posted July 18, 2007 09:43 PM               

The hull speed of this waterline length is 5.3 knots (give or take a few tenths, depending upon your equation.)

I also thought it would be useful to know the contour of the waterline, so I dropped the plumb bob from the waterline at 15 additional places, equally spaced, down the side of the hull and marked the locations on the garage floor. I snapped a chalk line down the centerline of the boat and measured the horizontal distance from centerline to the points dropped from the waterline. The data are shown in the graph below, which Dennis previously posted.

The line through the points on this graph represents the perimeter of the boat in the water (or half of the perimeter). The area under the curve represents the footprint of the boat in the water. The area of this footprint is 62.3 square feet (that’s the full hull area, not half).

If push the boat 0.1 inch deeper into the water, I force this footprint to submerge, and I displace 0.52 cubic feet of water which weighs 32.4 pounds. We now know the incremental buoyancy of the Sandpiper; for every 32.4 pounds you load aboard she will settle 0.1 inch. Actually, this number is only correct if your boat happens to be sitting at the same waterline as Duchess was at Lemington; that is, the number is only correct if your boat is loaded to the same weight as Duchess. But just the same, this starts to give us an idea of how buoyant the Sandpiper is. If Sid and I together weighed 324 pounds, we caused Duchess to settle 1.0 inch as soon as we stepped aboard.

posted July 18, 2007 09:44 PM               

I computed the area of the hull by integrating the above graph using Simpson's rule.
I got a wetted surface area of 70.5 sq. ft.

I wrapped a stiff string around the keel and transfered the length to a tape measure. the perimeter dimension is 49.0 inches. I confirmed that the maximum keel extension is 23.5 inches (94 turns on my boat) and computed the surface area of the keel to be 8.0 sq. ft.

Next, I calculated the surface area of my rudder as 4.2 sq. ft. (Duchess has a non-standard rudder, but the surface area is nearly the same as a standard rudder.)

Total wetted area of Duchess at the PITs: 82.7 sq. ft.
Hull 85.2%, Keel 9.7%, Rudder 5.1%

posted July 18, 2007 09:46 PM               

By integrating this curve I get the submerged volume.

More math and I got a submerged volume of 36.1 cubic feet, which corresponds to a weight of 2250 pounds. This is 1000 pounds above the published weight and is more than I was expecting, but I have gone over the measurements and the calculations and I am pretty certain that the numbers are correct, at least to the limit of experimental accuracy. I also believe the experimental accuracy is better than 10% (maybe much better).

Duchess was loaded with all the usual sailing paraphenalia, including motor, spare gas, battery, rigging, sails, anchors, anchor rode and chain, rudder, instruments, cook stove and provisions for several days, spare parts, etc. etc. Maybe this added up to 1000 pounds, or maybe the published weight is in error

posted July 18, 2007 09:47 PM               

The data indicate that the LCB occurs 93.4 inches behind the FP, which in this instance puts it about 3 inches behind the center of the keel screw. If I stand on the keel trunk 3 inches behind the center of the keel screw, Duchess should settle but shouldn’t tip fore or aft

If I sit in the middle of the cockpit, about 4 feet behind the longitudinal center of buoyancy (LCB), the stern of the boat will settle (more than 0.6 inches) and the bow will rise. I can level the boat again by getting Sid to sit 4 feet in front of the LCB, provided that he weighs the same as me.

Now it gets interesting. If I sit my 180 pounds as far forward as I can sit in the cockpit, I’m about 2 feet behind the LCB and the boat tips aft. I can level the boat by putting a 45 pound stone in the anchor locker, which is 8 feet forward of the LCB.. One quarter of my weight placed 4 times farther from the LCB and the boat is level. Is it worth the extra weight or will the extra weight slow the boat? That 45 pounds will settle the boat by 0.14 inches. The extra wetted surface area caused by the increased submersion is about 0.4 square feet. The keel has 20 times this much surface area yet raising and lowering the keel had negligible influence on speed, so I think that 0.4 square feet has no influence at all. Definitely, add the stone.

I am astonished. What made Denis put that stone in his anchor locker in the first place?

posted July 19, 2007 01:36 AM               

Notice how high she floats and how level she sits. Keeping the boat at this level means that while racing we can adjust the balance by crew weight only. We’re not hampered by rocks in the bow or large gas tanks in the stern. We achieve this by keeping the boat as free from excess weight as possible. The outboard and tank is the smallest we could get to keep weight out of the stern.

