With subsonic airliners ventral fins are usually a stopgap, put in place because flight tests have shown that the vertical tail as designed and built, lacks effectivity for stabilising. It is much easier to add a ventral fin than to extend the vertical tail: the tail root will need to be re-designed to accommodate the extra bending moment. Or they are added to compensate for the de-stabilising effect of a modification, as in this Gulfstream:
Design and dimensioning of the vertical tail of an airliner is not straightforward, due to the many interference effects from the fuselage and the fuselage-wing intersection. From Torenbeek section 9.6:
The design of the vertical tailplane is more complicated than that of the horizontal tailplane. It is generally quite difficult to calculate the lateral-directional aerodynamic characteristics, since they are closely connected with a complicated asymmetrical flow field behind the wing/fuselage combination, which meets the oncoming air at an angle of sideslip.
The book gives a design process for determining the tail volume (tail area * moment arm). There is a relatively large number of input variables:
- number of engines;
- location of engines;
- high/low wing;
- vertical position of horizontal stabilisers.
Figure 9-24 above from the same book is for rapid dimensioning of vertical tail volume of single engines or wing root mounted engines, Figure 9-23 is for multi-engined aircraft. There is no design procedure for sizing ventral fins in the book, but they would follow the same design principles regarding vertical tail volume.
With airliner size aircraft, a big part of the solution is numerical computation. The engineering simulator will have a detailed 6-DoF model of the aeroplane, including aeroelastic effects and the flow field behind the wing/fuselage intersection. Ventral fin dimensions and placement can then be test flown on the engineering sim first.