Martin Brenner's, Pilot Balloon Resources 

Computations to Convert Raw Data to Derive Wind Speed and Direction

A number of methods for converting theodolite observations to wind speed and direction are available.   A solution in the form of a java scripted web page is available on this web site at no cost.  It requires a Java enabled web browser.   Simply follow the instructions on the page to derive wind data from the recorded observations.  A downloadable Excel Spreadsheet is available also.  It is compliant with computational procedures of the United States Weather Service and all U.S. Military Branches for 100, 30 and 10 Gram balloons with specified nozzles.

Modern Methods include: Sophisticated commercial products such as the Custom Craft Windsock program and calculator used by competition hot air balloonists, An MS DOS (Microsoft Disk Operating System) programs used by the US Weather Service,  Excel Spreadsheets embedded with formulas to perform the necessary calculations (one developed here), and a Java Scripted Web Page which are freely available on this site.   The Windsock program is under development for use on other platforms besides HP48G+ calculators, with additional features as well.  

Historical Methods include: Complex Slide Rules manufactured specifically for pilot balloon use, and the large but more intuitive plotting boards (which are used with a simple trig slide rule).  

Notes on the Ascent rate of a pilot balloon  
An assumed rate of ascent is required for single theodolite ascents (unless the tail method is used).  

I recommend using the tables in the inflation section of this site, with Kaysam Mil Spec balloons.  These are the balloons for which these tables were developed.  For other untested balloon types, it is best to do double theodolite ascents and calculate the mean ascent rates for the balloon type and nozzle used.  

Various formulas used for approximation for the ascent rate of a 30 gram pilot balloon have been published.  One is listed below.  In my research I have not found consistency with the predicted ascent rates of the formulas, published tables and manufacturers test data.  Also the documentation for the formulas often do not list if the formula applies to helium or hydrogen gas filled balloons - a good assumption is hydrogen was used.  
V=72(l³/L²) ^0.208  Where: 
V= ascent rate in meters per minute
l=the free lift, or the actual lifting force in grams of the inflated balloon
L=the total lift, or the free lift, l, plus the weight of the balloon.

The accuracy of the formulas and ascent rates can be improved by increasing the calculated rates of ascent for the first 5 minutes by 20% for minute 1, 10% for minutes 2 and 3, and 5% for minutes 3 and 4.  

The ascent rate tables used by the US Weather Service and Military have increased ascent rates in the early stages of the ascent.  The web page included on this site used to compute wind speed and direction uses an assumed constant ascent rate.  The Spreadsheet uses the more accurate ascent rate tables.