M 6899 esd Mathematical Formulation of the TPF Design Problem EsD. TPF Design Vector: G=In, r2 Y3 Y4] 640 unique TPF mission Variable Allowable values Heliocentric Orbital Altitude(AU) y, 1.0,1.5,,, 3.0, architectures 35,4.0,4.5,5.0,55 Collector Connectivity/Geometry Y2 SC1-1D, SCI-2D, SSI Complete enumeration 1D. SSI-2D Diameter of Collector Apertures() 4,6,8, 10 Collector Apertur res determines accuracy 1,2,3,4 MDo methods limited to the Original Optimization Formulation evaluation of 48 design ∑Fy(G vectors(7.5% of the full- Objective factorial trade space) ∑?y lere Constraints Subject to Isolation 2.5≤.≤20mili- arcsec y= year in the mission g= cost O≤10 Integrity ￥= number of" images Surveying SNR≥5 8=angular resolution Med. Spectroscopy SNR210 22= null depth Deep Spectroscopy SNr> 25 O Massachusetts Institute of Technology-Dr. Cyrus D Jilla& Prof. Olivier de Weck Engineering Systems Division and Dept of Aeronautics AstronauticsMathematical Formulation of the TPF Design Problem TPF Design Vector: G = [γ 1 γ 2 γ 3 γ 4 ] • 640 unique TPF mission Variable Allowable Values architectures Heliocentric Orbital Altitude (AU) γ 1.0, 1.5, 2.0, 2.5, 3.0, 1 3.5, 4.0, 4.5, 5.0, 5.5 • Complete enumeration Collector Connectivity/Geometry γ SCI-1D, SCI-2D, SSI- 2 1D, SSI-2D determines accuracy # Collector Apertures γ 4, 6, 8, 10 3 Diameter of Collector Apertures(m) γ 1, 2, 3, 4 4 • MDO methods limited to the Original Optimization Formulation evaluation of 48 design 5 ∑ F y ( ) vectors (7.5% of the full￾G Objective : Min y =1 factorial trade space) 5 ∑ ? y ( ) G y =1 Where Constraint :s Subject to y = year in the mission Isolation 2.5 ≤ θ r ≤ 20 milli- arcsec Φ= cost O ≤ 10 −6 Ψ= number of “images” Integrity Surveying SNR ≥ 5 θr= angular resolution Med. Spectroscopy SNR ≥10 Ω= null depth Deep Spectroscopy SNR ≥ 25 © Massachusetts Institute of Technology – Dr. Cyrus D. Jilla & Prof. Olivier de Weck Engineering Systems Division and Dept. of Aeronautics & Astronautics 10