I am trying to rearrange the following equation (fletcher) to enable $LEV$ testers to measure the hood entry velocity $Vh$, and hood entry area $A$, and knowing the capture velocity Vc, required , calculate the maximum working distance x. I can simplify the equations for $\frac{W}{L}=1$, but when rearranging for any other aspect ratio the solution includes a complicated Lambert-W function in the middle of the solution. I need to try and get this into a format that can be included in an excel spreadsheet.
The series of equations are:
$Vh=Vc(0.93+8.58α^2)$
$α=(x/√A)(W/L)^(-β)$
$β=0.2(x/√A)^(-1/3)$
Which when incorporated into a singular equation gives:
$Vh=Vc(0.93+8.58((x/√A)(W/L)^(-0.2(x/√A)^(-1/3)))^2)$
Can anyone assist in rearranging this to find x as the subject, in a way that can be entered into an excel calculation?
Many thanks in advance!