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Math Help - Pitch of a rafter - Help Please

  1. #1
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    Pitch of a rafter - Help Please

    I need a formula that works out the pitch (theta) of a rafter with the known rise (o) and known run (a), and known depth of the rafter (d) but with an unknown plumb depth of the rafter (because the pitch at this stage is unknown)

    I would put a diagram in but i am afraid i don't know how to, sorry.

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  2. #2
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    Quote Originally Posted by rileysan View Post
    I need a formula that works out the pitch (theta) of a rafter with the known rise (o) and known run (a), and known depth of the rafter (d) but with an unknown plumb depth of the rafter (because the pitch at this stage is unknown)

    I would put a diagram in but i am afraid i don't know how to, sorry.
    The pitch here is the angle theta made by the rafter with the horizontal.

    tan(theta) = rise / run = o/a
    So, theta = pitch = arctan(o/a)

    Example, if rise = 2 meters, and run = 12 meters,
    pitch = arctan(2/12) = arctan(0.1666667) = 9.46 degrees.

    ----------------
    If only the depth ,(I assume you mean the total length of the rafter starting from its intersection with the run), and the run are known, then
    cos(theta) = run / depth = a/d
    Then, pitch = arccos(a/d).
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  3. #3
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    Revised Detail

    So given a=2000 and o=823.7 and d=90, we can iterate to an answer of 20 Pitch () .

    http://www.savefile.com/files/1673394

    My question may be more or an algebra question, I'm not sure.

    I need a formula that doesn't use iteration (ie. doesn't calculate the approx depth on the plumb (?) then work out the pitch then revise the plumb depth (?) and then revise the pitch again until an answer is whittled down.)
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  4. #4
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    Quote Originally Posted by rileysan View Post
    So given a=2000 and o=823.7 and d=90, we can iterate to an answer of 20 Pitch () .

    http://www.savefile.com/files/1673394

    My question may be more or an algebra question, I'm not sure.

    I need a formula that doesn't use iteration (ie. doesn't calculate the approx depth on the plumb (?) then work out the pitch then revise the plumb depth (?) and then revise the pitch again until an answer is whittled down.)
    Oh, so that is the sketch. You should have shown that in your original post so that we could have solved it at once.

    Anyway, the pitch now is arctan (o/a) = arctan(823.7 /2000) = arctan(0.41185) = 22.3843 degrees.

    So d, the depth, is the deph of the rafter.
    You want to find the vertical component of d that is marked "?" in your sketch.

    By Geometry, the angle between d and the "?" is also the pitch or 22.3843 degrees.
    So,
    cos(pitch) = d/"?"
    and so,
    "?" = d / cos(pitch) = 90 / cos(22.3843 deg) = 97.334 -----answer.
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