The 7-10-7 Rule: Perfect Spars Without Math

Welcome to Nomad Boatbuilding. My name is Mark Gruden, and I'm a boatbuilder on Vancouver Island, and today I want to share with you an old boatbuilder's trick called the 7-10-7 rule. Right now some people think that getting into wooden boatbuilding requires a lot of complicated math, and that can be true if you're designing boats. The corrected length of the hull, sea rule delta 0.6.3, plus twice the midship girth difference, sea rule delta 0.6.4, divided by 2.37, shall be equal to, or less than, 2.4 meters. Building them is quite a different story. In practice, wooden boatbuilding requires far more geometry than mathematics. Okay, so today I want to share a simple geometric trick that solves what might otherwise feel like a complicated, or at least tedious, math problem. The math isn't difficult, it just has to be repeated over and over, starting with different values. Geometry lets us bypass all of that. So when rounding something like a spar by hand, rather than on a lathe, the first step is all the same. Turning a square or rectangular cross-section into an octagon, and that's where the 7-10-7 rule comes in. The 7-10-7 rule is a straightforward geometric method for dividing each side of a square into three sections of 7 units, 10 units, and 7 units. That's 24 in all. Once you mark those divisions and remove the corners, you're left with an octagon. All right, now don't reach for a calculator, because the numerical math doesn't quite line up perfectly with this geometry. But the geometry is more than accurate enough for our work, and that's what matters. Now, using an imperial ruler makes this fast and adaptable. You can apply the same 7-10-7 proportions to almost any size stock without calculating or converting measurements. You just scale the ruler to suit the size of the stock. Because of the way imperial units work, breaking down into units of 8 within a given division, divisions stay visually the same whether we scale up or down. We can very quickly divide a surface into 24 units of 7, 10, and 7 very, very easily. This is a visual process, so let's look at it. So I've made up this little stick to help demonstrate what I'm talking about. So let's start by looking at the one in the middle here. This is a 12-inch scale, and it's broken up into 3 units of 4 inches. Each of those 4-inch units can be broken down into 8 units of a half-inch. And so, if we go to those major divisions of the 4 and the 4 and come back one unit on each side, we create 7-10-7 units. It breaks it up evenly into our 7-10-7, just by looking at what that one unit is back from that major division. If we're working at a 6-inch scale, for instance, we use the quarter-inch marks. 6-inch is broken up into 3 units of 2 inches. We come back one quarter-inch from each unit, and we get 7-10-7. Again, we go down to 3 inches, and it goes down to 8ths. 7-10-7. You can go down to inch-and-a-half, it becomes sixteenths. You get the idea. The top one is where I've gone up to 18 inches, and I did this to sort of demonstrate that this doesn't work very well once we go to that specific scale. Because now our markings, while they're there, they're three-quarter-inch markings, they're no longer visually obvious on the ruler. So the best thing to do is, if I'd gone up to 24 inches, that makes sense. Because then we have 8-inch units, and each of these increments that we're stepping off are just an inch wide. So that makes a lot of sense. But this particular one at 18 inches, the units are there, but they're not visually obvious. So you can figure it out, but the convenience breaks down. The convenience is in visually being able to see what unit is the 7 mark, and which units are the 10 mark. So it's just 7 from one end, 7 from the other end. Let's do it on a piece of material, and you'll see what I'm talking about. So allow us to pretend for a minute that this is a stock that we're working with. We'll say this is like a 6x6. Okay, we're gonna pretend this square is the cross-section of our spar. Now when we use this method, we don't do it on the butt end of a spar. We do it on the sides of a spar. But I want to show you this method to demonstrate exactly what we're talking about. So if I take this imperial ruler, and because the size of this, 6 inches is the closest thing to this size, I skew it across the work, touching the ruler off one end and touching the 6 off at the other, and then I come to our divisions here. So the 2 inches and the 4 inches are our two major divisions. And I come back one unit. In this case, the one unit is a quarter inch, because 2 inches breaks into 8 by quarter inches. I can draw this line across here to sort of show you where I've done those divisions. Now if I take that over to the edge of my spar here, that gives me 7 units, 10 units, and 7 units. So for convenience, I'll grab dividers to sort of move these dimensions around. So then I take that 7 units, and I lay that off here. There's 7. Lay it off here. There's 7. Lay it off here. 7 and 7. And at the very ends, 7 and 7. And then we connect those dots. What we end up with is that, that, that, and that. There's some inaccuracy in the way I've drawn this here because of the using these heavy pencil lines, but the beauty of this is across those flats is the same as the 10 units in between. The point is that now we just take these units, and we chop those away. Plane those off. And that will give us an octagon. And then we can use the same method to divide each of these smaller faces into 7, 10, and 7 units. 7, 10, 7. And we cut those off. And now we're down to 16 sides. And we keep going that way until we've reduced this thing down to a cylinder. Now the fun thing about this method is that it's not constrained to just doing it on a square. You don't have to have equal sides. We could do it with a rectangle. We know these two sides are the same, so I'll just visually bring those over. And then we need to divide up the other one. Now, this is where I would just cut it down to the next increment. I would go down to say 3 inches. We go down to eighths. So we go 1 eighth and 1 eighth back from the major increment marks. Oops, made that one wrong. 