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Thread: The physics of flotation, let's ask Achemedes, shall we?

  1. #1

    Default The physics of flotation, let's ask Achemedes, shall we?

    I've run into several raft manufactures telling what their raft will do...typically being told their 12-14 foot raft will float a moose drawing 2-3 inches of water.


    This is the case with the new raft I ordered. Let's take a look at the physics.

    To float a moose, camp, and paddler..I am going to use a figure of, 600 pounds for meat, 200 pounds for me, 125 pounds for camp.. modest figure of.. just under 1000 pounds.

    Archimedes law tells us to the amount of flotation you get is directly a factor of how much water you displace..

    So to float 1000 pounds you must displace 1000 pounds of water. 1 square foot of water weighs 62.416 pounds at 32 degrees... a bit less at 100 degrees...(your moose will float a bit higher in colder water!!)..


    So a 12 foot boat at 50 inches wide needs to displace 16.02 square foot of water to float the moose...


    hmmm... I don't have time right now to do the math on how many inches of draft on the raft it will take to get to 16.02 square feet, but imma guess it's more than 2-3 inches..lol

    It's just physics..

  2. #2

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    I took a short cut, and used a 12 foot by 4 foot square....drawing 4 inches this is 15.984 square feet...


    Using a real raft the displacement will be less.... so 5-6 inches is more realistic. The manufacturer who sold me the new raft, and told me because of the 6 inch inflatable floor would float the moose and camp drawing 2-3 inches of water, was simply wrong.

    Simple physics...no?

  3. #3
    Member Birdstrike's Avatar
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    With a non-bailing floor your assumptions might be correct. With a self bailer it will ride lower

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    Member ChugiakTinkerer's Avatar
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    Eureka!

    Sorry for being a nitpicker, but it's cubic feet we're talking about here.

    It gets worse if your dimensions are for the total width and total length. You have curvature of the tube and the curve of the bow and stern that mean your first inch submerged is substantially smaller in area than the last inch submerged. So for a 12' x 50" bucket boat you'll probably be looking at drawing an additional inch. It does seem that the salesdroid was being overly optimistic, or maybe thought you were hunting jackalope, not moose.

  5. #5
    Member bobmikk's Avatar
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    "Eureka, it floats"... now I know where that comes from.

    Attached a calculator for displacement... check it out...

    http://www.blueheronwings.com/bh/comps/bdesign.html

  6. #6

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    Quote Originally Posted by ChugiakTinkerer View Post
    Eureka!

    Sorry for being a nitpicker, but it's cubic feet we're talking about here.

    It gets worse if your dimensions are for the total width and total length. You have curvature of the tube and the curve of the bow and stern that mean your first inch submerged is substantially smaller in area than the last inch submerged. So for a 12' x 50" bucket boat you'll probably be looking at drawing an additional inch. It does seem that the salesdroid was being overly optimistic, or maybe thought you were hunting jackalope, not moose.

    yea, no doubt. I was giving him the complete benefit of the doubt using a square.. square edges, no rocker... no rounded bow and stern, and it needed more than 4 inches of draft to float the load. With real life application.. 5 or 6 seems realistic.


    What I don't get is how he can not know this. He supposedly has been doing this 30 years. So when an owner tells you an outright "lie" to sell his boat... and he repeated it again today ... "the floor alone floats 800 pounds"... "boat will float that load at 2-3 onches draft... doesn't the consumer have some course of action? Kinda frustrating...

    The flotation stuff is pretty interesting though. It's be neat if these boat manufacturers could give you the displacement numbers at various drafts... 1 inch =... 2 inch equals... I am pretty sure the boat in question will need 5 plus... maybe 6 inches draft to float 1000 pounds. Much if the river I am hunting is 1-2 inches by the end of the season..lol Pulling 4 inches of over load is a lot of work.

  7. #7
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    A better way would be to buy 20, #50 bag of sand. Weight each bag to make sure they are the correct weight. Put the proper amount of air in the boat and add the sand. Now measure the amount of free board. Using this method is the only way to remove all the variables.

  8. #8
    Member ChugiakTinkerer's Avatar
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    Mike Strahan did something like that recently, using fish totes filled with water. I'll see if I can find the link.

    Sent from my HTC One using Tapatalk

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    Member ChugiakTinkerer's Avatar
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    Thinking about that floor, let's say it's 36" x 10' x 6". That's 15 cubic feet. Displacing that much water it will support over 900 lbs. So he was probably correct on 800 lbs. But trying to maneuver a raft drafting 6" seems Like it might pose a few challenges.

    Sent from my HTC One using Tapatalk

  10. #10

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    The draft of any inflatable is determined by its tube diameter and overall waterline.

    Here's a computation formula that will get you in the close ball park (within a few pounds) of max capacity:

    M = Maximum load in kg
    V = Volume in cubic meters of the total buoyancy of the boat
    W = total weight (kg) of the boat as supplied by manufacturer including all installed accessories

    My new design the "KORK" has these specs and capacity statement:

    11' length
    14" tapered to 22" tube diameter
    44" width
    2" inflatable floor
    Capacity = 1200-lbs

    Formula to devise weight capacity:

    Max Load M = 0.55 X V X 1000 - W

    0.55 X 1.026 X 1000 - 17.8 = 546.5 kg (1202.3 lbs)

    This weight on board should submerse the boat 7" (roughly 50% of hull above and below the surface).

