Mathematicians . . . Please Help
I think most of us have either seen or heard of someone who could calculate rafter lengths in their head. I want to crack the mystery behind it, so I’m calling on you old-timers and mathematicians for help. Are there any tricks to calculating common rafter lengths IN YOUR HEAD (with no framing square either) besides memorizing the “lengths per foot of run,” or is it just plain number crunching after that? <!—-><!—-><!—->
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For example, suppose you have a building you measure at 33′. From this point you put your tape measure down and do the rest in your head with no aid of a square. <!—-><!—->
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33′ (span) divided by 2 (half the span) = 16′-6″ (unadjusted run). In this instance I’ll use the unadjusted run for the sake of simplicity and figure on subtracting half the thickness of the ridge board after the rafter is laid out. I’m also going to avoid a building width that has a run including inch fractions so that I don’t complicate this too much right now.<!—-> <!—->
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Say you want to frame the often used pitch of 4:12. The “common rafter length per foot of run” is 12.65: 16 (4 squared) + 144 (12 squared) = 160 The square root of 160 = 12.64911 or 12.65. If someone already knew the “length per foot of run” for a 4:12 pitch, he could skip the whole A2 + B2 = C2 thing and start with 12.65.<!—-> <!—->
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Now the problem becomes a matter of multiplication and conversion: 12.65 x 16.5. For most people it’s kind of difficult to multiply 12.65 by 16.5 and be sure of the answer (208.725) without writing it down.<!—-> <!—->
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Of course, the decimal inch fraction .725 must also be converted into an inch fraction of 11/16 (.725 x 16 = 11.6 or approximately 11/16). Answer: 208 11/16″ (17′-4 11/16″). <!—-><!—->
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Are there any ways to either BYPASS or SIMPLIFY these last two multiplication and conversion steps so as to make it easier to calculate in your head? <!—-><!—->
–T
Edited 11/7/2007 12:14 am ET by JourneymanCarpenterT
Replies
I don't know T, but in the time it took me to read your post I'd have had the answer with a square and a pencil, or a CM.
But you guessed it-what the hell do I know.
A great place for Information, Comraderie, and a sucker punch.
Remodeling Contractor just outside the Glass City.
http://www.quittintime.com/
That's why I'm looking for a shortcut. It just seems like it would have to take longer to calculate this equation in your head as opposed to a calculator. Yet, I've heard several experiences of rafter lengths being calculated in someone's head just as quickly.
Perhaps these are just stories that I've heard, although they are stories that I've heard confirmed again and again. I guess you've been around a while, have you ever seen or heard of this?
If these experiences aren't just stories, perhaps they're people who are simply gifted at number crunching and hence no other tricks will ever be found. However, after Jim Allen was able to explain the trick for eyeballing jack rafters, I just couldn't resist searching for a trick to this one also.-T
I'm old.
Been doing this for quite a while.
Don't believe I've seen anyone frame a roof without a square.
But I usually am wary of any story that starts out ...........
"you should see this guy, he can.............."A great place for Information, Comraderie, and a sucker punch.
Remodeling Contractor just outside the Glass City.
http://www.quittintime.com/
or;
"I knew this guy once..........."
I'm getting old too.
I like my framing square god dammit!
[email protected]
remember that thread about what you would take on an island with no power?
I don't remember anyone coming up with taking "that guy".A great place for Information, Comraderie, and a sucker punch.
Remodeling Contractor just outside the Glass City.
http://www.quittintime.com/
remember that thread about what you would take on an island with no power?
How about bringing "That Girl"?
eh? Am I old too or what?[email protected]
You do have a strange sense of humor.A great place for Information, Comraderie, and a sucker punch.
Remodeling Contractor just outside the Glass City.
http://www.quittintime.com/
I've been doing this for a long time and I've never seen anyone frame and entire roof without a square either. FKA Blue (eyeddevil)
I do know an individual who could do the calcs in his head. My ex partner. He also used to race seasoned bookkeepers using electronic 10 key adding machines through a string of numbers and beat them both for accuracy and speed. But he is one in a million as far as I am concerned. It is a gift. And he still cut the damn boards wrong sometimes.
They can't get your Goat if you don't tell them where it is hidden.
"And he still cut the damn boards wrong sometimes."
