Non-Dimensional Wind Velocity and other curious Scaling Laws

Engineering Scaling Laws are wonderfully complex. They cut both ways, helping or hindering up-scaling intentions. Total gravity force increases cubically with volume, and compounded stresses concentrate in structural discontinuities, while engineering material bond strength remains constant. Jumbo jets would never have grown so big, economically, if the unit-human had not remained the same size as everything else grew bigger cubically.

A similarly subtle Wind Energy Scaling Law, Non-dimensional Wind Velocity, has been identified in Airborne Wind Energy (AWE) R&D for some years now. As an AWES (AWE System) architecture grows in scale, most-probable wind velocity at a given deployment location remains constant; does not scale. This partly holds for HAWT scaling, that grow taller into better wind, but not as fast as their non-dimensional cubic mass grows in proportion to wind velocity. AWE design is less settled archetypally.

For an AWES, its Mass Scaling Exponent (MSE) predicts how well it will scale. Thin Membrane wings are quasi 2D, with an MSE near 1. Rigid wings are thickened, for an MSE of about 2. “Energy Drones” are fully 3D, with a severely scale-limiting MSE of 3 or more. High MSE of flying generators is further compounded by slow thermal transfer (cooling). The geophysical wind-field is itself scale limited to about 10km high, vertically, and limited to planetary-scale, horizontally.

For average most-probable-wind, 10kW is close to a practical and economic AWES scale limit for flygen “Energy Drones”. Hang-glider construction with groundgen placement takes this to 50kW or so. LEI (leading-edge-inflatable) construction can achieve about100kW effectively (KitePower). Fabric parafoils achieve about a MW or two (SkySails). Single-skin kites might do 10MW each (Kiteship, NASA Power Wing (NPW)). Tensile load-paths scale fractally fairly well. Tethers scale aerodynamically rather well, as cross-sectional strength increases quadratically as profile increases linearly. An odd scaling law limiting soft kite units is operational; fabric panels are too easily abraded by ground-handing a too heavy a unit-kite (>~300kg).

From there the AWES design game shifts to many-connected kite-networks of high unit-count (kPower), as a fractal non-dimensional scaling strategy. Kite Networks in principle could reach demo GW unit-plant ratings as early as 2030, and someday scale to even to TW ratings, by multiple altitude stages, all the way to 10kM, and >10kM horizontal extent, within basic non-dimensional wind velocity scaling law constraints.