    Maneuverability and safety limits are not considered in these figures. A "useful" load and "max" load are two different numbers.

    Useful load for any know legitimate weight capacity is 75% operational capacity. So, a stated 1200-lb capacity would perform best with less than 900-lbs on board. Can it hold an extra 200 lbs? yes, but with caution and slow speeds.

    Hope this helps,

    larry

  11. #11

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    Quote Originally Posted by ChugiakTinkerer View Post
    Thinking about that floor, let's say it's 36" x 10' x 6". That's 15 cubic feet. Displacing that much water it will support over 900 lbs. So he was probably correct on 800 lbs. But trying to maneuver a raft drafting 6" seems Like it might pose a few challenges.

    Sent from my HTC One using Tapatalk

    Yea, I believe the floor could support close to what he claimed... BUT... fully submerged... thus as you said..6 inches of draft.


    The reason I brought that comment up, was he used it to support his claim on his boat only drawing 2-3 inches with the 1000 pound load.... it's irrelevant. You can have a 24 inch thick floor at those surface area dimensions and it draws the same.


    Flotation IS pretty amazing. I stuffed 55 thousand pounds on my boat last summer, and drug a 20 thousand pound bag(49 foot boat at 14 wide).. and was surprised how much freeboard I had. If I touched bottom I was in trouble... floating the weight was not an issue though.

    And there is it.. the float hunt dilemma... float it high enough that you are not dragging the raft, bottom on the rocks every 100 yards..


    There is no doubt in my mind though that this raft manufacturer's claim of 2-3 inches is incorrect.


    If I was selling boats for 30 years... I am pretty sure I'd know this info...

  12. #12

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    Quote Originally Posted by Larry Bartlett View Post
    The draft of any inflatable is determined by its tube diameter and overall waterline.

    Here's a computation formula that will get you in the close ball park (within a few pounds) of max capacity:

    M = Maximum load in kg
    V = Volume in cubic meters of the total buoyancy of the boat
    W = total weight (kg) of the boat as supplied by manufacturer including all installed accessories

    My new design the "KORK" has these specs and capacity statement:

    11' length
    14" tapered to 22" tube diameter
    44" width
    2" inflatable floor
    Capacity = 1200-lbs

    Formula to devise weight capacity:

    Max Load M = 0.55 X V X 1000 - W

    0.55 X 1.026 X 1000 - 17.8 = 546.5 kg (1202.3 lbs)

    This weight on board should submerse the boat 7" (roughly 50% of hull above and below the surface).

    Maneuverability and safety limits are not considered in these figures. A "useful" load and "max" load are two different numbers.

    Useful load for any know legitimate weight capacity is 75% operational capacity. So, a stated 1200-lb capacity would perform best with less than 900-lbs on board. Can it hold an extra 200 lbs? yes, but with caution and slow speeds.

    Hope this helps,

    larry

    Yea, and as we have gone through here before, and I am sure you are aware, load capacity has everything to do with where you intend to float the load. I hunted the Tanana one fall with a 12 foot boat. I was really worried about getting back to town if I killed a bull. I got lucky, loaded the bull and camp... sat down about 8-10 inches, and felt completely comfortable going down river..nice and slow. That same raft on many on Alaska's other rivers, and I never make it out from either flooding, capsizing, or simply being unable to drag it..

    Thanks for the info though... I saved it. I'm not sure what tube diameter has to do with it though... overall water line is the only factor... correct? I mean a row boat can have sides 1 inch thick... and as long as these sides are ridged enough to hold the shape of the water line.. and displace the water... the force of flotation is there.


    In other words... the only reason a boat with 16 inch tubes would float higher than a boat with 12 inch tubes with identical water lines would be the rigidity the 16 inch tubes would afford you in maintaining the shape of the waterline..


    Much like the floor in the PR-49...since it is not ridgid, and under load it takes on a concave shape... that boat will sit down more than a boat with equal waterline, and a ridgid floor...more displacement with similar draws.. not saying anything wrong about that boat... at 10 pounds or what ever it is... it's a great hunting tool.

  13. #13

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    Coffee is taking affect..lol

    Larry... since I have you on the phone here.. and just to let you know, I really appreciate you taking on the questions here about your products! It's very helpful..


    Have you looked at a modest floor insert for the PR-49?

    I suppose as soon as you do that you introduce more weight... more abrasion.. more, more, more...


    But an insert would increase rigidity and floatation for some applications... and of course.. more weight..

    hahahaha.. back to square one..

  14. #14
    Member ChugiakTinkerer's Avatar
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    I have an Aire Trib 12' that I would be reluctant to haul a moose with. I've made a few assumptions and ran some calcs just to see how it compares with the raft you've described.

    Length is 12.33 ft, width is 73", tube diameter is 18" tapering to 17" in the bow/stern. Not sure of floor thickness but I do know it sits up above the bottom of the tubes by a couple inches.