1 eighth and 1 eighth back from the major increment marks. Draw those up. Down. We connect those dots. And we chop the corners away. And we get something that... it's an elongated octagon, but then we can do the same thing by dividing these sides up into further divisions. And slowly work our way down to sixteens that way, and we get an ellipse. Now the 7-10-7 rule can apply to shapes that don't have parallel sides as well. Let's say, for instance, you want to create a piece of molding for the side of a boat. We'll say a rub rail that looks interesting. That'll be the side that goes against the hull. And let's say it's... we'll just say it's got a 90 degree angle across the top, a 90 degree angle on the face. Say something like this. So we can use the 7-10-7 rule to divide that up as well. So we'll say you should... you could use a round over bit on a router to do this little corner here to round that off. But what about this one right here? Well, this is where we could use the 7-10-7 rule again. So because of the size of this, I got to go to my inch and a half mark. So if I touch up there, I swing over to here, draw that off, and then we're using sixteenths back from the half inch marks. So there's one sixteenth and there's another sixteenth over there. Carry those over. And then we could do the same thing down here. So how I would lay this off is I might lay this out on a piece of paper in order to get the scaling right. So say we'd have to extend these lines outward square to the face of this surface so that I could use my 7-10-7 rule. So we'll do that right here. And I'm coming in a quarter inch from that mark, a quarter inch from that mark. Skipping across this. And so here is my 7-10-7 marks right there for that particular surface. And so then this is where I would divide up my surfaces right there. So that would be the beginning of my round over. And so, of course, I would divide up the next one. I'd probably just do this visually at this point. But my point is is that, well, you could use a round over here. You don't have anything to guide us down here. And so this is an interesting way to sort of break up these surfaces. The point is is that this 7-10-7 rule can apply to any trapezoidal shapes. So if we're like this, for instance, you divide those. We divide those. Let's do this by eye, obviously. And as you can see, you're well on your way to becoming an egg shape once you've knocked all those corners off. So I use the 7-10-7 rule all the time, even if I'm not necessarily measuring it out. For this, for instance, I would just do it by eye. I wouldn't bother to try and measure out where the 7-10-7 lands on this molding, but I'm using this principle of picking these these spots that are proportionally about that 7-10-7 distance from the ends of my piece of stock in order to create nice, round, elegant, curved shapes. So now if we're doing this on a spar, we would just take each side. We decide what size scale is best for the spar. In this case, this is just a little under 6 inches, and so we use a 6-inch mark. If this was bigger, I'd have to go up to the 12-inch mark, come back to the 2, come back a quarter inch, come to the 4, come back a quarter inch, and there's my 7-10-7. Now I would do this every few feet, depending on the size of the spar. Maybe we do it every 3 feet or something like that. And then by connecting the dots of the batten, this will become a curved line that matches the taper of the spar. Now there's a good reason why we're not using a marking gauge or a square to draw lines along a spar like so. If this was just a cylinder, we could do that, but that's not the case because this is a spar. It's going to have a taper to it. It's going to have an elliptical taper to it, in fact. And so we can't just draw those lines parallel to the side of the spar. We have to keep doing this calculation every few feet in order to maintain the spar taper, because each of these surfaces has to get tapered along with the spar. That's why there's so much calculation involved, and that's why you need a fast way to sort of recalculate these divisions all the way down the length of the spar. There are tools for doing this. They're called spar gauges. There's three different ones. These two are obviously the same. Now the spar gauge is made using the same 7-10-7 rule. So there's seven units to this little nail point, and there's seven units to this little nail point. And I happen to have a center point on here too, which I use once in a while. Now the edges of them need to be taken down to a fine taper, because if they're left thick, that skews your results, depending on how much this is skewed across the work. This little one here has been made by a friend of mine, Mikkel Pau, at the small boat school, and his is designed so that it'll skew and maintain the same proportions as it rotates around here. So that's kind of a really nice little one. It zeroes out where these little bolts pivot. So using a spar gauge like this, you could put it on your work, and you could stomp little divots in if you want to different places, or you could take it and you could scratch a line down the length of your spar, which I find less effective, but you can certainly do that, because this will skew as the spar changes shape. Some people will do this with pencils. I've never found that to be particularly desirable, because one pencil is always going to get a little duller than the other, and pulling them out and sharpening them is a pain. So I've always found it's easier for me to just do some dots every now and then, and then I connect the dots with a batten. And of course, if your spar is smaller, you go down to a smaller gauge. Now, while the spar gauge is great for getting your initial octagon, it's useless once you've got to go down to 16 sides, because this can't hook on to the face of the spar once we've beveled off those corners. It lies on these edges. And so you're pretty much obligated to go back to using your ruler method for the next divisions. So there we go. Come back one eighth division from our major divisions. In this case, we're using three inches, so the one and the two are our major divisions, and the rest of them are eighths. If I were to go down to something smaller, use this at an inch and a half, my divisions would be sixteenth. Now, you can use metric, of course, but