extensively. References [8-14] are a small subset of published work on the subject. This section first  presents a summary of the fundamental equations used to estimate the rollable tape spring primary characteristics, such as roll radius and deployment torque, that are fabricated from FRP materials. Current and future research in flexible composites that is needed to have a comprehensive understanding of the underlying physics is then discussed. Finally, details of the tape spring design for this effort are reported. Tape Spring Design Basics Classical Laminate Theory (CLT) describes the linear-elastic relationship between applied loads and the  laminate strains by the ABD matrix [15]. The terms of the ABD matrix are a function of the lamina material  properties and the fiber orientations in the construction. For rollable tape spring applications, the terms in the Dmatrix are of particular interest. AFRL Space Vehicles directorate has developed a general  composite laminate construction [10] that exhibits high stiffness, is dimensionally stable, and can be  subjected to high strains, which are essential characteristics for this class of tape spring applications. Reference 11 provides further details and high strain flexure test data demonstrating laminate  performance. The laminate consists of unidirectional plies sandwiched between bias plain weave plies, as  illustrated in Figure 9. The unidirectional lamina stores the primary strain energy upon stowage, whichdrives the deployment upon release. It is also characterized by high axial stiffness, low susceptibility to  creep/relaxation along the fiber direction, and relatively low transverse and shear stiffness. The plain weave lamina provides the required transverse/shear stiffness and contributes to laminate transverse  bending stiffness. This significantly increases structural stability of the laminate. Due to the bias  orientation, the plain weave lamina is subjected to relatively high shear loads under bending conditions.  The viscoelasticity of the matrix significantly factors into the response, resulting in very high susceptibility to creep/relaxation. If solely used in the laminate design, it will fail to deploy due to excessive relaxation.  Figure 9. Typical laminate constr uction for rollable tape springs.  Rollable tape springs are fabricated and strain free in the deployed configuration. The defining geometric  characteristics (illustrated in Figure 10) are the cross-section radius,  R, subtended angle, /g69, and overall  length, L. Suitable tape spring laminates for this application will have local minimum strain energy state in  the rolled configuration in addition to the other local minimum for the deployed state. This property keeps  the tape spring from automatically billowing when in the rolled state without constraint. The corresponding inner stowed roll radius, Rs, tends to be approximately equal to the cross-section radius, but can be  further estimated by: (1) The central hub disk radius, RH, should be set equal to, or slightly larger than Rs. The tape spring is  capable of being wound at a tighter radius without failure, but will billow to the stable radius if not  constrained. A strain energy gradient exists between the rolled and the deployed states. To make the  tape spring self-deployable, it is constrained in an unstable configuration where free end and rolled  sections are in their respective low-energy states. Releasing this constraint allows the tape spring to proceed to the lowest energy state, which is the initial strain-free deployed configuration. The transition is  503