Stability Again

The stable Farmer

In his book, My Old Boat Shop,WestonFarmer observed that he had discovered a rule of thumb target for comfort at sea and that was the pounds per square foot loading of the waterplane. He surmised that the optimum loading was 64 pounds per square foot of the waterplane, or to put it another way the underwater volume should be the area of the waterplane times 1 foot. He theorized that this would make the vessel the same weight as the sea surrounding it and thus the vessel would move with the sea not out of sync with it as would a lighter or heavier vessel. But what about the stability of such a vessel?

This idea intrigued me so I did some follow up. To dissect this theory we'll use a closed box 10' long by 4' wide and 2' deep. In the first iteration the box weighs 64 lbs per cubic foot or 128lbs per sqft of waterplane.

The green line is the waterline, the centre of gravity and the centre of buoyancy coincide. Logic tells you that this arrangement would not be very stable as it would rotate about the centres completely underwater. Add some sides,

Stability increases but comfort doesn't as the boat would move out of sync with the movement of the water. A wave passing through would start the boat moving upwards but not at the speed of the wave. As the wave passed and the trough arrived the boat would continue upwards due to inertia and then start to fall as the next wave arrived creating a very uncomfortable motion.

So what would happen if we loaded the boat as Mr. Farmer suggests?

Here it is,

Mr. Farmer's theory is that this loading would be very comfortable as the boat would move in sync with the water, Stability is much improved as the centre of bouyancy is now below the center of gravity and would move outboard as the boat heeled. Let's take a look at how that would work.

Here is our box boat at 40 degrees of heel,

However the immersed volume is too great so we must adjust the waterline (WL) and then determine the center of buoyancy, which is a piece of cake with a triangle.

You all remember your basic geometry of course. From that we can determine the metacentric height for that angle of heel and the righting arm.

But what did I discover? Here it is - If you look at the diagram above where we found the center of the triangle you'll notice that the line from the top left to the middle of the right side cuts though the deck line exactly in the centre, from that we can deduce that the center of buoyancy falls on a line joining the mid points of the two parallel sides. But where on that line?

Jim Michalak in a post here,  http://www.jimsboats.com/1dec15.htm shows you how to find the centre of effort of a four sided sail, that same method can be used with the above knowledge to find the center of buoyancy of a four sided immersed section but without the math. Here we go.

Here's our boat at 15 degrees of heel, the immersed volume is four sided.

First we join the two mid points,

Then divide the four sided figure into two triangles, find the centre of each and join the two centres.

Where the two lines joining centres and midpoints cross is the center of buoyancy.

But will it work for boats that don't have two parallel sides or a round bottom boats. Next time.

Stability One

Staying upright or at least afloat

Here's the real deal on stability in small boats, modern sail boat design http://www.wavetrain.net/boats-a-gear/471-modern-sailboat-design-quantifying-stability. Which is perfect for larger boats with decks and a mostly fixed centre of gravity. But what about small open boats such as the one we've just been working on. Well here is the stability curve for RMSQ&D assuming a fixed centre of gravity.

So degrees of heel are on the X axis and righting arm, in inches, on the y axis. The reason we've only gone to 45 degrees is because beyond that water is coming in over the gunwale and you're going down.

You can see that this boat has a pretty good level of stability up to 45 degrees which is great. However the fact is that you, the person in the boat, has a huge influence on the stability through your ability to move the centre of gravity by moving yourself about.

The question is how did I calculate the data for this curve? It is mind numbing work involving drawing and redrawing waterlines at various degrees of heel and then calculating the centre of buoyancy using stations and Simpson's rule. It is not for the faint of heart. Information on the process is here, www.mi.mun.ca/media/mi/boatrace/files/shipcalculations2.pdf , and here, http://koti.kapsi.fi/hvartial/stab/stab.htm.

The one thing to remember is when you draw in the new waterline at a different angle of heel the displacement must remain the same. With the boat dead level the displacement of station 5 is 109.118 cubic inches, or .7578 cu ft or 48 lbs However when you heel the boat 10 degrees without altering the waterline the displacement is 136.706 cu in, or .9493 cu ft. So we must reduce that displacement by .1915 cu ft, so the waterline must go down but by how much?

If we measure the new waterline it is 3.4 ft, 3.4 into .1915 is .056 ft or .675 inches so we draw in the new waterline .675 inches below the old water line and measure the difference in volume which works out to 28.642 cu in which brings our displaced volume down to 108.064 which is close enough.

We then divide the new waterline into 10 sections, making sure one station line passes through the centre of gravity, giving us the measures for applying Simpsons rule and calculate the transverse centre of bouyancy for station 5.

And then we do it all again for different angles of heel.

Westlawn recommends using the trapezoidal rule instead of Simpson's I don't think there is much difference in the end result.

