Density of Salt water

[Willallison]

The weight of 1 cu.ft of salt water is 64 pounds.
Can anyone tell me the weight of 1 cu. metre of salt water - in kg?

I actually got this link from another post on this forum: http://onlineconversion.com/

Let's see:

1 cu meter = 35.314667 cu. ft.
(or 1 meter = 3.28084 ft)
1 kg = 2.20459 lbs

64 lbs x 35.314667 = 2260 lbs/cu.meter.
2260 lbs/cu meter / 2.20459 = 1025 kg / cu. meter

[duluthboats]

:D beat me to it. I have the same number.
Gary

[Willallison]

Ok, thanks - that's what I calculate.
Here's another one for you.
I use a metric planimeter. How do I convert the reading taken to square metres - how is the scale factor determined?
With an imperial unit, it is the inverse of the scales, squared. (so for 3/4" = 1', the scale factor = 4x4 / 3x3 = 1.778)
I can't see how to do this on my metric unit.
For instance, if I am using a scale of 1:25 and get a reading for a given shape of 100, how many square metres is that?

[duluthboats]

:confused: Will,
I'm not sure what your looking for, could you elaborate?
Gary

beat me to it. I have the same number.Well thanks for the link to the online conversion web site! I just realized it was from your post that I bookmarked it :)

[Willallison]

Gary,
When you use a planimeter, you run it around the edge of a shape in order to determine the shape's area. The resulting measurement must then be multiplied by a number - the scale factor - in order to take account of the drawing's scale.
The design course that I'm doing is based in the US, so almost everything is explained using the imperial system as its basis. (such as the scale factor I used as an example in my other post - 3/4" + 1')
However, my planimeter is a metric one, and the drawings that I'm doing are also metric.
I don't know how to obtain the scale factor for the scales I'm usiong - in this instance 1:25 and 1:15.
I could draw a square of a known area to scale, and then work out the scale factor backwards, but I'd like to know how to do it properly

[duluthboats]

Yet another reason for one standard. Sorry Will, I can't help you.
Gary

[james_r]

Will:

First let me state that I've never used a planimeter in my life so my solution may be out to lunch.

Using your example: 3/4"=1' is the same as 1"=1.333' (simply divide 1 by .75). Note that 1.333 squared gives you your result of 1.778. IOW it doesn't matter which order you perform the calculations. With a scale of 1:25 you would simply square the 25 to get a figure of 625. Assuming your planimeter measures in square centimeters you would have to divide the resulting figure by 10000 to get square meters. Alternatively, you could use a scale of 1cm=0.25m (same as 1:25). 0.25 squared is 0.0625 which when multiplied by your reading would give you a result in square metres.

Hope this helps.

[Willallison]

Thanks James.
I mucked about for a while last night & came up with a similar solution - though I think the scale factor I ended up with was different to yours by a factor of 10 - 0.00625 - so I think the planimeter must measure square mm, not cm. When I checked it against a square of known area I came up trumps.
Thanks for the input - it will make easier to calculate the scale factor for any other scales that I may use

[Nomad]

WOW!

[trouty]

Like your using one of the Planix planimeters Phil?...

Last time I used one was in forestry - we used to use it to take area's off scale maps for working out all manner of stuff - stocking densities for pine plantations - e.g. we could work out how many seedlings we'd need, or for aerial fertilising a plantation we could again work out superhosphate requirements - even for weed spraying in plantation establishment - again - the scale map and planix was the solution for chemical requirements. You've already got the answers you needed - fantastic instrument aren't they!

It occurs to me Will, that your asking about weight of water for bouyancy determination, and a planix for calculation of complex shapes areas....so are you trying to come up with some type of ullage calculations for a hull volume?

I'd have thought a computer could do that for you?...

