Lion: 13ft waterline / 1.15ft radius (27.5" tubes) / 2.5ft cones
    Cougar: 10.33ft waterline / 0.75ft radius (18" dual tubes) / 3.84ft cones
    Super-Leopard / 10ft waterline / 1.1ft & 0.67ft radii (26.5" & 15" dual tubes / 4ft cones

    Calulations accounted for both tubes of the Leopard & Lion and all four tubes of the Cougar and Super-Leopard.
    Total volume displacement means how much "weight" it would take to fully submerge the whole cataraft under water:

    Leopard = 6052 lbs / Lion = 7548 lbs / Cougar = 5682 lbs / Super-Leopard = 7992 lbs

    Surprised? So, was I! Turns out that having twice as many small tubes (i.e. Cougar), does not give you more load capacity.
    (Volume increases are "squared" with larger diameter/radius tubes, not just multiplied.)
    But, having big single tubes that carry their full diameter for a longer part of their waterline (i.e. Lion) does!
    And having a big and a small tube on each side (i.e. Super-Leopard) really displaces alot of water!

    Now, nobody would load their cataraft until it literally sinks! But, reduced loads will still be proportional.
    In other words, since all of these catarafts use the same round/cylindrical shaped tubes, and only vary in size (diameter/radius), if we load each cataraft until the tubes are only half submerged, the differences would remain the same:

    Leopard = 3026 # / Lion = 3774 # / Cougar = 2841 # / Super-Leopard = 4870+#

    Note that on the Super-Leopard, because the smaller (15") tube is attached to the larger (26.5") tube at the bottom, the smaller tube is nearly fully submerged (13.25") and providing almost all of it's total displacement, even when the Super-Leopard is only loaded until the big tube is half submerged. That is some real load carrying ability!

    In fairness, the Cougar does have one real important load carrying advantage over the regular Leopard and Lion, and that is a much shallower draft. Because it's four tubes are arranged side-by-side on each side, when carrying it's load of 2841#, it will only be drafting 9" of water, while the regular Leopard will sink to 13.25" carrying only 185# more. In shallow water, 4.25" of deeper draft can mean a lot less work (and damage) trying to drag a ton-and-a-half over the rocks, if it can be done without portaging at all? Most folks already give the Cougar high marks for having a lower profile above the water, which makes better against the wind.

    I'm not sure how the Cougar got such a reputation as a bigger load hauler than the single-tube boats?
    If you've got deep enough water, it would seem that bigger tubes are better than multiple smaller tubes.

    I'm also fully aware that my use of the published waterline length might have skewed some of the data?
    I sure didn't set out to prove any pre-conceived agenda. I'm just a guy who is shopping for a cataraft, while helping my kid with some math homework!

    Thanx for reading, Dave.
    Now

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    Member 6XLeech's Avatar
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    Cool post. Thx for sharing. The rationale sounds right on including the reasoning for approximations.
    Congratulations to you and your kids!

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    Member AlaskaTrueAdventure's Avatar
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    As much as I admire the math time you have spent with your kids....as much as I respect 6XLeech and his forum contributions.....

    I believe you are are over-thinking the entire raft and rafting concept. Get a raft. Get a boat in a color you enjoy.
    Go rafting and have fun.

    Or am i just too simple? And welcome to the forum with your very first, your #1post!

    dennis

  4. #4

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    good post, thanks for taking time to calc all this stuff out. not only helpful for buying a raft, but possibly helpful in deciding which raft for which trips as well.

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    Yes, thank you for the math, Dave. I believe it is helpful. And I agree that one of the reasons the Cougar has the high freight reputation is the lower draft at a given weight. Single tube designs can usually be rowed faster though.

    Personally, any time I am submerged to half my tube diameter, I consider myself to be well overweight. Not only do heavy cats handle like slugs, they tend to get tippy and feel like they are wallowing in big waves when overweight. I think 1/3 capacity is a better safe limit.

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    Member Ridgerat's Avatar
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    Awesome post...thanks for sharing!

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    Member BluNosDav's Avatar
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    The other "math" that I'm dealing with now is Co$t.

