Deployable flexible strips resembling carpenters' tape measures have been used to deploy and support devices such as antennas and solar panels for some time. These curved strips are often referred to as "booms", especially when they also act as structural members. Perhaps the most famous example was the Viking Lander soil collection arm, which could be reeled up or extended as required. These booms are usually constructed from thin curved sheets of metal, or laminates of fibre reinforced polymer. Some of these booms possess the property of "bistability", which means they do not need to be constrained once they have been coiled up. Flexible deployable booms have found other uses in deploying antennas and imaging systems on the battlefield, inserting monitoring equipment into nuclear power plants, deploying a flexible solar array from the International Space Station (ROSA experiment), and very recently in forming the masts of the InflateSail drag deorbiting sail: the first European sail to be deployed in space, and one of the first successful demonstrations of orbital debris removal technology. These booms have several advantages over deployable systems consisting of rigid links joined by hinges or sliders, including simplicity, a very small number of moving parts, and they often can be made to be very lightweight. However, two main limitations of these flexible booms are that the vast majority to those developed to date only deploy in a straight line, and that the exact geometry and deployed length of boom cannot be very accurately controlled. Recently, versions of these deployable booms that are not only curved in one direction (like a tape measure), but have "double curvature" have started to be studied in earnest. These booms can be deployed into a whole array of new shapes such as parabolas, a torus, and even helices. This opens up a number of new possible applications, such as lightweight deployable parabolic dishes, large tent supports, and as active elements in directional antennas. In our project, we will accelerate the technology readiness level (TRL) of this technology by developing the design and modelling tools required to work with doubly-curved deployable flexible booms (focussing mainly on fibre reinforced laminate materials), and improving the manufacturing methods and deployment mechanisms in an effort to make booms with the necessary geometric precision and dimensional stability to be used in RF and optical systems. To design these highly constrained flexible structures we will be adapting a very powerful equation solving technique called polynomial continuation to seek out the perfect laminate fibre angles and thicknesses to get the mechanical behaviour required. To model the behaviour of the booms we will be generating novel energy methods to predict coiled and deployed shapes, building on methods we have already developed in this field. To motivate the development of these technologies, the University of Surrey is partnering with Surrey Satellite Technology (SSTL) and RolaTube Technology Ltd. (RTL) to build two new devices making use of curved flexible deployable booms. With RTL we are constructing a directional helical antenna that unwinds from a small motorised hub, deploying its own ground plane at the same time. With SSTL we are developing a novel Earth imaging telescope barrel consisting of multiple curved strips which deploy simultaneously to form the outer barrel. The telescope strip is an especially interesting device because it requires a single curvature in the deployed state where it forms part of the barrel of the telescope, but quite a complicated double curvature when coiled into a ring around the base of the telescope.