Stability?

[Roger Long]

If you're trying to make a larger point go on and make it. If you never intended to give the full lesson should we not feel used?

I thought I might go through the whole thing over the next few days but it got crazy so fast I dispair of going further. I expected the craziness on the Usenet where it's part of the fun but thought, for exactly the reasons you point out, that it would be more orderly here.

The throw away is only the allusion to the the physics of gravity. It's essential to understand that buoyancy is just the mechanics of gravity (yeah, and wave accelerations, see below) and water.

Put a bubble level and a spinning gyroscope on the raft. As the waves pass under the raft the bubble level will stay centered but the gyro will rock back and forth. Down for the raft varies. So, too does buoyancy because it is not solely the result of gravity. In some dynamics this may be quite significant. How does your false assertion that buoyancy is just gravity help in understanding these very real phenomenon? This doesn't seem like nit picking to me.

Well, as I said above, I got the equivelent of 1 minute into what I took an hour to cover with benifit of blackboard and arm waving. Stability is generally considered in a waveless world as a convention of naval architecture. Without a clear understanding of what is happening in that regime, where buoyancy is strictly a function of gravity, the far more complex subject of ship motions is pretty hard to get a handle on. Now you don't want to just jump from the first minute to the end but clear into another subject.

It gets even more complex when you add waves. If you calculate buoyancy in the classical way as if waves weren't moving, you find that vessels should capsize far more often than they should. Inertia, response time, dynamic effects of the moving water, all make it horribly complex. There's no point in even trying to think about it though until you understand what's happening in still water.

 

[sailingdog]

TSM—

My point is that without the induced artificial gravity caused by the acceleration, you'd wouldn't be able to float a boat. It doesn't matter whether the "gravity" is provided by artificial means or a planet's mass... you still need to have weight for buoyancy to occur. Your previous argument stated zero gee but no acceleration.

You're missing my point. If you were in a rocket ship in zero gravity accelerating at 1g you would be able to fill a tub with water and float a boat on it. No gravity, but the equivalent buoyancy force you'd have on the surface of the Earth. If you were plunging Earthward in a powered craft and were accelerating faster than 1g you could float stuff upside down... A touch less esoterically, you can use a centrifuge for your experiments. At any rate, it is clear that gravity is not necessary to have buoyancy. What you need is a fluid or fluids and a force or forces that order them by mass. I would not typically make this rather strained argument, but RL's assertion that buoyancy is a make believe force and it is dependent on the real force of gravity and that seeing this will somehow provide particular enlightenment to the question of stability annoys me. First, buoyancy is a real force as is pressure. Second, of all the fundamental forces you need to have buoyancy, gravity is the easiest one to replace with some other force (not some imaginary force, but a real one). Third, I've seen Roger make this argument before and he's yet to get to the stage where he demonstates the usefullness of thinking of buoyancy as an imaginary force in the understaning of stabilty.

Anyway, I've got to go finish installing my new solar panels so I'll leave it there...

--Tom.

 

[tsmwebb]

Well, as I said above, I got the equivelent of 1 minute into what I took an hour to cover with benifit of blackboard and arm waving. Stability is generally considered in a waveless world as a convention of naval architecture. Without a clear understanding of what is happening in that regime, where buoyancy is strictly a function of gravity, the far more complex subject of ship motions is pretty hard to get a handle on. Now you don't want to just jump from the first minute to the end but clear into another subject.

I'm very much looking forward to the rest of the lecture. I'm good with the conventions of naval architecture. I thought you were tossing them out in your opening salvo and your follow-ups dising buoyancy and GM. Simplifications for the purposes of calculation and teaching are undeniably useful. Treating buoyancy as a side effect of gravity is a reasonabe simplification in statics. If that was all you were after you lost me on the roundabouts.

--Tom.

 

[tsmwebb]

TSM—Your previous argument stated zero gee but no acceleration.

No I didn't mean to argue that at all. I typed:

Moreover, the fundamental force of gravity is not required for bouncy to exist. You can float things in zero gravity just buy taking advantage of a little angular momentum or any other convenient acceleration.

I was attempting to suggest you need an acceleration to sort things by mass but that the acceleration need not be gravity.

--Tom.

 

[Bill Roosa]

a 150 lb man

Grizz
Sorry if I made your head hurt. Franklin made me do it!

Since you asked: the addition of a 150 lb man stepping onto the barge amidships (7.5' from the bow and 5 ft from the center-line of the barge) is the barge tilts by some angle, 150 more lb must be supported so the part of the barge under then new load sinks. The CG of the barge also is shifted as is the CB. A moment of 150*7.5=1125 ft-lb is generated and we need to figure out how the displacement of the CB and CG occur to provide a counter moment of the same size.

