axial tension should consist of either SWCNTs with small diameters or uniformly loaded MWCNTs with densely packed shells to maximize . The CNTs are arranged in groupings, generally bundles. The strain energy density must be reduced by a fill factor k to account for the spacing between the individual CNTs. Consider the cross-section of a bundle of closely packed SWCNTs of radius r, arranged into a two-dimensional triangular lattice with a lattice constant of 2r+h. Ideal packing is assumed with a spacing of h=0.34 nm which is taken equal to the graphitic spacing. When the CNTs are arranged in a bundle the best packing fraction is produced when they are packed in a hexagonal closed packed structure. Consider a cross section of one bundle. A hexagonal shape will be observed. The hexagonal shape with an area of is taken to be the repeating geometrical unit in the bundle. Calculations can be performed to show that fill factor k = 91%. In reality, there may not be ideal packing within a bundle, as the actual fraction k may be lower than the value calculated. The expression of strain energy shows that it is advantageous to apply a high tensile strain to the springs to maximize energy storage since strain energy is proportional to square of the strain. Axial compression Analysis is performed on CNTs subject to compressive loads. The CNT is assumed to be a hollow cylindrical beam of length L, Young's modulus E, and thickness n.h, where n is the number of layers and h=0.34 nm is the thickness of one shell (taken equal to the separation between graphene sheets in graphite). The continuous tube has a mean radius r and diameter d. The cylinder has inner and outer radii of and . The shell's cross-sectional area is and the total enclosed area is . The strain energy that can be stored in the bar under axial compression to a strain of is ) = The strain energy density is just the strain energy divided by the enclosed volume. High energy densities are achieved with a high ratio. Therefore, in order for CNT springs to achieve a high energy density either SWCNTs with small diameters or MWCNTs with densely packed shells should be used. Support structure The purpose of using a support structure is to be able to store energy before it is released for use. The support structure should