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Math Question (Finding an equation)

john_mcclaryjohn_mcclary Member, Developers Posts: 2,114 PRO
edited November 6 in General
Non-Onshape question, but I figure there are enough smart people here, someone could help me :)
I've always just had a CAD program available to me, I just let the software do the math. Silly me..

I have to make an excel sheet that can help quote some straight chutes. They can enter all the black numbers you see below in the form of variables, so I need the full equations to solve for the grey numbers.
The problem I have is I don't know how to solve for H₃ and L₃ which I need to ultimately find A₂

At the very least I need A₂ that is the number all of this mess is trying to solve for. It lets us know if packages will even slide down the chute, or if we need to add/remove friction surfaces.
H₃ and L₃ will help them visualize how large the swoop is without asking for a model.

Here is what I got so far:

H₃ = ? = ~13.875
H₄ = sin(A₁)L₂ = sin(5°)20 = 0.08716 * 20 = ~1.74311
L₃ = ? = ~42.741
A₂ = atan( (H₁-H₂-H₃-H₄) / (L₁-L₂-L₃) ) = atan( (144-22-13.875-1.74311) / (240-20-42.741) ) = ~30.97

Furthermore: the values of A₁ L₂ & H₄ can be equal to Zero


Tagged:

Best Answers

  • john_mcclaryjohn_mcclary Posts: 2,114 PRO
    edited November 10 Accepted Answer
    Thank you @konstantin_shiriazdanov I'm sure that works, but I was having a hard time simplifying it. :/  me no that smart :disappointed:

    Morgan shared a doc with me and we worked it out there. Here is the result he came up with which I transposed into VBA for excel.

    EDIT: Fixed bug in code
    Public Function AngleOfMainChute(HorizontalLength As Double, ExitHorizontalLength As Double, EntryElevation As Double, ExitElevation As Double, ExitAngle As Double, SwoopRadius As Double)
        toRad = Application.WorksheetFunction.Pi() / 180
        toDeg = 180 / Application.WorksheetFunction.Pi()
        l1 = HorizontalLength
        l2 = ExitHorizontalLength
        h1 = EntryElevation
        h2 = ExitElevation
        a1 = ExitAngle * toRad
        r = SwoopRadius
        
        h4 = Tan(a1) * l2
        arcEndX = l1 - l2
        arcEndY = h1 - h2 - h4
        arcCPointX = arcEndX + Sin(a1) * r
        arcCPointY = arcEndY - Cos(a1) * r
        triHypot = Math.Sqr(arcCPointX ^ 2 + arcCPointY ^ 2)
        
        hypotToMainLineAngle = Application.WorksheetFunction.Asin(r / triHypot)
        hypotAngle = Math.Atn(arcCPointY / arcCPointX)
        
        result = hypotAngle + hypotToMainLineAngle
        AngleOfMainChute = result * toDeg
    End Function
    Thank you everyone :) 


Answers

  • john_mcclaryjohn_mcclary Member, Developers Posts: 2,114 PRO
    Thanks, Give me time to digest that :)
  • philip_thomasphilip_thomas Member, Moderator, Onshape Employees, Developers Posts: 1,373

    Philip Thomas - Onshape
  • john_mcclaryjohn_mcclary Member, Developers Posts: 2,114 PRO
    Yea I know right? I only get part way thru it before I go crosseyed.

    :)


    Trying to take it out of featurescript notaion and get it back to simple math.  In the end I need to code it in visual basic in excel
  • konstantin_shiriazdanovkonstantin_shiriazdanov Member Posts: 931 ✭✭✭✭✭
    edited November 8
    you can set this repeatable piece from denominators to its own variable, for example:
    L0 = Sqrt(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))
  • john_mcclaryjohn_mcclary Member, Developers Posts: 2,114 PRO
    edited November 10 Accepted Answer
    Thank you @konstantin_shiriazdanov I'm sure that works, but I was having a hard time simplifying it. :/  me no that smart :disappointed:

    Morgan shared a doc with me and we worked it out there. Here is the result he came up with which I transposed into VBA for excel.

    EDIT: Fixed bug in code
    Public Function AngleOfMainChute(HorizontalLength As Double, ExitHorizontalLength As Double, EntryElevation As Double, ExitElevation As Double, ExitAngle As Double, SwoopRadius As Double)
        toRad = Application.WorksheetFunction.Pi() / 180
        toDeg = 180 / Application.WorksheetFunction.Pi()
        l1 = HorizontalLength
        l2 = ExitHorizontalLength
        h1 = EntryElevation
        h2 = ExitElevation
        a1 = ExitAngle * toRad
        r = SwoopRadius
        
        h4 = Tan(a1) * l2
        arcEndX = l1 - l2
        arcEndY = h1 - h2 - h4
        arcCPointX = arcEndX + Sin(a1) * r
        arcCPointY = arcEndY - Cos(a1) * r
        triHypot = Math.Sqr(arcCPointX ^ 2 + arcCPointY ^ 2)
        
        hypotToMainLineAngle = Application.WorksheetFunction.Asin(r / triHypot)
        hypotAngle = Math.Atn(arcCPointY / arcCPointX)
        
        result = hypotAngle + hypotToMainLineAngle
        AngleOfMainChute = result * toDeg
    End Function
    Thank you everyone :) 


  • john_mcclaryjohn_mcclary Member, Developers Posts: 2,114 PRO
    edited November 9
    Forum bugged out, and made a this a separate post when I edited my comment to add a photo... Which I could delete a comment :)
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