



Monterey Bay California
Joined Feb 2004
14,166 Posts

Excellent!




Looks great.




Rudder size and the CLR and CE
re: rudder and jibs  In a multimasted ship, the rudder is more of a guide than a master. If the sail plan is balanced, ie. if the sail forces fore of the center of lateral resistance of the hull (CLR) are equal to the sail forces aft of the CLR, then a tiny rudder would be as effective as a large rudder. A baby can control a teettertodder if the 2 adults on the seats are the same weight. Conversely, if the forces are not balanced, then it would take a massive rudder to make up the difference  and the rudder would be hard over all the time, which will slow the ship. Slow ships have ineffective keels. They make lots of leeway on a beat, or any other point except dead down wind. So, for a good sailing vessel, you need to balance the forces.
The force of sails is dependent on the sail area and on the distance of the sail's "CLR" (actually called the sail's center of effort= CE) from the hull's CLR. The CLR is the fulcrum of the tettertodder, the CE's are the adults on the seats. This can all be calculated on paper, if you wish. Or, you can just put the boat in the water and see what happens. The seewhathappens method has the disadvantage that if the boat is unbalanced, its course will be set by the unbalance, and the capt. will be unable to sail the boat back to the launching area....been there, done that :) A symptom of unbalance is a ship that can tack, but not wear, or vice versa.  The paper method is pretty simple. The math is exactly analogous to finding the center of gravity of a real airplane: 1) Obtain or create a scale drawing of the ship's side view. 2) Mark the 1/4 chord point for each sail (the sail's CE), and for the hull+keel+rudder (the CLR). The 1/4 chord point for a rectangle (eg the hull) is just 1/4 of the length of the waterline aft of the bow. For a sail, it's trickier to find, but I just estimate the point where the sail's area is split 1/2 and 1/2, then split the difference between the 1/2 and the mast. 3) Measure the distance from the 1/4chord point of each sail to a specific point, eg. the end of the bowsprit. This is the lever arm for each sail. If you have a separate fin keel (as I always do), then treat the keel as if it were an underwater sail, ie. measure it's 1/4 chord point distance from the bowsprit. Ditto the rudder if it's big. 4) Multiply each sail's area by it's lever arm. Add up these sail "moments". Do the same for the underwater bodies to get the underwater moment. 5) Divide the total sail moment by the total sail area. The result is the summation CE for all the sails. That is, it's the distance aft of the bowsprit (or what ever you chose as the datum) where the sails all act together. It's the "center of gravity" for the sails (or center of lift to be precise). Ditto for the underwater bodies to find the summation CLR.  If the summation CE is exactly equal to the summation CLR (say, they are both 20 inches aft of the bow), then the ship is perfectly balanced. More likely, there will be a difference. If the difference is "small", then the rudder will work to nudge the ship in the direction you want. You'll be able to tack and wear once you've had some experience sailing her. If the difference is "big" then you will have to do something to move the CLR and the CE closer together. Big and small are relative to the ship; in other words, it takes some experience to understand what is too big. For my 2 and 3 foot hull ships, an inch difference is probably ok, but more than that, and I know I'm going to have to change something. Easy changes: move the fin keel, if the ship has one, fore or aft so as to move the CLR to match the CE. Or, add or subtract jibs to move the CE. Or change the size of the rudder; this only works if you make the rudder bigger, to move the CLR aft, in my experience. If you put the calculations all on a spreadsheet, you can tell what the ship will do when you reduce sail on a windy day. Changing sails obviously changes the summation CE. If you take off a jib, you will have to reduce sail on the mizzen, for example. Note: You may not be able to wear even a balanced schooner, though, if the standing rigging prevents the booms from swinging out perpendicular to the hull on a run. This is the situation for my topsail schooner Aldebaran  she will only wear if she has her square topsails set....and the skipper is lucky with wind and wave :).  This calculation is for when the ship has a small heel angle. If the ship gets hit by a gust and heels over, then she will turn into the wind due to the asymetrical thrust of the bow wave. Your calculations won't be much use then, nor will you have much control over her course. The solution is to do as the real ships did, namely, reduce sail in a blow. Gusts are one time I find a big rudder helpful: it may allow me to control the ship's course enough to get her back to land so I can reduce sail area. And in a calm, a big rudder may allow me to scull the ship back to land; a tugboat is a more elegant solution :). Incidently, a long, shallow rudder works better sculling than a narrow, deep rudder. The former more closely approximates a whaleboat's sweep. It's all about moments :) 



Brooks:
Thank you very much for the explanation, once I have read through it 3 or 4 times maybe 5 time and comprehend it, I'll give it a try, between spring and now I might have the time to get it right, rater than the splash and hope method, witch I found not to be so much fun with my 36/600 witch is now a 36/900. 



