Math Question (Finding an equation)

john_mcclary

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

konstantin_shiriazdanov

at least it calculates A2

you need the formula for "result"

Here is a C form for A2:

ArcTan((R*(-H1 + H2 + R*Cos(A1) + L2*Tan(A1)))/Sqrt(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2)) + <br>     (L1 - L2 + R*Sin(A1))*Sqrt(1 - Power(R,2)/(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))),<br>    -((R*(L1 - L2 + R*Sin(A1)))/Sqrt(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))) + <br>     (-H1 + H2 + R*Cos(A1) + L2*Tan(A1))*Sqrt(1 - Power(R,2)/(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))))/Degree

john_mcclary

Thank you @konstantin_shiriazdanov I'm sure that works, but I was having a hard time simplifying it.   me no that smart

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  

konstantin_shiriazdanov

at least it calculates A2

you need the formula for "result"

Here is a C form for A2:

ArcTan((R*(-H1 + H2 + R*Cos(A1) + L2*Tan(A1)))/Sqrt(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2)) + <br>     (L1 - L2 + R*Sin(A1))*Sqrt(1 - Power(R,2)/(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))),<br>    -((R*(L1 - L2 + R*Sin(A1)))/Sqrt(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))) + <br>     (-H1 + H2 + R*Cos(A1) + L2*Tan(A1))*Sqrt(1 - Power(R,2)/(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))))/Degree

john_mcclary

Thanks, Give me time to digest that

philip_thomas

john_mcclary

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_shiriazdanov

you can set this repeatable piece from denominators to its own variable, for example:

Sqrt(Power(L1 - L2 + R*Sin(A1),2) + Power(-H1 + H2 + R*Cos(A1) + L2*Tan(A1),2))L0 = 

john_mcclary

Thank you @konstantin_shiriazdanov I'm sure that works, but I was having a hard time simplifying it.   me no that smart

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_mcclary

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