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Previous work has characterized electrohydrodynamic (EHD) thruster performance, determining that thrust-to-power ratios are comparable with that of conventional propulsion at the laboratory scale. Achievable thrust density of EHD propulsion has yet to be experimentally quantified and could be a limiting factor in its application. In this paper, we quantify the achievable thrust density for a wire-to-cylinder electrode geometry using positive corona discharges for electrode pairs operating in parallel and in series. Geometric parameters, including the non-dimensional inter-pair and stage spacings, are varied, and the effect on current and thrust is measured. We estimate a maximum thrust per unit area of 3.3Nm-2 and a maximum thrust per unit volume of 15Nm-3, which we compare with the characteristic thrust density of a range of aircraft. We find that trade-offs exist between thrust density and the achieved thrust-to-power ratio, where increases in the former through either increased power input or pair packing density lead to decreases in the latter. We conclude that EHD propulsion has the potential to be viable from both an energy efficiency perspective (our previous study) and a thrust density perspective (this paper), with the greatest likelihood of viability for smaller aircraft such as unmanned aerial vehicles. [ABSTRACT FROM AUTHOR]