These were the ullage calcs for mine... :D

Tank Sounding Ullage % Full Capacity Capacity LCG TCG VCG FSM
Name m m m^3 tonne m m m tonne.m
Tank 1 0.197 0.000 100.0 0.345 0.354 1.181 0.000 0.106 0.000
0.190 0.007 99.6 0.344 0.353 1.178 0.000 0.106 0.000
0.181 0.016 98.0 0.339 0.347 1.167 0.000 0.105 0.211
0.180 0.017 97.5 0.337 0.345 1.165 0.000 0.104 0.211
0.170 0.027 93.9 0.324 0.333 1.147 0.000 0.102 0.289
0.160 0.037 88.8 0.307 0.314 1.129 0.000 0.098 0.441
0.150 0.047 81.9 0.283 0.290 1.120 0.000 0.093 0.497
0.140 0.057 74.2 0.256 0.263 1.119 0.000 0.088 0.518
0.130 0.067 66.4 0.230 0.235 1.118 0.000 0.083 0.513
0.120 0.077 58.7 0.203 0.208 1.117 0.000 0.077 0.508
0.110 0.087 51.0 0.176 0.181 1.115 0.000 0.071 0.503
0.100 0.097 43.4 0.150 0.154 1.113 0.000 0.065 0.496
0.090 0.107 35.8 0.124 0.127 1.111 0.000 0.059 0.456
0.080 0.117 28.7 0.099 0.102 1.112 0.000 0.052 0.345
0.070 0.127 22.3 0.077 0.079 1.113 0.000 0.046 0.243
0.060 0.137 16.6 0.057 0.059 1.113 0.000 0.039 0.163
0.050 0.147 11.8 0.041 0.042 1.114 0.000 0.033 0.100
0.040 0.157 7.7 0.027 0.027 1.115 0.000 0.026 0.055
0.030 0.167 4.4 0.015 0.016 1.116 0.000 0.020 0.025
0.020 0.177 2.0 0.007 0.007 1.116 0.000 0.013 0.008
0.014 0.183 1.0 0.003 0.004 1.116 0.000 0.009 0.003
0.010 0.187 0.5 0.002 0.002 1.116 0.000 0.007 0.001
Tank 2 0.350 0.000 100.0 0.528 0.541 2.836 0.000 0.191 0.000
0.340 0.010 96.7 0.510 0.523 2.809 0.000 0.189 0.000
0.320 0.030 95.1 0.502 0.514 2.800 0.000 0.187 0.233
0.319 0.031 95.0 0.501 0.514 2.800 0.000 0.187 0.233
0.300 0.050 89.4 0.471 0.483 2.787 0.000 0.179 0.446
0.280 0.070 81.4 0.430 0.440 2.782 0.000 0.169 0.437
0.260 0.090 73.6 0.388 0.398 2.777 0.000 0.158 0.423
0.240 0.110 65.8 0.347 0.356 2.771 0.000 0.147 0.406
0.220 0.130 58.2 0.307 0.315 2.764 0.000 0.136 0.390
0.200 0.150 50.6 0.267 0.274 2.756 0.000 0.125 0.375
0.180 0.170 43.1 0.228 0.233 2.749 0.000 0.114 0.359
0.160 0.190 35.8 0.189 0.194 2.740 0.000 0.102 0.333
0.140 0.210 28.8 0.152 0.155 2.732 0.000 0.091 0.311
0.120 0.230 22.0 0.116 0.119 2.723 0.000 0.078 0.272
0.100 0.250 15.7 0.083 0.085 2.718 0.000 0.066 0.202
0.080 0.270 10.3 0.054 0.056 2.712 0.000 0.053 0.117
0.060 0.290 5.9 0.031 0.032 2.703 0.000 0.040 0.057
0.040 0.310 2.7 0.014 0.015 2.686 0.000 0.027 0.020
0.024 0.326 1.0 0.005 0.005 2.664 0.000 0.016 0.005
0.020 0.330 0.7 0.004 0.004 2.655 0.000 0.013 0.003

Will, If I told you how I did that - I'd have to shoot you! ;)

Cheers!:D

[Stephen Ditmore]

Simpler answer: 1 meter^3 of fresh water = 1 metric tonne
For salt water divide by 0.975.
Therefore 1 meter^3 of salt water = 1.0256 metric tonnes, give or take depending on temperature & salinity.

[Mike D]

Hello all

Integrators are excellent little machines to take the drudgery out of some boring calculations. I quickly reviewed about 20 sites out of a couple of thousand that I found but the theory side was overwhelming and the “how to” in practice was underwhelming so the following is my own experience.

I’m going to refer to the tracing arm, the fixed point, the disk (the revolving wheel) and the scale so I guess everyone is clear about the terms.

As you trace the closed curve the disk rotates and the scale changes and there are points where there is very little movement of the disk and others where it is big. So the start and stop point should be where there is little movement thus a small error in start/stop will register zero shift on the scale.

The convention is to track the curve clockwise, it is not mandatory so if you are more comfortable going the other way just do it. The readings are theoretically negative but so what!

More important is that you place the fixed point in a position so that you are not forcing the disk when either pushing or pulling the tracing arm. This becomes much more important with the age and the condition of the planimeter. They can seize up and repairs are expensive – does anyone repair them any more? So treat them gently and don’t leave them exposed in a dusty atmosphere and always put them back in a clean storage case.

The amount that the scale changes signifies the area but this depends on the size of the disk and the distance of the point from the disk. So a typical US or British machine would have answers in square inches while a European model would have square centimetres. The relationship of Pi*disk dia*distance is a stated area which is usually Engraved on the arm
Written on a card in the case or
Written in the book of instructions.If it is missing don’t worry, in a way it is better that you don’t have it.

The disks can wear over time, using them on rough tracing paper was a no-no, coarse blueprints were almost as bad so it will always give a false reading.

Then you are also depending on the accuracy of the drawing that you are using. Before CAD systems came into use the copy or blueprint was exactly the same as the original drawing – at least in the machine during the process. But the machine was hot and did the paper stretch the same as the master. Then the copy had to pass the "fixing" step and what happened there?

Along came the photo-copying machine that distorted copies in a complicated manner and caused more errors.

With a CAD system what do you have? Now, the tendency is to scale the drawing in the computer to some convenient, common scale but to print it so the drawing fills a sheet. So what does it mean when a set of body sections are in a computer but printed on say Legal size or Letter or A4, just what scale is it? (By the way, every drawing you produce should show the scale like a map so that when someone gets a shrunken version, it is at least possible to see what goes on without the frustration of measuring and calculating!)

The point is that you don’t know and you have to work around it. If you get a drawing made by hand it is almost certain that the draftsman/designer/nav arch made errors but anyone scaling it would find the errors simply by laying a scale across and then up a Body Section. It was simple to correct the error, or at least minimise it, by judiciously sliding the scale rule. But, of course, this is impossible with a planimeter.

The first thing is to find if there are errors on the drawing due to any of the foregoing points. This is done because you have to find the conversion factor that will be used to change the planimeter scale reading into the area. If it is a CAD drawing then only checking a few grid dimensions is necessary to see if there was a heat distortion.

You’ll be able to quickly find out if the error is general and over the whole drawing or local and only in some specific area. Now you have to find the factor.

Don’t draw a rectangle or anything else because you may have made an error yourself and suppose that you were exact is the drawing or copy exact also? All of these precautions are essential on small scales because a pencil line can be half an inch thick or more whereas it shrinks to 0.0something on very large-scale drawings.

If it is a general distortion take the largest rectangle that is drawn on the copy and go around the shape then convert the reading to the known area. If there is only a local distortion then eyeball the sections affected and judge the corner of a rectangle from there to the centreline or side (the greater distance) and to the top or the bottom (again the greater distance) and find the factor. If there is a bad distortion you may be required to break the sections into upper and lower or inboard and outboard. You may also have to have different factors for port and starboard.

You never know when the planimeter will act up so you must trace the curve at least three times. If it acts up once and you trace once you have an error but you don’t know that. If you trace twice you know you have an error but which one or both? You trace again and again until out of all your readings you have three are the same (some hopes) or within 1. If you have a large scale drawing you can accept a greater difference so just what error will you accept? Before computers, it was generally reckoned that half a percent on final data so half that on the calcs was normal but that was on ships and scales were usually ¼” = 1”. It’s your boat, call the shots.

