Calculating Buoyancy

If I remember, the buoyancy question was raised to help plan a floating
dock. Let me suggest two references - at your library or inter-library
loan. HANDMADE HOUSEBOATS by Russell Conder, International Marine, 1992,
which has a good discussion of using various sorts of floation and the
structure to contain it. Even better for the stated use is THE DOCK MANUAL
by Max Burns,Storey Books, 1999. Floating, fixed, design, calculations,
plans, hardware - it's got it all. Good luck.
Bill Shenk

John,

Back to the bouyancy problem - the waterline of the drums is indeed
non-linear, though I think you'll use 1/3 or so of the available
floatation and press ahead. (I don't think one could even estimate
the weight of the dock very closely.)

Anyway, if your dying to know the waterline and don't recall your
Calc 1 (this is a simple area-under-the-curve intergration problem)
do this: Draw a big circle on fine graph paper. Count the squares
inside. Divide your total bouyancy available by the number of
squares - assigning each square to some unit of bouyancy. Now, count
enough squares from the bottom up to equal the weight of your dock.
There you have it.

I just happened to see a photo of a similar project that was designed
as a trailer; the wheels and all just sunk and it was left hooked to
the truck. This let the guy run his dinghys and swim without a dock
permit. I believe he guyed it with two ropes, but I imagine you
could also make a rigid link or chains to the truck to achieve the
same result.

Regards,
Gregg Carlson

--- In bolger@y..., j.c.ewing@h... wrote:
> Yes, I had a similar idea at an earlier stage and went on to
explore
> what might be a 'simpler' approach. But I haven't yet dismissed the
> concept you describe. Thanks for the further input.
> John
>
> --- In bolger@y..., wmrpage@a... wrote:
> > In a message dated 5/13/01 11:46:47 PM Central Daylight Time,
> > j.c.ewing@h... writes:
> >
> >
> > > And if I were to use two rows of drums
> > > (and I think I will have to) the outer-most drums will submerge
> > > before the inner row.
> > >
> > >
> >
> > It occurs to me that if you were to arrange your drums
> in "catamaran"
> > fashion, on or under either side of the ramp, and attached the
ramp
> on a
> > horizontal pivot amidships on the "catamaran", somewhat shoreward
> of its
> > outboard end, then all of the "drums" would equally contribute to
> supporting
> > the load, regardless of the angle of the ramp (which would vary
> with water
> > level) and the outboard end of the ramp could be at or even below
> the actual
> > waterline, facilitating landing the boat and winching it out. How
> one would
> > construct such a contraption so that it can be put in and taken
> out, what
> > configuration the pivot bearing would take and the like, do not
> seem obvious
> > to me.
> >
> > I think this is an interesting problem and would appreciate
hearing
> from you
> > as you tackle the problem.
> >
> > Bill in MN

Yes, I had a similar idea at an earlier stage and went on to explore
what might be a 'simpler' approach. But I haven't yet dismissed the
concept you describe. Thanks for the further input.
John

--- In bolger@y..., wmrpage@a... wrote:
> In a message dated 5/13/01 11:46:47 PM Central Daylight Time,
> j.c.ewing@h... writes:
>
>
> > And if I were to use two rows of drums
> > (and I think I will have to) the outer-most drums will submerge
> > before the inner row.
> >
> >
>
> It occurs to me that if you were to arrange your drums
in "catamaran"
> fashion, on or under either side of the ramp, and attached the ramp
on a
> horizontal pivot amidships on the "catamaran", somewhat shoreward
of its
> outboard end, then all of the "drums" would equally contribute to
supporting
> the load, regardless of the angle of the ramp (which would vary
with water
> level) and the outboard end of the ramp could be at or even below
the actual
> waterline, facilitating landing the boat and winching it out. How
one would
> construct such a contraption so that it can be put in and taken
out, what
> configuration the pivot bearing would take and the like, do not
seem obvious
> to me.
>
> I think this is an interesting problem and would appreciate hearing
from you
> as you tackle the problem.
>
> Bill in MN

Victoria is at the southern end of Vancouver Island (in British
Columbia, Canada). I know my reference to drought and rain barrels
was a bit confusing but I didn't want to bore everybody with details.
But since you asked...

