displacement calculations

[AHall]

Hello group.

I am trying to find the displacement of a boat for which I have a set of plans.
The boat is an Arno Day designed lobsterboat (design #36) 28' x10'.
Would anyone care to critique my procedure?

1. I have run a planimeter over the underwater portions of the stations and calculated each station's area. (I didn't forget to double each)
2. Figured out the distance between stations (not uniform in my case)
3. Volume for each space between stations is the average area of the adjacent stations multiplied by the distance between them.
4. Summed up the volumes calculated above and multiplied by the unit weight of water (64 #/ft^2)

I come up with a displacement of approximately 5800# which seems light for this boat.
I looked at the website for an Ellis 28 which is a similar hull form, and it's displacement is 8,000-10,000#

I understand that Naval Architects use Simpson's Rule for these types of calcs, but cannot seem to make it work with uneven station spacing.

Anyone have any suggestions?
Thanks,
Andy Hall

[Ed Burnett]

If you have an uneven station spacing Simpson's rules will be hard to make work.

In this case, I would draw a sectional area curve and run the planimeter around that - the area under the section area curve represents the volume of displacement. You can also cut out the shape made by the curve and find the balance point to locate the LCB.

Alternatively, having drawn the section area curve you can then pick off the section areas at a regular spacing and use simpson's rules.

Have fun!

[FG]

you're missing something as a block 28 X 10 X 1 foot displces almost 18,000 lbs.

estimating 1 foot depth and 60% of block filled by hull you have almost 11,000 lbs.

[Ed Burnett]

One other thing:

It would be worth while checking the calibration of your planimeter. Run it around a circle or square for which you can easily calculate the area and check the figure you get with the planimeter is correct.

[mmd]

Andy, I can't add anything to what Ed Burnett has posted - his procedure should give you fairly accurate numbers. As for the discrepancy between the Day deign and the Ellis 28, are they the same breadth at the LWL? Is draft the same? Are you including the skeg in your section areas? All of these can make a significant difference in figures. Also, some lobsterboats have quite flat buttocks and others have a considerable S-curve from the fore-quarter to the stern - the former are light and go fast, the latter are heavy and carry more stuff.

FG, your block coefficient for a lobsterboat is a bit high at 0.60; it is more likely to be around 0.50 to 0.55.

[ 12-23-2004, 04:18 PM: Message edited by: mmd ]

[FG]

I don't know lobster boats. Canoes and Kayaks. Just thought I'd suggest a simple method to see if the 5800 was in the ballpark. Is there a good place to look up ranges of block coefficients for common boat types?

[mmd]

Nope; not that I know of. That's one of the things a pro designer laboriously compiles for himself and guards like his daughter at a biker's convesntion. We get paid for what we know, not so much what we do.

[AHall]

Thanks all for the quick replies.

I was originally wondering if my method of finding the submerged area (assuming my sectional areas are correct)is correct.

Ed: can you suggest a website explaining how to plot a sectional area curve? I hope by mentioning a planimeter, you guys don't think I know what I'm doing.

MMD: I did include the skeg in the sectional areas, and the Day boat versus the Ellis: they are similar, with the Ellis slightly flatter aft, and a bit narrower.

I will have to check the planimeter. I am always amazed at this device with little wheel moving forward and backward and after running the test pattern thingy (in the planimeter kit) my measured area comes out right on. I'll bet I screwed up the scale factor.

FG: thanks for the reality check. Your 11,ooo # displacement looks a lot like double my calculated volume (I did double the half-section areas however)

My things are at work, so I will not be able to give concrete answers as to where my errors lie until tuesday.

Thanks again,
Andy

[John E Hardiman]

AHall,

One thing to point out is that the way you did the calc will always underestimate the displacement as it effectively draws a straight line between sections rather than a fair curve. Depending on the hull shape, this could be as much as 30-40%. There are other rules out there that can use irregular spacing, such as Tchebycheff's rules, but it is probabily better to work up a sectional area curve.

Also, check which waterline you used. You might have used the lightship line.

[TR]

Andy;

It's probably your scale correction, if the lines are at 1/2" scale the SCF is 4, if they are at 3/4" the SCF is 1.778.

An easy and quick check is to just estimate triangular area for each station area. Use a clear plastic drafting template to estimate the in/out areas and draw a line from centerline to waterline. Measure the lengths on the waterline and centerline, multiply, divide by two, and you have half area (or pretty close).

To lay out a curve of areas, just measure and mark each stations area, (it's easy to use the same scale as the drawing) along the station line right on your lines drawing, on one side of the centerline or waterline. Station 0, if the stem, will be nothing. (that will be up or down the station line from CL or LWL) The largest section will be about midships, and the transom will be slightly smaller. So you get a curve, starting at nothing, curving up to max at station 5-6, then tapering slightly and chopped off square at the transom. Run your planimiter round it, (perhaps in two sections) apply your SCF, and you have the volume.

FG,
Some ballpark Cb's (block coefficient) no keel!

22' Vee-bottom planing = .324
25' semi-planing = .337
25' Vee-bottom planing = .326
31' round-bottom displacement power = .34
24' very fast vee-bottom = .30
28' round bottom power = .418
38' vee-bottom planing = ..364
Sailing yachts = .35 - .45
Traditional hulls = .35
Fin keel = .45
These are not ideals in any way, only a general guide.

Tad

[ 12-24-2004, 12:42 AM: Message edited by: TR ]

[Alan Peck]

My plans have a curve of areas. It is labeled:

2 sides included. Scale 2"=1.0 (square symbol)

Can anyone tell me what scale factor to use to calcuate the displacement?

[Ed Burnett]

AHall,

Tad's explanation of the curve of areas should get you there. There was an article in Professional Boatbuilder a little while ago (written by Tad also but I can't find the issue right now) which you might find interesting. It's not so much about how to draw the SA curve but explains various factors of power boat design that are illustrated by it. The curve of areas is one of, if not the most descriptive thing on a lines plan.

I picked up my planimeter at a boat jumble a good few years ago. A more delightfully mysterious instrument is hard to imagine. I did go through the mathematical proof of how they work in college, but I seem to remember that was even more mysterious than the instrument itself. It is a bit of a shame that it stays in the drawer most of the time now. These days my hull fairing software runs all the calculations in about three seconds flat which is fabulous but a bit cold.

[TR]

Alan P,

The SCF for an area that is drawn to the same scale in both vertical and horizontal directions is;

The architectural scale inverted and squared, so -

1/4" scale = (4/1 * 4/1) = SCF of 16

1/2" scale = (2/1 * 2/1) = SCF of 4

2" scale = (.5 * .5) = SCF of .25

Things get a little tricky if vertical and horizontal scales are different, and this is often done to emphasize the curve. This is also the reason for including both sides, effectively doubling the vertical scale.

Ed's mention of planimeter mysteries reminded me of a Weston Farmer article on making a 50 cent knife-blade planar planimeter. It does work, and its workings are a bunch more obvious (for all you mathematicians!) than the mysterious polar type. See "From My Old Boat Shop" for details.

All the best, Tad

[Alan Peck]

TR: Thanks very much.

Happy Holidays to all

[AHall]

Head hanging low, AHall writes: checked my calculations today, and discovered an error in the scale factor I used with the planimeter (inverted it but didn't square it)

I come up with a displacement of 7760#. This is much more in line with similar hulls.

Thanks for all your help and have a great new year,
Andy Hall