The thing to remember is that beam is directly proportional to initial stability. But too much beam can create problems with dynamic stability.

We'll talk more about stability next time and about a discovery I have made whilst working on this.

Quick and not so dirty

Quick and Dirty

When I first approached this design I took the section lines of the skiff,

and simply rounded the chine corners. Then I adjusted the rounding so that the curves were parallel. I also narrowed the pram bow at the waterline to give a finer entry

I then went through the process of waterlines, buttocks and diagonals to get this,

 

Compare that to this, which is the hull we've developed over the past few weeks

 Here's a comparison of the sections side by side, the red being the lines developed from the skiff by rounding and the black being our skiff, and also superimposed.

On the face of it I can't see much difference and it was very much quicker. Our skiff is a little finer in the bows and the Q&D version has a bit more displacement, that's about it.

Now that that is done I will run some numbers on the two versions to see what difference, if any, there is.

Numbers

BY THE NUMBERS

I ran the numbers on these two versions, here they are,

Version	RMSQ&D	RMS
Displacement	304.89 lbs	266 lbs
Block Coefficient	0.18	0.16
Prismatic Coefficient	0.48	0.53
Area of the waterplane	25.55 sqft	27.78 sqft
Centre of flotation (aft or forward of Station 5)	.4381 ft aft	.4772 ft Aft
Lbs per inch immersion	152.29 lbs	137.49 lbs

So what does that mean exactly?

Well Q&D can carry more weight at the designed waterline by about 40 lbs and it takes more weight to sink it any further into the water.

Skene's sets out that a prismatic coefficient between .49 and .55 is best for sailing vessels, any more than .55 and you have a tub, any less than .49 the vessels is so fine it drags a huge quarter wave. So Q&D is on the fine side and RMS is within the parameters set out by Skene's. However the block coefficient tells us another story, by that coefficient RMS is the finer vessel.

Skene's also sets out that the center of flotation should be between 54 – 59% of the LWL aft of station 0 or in our case, between .48 ft aft of station 5 to 1 ft aft. So Q&D is a bit too far forward and RMS is just about right.

The LWL is 12ft for both these vessels and the beam at the WL is 5ft 4in which is a beam to length ratio of 2.5 which is a little beamy, anything from 3 to 5 is better, but the beamyness in such a small vessel adds to the initial stability.

Next time we'll look at stability.

On the Fiddle

The Fiddly Bits

Adjusting each of the lines so that they are fair takes a fair bit of time because they have to be fair in all three views. With pencil and paper this takes more hours than you can count as you try a new curve and erase the old one only to find that some other line is not fair because of the change you made.

This takes much less time on the computer. Each curve has nodes where they intersect with other lines,

The blue squares are the nodes. Each of these nodes can be moved to adjust the curve. I use this little gadget to determine how far to move the node.

The concentric circles are 1/8^th inch apart and at the centre is a reference point. I put the reference point on the curve I want to adjust,

and move the node an 1/8^th inch at a time until the curve looks right.

Then of course you have to transfer the new intersection to the other views and adjust those curves. After about a half hour of fiddling I got to this.

The lines are all fair to one another and the flow aft is smooth. In the next post I will show you another set of lines for this same boat which took only two hours to do from start to finish and I'll tell you how I did it.

Buttocks - not that kind!

Buttocks

Buttocks are also fairing lines and show the flow of water around the hull. Usually two buttock lines are used and are shown only on the profile as they will be straight lines in plan. They are drawn first on the sections, the blue lines,

and then the intersections transferred to the profile and then joined by curves.

You can see that we have the same hump at station 1 as we had in the diagonal. The flow aft appears good, perhaps we should have a third buttock line to better define that flow.

That third buttock shows a definite problem aft of station 5. This where the fiddly bits come in, adjusting all the lines so that they are fair to one another

Somewhat askew

Diagonals

Diagonals are fairing lines that help develop the shape of your boat so that it presents less of an obstacle to smooth movement through the water. Most designers will tell you that diagonals are shown on the plan view on the opposite side from the water lines. I prefer to simply use a different colour, in this case magenta. They will also tell you that diagonals are not shown on the profile. I prefer to show the diagonal as it helps me “see” the hull.

Diagonals usually go from some defined point on the centreline to the turn of the bilge, there may be more than one diagonal in a larger vessel in which case they are not numbered but identified by letters. In our case only one diagonal is needed.

The intersections are then transferred to the plan and profile using the method we have already discussed here.

The transferred intersections are then joined to form curves.

First in plan,

and then in profile.

These look very smooth and fair but if you look closely at the intersection with station1 in profile you can see a definite hump in profile and hollow in plan.

We'll put the buttocks in first before attempting any corrective action.