Another way to change the balance is to change the ballast location. Real ships did this by shifting cargo. This is why ships have draft marks at the bow and stern; the captain can more easily see if his ship is ballasted to sail level, or is she is down by the stern, etc. In one of the Hornblower books, he has the crew shift the cannons to make his new vessel tack more easily. More weight aft makes the ship easier to wear. More weight forward makes the ship easier to tack.
Besides making the sailboat stiffer (by putting the ballast down lower), a fin keel makes it easy to change the CLR. That's one of the reasons I always put a fin keel on my sailboats. Move the fin keel aft to make it easier to wear, or forward to make it easier to tack. My fins are bolted to an aluminum L attached to the keel of the hull. It's easy to drill a new hole in the aluminum if I find I need to move the fin. I drill several holes in the aluminum L before taking the ship out for it's maiden voyage. That makes it easier to adjust the fin pondside. If you don't like calculations, then just drill lots of holes in your aluminum L, and use the sailitandsee method in a small pond with full access to the shoreline. Once you find out where the fin keel needs to be, then make a new L with only one hole (or bolt the fin directly to the ship's keel). The calculations tell me the likely location of the fin. Actual sailing tells me the true location. The reason the true is not always the calculated is that sails are not equally efficient. The masts farther aft set sails which are working in "dirty air", i.e. the turbulent air spilling off sails closer to the bow. The CE/CLR calculation does not take sail efficiency into account (I don't know how to calculate that). The effect is that the fin keel will likely need to be set a little bit farther forward than the calculation suggests. One interesting effect of dirty air is that for maximum speed, you will need to trimin the sails aft more than the sails forward. On your 3 master, the Mizzen sail will likely work better if it's trimmedin more than the Foresail, for example. This is because the sails (acting like wings) create downwash. This makes the air change direction, so sails aft don't see the same wind direction as sails forward. This is very apparent on my Aldebaran: the square sails on the mainmast must be bracedin more tightly than the squares on the foremast. Or to put it another way, if the squares are all trimmed the same (with parallel yards), the squares on the mainmast will luff before the sails on the foremast. If your 3 masts are all trimmed the same, say off one servo, then the mizzen will luff before the fore. It will be harder to work to windward with a single servo setup: as you point up, the mizzen will luff, and the ship will fall off. You'll need "lee helm" to keep her pointing up. Lee helm reduces the efficiency of the hull lift (which is the true reason ships can sail upwind: the hull lift counters the natural tendency of everything to blow downwind). Conversely, when a ship carries a little bit of "weather helm" (you are continually trying to keep the ship from pointing up too much), the rudder acts like a wing flap; flaps increase the coefficient of lift for a wing, thus your rudder/flap makes hull lift stronger than it would be if the rudder was centered. If you are copying a historic ship and have reasonable plans, then most of the balancing of sails/masts/hull has already been worked out for you. The only questions are where to attach the fin keel, and how big to make the rudder. While a tiny rudder (historic size) may work, and certainly looks best, a model usually is easier to control if you have a bigger rudder, I find. Making the model rudder 45 times as large as the historic rudder seems to work for me (I prefer ships that are maneuverable). If I make the extension out of clear plastic, the oversize is not visible when she's sailing. If shiponthemantle appearance is important to you, then making the plastic easily removable is an option. My fin keels are always removable to make transport (and home storage of the hull) easier. 



Worksheet for calculation of CE & CLR
Here's a Excel worksheet to make the CLR/CE calculations easier. I've set it up for 3 jibs and 3 masts. You only need type in the sail dimmensions and their CE's, along with the hull parts and their CLR's. The jibs are treated as triangles, so you need the luff length, and the perpendicular from clew to the luff. The quadralateral sails are treated as rectangles, so just estimate/measure their average base and heights. All underwater parts are treated as rectangles.
Worksheet experts will know how to modify it for other vessels. If you run into trouble, email me and I'll try to help. There are some instructions on the worksheet, but feel free to ask questions.  For fun, I ran the worksheet for the 2 masted schooner I drew for the preceding post. I just put in zeros for the missing jib and mizzen. I measured the model values, in cm, off the screen using the full size drawing. The results were that the fin keel would have to be moved aft from where I'd drawn it at the center of the hull: To balance the boat, the fin keel's CLR needs to be just fore of the mainsail's CE. This explains why most real 2 masted schooner hulls had "drag". That is, most of the underwater area of the hull was aft, leading to a hull that had lots of draft at the stern, but not much at the bow. The nautical architect needed to move the real CLR aft to balance the large mainsail. He did this by "cutting away" hull in the bow area, giving the underwater portion of the hull a triangular look when viewed from the side. I might mention that when I sail Aldebaran as a schooner (no square topsails set), I need to move her fin keel aft from the topsail schooner position...showing that models (and spreadsheets) mimic real life :) Figuring this out by hand would have tried my patience. But with a spreadsheet, I could play whatif and move the finkeel aft, mathematically, until the summation CE equalled the summation CLR.  For the imaginary 3masted schooner (on the spreadsheet as an example), the fin keel CE would need to be 3.5" inches fore of the center of the hull. For terns (3masted schooners), drag is apparently not needed; the sails balance themselves around the rectangular hull form typical of terns.  I'd be happy to type in the values for your schooner, if you would like. I'm curious what a scale model tern will need, if anything, to balance. 



