  We propose and develop an electrical and mechanical system model of a
single-axis linear-motion kinetic energy harvester for impulsive excitation
that allows its generated load power to be numerically optimised as a function
of design parameters. The device consists of an assembly of one or more spaced
magnets suspended by a magnetic spring and passing through one or more coils
when motion is experienced along the axis. The design parameters that can be
optimised include the number of coils, the coil height, coil spacing, the
number of magnets, the magnet spacing and the physical size. We use the
proposed model to design optimal energy harvesters for the case of impulse-like
motion like that experienced when attached to the leg of a human. We generate
several optimised designs, ranked in terms of their predicted load power
output. The three best designs are subsequently constructed and subjected to
controlled practical evaluation while attached to the leg of a human subject.
The results show that the ranking of the measured output power corresponds to
the ranking predicted by the optimisation, and that the numerical model
correctly Predicts the relative differences in generated power for complex
motion. It is also found that all three designs far outperform a baseline
design. The best energy harvesters generated an average power of 3.01mW into a
40$\Omega$ test load when driven by footsteps whose measured peak impact was
approximately 2.2g. With respect to the device dimensions, this corresponds to
a power density of 179.380$\mu\text{W/cm}^3$.