The CG is pretty easy but we need to know some more specifics about our barge to actually tell a) where it was before the boarding and b) where it is after. I ass u me that the barge is 4' from keel to gunnell and still has the 10' beam and 15' LOA. All the "hull plates" are made of super-strong 0 thickness unobtainium. The plates have the following dimensions:
Bow and stern - 4' x 10' the area of each is 40 ft^2
Starboard and Port - 4' x 15' with area 60 ft^2
bottom - 10' x 15' with area of 150 ft^2

The total area of unobtainium hull plates is 80+120+150=350 ft^2
Since the whole barge weights 10k lb that means each square foot of plating weights: 10,000/350=28.6 lb/ft^2

One of the things we know about rectangles (but not generally curved shapes) is that the center of gravity is located at the intersection of the diagonals or the exact center of the shape. This is true of any symmetrical shape BTW. From this we can deduce that the barge CG is located 7.5' back from the bow and 5' from the port side. All that is left to figure is how height above the keel it is. To do this we need to average the contributions of each of the hull plates and then divide by the total weight. Since I'm going to measure from the keel upward I'll consider a point 7.5' back from the bow and 5' in from the port side and 0' from the keel to do my measuring from.

(40*28.6*2+40*28.6*2+60*28.6*2+60*28.6*2+150*28.6*0)=10000*x
(area*specific weight* distance above the datm+....)=total weight*distance CG is above the chosen point
solving for x gives 11440/10000=x=1.14 ft above the keel. So the CG before boarding is 7.5' from the bow, 5' from the port side and 1.14' above the keel.

After boarding the CG will clearly still be 7.5' from the bow. If we assume a 6' tall person who has a CG 3' from the bottom of his shoes we can calculate the new CG first for the distance it is from the center-line and then its distance above the keel. For both I'll assume the same point to measure from as before, centered fore-n-aft, port-n-starboard and on the keel. Moments that tend to turn the boat bow down or port down are positive

For the distance from the center-line we write
28.6*(40*0-40*0+60*5-60*5+150*0)+150*5=100150*x
Hay, looky there the bow and stern plates don't change the moment at all because their moment arms are 0 and the port and starboard plates cancel each other out because they are on opposite sides of the reference point by the same amount. It is smart to pick the right reference point to make the math easy.
x=150*5/100150= 0.00749 ft toward the guy boarding

For the distance above the keel we write:
28.6*(40*2+40*2+60*2+60*2+150*0)+150*(4+3)=100150*x
Identical to the first calculation but with one more term for the guy and the addition of his "mass" to the total "mass"
x=(28.6*400+150*7)/100150=0.125 ft above the keel

so the CG after boarding is 7.5' from the bow, 0.00749 ft from the center toward the guy boarding and 1/8' above the keel. Not what I expected but the math don't lie.

The CB is much harder since we don't know where the MC is located and have to use calculus to calculate the actual force upon the now tilted barge bottom. The amount of heel is not going to be much though because the CG only moved 0.007' from the center-line. We could "cheat" and use the "displaced water and wedge method" but I'm not sure Roger where Roger wants to take the class. My calculations are that the gunnell will drop by 0.096 ft or about 1.15" under weight of the guy boarding which is an angle of 1.1 degrees.
Hint: A wedge of water must be moved from one side of the centerline under the keel to the other as the barge heels. That water wedge weighs 150 lb

 

[All U Get]

What?

Hi Roger,
You kinda lost me after the steamer box. I have a lot of questions on how the set-up works. But for your question stuff floats if it displaces slightly more weight than the water does by volume. The heaviest portion, Center of Mass, is always at the lowest point, like an iceberg. If you remove any part of the iceberg the remainder will roll until the CM is again on the bottom. You can push the bottom up or the top down and eventually the ice will return to its balance point. I believe the Coast Guard has a few roll-over boats that work like this. Keep the water out and they pop up to continue on their way. They're like a penguin and my sailboat is like an ostrich, pretty good for 2 AM eh.
Now that steamer box, do you keep it hot enough to warm some of those B&M baked beans on top?
All U Get

 

[sailingdog]

Thanks for clarifying.

I was attempting to suggest you need an acceleration to sort things by mass but that the acceleration need not be gravity.

--Tom.

 

[Roger Long]

Treating buoyancy as a side effect of gravity is a reasonabe simplification in statics. If that was all you were after you lost me on the roundabouts.