Two model hull options
Here's what the 2masted schooner would look like with a balanced CE/CLR setup. The drawings are to scale, with the underwater bodies based on the worksheet.
1. Moving the fin keel aft to balance CE and CLR. 2. Making a Dragged Keel hull, with balanced CE and CLR. This will look familiar to anyone who's studied 2masted schooner hulls, I think. No fin keel, so she looks more authentic. But without the deep fin keel, it would take more ballast to achieve the same heel resistance. The dragged keel was treated as a delta wing for figuring out the center of lift. Hopefully, I did it correctly. Aerodynamic calculator: http://adamone.rchomepage.com/cg_calc.htm 



Well, being too curious to wait for dimensions, I measured sails, hull, and rest of data needed for the worksheet off your photo 21962. The photo is not quite square to the hull, so there will be errors in measurement. Hopefully they are not too big, but .....
Anyway, looks like your tern schooner will need a fin keel to balance the rig. I edited your photo to show the location and size of one that I'd use if she were in my fleet. Without the fin keel, Wawona will have a pretty big weather helm, if my calculations are correct. This is similar to what I experienced with my 2masted schooner model Aldebaran. You'll notice, though, that 3masted Wawona's fin keel is located closer to the center of her hull than the fin keel on the 2masted schooner example of previous post. I was sort of surprized that she'd need one. As I said earlier, I thought terns were probably more balanced than 2masted schooners, based on the hull shapes used on real schooners. So, either there is a scale effect going on (quite possible since sails scale as a square but hulls scale as a cube), or my method is wrong. I've had good results with the method on my other multimasted ships. It's be nice to go back in time and talk to a tern skipper; maybe the fact that she has 3 jibs, complicating the rig, is a sign that real terns had some weather helm problems. Hope this helps. It was fun for me, since I like math and worksheets :) Remember, you need to actually test a model in the water, math alone is not the defining test. 



One nice thing about fin keels: They make the ship run aground possibly before it pokes it's bowsprit/jibboom into the shore. :)
Incidentally, if the fin keel was the same width, but was twice as long(deep), it would be positioned farther forward. My photo shows a square fin keel. My Aldebaran's fin keel is actually rectangular. If you are having fore/aft trim problems, and need to move your ballast (on the end of the fin keel) farther forward, making the fin deeper will allow you to do this and maintain the same balanced rig. And, of course, if the ballast lever arm is doubled, you can cut the ballast in half, and still have the same righting force. Lack of spare buoyancy to support my original ballast was the reason I went to the very deep fin keel for Aldebaran. 



Thank you Tim:
Brooks: May be this will help find the cg I'm looking for, the over all length of Wawona is 72"over all hight 37 3/4" over all 13 5/8" wide, when loaded to water line, she has very little free board to catch the wind. A pic at water line. I can't really install a drop keel, as it is to get to and from the lake I have to roll her on her side to get her in my van, and then roll her back on to her stand for travel. So I need to get the CE/CLR with the ballast. By the way you do very nice work, on your boats and on your calculations. 



All of my keels are separate from the hull. I attach them at pondside.
The easiest way for me is to lay a towel on a picnic table, then lay the hull on the table edge, spars extending out into space. I can then bolt/screw the keel to the aluminum L on the bottom of the hull. The table supports the finkeel&ballast while I am attaching it to the L. An additional reason I lay mine on the table edge is so I can let the square sail yards extend into the open space and not hit the table top. I've also laid the boat on it's side in the grass. If I move the yards to a beat (brace them in), then I can safely let them rest in the grass. It also helps to find a slope; if the hull is upslope, then the yards have a little bit more room since the hull does not have to lie exactly flat to attach a keel. At any rate, if you later decide that your interior ballast is not working out, I think you would find that attaching external ballast and a fin keel not hard. By "not working out", I"m thinking: excessive heel in a light breeze, excessive leeway on a beat. These are the problems I ran into prior to developing my fin keel system. They are a consequence of scale effects, which is why model boats need, in my experience, nonscale features to enable them to operate like the real ships. Internal ballast problem  I rue the day I glued my internal ballast into my steam launch  I later had to replace the boiler, and the replacement was much heavier. So the launch now rides below it's painted waterline, sigh. The ballast is epoxied below the epoxy installed floorboards; it'd take more skill than I posses to remove it from the ABS hull. You might consider making your internal ballast removable. That way, if you decided to later add features to your schooner, you can avoid the "ride below waterline" problem I had. 
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