I'd guess that's why he's your ex - partner
Nope. He and his wife chose to move away from the area. I was just joking about how being a mental whiz at math wasn't proof against marking and cutting a board wrong.
They can't get your Goat if you don't tell them where it is hidden.
it was just my sick sense of humor
First, with the advent of construction calculators, why bother? Less chance for error on a clac. or paper.
If you want to do it in your head, why not start with the total rise and toal run to get the length. Calculate: total run = 16' 6" x 4" pitch = 5' 6" rise, and apply the A2 + B2 = C2 to the 16-6 & 5-6 numbers.
I would guess that there are not many in the population who can do this in their heads, and of those who can, not many are carpenters. Being in the big group, I started out using the numbers on the rafter square and doing the math on a scrap of lumber. Now I use a CM Pro.
Woodroe, it would be very hard to mentally calculate the square root of the sum of your two legs. Actually, it would be very hard to mentally do the squaring.So, if I'm going to do this problem in my head, I WOULD NOT use total run and total height....on this problem. I might use it on other problems though. Usually when I calculate rafters with my calculator, I run my numbers with the net total run. I'd start with the 6" and subtract .75" That would leave me with 5.25" which I would divide by 12 (.4375) and add into memory. I'd then punch in 16 (the run) and put that into memory. I'd then add 1 (the overhang) and put that into memory. I'd then put in 160 sqrt x M+ =220.56". That would be my rafter length from the tip of the subfascia to the tip of the rafter. It would already be shortened for the ridge. I normally use a level cut at the fascia line. FKA Blue (eyeddevil)
This is why God invented construction calculators.
I can only think of 2 shortcuts off the top of my head.
At a 5/12 pitch, there are 13" of slope for every 12" of horizontal run. So in the case of a 30' wide building, your 15' horizontal run would be 15' plus 15" of slope. (Or 16' 3")
A 9/12 pitch is the same as a 3-4-5 triangle. (Or a 9-12-15 triangle) So the slope length is 5"for every 4" of horizontal run. In your case of a 15' horizontal run the slope length would be 15 X 5/4, or 18.75', which is 18' 9".
In both cases you'd have to adjust for the thickness of the ridge board and overhang.
Thanks, this is exactly the kind of insight I was looking for. Your explanation of the 5/12 is especially helpful. Thanks again.-T
Actually the short cut you are looking for involves the diamonds on a tape measure and converting all dimensions to "cubits".But since you are a mere journeyman, I can't tell you or I'd have to kill you....
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I have Transcended the need for Pants....oooohhhhmmmmmm......
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I have Transcended the need for Pants....oooohhhhmmmmmm......
I have transcended the need to measure.
If your view never changes you're following the wrong leader
I have transcended the need to read BreakTimeView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
I believe that about as much as the pants thing.
If your view never changes you're following the wrong leader
I have transcended the need to make senseView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
That's good, because I've transcended the need to understand you.
If your view never changes you're following the wrong leader
You are right, those are the two simplest mental pitches Boss.The other relatively easy one is 12/12, where we mentally use 17" as the multiplier. In this case, since the run is 16.5 units your 30' building would be (15' + 65" + 8.5") which = 20' 5" +8.5" which = 21'-1.5".I normally don't think in terms of 1 1/2". I always leave the inches as 1.5" and just mark it out on the square to the nearest 1/16". So, if I'm in the mentally calculating mood, I'll sometimes start with these easy examples and add or subract from them as I suggested in my first response to Journeyman. They become the basis for the secondary math. Another somewhat easy pitch is 7/12. I would punch that in as 193 sqrt which returns 13.89. You 15' run might turn into something like this in my head: (10 x 14)+ (140/2) =(140) = (70) = 210. That 210 represents 14" x 15 units. I now have to subtract .11 which I'd round to .1 = so (.1 x 15)= 1.5 which comes off the 210. So 210 -1.5 =208.5When I start doing this stuff in my head, I get anal and would think about that final .01 and decide that it amounts to about (.01 x 15) = .15 which I call 1/8" I'd deduct that from the 208.5My answer on your roof would be 208 3/8" less ridge thickness if this roof was a 7/12.I most likely would run the mental numbers on a set of rafters with those numbers, even if I had done it with a calculator! As I was stacking, crowning and getting ready to mark my rafters, I'd be running that number in my head. I don't know why....it's just something I do. I dont' talk about the movie I saw last night with my co-workers....I'm too deep into this kind of twilight zone.And no...I'm not one of the one in a million guys that can calculate anything. I can do a lot of the rafter stuff on easy runs but mostly only on the commons and jacks. I don't know any of the hips and valley numbers but I have a few tricks for those too but its not too much mental math. FKA Blue (eyeddevil)
I remember a Saturday, working with one of my crew, finishing some framing details to button up a house for a client's Sunday visit. In other words, a lazy short day.
There was a set of horses on one side of the room, a small stack of eight foot 2X4s in the middle of the floor and a number of cut offs lying around.
I'd just been looking for a three foot piece, had spotted one near the other side of the room and had walked over to measure it. Finding it to be only thirty-five inches, I'd left it there, picked up a full one off the pile and walked back around to cut it on the horses.
The other guy was outside working on the deck railing. He stuck his head in the window on the other side of the room and asked me for a thirty-six inch 2X4. I said, "OK, just a second, I'll cut one for ya".
He replied, "That's OK. I've gotta cut it to fit, just a tad under thirty-six". Then spotting the piece I'd just measured on that side of the room he said, "Hey, there's a piece over here. Can you hand it to me?"
Deciding to mess with him, I studied the piece for a moment from ten feet away and said, "Nooo...that one's about an inch too short. Lemme cut one for you."
"No wait", he said, stepping through the window. He pulled out his tape and, of course, found it to be exactly one inch too short.
Obviously perplexed, he looked at me and said, "How in the fawk could you tell that piece was an inch short, from over there?"
"I'm de man", I said with a smile, "and don't you forget it."
A few people have a gift for math which far exceeds the rest of us. Among those of us who don't, there are many with good memories and enough experience to know what will work in certain situations. A large percentage of the latter group will do something like what I just described, for their own amusement, given the opportunity.
When you're the boss, it helps to have a small edge. A little awe goes a long way. ;)
Edited 11/8/2007 5:35 am ET by Hudson Valley Carpenter
You could draw it on the floor quick and easy without a calculator. Since you know the pythagoreon theorem and the slope, you can throw away your square. Or calculate the rafter length for any slope with a 5 dollar calculator.
Roof math always comes down to similar triangles and pythagoreon theorem.
Have a good day
Cliffy
"Roof math always comes down to similar triangles and pythagoreon theorem."Thats how I do it...with a five dollar calculator. There are a lot of guys in here that use trig though and I'm sure they have their own mental tricks which I can't relate to at all. FKA Blue (eyeddevil)
My first instinct to do something like this in my head would be to break the multipliers into easy segments.
I do know the 12.65" unit length of a 4/12 rafter so I wouldn't have to mentally do that math.
I'd mentally start by carving up the 12.65 into 12 and .65. Your span is easily cut in half too into 16.5 units. I'd mentally call the 12" one foot and know that the rafter length was 16.5' (16' 6") + .65" x 16.5. The latter is a tricky one. Because the math would be more challenging than I prefer, I'd probably opt to skip to the 2nd method that I describe later in this post.
Heres the first method.
I'd mentally cut the .65" into .50 and .15. These are multipliers that are easy to work with so: 16.5 units turns into 8.25". That's easy enough. The balance is .15" x 16.5 units. = (.10 x 16.5)=1.65. I still have to add half of that again to pick up the last .05" x 16.5units. That would be another .825.
Thats a lot of adding.
I'd probably do that mental math as a double check, but not as my primary.
The second method would be to mentally calcuate a 5/12 roof which is 13" per foot of run x 16.5 units. That would give me a starting length of 16' 16" + 6.5". In my mind I'd calc that to be at 17' 4" + 6.5" which equals 17'-10.5". Then, I'd have to subtract the difference between 13 and 12.65 which is .35. I'd round the .35 to 1/3 and mentally divide the 16.5" into 5.5". So, my final mental tally on this rafter is 17-10.5" - 5.5" which equals 17-5.
If I was in an anal mood, I'd remember.02 that I rounded. That would give me another .33" or 3/8" to adjust downward.
My final answer would be 17' -4 5/8" I probably would calculate that number about as fast as I could pull out my calculator and run the numbers.
Incidently, my calculator would be about 1/16" different. That's plenty close enough for me.
It's highly likely that I've mentally calculated a lot of numbers like these even though I carry and work with a calculator. I normally would scribble a couple of key numbers on a board somewhere to facilitate the mental math. This sounds a bit weird, but there is a very good chance that I'd mentally calculate a set of common rafters in my head on the way home, to double-check the calculator. When I'm working on stuff like this on-site, I do a lot of double checking inside my head as I'm setting up the stock for cuts.
Fun exercise. The more I do, the easier it is on me.
FKA Blue (eyeddevil)
Subtracting the 4:12 from a 5:12 is a pretty clever concept. Thanks for the tip.-T
I recently was watching a kids educational show that was teaching mental math tricks and one of the ways they taught was rounding up to an easy number, then subtracting. I then realized that I had been doing that in my head for years in a lot of different applications but I don't ever remember getting that type of instruction in schools. I think it's probably a trait of my contrarian personality. I don't consider myself gifted in math to any degree. There are hundreds in here that blow me away with their mathematical prowess I struggled with algebra, but I use the associative principle in my mental math calcs a lot. I still cant do simple story problems.In my last year of carpentry school, everyone had to take a four year test that was thought to be too long to finish. One section contained a lot of (useless) board foot measurement calculations and we weren't allowed to use a calculator. I flew through that section by doing very basic mental associative steps and I think that contributed greatly to me finishing the test. No one had ever finished it and the instructor didn't believe me! It's too bad I'm not active onsite anymore because theres no way to remember the multitude of mental shortcuts that occur in our everyday routines. I was hoping that we'd get a few more shortcut/tricks. Usually, if someone starts talking about one trick or another, it spurs my memory and I'm sure a few more would come up. Thanks for the thread. FKA Blue (eyeddevil)
Now, I’m not a math wizard either, but I could see marking the rafter length (for regular pitch roofs) correctly, without calculating the actual length, referencing the framing square ‘per foot run’ tables to head calc the even footage dimension and stepping off the ‘odd’ or left over inch/fraction dimensions.
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The framing square tables give you the “Run per Foot” unit for the slope, (Both Commons and Hip/Val), so subtract 12” from it, to get the gain, and multiply that by the largest whole footage of your Run to get the head calculated gain length, do a quick decimal to fraction conversion…/addition, add that to the whole footage that gained that amount, and use the framing square to step off the additional inch and fraction portion of the run. * (For Hip/Val rafters mark/step the leftover run as a common (on 12) length first, to get the height, and then step and convert the height to an ‘on 17’ step-off.)
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Do the (Whole feet) easy stuff in your head and step-off the (Inch & Fraction) awkward stuff. You won’t know what the actual length is, but it will be marked the right length.
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I understand what your doing and it makes sense to me. I'm going to have to digest that a bit and think about which pitches that makes the most sense for. I'm going to go find a framing square with the tables on them. That might refresh my memory about some tips. I wonder if there is a version of it online? FKA Blue (eyeddevil)
I had a double-E prof who was real good at quick approximate calculations. He knew how to round up, do the figuring, and then throw in a fudge factor for the rounding, eg. He tried to teach us some of it, but it was too much info to cram through too small of an orifice.
If your view never changes you're following the wrong leader
Thats kind of my approach. I do the mental approximations and keep the fudge factor somewhere in the back of my mind. A lot of times, I use that technique to mentally double check critical calculations on stuff that will take a long time to repair if I'm wrong. Sometimes I drive myself nuts. I remember one time trying to mentally calculate the square roots of some rafters. I had to put my "mental" foot down on that....I never did get to the end of that exercise. I don't even remember how to do square roots without a calculator anymore. FKA Blue (eyeddevil)
This guy could do squares and square roots pretty well. You know about powers of 2&10, know the square roots of 2&10 (or at least could), so you can get halfway close.Like I said, he was an EE prof and specialized in power, so being able to estimate watts, etc, quickly was worthwhile. I actually have some fudge factoring I do in programming, but it's not as applicable to general use. And I'll never be as good at it.
If your view never changes you're following the wrong leader
I don't know anything bout the powers of 2 and 10. I don't remember anything about mentally figuring square roots. It was a trial and error method and quite lengthy. I used to do the mental exercises in my truck because I had a long ride home. I'd be figuring pine lines, stair risers, rafter lenghts, etc as I drove. I drove past my exits a few times.... FKA Blue (eyeddevil)
1.414 is the square root of 2, 3.16 the square root of 10. The square root of 100, of course, is 10 (divide the zeros in half). The square root of 1000 is 31.6 -- the square root of 100 times the square root of 10.The square root of 4 is of course 2. The square root of 8 is 2 * 1.414 = 2.818.With this much info you can calculate the square root of a number within about 30%. Add in remembering the square roots of 3, 5, and 7 and you can get probably within 5%.
If your view never changes you're following the wrong leader
I was hoping that we'd get a few more shortcut/tricks
I've posted some of these here before, but because of so little positive response, I figured maybe my way of figuring and cutting roofs is so different that my methods just aren't practical for others. But you were actually one of the few who commented that you might find some use for one of my shortcuts, so I'll re-post a couple here.
I tend to figure my roof parts ahead of time, rather than on the jobsite. Using Google Sketchup, the free version, its ridiculously easy to calculate rafter lengths, hip lengths, etc.
I'll post a few examples that took me a matter of seconds to arrive at. View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
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View ImageView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
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View ImageView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
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View ImageView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
The next picture is a mockup - all it does is give you the angles for a hip roof with a square-cut fascia (common out here), but the angles are a big thing. I've sacrificed a lot of time and wood to those pesky angles. The angle for the roof sheathing panels, the angle for the fascia at the miter, the angle for the square-cut fascia at the end of the hip or valley rafter (its not square there!). To go into a complex hip roof with those angles already known is a big confidence booster and time saver. While I seldom backed the hip or valley, occasionally it made sense to do it, with a doubled-2-by, or a structural beam for a hip, for example. You have to actually cut the mockup out of the block of wood to get the backing angle, but its right there, along the "hip" portion of the mockup. The mockup, once its cut out, can be used to adjust a saw angle, or set a sliding t-bevel. It might take a few minutes to cut the mockup out of a block of wood, but then you can use it every time you frame a roof with that pitch. Originally, I made them out of stiff paper and scotch tape, which was tedious, but man what a timesaver on the jobsite. To arrive at this, I studied all the roof-cutting books and articles I could find, I studied all the geometry and trigonometry books I could understand, I took a trig class at night school (I dropped out when they got to sine waves), I really wrestled with this, because I wanted to get a grasp of the relation of the various planes, and angles. All the methods I encountered were heavy on the math, and difficult to explain (or understand!). I began making paper pyramids, or mockups (I'll post some pics), as a way of wrestling with the simplification of the angles and planes to a basic 3-dimensional object that I could hold, put a sliding t-bevel up to, or set on my saw base while I adjusted the angle of the blade. It wasn't until years later that I looked at my paper mockup, and realized it resembled the corner of a 4x4. Then I thought it out, and realized how it could actually be easily figured and cut out from a scrap of square lumber. It was like an epiphany for me, to grasp how easily the angles could be found, which I had struggled so mightily to arrive at. I've never seen or heard of this method mentioned anywhere, from any source other than my own. I know us old-time cut-and-stack roof-cutters have gone the way of typewriters and transistor radios, but even with truss roofs you still gotta get those angles, to do roofs right.
View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
Edited 11/11/2007 1:20 pm by Huck
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View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
Angle A represents the pitch of the roof.
Line 2 is drawn at 90 degrees to line 1, from the corner. It represents the run of the roof. And the green side of line 1 represents the rise of the roof.
Line 3 is drawn at the same length as line 2. Lines 4 and 5 are drawn once the length of line 3 is determined. Line 5 represents the hip rafter, as line 6 represents the common rafter.
If you cut away the dark brown portion, the piece remaining contains all the pertinent angles, in 3D, including the fascia compound miter angles, the roof sheathing compound miter angles, and the backing angles for hip and valley rafters.View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
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View ImageView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
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View ImageView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
I'm going to study your models a bit Huck to comment intelligently.I do know what you mean about having that epiphany regarding the 4x4. The angles reveal themselves in many of the parts that you cut with a saw. If you mark a pitch cut for a jack, then run your saw through on the proper angle, the cuts that expose themselves on the lumber will give you every angle you need to know. I don't have my paperwork from when I went through carpenter school but there was one particularly useful drawing that clued me into how every angle related to one another. The instructor called it the "butterfly" because it was several triangles interconnected by the lines in the middle and it had the shape of a butterfly in a two dimensional drawing. If I remember correctly, every angle you would need to know revealed itself in this drawing. Maybe I'll call my old high school buddy that went through the apprenticeship program. I'm sure he did his paperwork and saved it all. I didn't even buy the books....I borrowed them and I was never good at doing my homework or taking good notes, so that drawing was something that I should have saved but didn't.Thanks for the pics. FKA Blue (eyeddevil)
The "butterfly" intrigues me, because it sounds like he and I are on the same wave length - when all the complex math and calculating is over, what's left are a few simple planes and their relationships to one another. Once you boil it down to that, you've got the essence of the roof-figuring process.
Height-above-plate, shortening for thickness, converting fractions to decimals and decimals to fractions, these things are just distractions farther down the priority chart. Get the dimesions and angles first. Then follow up with the fine-tuning on the above stuff. Double-check yourself as you go.
The dimensions are not hard - calculators make it easy. With Google Sketchup for example, you draw the run, punch in 12', say, and the length of the line is automatically adjusted. Then draw the rise, punch in 5', same thing. Now draw the line connecting them, click "tools", then click "dimensions", put your cursor on the angled (rafter) line, and it gives you the length. Do the same with inches, do the same with any dimension less or more along the same angle (interpolate or extrapolate - so simple with a cursor), and you got it.
So the lengths tend to be pretty easy to arrive at. After that, all that remains is the angles. If you can simplify a system to arrive at those, you're on your way, with a minimum of headaches, hassles, and a minimum of math.
I love sitting at home and figuring the math on a complex roof. But when I'm on the jobsite, with a crew that costs a thousand dollars a day or more, all I want is production. I try to minimize math on the jobsite. Too many distractions (cell phones, questions from the crew, conversations with the client, or super, or developer, etc., etc.), from my experience, to really figure efficiently, and double-check effectively.
View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
Edited 11/11/2007 2:23 pm by Huck
...and so it goes - everytime I've posted those tips, they are completely ignored. Or worse yet, the thread just dies, and I feel like I killed it!
I'll wait a few days, and then delete them, because I really hate posting to myself. Like I said, I posted the tips because you asked, but my ways of figuring and cutting a roof must be so different from others that my tips are of no use to anyone but me! View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
Huck,What tips on cutting rafters are you talking about?Joe Carola
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Angle A represents the pitch of the roof.
Line 2 is drawn at 90 degrees to line 1, from the corner. It represents the run of the roof. And the green side of line 1 represents the rise of the roof.
Line 3 is drawn at the same length as line 2. Lines 4 and 5 are drawn once the length of line 3 is determined. Line 5 represents the hip rafter, as line 6 represents the common rafter.
If you cut away the dark brown portion, the piece remaining contains all the pertinent angles, in 3D, including the fascia compound miter angles, the roof sheathing compound miter angles, and the backing angles for hip and valley rafters.
View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
The top part of your contraption makes sense Huck. I don't understand what line 4 or the white portion of line 1 tell you though.
OK, now I feel like I'm getting somewhere. You're right, the top portion is the essence of the hip (or valley) roof angles. The bottom portion really only relates to a square-cut fascia, which is common here. Vertical fascia is far less so.
Line 4 represents the corner of the fascia at the hip - its not square there, and I've seen carpenters (like meaning, me!) really struggle with that compound angle. They seldom get that miter tight, because the angles are odd.
The white portion of line 1 is just the continuation of the ridge plane. By running the line all the way down until the square-cut fascia line, or plane, meets it, it just finishes off the mockup in a simple manner.View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
AHA!
Now I get it.
Not being an expert framer myself, on a recent job we had fascias that were square cut for a 10 pitch, IIRC. There were multiple pitches but the fascia angle stayed the same. And there were several outside hipped roof corners, where the two slopes had slightly different pitches. I could almost figure out how to do the hip rafters but something didn't quite click. I can see where a mockup like yours would have helped a trim guy like me figure out the math.
Post #51 ... Huck wrote:
"...and so it goes - everytime I've posted those tips, they are completely ignored. Or worse yet, the thread just dies, and I feel like I killed it!
I'll wait a few days, and then delete them, because I really hate posting to myself. Like I said, I posted the tips because you asked, but my ways of figuring and cutting a roof must be so different from others that my tips are of no use to anyone but me!"
Don't delete your posts and/or diagrams. These concepts do not always fall on deaf ears and other readers in future may find your insights exactly what makes everything click in place.
The tetrahedron composed of four right triangles is the basic unit of complex roof geometry. I do a bit of roof (and other) math tutoring/consulting/advising and always tell folks "I don't give a %#&@ if you forget everything else we do here ... but remember this!"
I've posted the links below before but here they are again. The point of all this is: the geometry of any compound angle is exactly the same as the geometry of a Hip roof, the formulas for a Hip roof apply to any compound angle, and in essence all compound angles are the same.
Compound Angle extracted from the Stick and Developed
Development of a Compound Angle
Comparison of Compound Angle and Hip Roof Geometry
Development of a Hip Roof
Taking the geometry and applying it to understand square cut fascia ...
Square Cut Fascia intersects foot of Hip Rafter
There are links to other diagrams, formulas and notes.
Hey Blue! You changed you handle ... ?
Joe Bartok
Edited 11/17/2007 11:02 am ET by JoeBartok
Here are some links to a few more examples of the tetrahedra modeling different compound angles. The triangles can be determined with nothing more than a compass and straightedge. Or the lengths of the sides may be solve using trigonometry.
The lengths of the sides are trig functions of the angles, scaled with respect to the side equivalent to the "Hip run" being equal to one. If anyone wants to try making the models the lengths of the sides may be multiplied by any number to scale them to a size convenient to work with. Just lay out the lengths on bristol board, cut and tape. Or cut the compound angle on a stick.
Compound Angle ... Jack Rafter
Compound Angle ... Jack Purlin
Compound Angle ... Hip Rafter Side Cut
Joe Bartok
Yes. I couldnt remember my passwords and name. Excellent work on those diagrams and formulas. In my younger days, I'd have eaten them up. FKA Blue (eyeddevil)
Edited 11/17/2007 9:34 pm ET by Jim_Allen
I couldnt remember my passwords and name.
Happened to me several times. I think I was Huck orginially, maybe Huckleberry?, then Constructamundo, Gumshoe, then Huck again with different "official" name but same screen name.View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
The trick is to only have one or two basic user names and just a few passwords -- one for blogs/forums, a different one for insurance/financial sites, and a third for your email account, eg. Also, keep a file on your home or work computer (if it's reasonably secure) with all the passwords in it. Update it religiously.
If your view never changes you're following the wrong leader
There is no way I could possibly manage all the usernames, login and passwords and do it "religously". Heck...I'd have a better chance at getting elected president. FKA Blue (eyeddevil)
That's why I use just a few if I can. I mostly use the file because there are about 20 systems I have to change the passwords on every 4 months, and there would be no way to manage otherwise.
If your view never changes you're following the wrong leader
I"ve forgotten more than 20 and have a file with more than 20. Everyone is asking for names and passcode nowadays. It's insane. FKA Blue (eyeddevil)
Use the same password on as many systems as possible (but separate separate ones for leisure/financial/personal/work, etc). Most of these you never change, or only if compromised. For passwords that you must change regularly, keep a record of prior passwords, so if you forget to change one system you can guess what its password was.
If your view never changes you're following the wrong leader
If I had any say in it, I'd use the same password everywhere for everything and I'd NEVER change it. Unfortunatly, every system has their own requirements....some want 4 digits, some want at least 8, etc. I can't even remember where all my password folders are! FKA Blue (eyeddevil)
Thankfully there's a common denominator for 98% of the systems I have (one #$%! system requires at least one #$%! character) so I have a Java program that generates 10 random PWs at a time according to the common rules and I select one that "feels" good when you key it.
If your view never changes you're following the wrong leader
And my password folder is my Unix .netrc file where you naturally keep ftp passwords anyway. So no new security measures are required.
If your view never changes you're following the wrong leader
Use the same password on as many systems as possible
The downside to that is if one system is compromised, your password to other systems is also known. That's also a risk to keeping the passwords on your computer - one rootkit or virus and all your passwords can be discovered.
IMHO, the thing "one should never do" is the answer - write them down. I write them on a piece of paper, which I store in a safe. On those rare occasions when I forget one of about 67 passwords, I can look it up.
Another tip is to ALWAYS use weird characters in passwords - like $ or # or % - and mix upper and lower case. This makes your passwords much, much harder to crack.
The best tip, though, is one a former operative taught me - develop your own unique system for mentally generating passwords, and memorize it. Then you will always be able to recreate your passwords easily. For example, you might decide to use the text on the phone keypad as a key. You might use the month and the name of the site to decide where to start on the keypad, then following a predefined (memorized) pattern. Works great, once you get the hang of it.
I would like to hear more about it as well.
I am kind of confused with your paper triangle. I see the triangle on the top that you have drawn 22 and 67 degrees, does the bottom below the triangle serve any purpose?
Matt- Woods favorite carpenter.
see post aboveView Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
I think I'll give this a try this weekend. I'll cut up a scrap 4x4 to see it in person.
The more I read that post the more it makes sense to me, it's just taking a little time to sink in.
Don't delete the posts either, I may need to look at them when I try to make a model of it.
Matt- Woods favorite carpenter.
OK, cool. Good to know my message in a bottle finally washed up on someone's shore! Let me know if I can clarify anything.
Like I said to Blue, its a simple concept, but I struggled long and hard to arrive there. The paper pyramid was the intial concept being worked out - I didn't realize until much later I could do it from a scrap of wood. I worked out all the angles with trig and protractors, and carefully drew and cut them, and taped them into the 3d pyramid. This allowed me to study the relationship of the planes.
Years later, I looked at my paper model, and it just hit me - how easy it is to arrive at all the complex angles on a hip roof with square-cut fasica!
edited to add: the bottom portion of the pyramid represents the line of the square-cut fascia (as opposed to vertical fascia) carried down until the plane of the fascia intersects the vertical plane of the ridge.
View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
Edited 11/16/2007 10:14 pm by Huck
The difference between you and I Huck is that I've never wrestled with that square cut angle problem. I think I did one back in the early 80's and I do remember me needing a couple of whacks at it before I got the angle.I have noticed though, that every angle needed for all the things discussed in thie forum expose themselves in the drop offs of the stuff we cut. Take a look at the angels formed on the common rafters on jacks. Notice the angles revealed on the compound cuts. Its all there in living color.Nice job on your little model. It makes my head hurt to try to understand why it all relates but I know it does...I'm just too lazy, or into something else to go at it with enough gusto to really understand it. What does the angles on the cutoffs of those square cut compound mitres tell you? I think you'd be surprised if you would put your framing square on them, like I have on all the cuts of the commons and jacks. It's all there, repeating itself over and over like a broken record but no one has a framing square anymore to see and understand it.It's their loss. The speed square guys think they have something faster... FKA Blue (eyeddevil)
Like Blue I don't run into square cut fascia. But thats not the only purpose of that model, or is it?
Matt- Woods favorite carpenter.
Like Blue I don't run into square cut fascia. But thats not the only purpose of that model, or is it?
No, all the angles are there. The angle of the backing for hip or valley. The angle of the roof sheathing - which is actually a compound angle, although you don't generally think of it as one when you're running 1/2" osb sheathing - but you will notice it big time when you run 2x sheathing, which we would sometimes encounter.
I hadn't encountered much square-cut fascia before I came here (Bakersfield), which is why it threw me for a loop when I tried to get that mitered corner right. Even the angle that the hip or valley needs where it meets the fascia is tricky. The common rafter ends are square, but because the hip and valley run 45 degrees (in plan view), the angle is not square, and the bevel is not at a true 45, because of the roof slope (it would only be a true 45 on a flat roof, or on a vertical fascia).
View Image “Good work costs much more than poor imitation or factory product” – Charles GreeneCaliforniaRemodelingContractor.com
Edited 11/17/2007 1:06 am by Huck