    It seems obvious that the Super-Leopard offers the largest load carrying capacity and at the shallowest draft. But, it costs nearly twice as much as a regular Leopard! ($4999 vs $2680) Cougars are also expensive ($4000). My guess is that all of the lacing between the dual tubes on each side requires a lot of manufacturing expenses?

    Given the large price difference, I'm more inclined to get a regular Leopard and a second boat; like a Soar Pro Pioneer? These two rafts could share large loads and provide a shallower draft overall whenever that is a factor. And provide additional versatility when only one boat is required for different kinds of trips. Maybe even carry the Pioneer rolled-up on the Leopard until the cargo suddenly increases during a float trip (i.e. after the moose is dead).

    Decisions, decisions . . . .

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    And actually the draft of the double tube boats isnt automatically lower than the single tube boats......

    Since the double tube boats have small diameter tubes, the diamater change to volume ratio is less at the bottom of the tubes that a single tube boat. So under small load capacities, the "feighter" boats actually sit lower in the water than single tube boats.

    Once the boat is under a great load, and is sinks deeper, then the freighter gains more boyancy with a larger submergered airspace because of the width of the double tubes, which have then closed the gap in airspace on the bottom between the tubes. So in its use, under a very heavy load, the freighter will draw less water. But under a light load to a certain point, it will draw more.

    We had a cougar, and compared to our friends jaguarundi under light loads, his boat was much more nimble, and floated over rocks much easier. Needless to say the cougar loved getting rocks hung up in its "crack"

  9. #9

    Lightbulb

    Nice job doing math with the kid and making it relevant!

    Quote Originally Posted by BluNosDav View Post
    I've always been perplexed by how different raft manufacturers can advertise vastly different "load capacity" numbers for tubes that are almost exactly the same shape, diameter, and length??? With watercraft of all types, load capacity is actually the "displacement" (volume) of the water supporting the "weight" of the vessel, and cataraft tubes are just about the simplest hull shape in the boating world.
    Well, it's just a teensy bit more complicated than that. You made a very good approximation using geometry, but all heuristics are inherently fallible. Boat designers mostly use calculus for hydrostatic calculations of hull geometry. It's pretty darn complicated, here's the simplest explanation I've seen: http://en.wikipedia.org/wiki/Buoyanc...nd_equilibrium (The 8th equation is the volume integral.)

    If you actually read that link, it's probably time for a beer!

    Surprised? So, was I! Turns out that having twice as many small tubes (i.e. Cougar), does not give you more load capacity.
    (Volume increases are "squared" with larger diameter/radius tubes, not just multiplied.)
    No, but if the tubes are separately inflated, then additional tubes could be a huge safety factor in case of a puncture. Worst case, it might mean the difference between getting that load of gear and meat safely to shore for repairs, or having a cold swim followed by a survival situation.

    Now, nobody would load their cataraft until it literally sinks! But, reduced loads will still be proportional.
    In other words, since all of these catarafts use the same round/cylindrical shaped tubes, and only vary in size (diameter/radius), if we load each cataraft until the tubes are only half submerged, the differences would remain the same:
    Not necessarily proportional. Consider that the tubes become deformed as the load increases, especially as they are submerged further into cold water, which reduces the air pressure.

    None of this is to criticize the original post, just to add some additional thoughts to a good analysis.

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    Member BluNosDav's Avatar
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    Decided to bring this thread back up from the past, with an update and a different angle on the load capacity of a cat-a-raft.

    Finally bought an 18' AIRE Leopard, complete with an 11' long, 72" wide frame, 25" cargo extensions fore & aft, and 4 swivel seats on the corners. So, there's plenty of "room" to load it up (or is that down?), and we did! For it's maiden voyage, my family took it up to the Fortymile River country, and we packed for comfort, rather than weight-savings. Since we'd done the earlier theoretical calculations three years ago, my daughter & I took the time to gather the actual weights of everything that we loaded into the raft using a scale (except the frame which is fully assembled right now). As we shoved off into the Mosquito Fork, we had 768 pounds of gear, 795 pounds of people & dogs, and if the frame was approximately 150 pounds, that was right around 1700 total pounds pressing the Leopard's 26.5" tubes down into the water.

