Hmm. I'd say proportional to current weight... dweight/dheight=weight, dweight/weight=dheight, ln weight = height + c', weight = c*exp(height) Let's say yo

Hmm. I'd say proportional to current weight... dweight/dheight=weight, dweight/weight=dheight, ln weight = height + c', weight = c*exp(height) Let's say you need 1000 kg for 10 meters of tower supporting another 1000 kg of load. A mass ratio of 2. To extend that another 10 m, you need to support the above 2000 kg, so you need more beefy stuff for the next 10 m below, 2000 kg of tower. Now you have 4000 kg to support for the next 10 m so you have to use 4000 kg of tower, 8000 for the next etc. That's exponential. Of course, in reality the base is less than two every 10 meters, steel is stronger per weight than that. Though yes, on the other hand, the bending moment grows linearly only with height, and different buckling things are only power things. I don't know then if structural frequencies etc start coming in at some point.