Down below we keep it fairly sparse; no cushions, floorboards or hatch covers as they all add up to quite a bit of extra weight.

I wouldn’t recommend going to this extreme if your cruising though. A larger motor could provide much safety through a squall. A few cushions would also be nice for sleeping. However you might take stock occasionally to see what you might take off your boat. It’s amazing how stuff accumulates over a season. Last year we removed approximately 100 lbs of gear we were not using. That not only made us lighter but it also gave us a bit more room to stretch out in.

D’Arcy, Shortwave

posted July 19, 2007 04:53 AM            

I have a copy of Arthur's raw and computed data. There is a lot of work and a lot of information here. It will take a very long time to analyze it all.

All of this data refers to the hull shape while the boat is at rest. As soon as the hull starts to move through the water, everything changes. For example, my transom is 4 - 6" above the water while the boat is tied to the dock. I can stand on the very back of the boat and the transom will still be clear of the water. But as soon as the hull starts to move, the waveform will come up and bury the transom. Plus, the bow will lift.

At station # 2, 23.2" back from FP, the half-width of Arthur's boat is 11.6". Therefore the half-angle of entry is 25.7^o. I think that racers look for an entry half-angle nearer to 15^o. A Sandpiper has a very blunt entry.

Is it better to bury the blunt bow or to drag the transom? Does a Sandpiper sail faster at some magical angle of heel because the entry angle for the heeled waterline is changed?

posted July 19, 2007 09:49 AM               

He shrugged the whole thing off as he figured there was so mutch turbulance behind the centreboard that the formulas really didn't work. He felt your best speed advantage was to play shifts well. I think Arthur's analysis is sort of confirming this in that there is minimal gain with the board up or down.

The one important factor does seem to be getting your weight right fore and aft. I would be cautious though in putting a rock up front as there are times when you want the weight back. We've had a few beautiful runs through steep waves where if we were not both sitting in the stern, our bow would be digging into the next wave. I wouldn't want to have a rock in the bow then.

posted July 19, 2007 10:29 AM               

quote:

---

Originally posted by Tailpiper:
snip
Don White, when you pack your 'Piper for the trip west, only load rudder, sails and rigging into the boat. Load the anchor, outboard & tank, camping gear and stuff into the truck. At some point in the drive we are sure to find an unattended weigh station. You already know the weight of your trailer. Let's settle this issue about the weight of our boats.[/B]

---

We'll pass right by a Provincial Dept of Highways weigh station within 20-25 miles of my house. (out by the airport on Hwy 102)

posted July 20, 2007 04:22 AM            

Again, through trial and error, the submerged cross-section of the Sandpiper was drawn. The diagram on the left was an earlier estimation of the Sandpiper. The diagram on the right is an estimation using data that Arthur had collected.

The cross-sectional area was calculated to be 601.2 sq.in.. This area x the length that Arthur measured (185.6") defines a prism of 111,582 cu.in.. But Arthur's 2238 lb 'Piper displaced 61,948 cu.in. of Lake Erie water. This ratio is known as the Prismatic Coefficient.

Therefore, a Sandpiper's Prismatic Coefficient is 0.56.

I found this on a website:

Opinion varies regarding the range of ideal prismatic coefficients. Most sources suggest that for average conditions, the optimum prismatic is between .54 and .56.

Light winds and calm water favor a lower range of about .53 to .55. Heavy winds and ocean sailing favor a higher range of about .55 to .58. The higher prismatic gives greater buoyancy in the ends, and displacement in the ends contributes favorably to stability.

Any errors in my assumptions for calculating the cross-sectional area may suggest that the true prismatic coefficient may actually be a little less than 0.56. However, the fact that Arthur's data generated a prismatic coefficient that seems reasonable, implies that his Sandpiper really does weigh 2238 lbs !

posted January 05, 2008 05:47 AM            

Here are the bows of some finalists in the America's Cup Regatta last summer. From left to right: Alinghi, Luna Rossa, Team New Zealand, BMW-Oracle.

posted February 02, 2008 11:45 AM               

This doesn't change the analysis much, but it means the stone in the anchor locker has more influence than expected.

It also means that sitting at the very front of the cockpit puts you nearly at the LCB.