it doesn't scale quite as easily or as much. That is, you can start with like 24 centimeters in total, and divide that into 7 centimeters, 10 centimeters, and 7 centimeters, and you can cut that in half and work with 12 centimeters and use half centimeter increments. But beyond that, it gets all very fudgy, and it doesn't work very well. You can't really go up from 24 centimeters, because it gets ridiculously large, and going down from 12 gets... I mean, you can do it, but it's, it's, it starts to lose its immediate accessibility. With an imperial ruler, we have the visual cues of how the ruler is broken up into equal divisions in each unit. That is, every unit within the imperial ruler that we're interested in will break down into eight identifiable units, and that's where it becomes really accessible, because within any one unit that is divisible by eight, there's a little line already drawn in there, so we just need to work back one line from that one unit. So if it's an inch, we go to 7 eighths, and if you go up, we're going back by a quarter inch, or by a half inch, and so on. So with imperial, you can work in half inches, quarter inches, 16ths, 30 seconds, even 60 fourths, although that's getting pretty small and kind of impractical at that point. But the point is that the markings are already there. That flexibility makes it very easy to adapt this method to very small or very large stock. A little while ago, I needed to make an octagonal plug for this hollow mast I was building, and using the 7-10-7 rule, it was pretty easy to do that. I just needed a few dimensions to get started. I could use dividers to find some widths of these staves, and then I could lay this out on paper very easily. Then I just make myself a rectangular blank that's tapered, and use the 7-10-7 rule to turn it into an octagon. So I did all of my initial tapering on the bandsaw, and just cleaned it up by hand with a block plane. Now I just want to plane down to my lines. When I get there, stop, and then we will check our work. Bear in mind, at the smaller end, this is going to be a narrower amount of material. There's less to take off down here, so I need to actually taper my strokes up at this end a bit more, just to bring a bit more even. Now, there's no point in trying to do this with machines. It's pleasant work. I'm sure you can do it with machines. I'm sure you could do this on the table saw. You need a little bit of ingenuity, but spend more time thinking about it and making a jig than it will take me to just make it. About right at the front end. Back end, we're still a little oversized. If you're going to trim down something like this, it's a good idea to mark one side so you know where you started and stopped, because it can be really easy to lose track of that. The way I made the hollow spark created an octagon to start with, but I still needed to divide the eight sides into 16, so again, I turned to the 7-10-7 rule. I'm just going to mark these edges so I can see them a bit better. I want to swing this rule over as close to square as possible, so the closest I can get is going to an inch and a half. So that gives me three equal half-inch units. I'm just going to draw a line across here as a reference. And if I go to the first half mark, and then come back one sixteenth, and the other half mark, and come back another sixteenth the other side of it, leave 7 sixteenths, 10 sixteenths, and 7 sixteenths in between. 7 10 7. We do that on all the sides, and then we connect those dots by planing away the 7 portions, and that will leave us equal divisions between all of them. So I came up with a nice little trick using a small ruler here, so if I slide this across till I'm butting up to one of my divisions, I drop this piece of tape very carefully across my edge, and we wrap that around gently. So there's just enough thickness in this tape that I can feel it against the edge of the stave. So if I rotate this now, there's my division. There's my division. So I only have to lay it out once. You can't really use a marking gauge to do this because the the facets are not going to let you register against them very easily, but this works fine. A lot of this gets done by eye. Once you start planing, you don't have to be perfect. Just pretty close. We'll be sanding, and that will fair it all together. So I'll come down about roughly another three feet and do that again throughout the length of the mast. So these divisions are set far enough apart that if I've got a plan and I'm stroking, I'm sort of starting at one and I'm finishing off at the other so I can easily control the length of that stroke. I don't need to draw lines all the way along. Some people do that, but that's a crazy amount of work. There's no need for it. Okay, now I don't just use this in boat building. I also apply the same principle when making banjo necks, for instance. I'm not necessarily chasing the exact same 7-10-7 ideal that you would to create a perfect circle or ellipse, but I'm using those proportions to lay out some guidelines or something close to that. Now over the holidays, I managed to fracture my ankle and I've been bombing around on a scooter and on crutches for a little while and I've just finally gotten back to walking and so made myself a walking stick and well, you can take one guess what principles I used in order to make this shape. Even though I'm still shaping something by eye, the process is still grounded in using the 7-10-7 rule and that allows me to get from square to round in a really short time period and in a very reliable way that leaves me with something that looks nice and round and isn't something square with rounded corners. That's kind of the key here. Now at its core, this method is about using simple geometry to replace repetitive calculations and to turn a rough boxy shape into a clean, flowing, smooth, curved shape with accuracy and efficiency. Okay, I want to thank you all for watching and I especially want to thank all my followers on Patreon whose support makes these videos possible. If you like this content, you'd like to support the channel, please consider joining me over on Patreon. You can find links in the corner or down in the description. Alright folks, that's it for this week. We'll see you later.