When you trace the curve try to do it continuously, get comfortable, and well supported before you draw the arm around. If you stop and move around a bit the chances are you’ll nudge the arm. If you do you can be sure that Murphy’s Law kicks in because you stopped at a position where a small trace point shift makes a big scale shift.

When you read the scale try to run your eyes over the Vernier without studying it and you’ll get the hang of somehow just noticing where the lines match. This allows you to see better otherwise you are trying to concentrate at extreme short range maybe even using a magnifying glass then at two longer ranges and it is tiring. Or study the Vernier and take your time.

Scales – a lot of confusion around eh – meters, rulers, proportions. Scales in metric were invariably 1 to something. I have a few metric scale rules and a small set of them on a swivel that were given to me by a salesman many years ago – 1:10, 1:15, 1:20, 1:25, 1:30, 1:331/3, 1:40, 1:50, 1:75 and 1:125. Made by the German company Aristo, beautiful things and they even fold into a leather case. Notice there’s no duplication and there are 5 plastic rules each with one scale on the face, the backs are blank.

The UK and the US rules use something = 1’, the metric versions are the true scales in the other sense. The inch rules are on a scale of 1:12 or 1:48 for 1” = 1’ and ¼” = 1’, for example. So when you convert the planimeter constants you could convert using (48/12)^2 or (1/ 1/4)^2. The metric versions are just (50/10)^2 or whatever the drawing scales are. But as you are finding out the factor yourself you won't be using this.

Avoid the scale rules that have two scales on one edge, some metric rules have 1:10 and 1:100 together, dumb. The same divisions just with different numbers and one is 10 times the other. The rules should have one scale on each edge and they should be fully divided for the full length. Fully divided means that all the divisions are marked, like a tailor’s measuring tape or a normal carpenter’s rule or tape. Some rules have the major divisions only and the minor marks are at one end only, like a map.

The fully divided scales are always more expensive and they only have half the number of scales so they are more than double the cost per scale. But the enormous advantage is when using a lines plan and measuring say half breadths. With the fully divided version set zero to the centreline and read off the breadths just reading along the scale. On the other side turn the scale upside down or turn the paper around. With the other type you are continuously shuffling the rule.

If anyone asks for an explanation of calculating the area rather than using the planimeter I’ll be happy to explain it. Don’t forget that a planimeter gives only the area and you will need the centre of area (the “centre of gravity” of the shape) for stability and other calculations. There is another instrument that is big brother to a planimeter and it is called an integrator, the simple one gives the area and its first moment the better version gives also the second moment.

None in eBay compared to the selection of planimeters and I only checked one manufacturer – a planimeter about $500, simple integrator about $1,300 and the good one about $1,500. There's even an antique for $1,950.

There are tricks in manual calculations that aren’t in any text-books nor on any site I have found. If others wish to learn them I’d be pleased to help.

Michael

[Mike D]

Hello again

Water density
Ship designers use different densities than boat designers. In the ft-pound systems ships in salt water would use 35 cu. ft./long ton of 2,240# and 35.96 in fresh water. They were standard values and I don't remember anyone using #/cu.ft. for displacements etc. These rates work out to 64.0#/cu.ft. and 62.29#/cu.ft.

But in ship-model testing tanks they were much more particular and took into account temperature and salinity etc so the standards were
Fresh Water (salinity = 0%)
49 deg F, density 62.408 #/ft^3
59 deg F, density 62.366 #/ft^3 this being the standard
69 deg F, density 62.305 #/ft^3
Salt Water (salinity = 3.5%)
49 deg F, density 64.110 #/ft^3
59 deg F, density 64.042 #/ft^3 this being the standard
69 deg F, density 63.959 #/ft^3

Then the world, except a few irrationalists, went metric and the values became
Fresh Water (salinity = 0%)
10 deg C, density 999.59 kg/m^3
15 deg C, density 999.00 kg/m^3 the standard
20 deg C, density 998.12 kg/m^3
Salt Water (salinity = 3.5%)
10 deg C, density 1027.64 kg/m^3
15 deg C, density 1025.87 kg/m^3 the standard
20 deg C, density 1024.70 kg/m^3

There are standard tables from 32 to 86 F and 0 to 30 C in increments of one degree, I just gave one value on each side of the standard.

