Christof Beaupoil Administrator

Will it scale?

One (of many) key questions for all Airborne Wind Energy Systems is: Will it scale?

If the square-cube scaling law limits the size of conventional turbines, it will certainly limit the scaling of any airborne structure.

Here are some initial thoughts on scaling the OTS system up:

The Rotor:

The rotor is a rigid structure and the square-cube law will certainly apply. The most obvious way around it would be to stack multiple rotors. By stacking the scaling becomes linear. Twice the number of rotors will generate twice the power (ignoring shadowing effects) and have twice the weight.

The OTS transmission to the ground:

For the OTS scaling up in length and scaling up the transferred power have to be considered. Scaling up in length is linear. Twice the length will have twice the weight - under the assumption that the OTS weight can be ignored for its own dimensioning. This is true if the tether forces used for power transmission are large in relation to tether forces needed to support its own weight.

The current OTS weights 3.2 lb/100ft (50g/m). This is 1/100th of its strength or in other words if you scale it up to a length of 10,000 ft you would have to double its strength to support its own weight.

Do not try to power your space elevator with an OTS but for your AWE system you will be fine.

To double the power you can double the speed/rpm or double the torque. Doubling the torque as a first approximation will double the tether forces and double the buckling load on the struts.

I assumed that tether strength would scale linearly to its cross section and therefore its weight. When looking at specs you will see - for reasons I do not understand (yet :) - that strength growth faster than weight. If you are a tether experts, please enlighten me. But for now this brings us on the safe side.

The struts are Euler's columns type 1 (pivoted in both ends). If we want to double the allowable load we have to double our Moment of inertia. For a strut with a cylindrical cross section this is Ix = π (do4 - di4) / 64 . Weight will go squared with diameter while buckling force will go in forth power. Who cares about square-cube if you can beat it with square-forth power :)

Summary: According to my cocktail napkin calculations the OTS system should scale very nicely! But then again don't trust an engineer that has not engineered for a quarter of century! PLEASE correct me if I am wrong - I can handle public shaming :)

What I haven't considered in this calculation are drag based losses of the OTS. It is moving multiple tethers cross wind at high speed - so there will be losses that can not be ignored when scaling up. For now I lack the skill to simulate and the data to calculate. Anybody up for the challenge? If not I will have to take some data from my next version. Until then: