Hello all,
Let’s say for fun, I wanted to measure, mark, and layout diagonal bracing and/or bridging with nothing but tape measure, speed square, and construction master calculator. The angle given in the construction master doesn’t match up with actual angle. Please see attachment- a picture here is worth 1000 words. I know I’m probably missing something easy, but I want to know the math behind it.
Thanks in advance for your knowledge,
Paul
Replies
There must be an error in your drawing. The notes show the rise and run to be equal, but the drawing doesn't. If the rise and run are equal, the angle would be 45 degrees - and you wouldn't need a construction master calculator to know it LOL!!
my bad on the drawing. and yes i made those measurements an obvious 45. That said, the measuring line is long point to long point- and i want my brace to have plumb cuts on both ends, which should be 45 deg. but the angle is actually something else- something to do with the measuring line being across the width of the 1x6... i think.
Actually, your 2x6 does not lay on the 45 * line. Therefore, the angles at the ends will not be 45*. I could calculate them for you, but you can to.
I'm really not sure what you're asking, but as far as the descrepancy between actual, and theoretical.....
I think where you're losing it is the same as where some folks get confused cutting roof rafters the first time. The measurement is on the top leg, parallel cuts. If you deduct the height of the 2x6 cut on a 45 from the total rise, then it is a 45 degree brace, yes.
I'm reading this over, and even though I know exactly what I mean, I'm not sure that what I said will come across as what I actually meant. Clear as mud......:)
Bing
That diagonal measurement given by the Construction Master would be from long point on one end to the short side on the other end. I think your problem is measuring from long to long across the width of the board.
Edited 10/4/2009 9:56 pm ET by Doobz26
Let's say for fun, I wanted to measure, mark, and layout diagonal bracing and/or bridging with nothing but tape measure, speed square, and construction master calculator.
Why throw the calculater in the mix? Just lay out a scaled down triangle on a piece of ply or on a slab. Any angle you need is then visible and can be duplicated.
Here is a webpage I use to cacuate angles and side lengths;
http://www.csgnetwork.com/righttricalc.html
Mike
Small wheel turn by the fire and rod, big wheel turn by the grace of god.
Thanks for the great website, Mike. I am trying it asap. Ya gotta love this Breaktime conversation.
Breaktime has been good to me. Mike
Small wheel turn by the fire and rod, big wheel turn by the grace of god.
Actually the red line is measured long to long and the black line is measured long to short.
These are two completely different lines. A construction master calculator won't give you an across the board measurement. It gives angles that are relative to only one side of the board.
Using your example of 22 9/16 rise and 34.8 degree pitch, the rise = 15 11/16 which when added to the plumbcut depth of a 2x6 cut on a 34.8 degree angle (6 11/16) is 22 3/8.
So if you want to use your Construction Master in this way, you could snap a line across the board at the calculated distance then make your angles relevant to this line.
It's all about marking and measuring from the same reference points.
you talking to me? This ain't my example.
Edited 10/4/2009 10:45 pm ET by Doobz26
I was posting back for the OP. In your post you said :That diagonal measurement given by the Construction Master would be from long point on one end to the short side on the other end. I think your problem is measuring from long to long across the width of the board. Which is opposite of what was in the drawing. The CM measurement and angle is based on long to long, while the OP wants to measure long to short, or plumb to plumb. But basically we are saying the same thing. One measurment is "across the board" and the other is "along the edge".They are different lines and different angles as well as different lengths.
What I want to know is why everyone jumped to the conclusion that you were using a 2X6. You never stated that and it isn't shown in the enclosed drawing, either.
One thing that always helps you to get the math right is to have a decent sketch. Your drawing is so far out of scale (assuming you really were referring to a 2X6) I think it confused you more than it helped you.
THE MATH:
W = board width
X = run
theta = angle from level
Y = rise - slant height of board
Y = X * Tan (theta)
Y = X - W / Cos (theta)
X * Tan (theta) = X - W / Cos(theta)
I solved this iteratively as follows (each column is an iteration):
I can't seem to post pictures or tables of the iterative calculations but I converged on a solution of 35.074 degrees.
Edited 10/6/2009 6:34 pm ET by Mike_Mills
http://www.hunt101.com/data/500/medium/untitledx.jpg
Why can't I attach photos and tables on this web site. I cannot even attach files I've uploaded here.
Edited 10/6/2009 10:42 pm ET by Mike_Mills
View ImageView Image bakersfieldremodel.com
What I want to know is why everyone jumped to the conclusion that you were using a 2X6
He called it a 1x6 in one post - seemed like a typo, since 2x6 seemed a lot more likely for that situation.
I can't seem to post pictures or tables of the iterative calculations but I converged on a solution of 35.074 degrees.
Pretty close to what I came up with: 35.024 degrees.
View Image bakersfieldremodel.com
Edited 10/7/2009 3:41 am by Huck
One thing that always helps you to get the math right is to have a decent sketch. Your drawing is so far out of scale (assuming you really were referring to a 2X6) I think it confused you more than it helped you.
2nd that!View Image bakersfieldremodel.com
Mike, when I first attempted the math I thought the solution required iterative calculations as well (and I still think it's a legit means of solving this problem). Check out the Math Notes and Diagrams link in the calculator I posted to Paul; there are several closed form resolutions. (Er ... I hope I'm understanding the OP's problem/question correctly).
Joe Bartok
Edited 10/7/2009 10:43 am ET by JoeBartok
I'm sure there are many ways to solve it. I was in front of my PC with Excel loaded, so an iterative (a numerical solution) was easy to do.
I think of an iterative solution as the mathematical equivalent of "cut it and see if it fits, if not, cut it some more and stop when it's close enough" method of solving the problem.
Edited 10/7/2009 11:03 am ET by Mike_Mills
Paul, I think the comments by others regarding your working points are on the money. Try this Rafter to Fixed Ridge Height Calculator (based on a solution originally posted by Joe Carola; click on the "Imperial Units Rafter Calculator").
Here are the numbers I entered ...
x = 22.5625
y = 22.5625
Plate Width = 0
Design to ... select "Rafter Depth"
Entering a "Design Value" of 5.650454 returns an angle of 34.8°, a diagonal (the Square Root of x² + y²) of 31.908194 ... that's damn close to your 31 15/16. Also note that the arctan (x/y) field returns 45°. So it seems you are using a 2×6.
Edited 10/7/2009 10:36 am ET by JoeBartok
Edited 10/7/2009 10:49 am ET by JoeBartok
Edited 10/7/2009 10:51 am ET by JoeBartok
Edited 10/7/2009 10:51 am ET by JoeBartok
Here are a couple of links to related threads with text and images in the JLC Forums. There used to be a thread in Joe Fusco's old forum but that's history now ...
Fixed Ridge Height and Rafter Pitch ... Joe C. posted a CM solution. The calculator isn't wrong, it's how you are inputting the values.
The math, please
Hope this helps.
Edited 10/7/2009 11:19 am ET by JoeBartok
Edited 10/7/2009 11:21 am ET by JoeBartok
LOL ... the Construction Master/speedsquare answer to your riddle is right here in the forums
http://forums.taunton.com/tp-breaktime/messages?msg=64231.1
Edited 10/7/2009 3:33 pm ET by JoeBartok
Joe, thanks so much for all your help on this. I know how easy it is to scribe the angle i need- then just go and cut it...but sometimes I just want to know why things work the way they do.
I intend to take some time and really draw this stuff out on some paper so i can digest it.
I'm not sure if this analogy works or not but... this problem with the math is alot like trying to cut bridging-- with nothing but a protractor and math. Sure its easy to do with a rafter square, but doing it with something that only has degrees on it is a different monster. Nobody would ever want to do it that way...but i know it can be done. thanks again for you help and know how.
Hi Paul - I posted this earlier, but neglected to direct it to you, so in case you missed it, I'll post it again for your benefit.
I'm thinking your question pertains to this situation:
View Image
...in which case, the run entered should be 22 9/16", but the rise should be 15 13/16", in order to yield the correct angle, which the online calculator I found at http://www.1728.com/gradient.htm gives me as 35.024 degrees. Subtracting that from 90 degrees, I'm thinking the angle for the cut is gonna be 54.976 degrees.
View Image bakersfieldremodel.com
Edited 10/7/2009 7:16 pm by Huck
...and here's the other one you probably missed - this time figured with a 2x4.
The run is 22 9/16 (22.5625) and the rise is 18 1/16 (18.0625). The angle is 38.679 degrees, so the angle of the cut would be 51.321 degrees.
View Image
View Image bakersfieldremodel.com
Edited 10/7/2009 7:18 pm by Huck