Victoria (and other parts of what's normally the 'Wet Coast') had a
pretty dry fall and winter. Our reservoir should have been raised
years ago but wasn't (partly because of environmentalist opposition)
and so there wasn't much water in reserve and the regional government
has already imposed severe water restrictions (such as a ban on water
sprinklers and lawn watering). In response, Home Depot and many other
outlets have finally begun to make rain barrels more widely
available. This might seem a bit like closing the door after the
horse has fled but, as it turns out, we have been getting some spring
rain -- perhaps to be captured in those barrels.

John (who has finished applying four coats of varnish to Nandessa's
bottom and hopes to turn her right-side-up tomorrow)

--- In bolger@y..., wmrpage@a... wrote:
> In a message dated 5/13/01 11:46:47 PM Central Daylight Time,
> j.c.ewing@h... writes:
>
>
> > We are in drought conditions here in Victoria and Home Depot has
> > brought in a huge stock of plastic drums that they are selling as
> > rain barrels, at $28 each.
> >
> >
>
> Where is Victoria? And what do people do with "rain barrels" when
there is a
> drought?
>
> Very Curious,
> Bill in MN
>
> P.S. Could you find means to send a diagram of what your intention
is, or
> what local practice is? I was thinking in terms of a simple float,
but it
> seems that you are aiming at something outside of my limited
experience. Do
> you have to cope with tides or otherwise substantial changes in
water levels?

In a message dated 5/13/01 11:46:47 PM Central Daylight Time,
j.c.ewing@... writes:

And if I were to use two rows of drums
(and I think I will have to) the outer-most drums will submerge
before the inner row.

It occurs to me that if you were to arrange your drums in "catamaran"
fashion, on or under either side of the ramp, and attached the ramp on a
horizontal pivot amidships on the "catamaran", somewhat shoreward of its
outboard end, then all of the "drums" would equally contribute to supporting
the load, regardless of the angle of the ramp (which would vary with water
level) and the outboard end of the ramp could be at or even below the actual
waterline, facilitating landing the boat and winching it out. How one would
construct such a contraption so that it can be put in and taken out, what
configuration the pivot bearing would take and the like, do not seem obvious
to me.

I think this is an interesting problem and would appreciate hearing from you
as you tackle the problem.

Bill in MN

In a message dated 5/13/01 11:46:47 PM Central Daylight Time,
j.c.ewing@... writes:

We are in drought conditions here in Victoria and Home Depot has
brought in a huge stock of plastic drums that they are selling as
rain barrels, at $28 each.

Where is Victoria? And what do people do with "rain barrels" when there is a
drought?

Very Curious,
Bill in MN

P.S. Could you find means to send a diagram of what your intention is, or
what local practice is? I was thinking in terms of a simple float, but it
seems that you are aiming at something outside of my limited experience. Do
you have to cope with tides or otherwise substantial changes in water levels?

That site looks fantastic, Dick, and should do the trick quite
nicely. Many thanks for steering me there.
John

--- In bolger@y..., dickpilz@g... wrote:
> Hi, John,
>
> By now, as you know, there are several considerations when you want
> to find the volume of a cylinder that is lying down on its side.
>
> Fortunately, this problem isn't new or unique. I used to use the
> tables in "Machinery's Handbook" but there is an easier way.
>
> Just browse to:
>
>http://grapevine.abe.msstate.edu/~fto/tools/vol/parthcylinder.html
>
> It is an online calculator for finding out this volume, or you can
> switch the problem around and find out what the depth immersion
will
> be, for a certain volume. Using feet for diameter and length, you
> can plug in 62 to 64 pounds for each calculated cubic foot.
Whatever
> floats your boat - or raft :-)
>
> There are other volume calculators at this site as well. Sure, you
> can gut it out with all of the formulae, but somebody has already
> done it for you and is offering it for free use.
>
> Enjoy!
>
> Dick Pilz
>
> --- In bolger@y..., "John Ewing" <j.c.ewing@h...> wrote:
> > This is probably something I should know but high school was a
long
> time ago, so...
> > I want to calculate how much dock weight I can support by
floating
> plastic drums, 1.75' dia. by 2.66' long/high. Presumably I'd
multiply
> volume by some factor, but what is it? (Of course, I'll need to
take
> into account the weight of the drums themselves.) One complication
is
> that our inlet here is not fully fresh water and not fully salt
water.
> > Thanks for any assistance anyone might be able to offer.
> > John

Hi, John,

By now, as you know, there are several considerations when you want
to find the volume of a cylinder that is lying down on its side.