    If I drop the raft in the water empty, the side tubes will start to submerge but the floor will be above the waterline. According to Aire the 2" waterline is 100". Initial displacement will the 2" portion of the side tubes times the length, which my simple calculation says is 1.8 cubic feet. At 62 lbs per cubic ft that equates to ~118 lbs. It turns out the boat weighs in at 110 lbs, so it's a draw. My empty boat will sit in the water 2".

    Further calcs will treat the floor as if it were a solid floor. That's probably viable until I submerge the floor completely. Without getting into fancy calculus, I'll treat the boat as a box that is 5.5' wide and 10.9' long. That's an area of 59.95 square feet, so each inch of additional draft displaces 5 cubic feet of water, or 310 lbs. To get to a 1,000 lb load I need to draft an additional 3.22 inches.

    My back of the envelope math here should be in the ballpark of what actual load measurements will reveal. If you were willing to be generous to the manufacturer, you could say that if the boat you were looking at had the same dimensions and he was referring to draft of the floor, then maybe his statement was correct. That's a lot of stretching though, and at my age I'm not that limber!

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    The other all important question is how well your load is attached to the tubes. If it is resting on the floor, it will push the floor lower than the tubes, creating an even deeper draft. Are there plenty of d-rings to run straps through? If you have a rigid floor tied to the tubes, will it support 7-800 pounds of meat, antler, cape and gear without sagging or breaking? With an inflated floor, will it be able to handle the extra wear and tear from rocks and bottom that will come as a result of all the weight on it? Because when you add weight to the floor, it loses the ability to flex and float over rocks and obstacles; instead it will drag over them.

  16. #16

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    Quote Originally Posted by willphish4food View Post
    The other all important question is how well your load is attached to the tubes. If it is resting on the floor, it will push the floor lower than the tubes, creating an even deeper draft. Are there plenty of d-rings to run straps through? If you have a rigid floor tied to the tubes, will it support 7-800 pounds of meat, antler, cape and gear without sagging or breaking? With an inflated floor, will it be able to handle the extra wear and tear from rocks and bottom that will come as a result of all the weight on it? Because when you add weight to the floor, it loses the ability to flex and float over rocks and obstacles; instead it will drag over them.

    that will be one good aspect about this raft. It has a 6 inch inflatable floor that sounds pretty rigid... with that rigidity, additional demands will be made of the bottom fabric, which I have concerns about... guess we'll see.. I'm also pretty convinced I'll still need the PR-49. I will not be a mean clean floating machine...lol Last year with the PR-49 tied to the bow of the canoe was pretty maneuverable.. but I managed... the PR-49 tiedto the bow of a 16 foot SOAR canoe(no real keel).. was remarkably maneuverable with the single canoe paddle..

  17. #17

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    anchor...the tube diameter matters because this factor determines the available fabric of each tube, which adds to the waterline.

    In your example, a boat with 12" tubes vs the boat with 16" tubes will have different waterlines and capacity.

    Imagine a 12" tube with 200-lbs resting on it. Now take that same length of tube and add 4" to its girth...that tube will hold more weight because there is more surface of the larger tube diameter making contact with water and supporting the weight with more air.

    Yes, the floor inserts are 2" drop stitch. They weigh about 6 lbs, but add rigidity and allowance.

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    Quote Originally Posted by willphish4food View Post
    The other all important question is how well your load is attached to the tubes. If it is resting on the floor, it will push the floor lower than the tubes, creating an even deeper draft. Are there plenty of d-rings to run straps through? If you have a rigid floor tied to the tubes, will it support 7-800 pounds of meat, antler, cape and gear without sagging or breaking? With an inflated floor, will it be able to handle the extra wear and tear from rocks and bottom that will come as a result of all the weight on it? Because when you add weight to the floor, it loses the ability to flex and float over rocks and obstacles; instead it will drag over them.
    Now your just dreaming. There is no rubber boat that will have the same performance loaded at 100% as it does with a normal load.

  19. #19

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    Quote Originally Posted by Larry Bartlett View Post
    anchor...the tube diameter matters because this factor determines the available fabric of each tube, which adds to the waterline.

    In your example, a boat with 12" tubes vs the boat with 16" tubes will have different waterlines and capacity.

    Imagine a 12" tube with 200-lbs resting on it. Now take that same length of tube and add 4" to its girth...that tube will hold more weight because there is more surface of the larger tube diameter making contact with water and supporting the weight with more air.

    Yes, the floor inserts are 2" drop stitch. They weigh about 6 lbs, but add rigidity and allowance.


    Hmm... I guess I follow along when you say the 16 inch tube boat will have a different waterline than the 12 inch tube boat...

    We also seem to be talking about a non rigid floor. Once the floor is rigid, and the waterlines are equal...the 12 boat should pack the same as the 16 boat... up to the point the 12 inch tube boat loses freeboard..no?

    So you make a floor insert for the PR-49? I was unaware of that.. I'll check your site... would be interesting for me..

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    Holy crap, I was told there would be no math on this forum...

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