  This paper proposes and simulates vertical airborne wind energy (AWE) farms
based on multi-aircraft systems with high power density (PD) per ground area.
These farms consist of many independently ground located systems that are
flying at the same inclination angle, but with different tether lengths, such
that all aircraft fly in a large planar elliptical area that is vertical to the
tethers. The individual systems are assigned non-overlapping flight cylinders
depending on the wind direction. Detailed calculations that take into account
Betz' limit, assuming a cubically averaged wind power density of 7 m/s, give a
potential yearly average PD of 43 MW/km$^2$. A conventional wind farm with
typical packing density would yield a PD of 2.4 MW/km$^2$ in the same wind
field. More refined simulations using optimal control result in a more modest
PD of 6 MW/km$^2$ for practically recommended flight trajectories. This PD can
already be achieved with small-scale aircraft with a wing span of 5.5 m. The
simulations additionally show that the achievable PD is more than an order of
magnitude higher than for a single-aircraft AWE system with the same wing span.