Fortunately, this problem isn't new or unique. I used to use the
tables in "Machinery's Handbook" but there is an easier way.

Just browse to:

http://grapevine.abe.msstate.edu/~fto/tools/vol/parthcylinder.html

It is an online calculator for finding out this volume, or you can
switch the problem around and find out what the depth immersion will
be, for a certain volume. Using feet for diameter and length, you
can plug in 62 to 64 pounds for each calculated cubic foot. Whatever
floats your boat - or raft :-)

There are other volume calculators at this site as well. Sure, you
can gut it out with all of the formulae, but somebody has already
done it for you and is offering it for free use.

Enjoy!

Dick Pilz

--- In bolger@y..., "John Ewing" <j.c.ewing@h...> wrote:
> This is probably something I should know but high school was a long
time ago, so...
> I want to calculate how much dock weight I can support by floating
plastic drums, 1.75' dia. by 2.66' long/high. Presumably I'd multiply
volume by some factor, but what is it? (Of course, I'll need to take
into account the weight of the drums themselves.) One complication is
that our inlet here is not fully fresh water and not fully salt water.
> Thanks for any assistance anyone might be able to offer.
> John

CORRECTION: 14 drums not 12. With this design there are approximately
.54 cubic feet of flotation (steel drums) per square foot of float
which is constructed of 2x8 joists etc and 2x8 decking. Using your
slightly smaller plastic drums you would need 16 for the same
structure.

--- In bolger@y..., cha62759@t... wrote:
> Hi John, In referring to "Marinas, Recommendations for Design,
> Construction and Maintainence" published by the National Association
> of Engine and Boat Manufacturers here is what their design for
floats
> using steel 55 gallon oil drums looks like. Their basic design for a
> floating
> dock is 8' wide by 24' long. At each end of the float there are 2
> pairs of drums across the 8'width. The pairs of drums are placed
> right
> up to the edge with a space between the 2 pair. Between the ends
> with the pairs of drums there are 4 more drums spaced equally again
> across the 8' width. 12 drums in all. From this basic design you can
> come up with requirements for the size of float you want. This is
> easier to draw than to descibe.
> The point they make is that flotation should be close to the edges
> for
> stability. They also emphasize that this is a fresh water solution.
> For salt water you would need to use foam or plastic. If you wish I
> can copy the relevent pages and fax them to you.
>
> Bob Chamberland
>
>
>
> --- In bolger@y..., "John Ewing" <j.c.ewing@h...> wrote:
> > This is probably something I should know but high school was a
long
> time ago, so...
> > I want to calculate how much dock weight I can support by floating
> plastic drums, 1.75' dia. by 2.66' long/high. Presumably I'd
multiply
> volume by some factor, but what is it? (Of course, I'll need to take
> into account the weight of the drums themselves.) One complication
is
> that our inlet here is not fully fresh water and not fully salt
water.
> > Thanks for any assistance anyone might be able to offer.
> > John

Hi John, In referring to "Marinas, Recommendations for Design,
Construction and Maintainence" published by the National Association
of Engine and Boat Manufacturers here is what their design for floats
using steel 55 gallon oil drums looks like. Their basic design for a
floating
dock is 8' wide by 24' long. At each end of the float there are 2
pairs of drums across the 8'width. The pairs of drums are placed
right
up to the edge with a space between the 2 pair. Between the ends
with the pairs of drums there are 4 more drums spaced equally again
across the 8' width. 12 drums in all. From this basic design you can
come up with requirements for the size of float you want. This is
easier to draw than to descibe.
The point they make is that flotation should be close to the edges
for
stability. They also emphasize that this is a fresh water solution.
For salt water you would need to use foam or plastic. If you wish I
can copy the relevent pages and fax them to you.

