What you need to do is look closely at the physics of the inflated envelope and how the shape is determined. Let's limit the variables and hold the temperature differential constant as we make the balloon bigger. As the envelope height dimension grows, the pressure differential between the inside and outside grows. So that if the envelope tension is the same, the Gaussian curvature will increase. That's not what you want, you want the curvature to decrease in order to make the balloon bigger. So now you have to
decrease increase the envelope tension in proportion to the square of the size change in order to maintain dimensional similitude. You want most of the envelope tension to come from the payload support tendons, and little from the hoop tension.
So you have to solve a fairly complicated but reasonably well conditioned set of equations that account for -
- Envelope weight (lbs/sqft) as a function of size and temperature difference.
- Envelope shape as a function of construction details, payload, temperature, and size.
- Envelope thermal performance wrt fuel system cost and weight.
You can definitely set this up in Excel and use the add-in solver to optimize the envelope parameters.
As sanity check, if we start with a balloon with 20 tendons at 25# tension each, and double the linear scale, we now need 40 tendons to maintain panel size, and need to tension them at 100# to keep similarity with the original. Thus lift (total tension) goes with volume, as we would expect for similar shapes.