Preliminary Design of the NB$_3$Sn $cos$ $\theta$ Short Model for the FCC

The next generation particle accelerators will need to increase by an order of magnitude the center-of-mass energy: a viable solution is a 100 TeV circular collider, temporarily called Future Circular Collider (FCC). To achieve this goal, a new generation of double aperture superconducting magnets, capable of generating a high quality, stable 16 T magnetic field in a 50 mm bore is being developed. In order to achieve this challenging task, the CERN's plan includes several intermediate steps in the development of accelerator-grade Nb3Sn magnets. The first constructive phase will be a 1.5 m long, single aperture cos-theta dipole, with a target central magnetic field of 12 T and an ultimate field of 14 T. In this contribution, the preliminary 2D design of this short model, named Falcon Dipole (Future Accelerator post-Lhc Cos $\theta$Optimized Nb$_3$Sn Dipole) will be presented in detail. It features a 2-layers design, with Nb3Sn state-of-art conductor in order to generate the required field. A solution for the mechanical design will also be presented: the necessary pre-stress will be given by a shell-based concept using bladders and keys. This technique avoids giving all the pre-load with just the collaring and it allows to obtain about half of the pre-stress during the assembly of the magnet at room temperature, and full pre-stress in second instance thanks to the cool down. The FalconD project aims at gaining experience on the technology involved to reach fields above 11 T with Nb3Sn coils.