Bob Chamberland

--- In bolger@y..., "John Ewing" <j.c.ewing@h...> wrote:
> This is probably something I should know but high school was a long
time ago, so...
> I want to calculate how much dock weight I can support by floating
plastic drums, 1.75' dia. by 2.66' long/high. Presumably I'd multiply
volume by some factor, but what is it? (Of course, I'll need to take
into account the weight of the drums themselves.) One complication is
that our inlet here is not fully fresh water and not fully salt water.
> Thanks for any assistance anyone might be able to offer.
> John

Wow, Bill, that was some detailed reply!! I'm not sure I can take it
all in in one quick go but I'll try to pick up on a couple of your
points...

> You have an engineering design issue here, not just a mathematical

problem.

> I think the issue can be more precisely stated as: "How do I

achieve a

> tolerable level of vertical movement of the structure for a given

load?" As

> you have not specified your tolerance for vertical movement, nor

the maximum

> load, I don't think there is any simple answer to be derived from

any

> mathematical formula.

Ya, and it's more complicated than that, even. What I really want to
do is float the outside end of a ramp into the water (the ramp being
hinged at the land end) and then to add rollers and a winch in order
to haul out and 'park' my 16-ft. rowing skiff, Nandessa. So the
barrels would have to support the weight of the ramp itself (or
actually 50% of the weight, plus a bit for downward weight shift),
the boat and a person or two. And if I were to use two rows of drums
(and I think I will have to) the outer-most drums will submerge
before the inner row.

> If the drums are to be conventionally mounted under the dock, with

their long

> axis' (axes?) parallel to the waterline, you face an interesting

phenomena.

> As long as the waterline is below the diameter of the drum parallel

to the

> waterline, each increment of immersion reflects progressively

greater

> displacement of water, or conversely, each increment of weight

results in

> less vertical movement. Once the waterline passes that diameter,

the opposite

> result would obtain, with probably undesirable results...
>
> If I were in your shoes, I would look to the empirical experience

of my

> neighbors and adjust my plans accordingly, as local conditions and
> expectations probably have been and will continue to be adapted to

a host of

> empirical factors, not readibly reducible to mathematical

resolution.

There is so little boater use of Portage Inlet that most of what
docks that do exist are old and rotting. Many are just based on now-
waterlogged logs. However, there is a pretty new dock on drums on the
other side of the point and, although its much larger than what I
contemplate, I agree I should go talk to the owner.

> Failing that, I would use 1/2 the immersed displacement of the

drums, reduced by a

> very substantial "fudge factor", to allow for the density of the

drums, the

> weight of the supporting structure, marine growth, imprecision in

estimating

> the "live" loads, and other "factors of ignorance".

Ya, it did dawn on me following earlier replies that, after
submerging to its mid-point, a barrel lying flat will gain less and
less buoyancy as it sinks further into the water. So, my thought is
to count only the buoyancy to the midpoint and leave the rest for
margin-of-error (or fudge factor, as you termed it).

> I am curious about the source of your "drums". Would you care to

share with

> us what your source is (after you secure an adequate supply for

your

> purposes, of course)

We are in drought conditions here in Victoria and Home Depot has
brought in a huge stock of plastic drums that they are selling as
rain barrels, at $28 each.

Thanks for your reply, Bill, and thanks to Chuck and the others. At
least I now have a starting point. --John

Yes, see what your neighbors are doing and find out which raft is
stable and which raft sinks when someone gets on it.

Around here (northwest lower Michigan) there are plastic 40 or 50
gallon drums for sale in a number of places. One cost me $17. but in
quantity probably available for less. You could probably find steel
drums too but the plastic drums are a lot easier to handle and don't
rust. They are difficult to puncture also. Mine, ironically, had been
filled with Argentine cherry juice. (I am in the middle of the cherry
capital of the world).

--- In bolger@y..., wmrpage@a... wrote:
> In a message dated 5/12/01 4:33:32 PM Central Daylight Time,
> j.c.ewing@h... writes:
>
>
> > I want to calculate how much dock weight I can support by
floating
plastic
> > drums, 1.75' dia. by 2.66' long/high.
>
>
> If I were in your shoes, I would look to the empirical experience
of
my
> neighbors and adjust my plans accordingly, as local conditions and
> expectations probably have been and will continue to be adapted to
a
host of
> empirical factors, not readibly reducible to mathematical
resolution.

I am curious about the source of your "drums". Would you care to
share with
> us what your source is (after you secure an adequate supply for
your
> purposes, of course)
>
> Ciao for Niao,
>
> Bill in MN,
>

Bill,
After reading your thoughtful response,I must say that you have convinced me to stick to boatbuilding.....docks are way too complicated for me!.....;-)

Sincerely,
Peter Lenihan,visualizing the arcs described by the wine glass as it approaches the hole in my head,from the sunny St.Lawrence...........

---wmrpage@...

> wrote:
>In a message dated 5/12/01 4:33:32 PM Central Daylight Time,
> j.c.ewing@...writes:
> 
> 
> <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">I want to calculate how much dock weight I can support by floating plastic
> drums, 1.75' dia. by 2.66' long/high. </BLOCKQUOTE>
> 
> This is not a trivial question. Calculating the displacement of an immersed
> cylinder is a trivial problem, as someone will probably point out. Your
> problem is not so simple.
> 
> I think that as far as mathematics are concerned, you need to be able to
> calculate the areas of the portions of a circle circumscribed by chords and
> arcs, where the chords are parallel to the waterlines of the (partially)
> immersed float and the arcs described by the immersed diameter. This is
> probably a trivial exercise to a numerate human, but I don't know that I
> would be able to figure it out. The computational methods used to determine
> the displacement of vessels from plans would certainly suffice, but with so
> simple a shape as a cylinder there is certainly a simpler mathematical
> solution.
> 
> You have an engineering design issue here, not just a mathematical problem.
> I think the issue can be more precisely stated as: "How do I achieve a
> tolerable level of vertical movement of the structure for a given load?" As
> you have not specified your tolerance for vertical movement, nor the maximum
> load, I don't think there is any simple answer to be derived from any
> mathematical formula.
> 
> Any floating drum is going to sink until the weight of displaced water equals
> the supported weight, or sink until it strikes bottom or implodes. Since you
> do not want your dock to sink, and you want walk along it dry-shod, the
> relevant inquiry is probably the increase in displacement per unit of
> vertical movement that will keep your platform at the desired minimum height
> above water when subjected to the maximum load.
> 
> If the drums are to be conventionally mounted under the dock, with their long
> axis' (axes?) parallel to the waterline, you face an interesting phenomena.
> As long as the waterline is below the diameter of the drum parallel to the
> waterline, each increment of immersion reflects progressively greater
> displacement of water, or conversely, each increment of weight results in
> less vertical movement. Once the waterline passes that diameter, the opposite
> result would obtain, with probably undesirable results.
> 
> In the unlikely event that you plan to mount the drums with their long axis'
> (axes?) vertical, the familiar "Pi x R^2 x L" formula will give a
> displacement per unit of vertical position solution which even an innumerate
> such as I could calculate, but that does not address the practical
> engineering considerations your question raises.
> 
> If I were in your shoes, I would look to the empirical experience of my
> neighbors and adjust my plans accordingly, as local conditions and
> expectations probably have been and will continue to be adapted to a host of
> empirical factors, not readibly reducible to mathematical resolution. Failing
> that, I would use 1/2 the immersed displacement of the drums, reduced by a
> very substantial "fudge factor", to allow for the density of the drums, the
> weight of the supporting structure, marine growth, imprecision in estimating
> the "live" loads, and other "factors of ignorance".
> 
> I am curious about the source of your "drums". Would you care to share with
> us what your source is (after you secure an adequate supply for your
> purposes, of course)
> 
> Ciao for Niao,
> 
> Bill in MN,
> 
> contemplating whether he can calculate the area between a chord and a circle
> 
> 
> 
>
>
>
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In a message dated 5/12/01 4:33:32 PM Central Daylight Time,
j.c.ewing@... writes:

I want to calculate how much dock weight I can support by floating plastic
drums, 1.75' dia. by 2.66' long/high.