That is all I was after. I've found the experience of trying to present this on the net a fasinating insight into teaching dynamics. This is the second time and also with you throwing peanuts up on the stage

The difference is not, as you suggested above, that my students were bored and people here interested. I gave the same lecture to the Society of Professional Sailing Ship Masters a couple years after a sail training ship capsized and killed 19 people. I also gave it to the Council of Educational Ship Owners while the Coast Guard had a Notice of Proposed Rule Making out that would have made deep water sail training virtually impossible. I even gave it in the forecastle of a large Russian square rigger just after going through the tail end of a hurricane. I would assign the interest level of these groups the color Red.

Not once, speaking to all of this wide spectrum of groups with chalk in hand, did everything in this whole long thread occupy more than the first minute or two of my talk.

I'll have to think about going on with it. I'm not sure this is an effective venue for such a presentation.

 

[Todd Smith]

Roger,

I think the difference in group dynamics between the lecture hall and here, is that in the lecture hall you can control the direction of discussion before it diverges too much. So the throw away line can then be followed by some direction control immediately. You can get the conversation flowing into the correct topics.

Here though, you threw that line in and it causes ripples like a rock into a pond. They go in all directions and you can't control the direction of flow because of the time lag and diverse nature of your audience.

I think a group like this is an effective venue for discussion of vessel stability, but the techniques will be different than in a face to face group of people.

Todd

 

[Beija Flor]

Is it buoyancy that makes this thread float - or levity?

 

[LANCE ON CLOUD NINE]

Cash, Lots Of Cash!

 

[Ross]

I think that all of the high flown explanations complete with mathmatical proofs was absurd. Any kid playing with a sink full of dish water knows that the water tries to push any floater out and return to its normal level. Just put a jar with the lid on it into the sink full of water and watch how quickly the water fills the hole made when you pull the jar out.

 

[Bill Roosa]

Floaters

Ross!
I never meant my math to be a proof. The math works. It does give you the answers. It does not ask the questions however.

What stability questions do you have?

I wanted to know how to make my boat stiffer, how moving stuff around or just packing my boat for a cruse would effect my stability, and what I can expect from my boat in a knock down.

To do that I believe "we" have to learn how these things are calculated. I know that my 40.5 does not have any of the really nice documentation and I'll have to produce it myself if I want it. And yes Don, if I do produce a righting moment plot I will make it available to the knowledge base.

To me, this is like the Linux community. Give me the code (procedures) and I'll go get my own data and then share it with the community. Unfortunately I do not know all the in's and out's of stability. I can do my own calculations (math) but don't know any of the "cheats", the faster, smarter ways to get to the answer. Stuff like meta center. REALLY handy concept I had no knowledge of. A quick search of the Internet on meta center arms me with the math tools to answer a lot of my questions. But without Roger asking the question I would never have pulled meta center out of my arse in a thousand years.

The math is HOW you do it. WHAT it do is the question. I'm looking for more HOW and WHAT.

 

[Ross]

Bill, Some while back on the evening news they were showing a floating pier in California that the harbor seals or sea lions had taken over. They were sunning themselves and peasefully snoozing when one more tried to climb aboard and raised the CG above the CoB. Tilted the whole raft into the harbor, dumped the load and righted itself. During world war 2 the Navy liked to line the decks of their battleships with all the shells before they stowed them in the magazine. They nearly capsized a ship one time and decided that it wasn't a good practice.

 

[tsmwebb]

I've found the experience of trying to present this on the net a fasinating insight into teaching dynamics. This is the second time and also with you throwing peanuts up on the stage

I'll have to think about going on with it. I'm not sure this is an effective venue for such a presentation.

I wrote a nasty reply to your post initially. I've deleted it, but I'm sorry if it offended.

I very much hope you'll go on with presenting your ideas here or on a web page (and wish you had done so in RBC). I presume that you really aren't trying to be offensive. Nevertheless, you have done a good job of irritating me. I'm not really throwing peanuts on your stage I'm just annoyed that you aren't getting on with the lesson. And quickly, too! I'm hoping that FedEx will come and remove my old solar panels today and the new panels are almost installed (a little paint and a couple of coves some massive re-stowing and I'm good) so I'll be out of the Marina and off the net soon... If you'd just write up a post explaining life, the universe and stability and post it right away I'd be happy.

--Tom.

 

[Jim Kolstoe]

With due apologies Rodger, I will make a further comment.
Air pressure has nothing to do with bouyancy. Any air pressure bearing on the boat is transmitted through to the water, with the same net effect as that same air pressure bearing directly on the water.
Instead, visualize putting a boat in a basin of water barely big enough for the boat, but which is higher that the water's surface. As you ease the boat into the water, water will be displaced upward in the basin because the boat is occupying the volume that the water had been using. Remember that any liquid or gas, including water, always sinks as low as it can. The volume of water raised above the initial level will equal the weight of the boat, and no more. The reason is that gravity, acting on the boat, is powering the whole thing, and therefore the amount of power available to lift the water is equalent to the weight (not mass or volume) of the boat. (As a side note, if the density of the water is known, you can determine the weight of the floating boat by measuring the volume of water raised above the initial level and multiplying that by its density.)
When you move your boat from a basin to a lake or ocean, the same thing occurs even though it may not be reasonably measureable, since the increase level of the water will be spread over the entire surface of the body of water - a sheet of standard writing paper is very light, but the same thickness of paper ten miles square would be very heavy.
In otherwords, bouyancy results from the boat trying to raise the water level as it sits down into the water's basin - irrespective of the size of the basin.
Now then Rodger, I hope you will continue with your "lecture" as it has been fun and educational. Many thanks.

Jim Kolstoe, h23 Kara's Boo

 

[Bill Roosa]

Rising water

Hi Jim
While I do not disagree with you I'm curious how you would explain the following:

I have two hemispheres 1' and 1.1' in diameters. They nest. If I pour a little water in the bottom of the 1.1' hemisphere and nest the 1' one in it I can find a quantity of water that fills the space between the two. I can then add lead to the inside of the 1' hemisphere and get the 1' hemisphere to float in it instead of having to force it down with my hand.

So how can the weight of the water be less than the weight of the 1' sphere floating in it?




You can imagine a form fitting mold exactly 1 nanometer larger than the hull of an aircraft carrier and "float" the carrier in a teaspoon of water.

I would suggest that it is not the quantity of water displaced but it is the force generated by the volume surrounded by a fluid (in a gravity field for you purist)

 

[Roger Long]

I wrote a nasty reply to your post initially. I've deleted it, but I'm sorry if it offended. I very much hope you'll go on with presenting your ideas here or on a web page (and wish you had done so in RBC). I presume that you really aren't trying to be offensive. Nevertheless, you have done a good job of irritating me. I'm not really throwing peanuts on your stage I'm just annoyed that you aren't getting on with the lesson. And quickly, too!

No offence taken at any point. Maybe if I'd seen the post you deleted though... I'm sorry you didn't see the peanut thing as the joke is was. I would like to get on with the discussion but there is quite a bit of stuff going on away from the computer right now. A web page is a good suggestion. It would be more coherent than a thread. You may have to wait a little while though.

As to your earlier question of why the gravity / buoyancy business is important: Over the last 30 years, I've had occasion to talk about stability with a wide range of people, from high school and boatbuilding students to meeting with USCG naval architects at headquarters in Washington working on developing new stability regulations. I have encountered a surprising number of people, even some with advanced education, who just saw in the textbook that there was an upwards force called buoyancy and never thought about or formed a clear idea of what causes it. If you are going to try and understand something then its source and true nature is fairly important, don't you think? You don't know who is in an audience so you have to cover all the bases. I therefore start with the basics.

I warn you though. When I continue, I will have to belabor the concept of centers (of gravity and buoyancy) a bit because it’s another concept that people think, “Oh, yeah, I know what that means.”, but, often, they really don’t. My objective is to get people to understand stability and not just the simple mathematical models used to analyze it.

 

[sailingdog]

The amount of water remaining means nothing...it is the amount of water that the hemisphere displaces that is important. Provided you don't add too much lead to the smaller sphere, it can float inside the larger one in very little water, since the weight of water it is displacing still equals the weight of the smaller hemisphere.

In fact, you could fill the 1.1' hemisphere entirely with water, and then lower the weighted 1' hemisphere into it. The amount of water that spills out would equal the mass of the weighted 1' hemisphere, provided the 1' hemisphere was weighted so that it still floated.

Hi Jim
While I do not disagree with you I'm curious how you would explain the following:

I have two hemispheres 1' and 1.1' in diameters. They nest. If I pour a little water in the bottom of the 1.1' hemisphere and nest the 1' one in it I can find a quantity of water that fills the space between the two. I can then add lead to the inside of the 1' hemisphere and get the 1' hemisphere to float in it instead of having to force it down with my hand.

So how can the weight of the water be less than the weight of the 1' sphere floating in it?




You can imagine a form fitting mold exactly 1 nanometer larger than the hull of an aircraft carrier and "float" the carrier in a teaspoon of water.

I would suggest that it is not the quantity of water displaced but it is the force generated by the volume surrounded by a fluid (in a gravity field for you purist)

 

[Don12364]

Gentlemen,
This is all very well but when are you guys going to stop throwing brickbats (and apologies) at each other and get on to talk about STABILITY?

BTW nobody has yet mentioned that old Greek guy who ran down the street naked and wet yelling "Eureeeka"!
Archimedes knew then what many have yet to appreciate.