What is the theoretical maximum height of a herbaceous plant stem?
Update: I have edited the answer for a better structure and for providing reliable references.

Some of the factors that influence growth, while keeping in mind that every species has particular needs:

•   light, temperature 
•   insufficient light leads to etiolation 
•   water 
•   amount of water and dry substances, page 185 
•   water influences diameter 
•   soil 
•   wind 
•   macronutrients 
•   citokinin 
•   genotype 
•   heterosis 
•   inbreeding 
•   pinching the stem stops its growth and promotes lateral stems (I understand that you don't want to, but I list it here so that you can watch out accidents - involuntary pinching has the same effect) 
•   root type 
•   shelter near a fence or a wall 

You might find some info as to what to consider in your calculations in this paper, although it's about trees.

Just for the purpose of knowledge, herbaceous vines like Ipomoea are also stems and they can grow longer than vertical ones. There may be more to add, but I'm only a Horticulture student, not a plant physiologist.

I strongly recommend to ask plant related questions on Gardening and Landscaping SE, a small community, but a very enthusiastic one. Also, hardly can someone become a good gardener without knowing at least the basics of plant biology and psysiology, so you have a major chance there of receiving answers in a few hours, not days.

Good luck with your project and I hope you'll return to tell us your conclusions. We will be happy to see you interdisciplinary approach.