I must add that although these are internationally agreed the Class Societies and other Regulatory Bodies use a very simple standard of FW is 1 and SW 1.025 specific gravity and these are used "in the trade". Ships operating in specific areas only may have something slightly different but it is not common practice.

Even so, if I had a boat on Lake Champlain in New England I would use a different value to the guy in Louisiana. The advantage of doing many of the standard calculations on computer is that you can change the water density easily. It won't make too much difference but if you need to produce documentation of some sort on drafts etc it is easily accomplished. There are other, simpler ways but I believe that most have signed on to various yacht design courses so the instructor will explain all that.

So let us have a look at trouty's "ullage table" which is not an ullage table but presumably a statement of volume and weight of something undefined on a scale of metres of something that is not defined. But as there are two tables together indicated as Tank 1 and Tank 2 perhaps they are ullage tables after all. :)

It is standard practice to state on capacity tables the volume and the corresponding weight in #, kg, t, LT or whatever. Dividing the weight by the volume and we see it is salt water.

An ullage table is something like a gas gauge on a car telling you the contents of the tank. The tank on the boat is assumed to be of an odd shape and that there is a pipe inside to guide the "ullage tape" around bends etc. So when you check the oil in your car you are checking the ullage because you see the space from the top of the filling pipe down. The sounding is from the bottom up to the oil level or water or whatever is in the tank.

The sounding measurement plus the ullage is constant, if it isn't there is a mistake. The values can be declared at any interval the designer or the owner wishes, trouty took 10mm and the funny values near the top and the bottom indicate the 98% and the 1% full. 98% is standard for oil tanks which are never 100% full on ships and the 1% is probably the minimum and it is common to have warning devices top and bottom. So while the tanks are carrying salt water it is unusual to have the precision of only 10mm reading as ballast tanks should not be slack because of the free-surface effect on stability.

Eyeball the weights or volumes on Tank 1 and the tank seems to swell towards mid-depth and then shrink again, unusual but not impossible.

Computers will indeed do that for you, as trouty says, but it is not necessary to buy a program to do it. If you have a computer I guess there was a spreadsheet bundled with it. Whatever spreadsheet you have will do the calculations necessary and you'll be able to exercise more control than the nav arch program.

Last comment about trouty's tables. It is unusual for a table of ullages to begin with zero ullage. When the tank is full there is some sort of vent pipe that is above the top of the tank and it could have liquid in it. So a zero ullage reading means that the measuring point coincides with the top of the tank and the plug could be under pressure. I once knew a guy whose face was very badly disfigured because the ullage or the sounding cap was in the wrong place, he unscrew it and it hit him in the face due to the head of almost 15 feet. So the sounding point should be well above the top of the tank making it higher than the vent pipe.

Just pulling your leg trouty :D good to see somebody generating "technical stuff" on a design forum.

Michael

[Willallison]

So the start and stop point should be where there is little movement thus a small error in start/stop will register zero shift on the scale.


Thanks for that very important tip MD. It probably goes a long way towards explaining why 9 times out of 10 I get excellent triplicate results and then out of the blue some of them are completely different......


I agree with your remarks regarding a zero ullage. For many years I have been involved with surveying ship tanks and am yet to come across one without some sort of 'riser' for the tape entrance.

[caroline]

so what IS the density fo salt water

[Willallison]

It is generally taken as:
64 pounds per cubic foot, or
1026 kilograms per cubic metre
....depending on where you are.... ;)

[yipster]

:idea: than how much faster do we plan on salt water and will we go slower in displacement mode than in sweet? eh...:confused: