I need to solve an implicit equation in VBA - vba

Question

I want to give the other parameters that are mentioned in the function, and get a solution for a (the angle), but I get error: "invalid procedure call or argument" Run-time error 5.
I need to call the function in excel worksheet. It is a pretty long equation. Also, it could be that I enter a infinite loop but I don't know how to avoid that.
Function calculateangle(r, h, C, g, d, m, t, x, y As Single) As Single
Dim a As Single
a = 0
While y <> (d + r - r * Cos(a) + (x - (t - r + r * Sin(a))) * Tan(a) - (g
/ (2 * ((((C * m * (2 * g * (h - (d + r - r * Cos(a)))) ^
(1 / 2)) + m * (2 * g * (h - (d + r - r * Cos(a)))) ^ (1 / 2)) / (m +
0.04593)) ^ 2) * (Cos(a)) ^ 2)) * (x - (t - r + r * Sin(a))) ^ 2)
a = a + 0.01
Wend
MsgBox Round(a, 2)
End Function

Answer 1

One obvious issue is that you are using a Function but not returning a value.
This really is a complex piece of spaghetti! However, I suggest an approach like below which will help separate out various bits and thus make it easier to do debugging
Function calculateangle(<...all the bits ...>) As Double
Dim a As Double
Dim tTolerance as Double
dim f1 as Double ' sub sections to help untangle the spaghetti
Dim f2 as Double
Dim f3 as Double
Dim fFinal as Double
Dim tWithinTolerance as Boolean
tWithinTolerance = false
a = 0
tTolerance = 0.01
While not tWithinTolerance
f1 = d + r - r * Cos(a)
f2 = m*2*g*(h - f1)
f3 = x - (t - r + r * Sin(a))
fFinal = (f1 + f3 * Tan(a) - (g / (2 * ((((C * f2) ^
(1 / 2)) + f2 ^ (1 / 2)) / (m + 0.04593)) ^ 2) * (Cos(a)) ^ 2)) * f3 ^ 2)
tWithinTolerance = (Abs(y - fFinal) < tTolerance)
a = a + 0.01
Wend
Calculateangle = a ' note how this sets a return value for the function
End Function
I have left the rounding (which is a presentation issue) to the code that calls this function - this way you can display the answer to whatever level of detail you want!
(apologies if I have mangled any of the calculation on the way through - but you get the concept!)

Answer 2

For the author and those who want to deal with his solitaire. I hope I did not confuse anything in parentheses and simplifications.
Do
vCosA = Cos(a)
vCosADR = d + r * (1 - vCosA) ' d + r - r * vCosA '
vCosMGHADR = m * (2 * g * (h - vCosADR))
vSinAXTR = (x - (t - r * (1 - Sin(a)))) ' - r + r * Sin(a)
'((C * vCosMGHADR) + vCosMGHADR) == ((C + 1) * vCosMGHADR)
If (y = _
(vCosADR + vSinAXTR * Tan(a) - _
(g / _
(2 * _
( _
( _
((C + 1) * vCosMGHADR) / _
(m + 0.04593) _
) ^ 2 _
) * (vCosA ^ 2) _
) _
) * vSinAXTR ^ 2 _
)) Then Exit Do ' *** EXIT DO ***
a = a + 0.01
Loop