This is not a trivial question. Calculating the displacement of an immersed
cylinder is a trivial problem, as someone will probably point out. Your
problem is not so simple.

I think that as far as mathematics are concerned, you need to be able to
calculate the areas of the portions of a circle circumscribed by chords and
arcs, where the chords are parallel to the waterlines of the (partially)
immersed float and the arcs described by the immersed diameter. This is
probably a trivial exercise to a numerate human, but I don't know that I
would be able to figure it out. The computational methods used to determine
the displacement of vessels from plans would certainly suffice, but with so
simple a shape as a cylinder there is certainly a simpler mathematical
solution.

You have an engineering design issue here, not just a mathematical problem.
I think the issue can be more precisely stated as: "How do I achieve a
tolerable level of vertical movement of the structure for a given load?" As
you have not specified your tolerance for vertical movement, nor the maximum
load, I don't think there is any simple answer to be derived from any
mathematical formula.

Any floating drum is going to sink until the weight of displaced water equals
the supported weight, or sink until it strikes bottom or implodes. Since you
do not want your dock to sink, and you want walk along it dry-shod, the
relevant inquiry is probably the increase in displacement per unit of
vertical movement that will keep your platform at the desired minimum height
above water when subjected to the maximum load.

If the drums are to be conventionally mounted under the dock, with their long
axis' (axes?) parallel to the waterline, you face an interesting phenomena.
As long as the waterline is below the diameter of the drum parallel to the
waterline, each increment of immersion reflects progressively greater
displacement of water, or conversely, each increment of weight results in
less vertical movement. Once the waterline passes that diameter, the opposite
result would obtain, with probably undesirable results.

In the unlikely event that you plan to mount the drums with their long axis'
(axes?) vertical, the familiar "Pi x R^2 x L" formula will give a
displacement per unit of vertical position solution which even an innumerate
such as I could calculate, but that does not address the practical
engineering considerations your question raises.

If I were in your shoes, I would look to the empirical experience of my
neighbors and adjust my plans accordingly, as local conditions and
expectations probably have been and will continue to be adapted to a host of
empirical factors, not readibly reducible to mathematical resolution. Failing
that, I would use 1/2 the immersed displacement of the drums, reduced by a
very substantial "fudge factor", to allow for the density of the drums, the
weight of the supporting structure, marine growth, imprecision in estimating
the "live" loads, and other "factors of ignorance".

I am curious about the source of your "drums". Would you care to share with
us what your source is (after you secure an adequate supply for your
purposes, of course)

Ciao for Niao,

Bill in MN,

contemplating whether he can calculate the area between a chord and a circle

John:

The math is the easy part. Multiply the volume in cubic feet times 62 pounds for the displacement. It would be 64 pounds for seawater, so the difference is negligible. What that number gives you is the weight the drum will support (including the weight of the drum itself) before it sinks. What I don't know is how far you want the drum to submerge. Halfway? One third? Two thirds? You might look at some existing docks for help. That or ask some who knows.

Chuck

-----Original Message-----
From:John Ewing [mailto:j.c.ewing@...]
Sent:Saturday, May 12, 2001 4:33 PM
To:Bolger Yahoogroup
Subject:[bolger] Calculating Buoyancy

This is probably something I should know but high school was a long time ago, so...
I want to calculate how much dock weight I can support by floating plastic drums, 1.75' dia. by 2.66' long/high. Presumably I'd multiply volume by some factor, but what is it? (Of course, I'll need to take into account the weight of the drums themselves.) One complication is that our inlet here is not fully fresh water and not fully salt water.
Thanks for any assistance anyone might be able to offer.
John

This is probably something I should know but high school was a long time ago, so...

I want to calculate how much dock weight I can support by floating plastic drums, 1.75' dia. by 2.66' long/high. Presumably I'd multiply volume by some factor, but what is it? (Of course, I'll need to take into account the weight of the drums themselves.) One complication is that our inlet here is not fully fresh water and not fully salt water.

Thanks for any assistance anyone might be able to offer.

John