    Well, it floated, barely! The front & rear bottom cross-bars were literally right down at the waterline. And at the center rower's position, because the lower side rails were bending even lower under the weight of all the coolers, there was a couple inches of river water sloshing on top of the taught, new, AIRE mesh floor! Given the standard 10" drop between the top & bottom of the frame, we were drafting around 16 inches, which is over half the diameter of the tubes.

    Everything worked out for the next week as we floated downstream. The river gained water depth, and we ate our way through a lot of groceries. But, during the first few days, there were a few times when we ran aground. All Hands just stepped off into the shallow water, and with that instant load reduction of about 800#, we were able to walk our boat until deeper water was available.

    AIRE's published capacity for the Leopard is 1427 pounds, but, we exceeded this by a few hundred pounds, without any real issues. So, there is some extra room in the factory numbers. Don't know what AIRE uses for their measuring criteria?

    But, one thing that the above experience has brought to my attention, is the concept of a floor capacity limitation. While the top of the frame rests directly on the tubes, the bottom rails and cross-bars do not, and the bending in the middle concerns me. The bottom D-rings on the tubes are not load-bearing. They merely keep the tubes from rotating outward away from the frame. Because, all of the seats are located on the top, almost all of the people-weight is not being carried by the floor. But, when we swapped out rowers, (or if anyone decide to move around the boat, suddenly hundreds of pounds shifted from butts to feet, and onto the floor. Considering how much the lower rails bent in the middle, it seems to me that some extra frame support is needed. I'm considering adding a couple of short vertical bars to connect the rower's seat & foot bars to the bottom side-rails, as one way of providing more support to the middle section of the floor. Adding a couple top cross-bars and "hanging" the coolers from them would be another solution. Anyway, the practical math is just as interesting as the theoretical.

    Thanx for everyone's input, Dave.
    "Luckily, enforcement reads these forums, and likely will peruse this one...Especially after a link of it is forwarded to them....." - AlaskaHippie.

  11. #11

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    What about a simple raft? Why do you think all the military in the world uses them? And not cats? Personal thoughts and LOTS of experience--
    Goo

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    Member BluNosDav's Avatar
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    Simplicity is nice, I gotta agree with ya there.

    But, the main reason that I chose a cat-a-raft instead, is portability. I.E. the ability to break down the vessel into smaller pieces. As a remote hunter, and a dad with a wife & small kids, it's mostly me that gets everything down to the river (and back up to the truck). Each of my cat tubes weighs a little over 50# and rolls up into a nice bundle, that I can carry on one shoulder for short distances, or strap onto my pack-frame for longer portages. My frame will (soon) break into ~60# halves, that can be carried the same way.

    A round-boat raft can only be reduced into one BIG piece of rubber/plastic that weighs 150+#. I can't carry that. Hell, those are hard to even move around the garage & basement.

    Now, back when I was in the Navy, with a half dozen 19-year-old Bos'n Mates under my command; they could each grab a corner of the raft, hoist it over their heads, and shout cadence all the way down to the water's edge & back. Ah, those were the days . . . . .

    Thanx for the memories, Goo!
    "Luckily, enforcement reads these forums, and likely will peruse this one...Especially after a link of it is forwarded to them....." - AlaskaHippie.

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    Member Birdstrike's Avatar
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    Now you can go back and figure out a way to reduce your gear weight by consolidating, upgrading, etc. . I was very heavy on my first overnighter too. I've since reduced that weight significantly but without sacrificing comfort.

    i just got back from a semi-remote trip using the AKRR Hurricane Turn Train from Talkeetna. Yes a round raft is heavy but the frame sure is simpler to breakdown and setup. One of my sons and I just strapped the rolled up raft to the side rails, lifted those to our shoulders and carried it 200 yds to the river. The frame took about 6 minutes to reassemble. Of course if you could split your frame in two pieces you would save lots of time too.

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