Standard conditions for a heliacal rising I imagine there are several possible conditions for determining the time of a helical rising of a star, the elevation of the star at sunrise, the latitude of the observer, and the azimuth of the star. 

Is there any kind of equation (or plot/graphic) that relates these variables and can be used to predict whether a star will be visible? (Ignoring weather, ie assuming some standard atmospheric condition).
What I do is compute the limiting magnitude for the position of the object I am interested in, and subtract it from the magnitude of the object (I call this the magnitude contrast).  If negative, it should be visible with the naked eye.  I use the function limmag_jd() in the Fortran library libTheSky for this.

In order to find the best moment in a given night, I compute the contrast for say every 15 minutes, and find the minimum.  You can do this for a number of nights, until the best contrast found is negative, which would be the heliacal rising.

I'm not sure whether there is an easy way using a simple equation - the limiting magnitude will depend on things like the positions of Sun, Moon and the object in question, the phase of the Moon, the magnitude of the object, etc.