Constraint Diagram Updates for E9X Case Study

+AerodynamicsPkg/TrimDrag.m

@@ -2,7 +2,7 @@
 %
 % [dCD0] = TrimDrag(Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 08 jan 2026
+% last updated: 22 jul 2026
 %
 % estimate the trim drag from any failed engines.
 %
@@ -38,18 +38,24 @@
 
     % return an array of zeros
     dCD0 = zeros(npnt, 1);
-
+    
     % exit the program
     return
 
 end
 
+% get the component
+icomp = Aircraft.Mission.History.SI.Power.Windmill(SegBeg);
+
+% get the number of sources
+nsrc = length(Aircraft.Specs.Propulsion.PropArch.SrcType);
+
 
 %% PRE-PROCESSING %%
 %%%%%%%%%%%%%%%%%%%%
 
 % get the SLS thrust
-Tsls = Aircraft.Specs.Propulsion.Engine.DesignThrust;
+Tsls = Aircraft.Specs.Propulsion.SLSThrust(icomp - nsrc);
 
 % get the moment arm between the fuselage and most outboard engine
 Arm = Aircraft.Specs.Aero.Fuse.DistToEng;

+AerodynamicsPkg/WindmillDrag.m

@@ -2,7 +2,7 @@
 %
 % [Aircraft] = WindmillDrag(Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 05 jan 2026
+% last updated: 22 jul 2026
 %
 % estimate the windmilling drag from any failed engines.
 %
@@ -99,6 +99,9 @@
 ThrCD(isnan(ThrCD)) = 0;
 DelCD(isnan(DelCD)) = 0;
 
+% if there are any theoretical drag coefficients less than 0, convert them to zero
+ThrCD(ThrCD <= 0) = 0;
+
 % compute the adjusted drag coefficient
 TotCD = ThrCD - DelCD;
 

+ConstraintDiagramPkg/+ConstraintSpecsPkg/ElysianE9X.m

@@ -2,11 +2,22 @@
 %
 % [] = ElysianE9X()
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 30 mar 2026
+% last updated: 22 jul 2026
 %
 % create a constraint diagram for a battery electric aircraft
 % representative of the Elysian E9X.
 %
+% data was extracted from the following papers, published in 2024 and 2025:
+%     1) de Vries, R., Wolleswinkel, R. E., Hoogreef, M., & Vos, R. (2024).
+%        A new perspective on battery-electric aviation, part II:
+%        Conceptual design of a 90-seater. In AIAA Scitech 2024 Forum 
+%        (p. 1490). https://doi.org/10.2514/6.2024-1490
+%
+%     2) de Vries, R., Wolleswinkel, R. E., Exalto, J., van den Berg, P.,
+%        Vos, R., & Hoogreef, M. (2025). Conceptual Redesign of a 90-Seater
+%        Battery-Electric Aircraft. In AIAA AVIATION FORUM AND ASCEND 2025
+%        (p. 3153). https://doi.org/10.2514/6.2025-3153
+%
 % INPUTS:
 %     none
 %
@@ -137,41 +148,20 @@
 % number of engines [2024 paper]
 Aircraft.Specs.Propulsion.NumEngines = 8;
 
+% lapse rate exponent correction factor for cruise/diversion/etc.
+Aircraft.Specs.Propulsion.LapseRate.Crs = 0.10;
+Aircraft.Specs.Propulsion.LapseRate.Div = 0.28;
+
 
 %% RUN THE CONSTRAINT ANALYSIS %%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-% determine which constraints to use (0 = 14 CFR 25; 1 = novel)
-Aircraft.Settings.ConstraintType = 0;
+% determine which constraints to use (0 = 14 CFR 25; 1 = novel; 2 = Steiner
+% et al. [extrapolate exiting reg's for >4 engine aircraft])
+Aircraft.Settings.ConstraintType = 2;
 
 % create a constraint diagram
 ConstraintDiagramPkg.ConstraintDiagram(Aircraft);
 
-% add the existing sizing point
-hold on
-scatter(Aircraft.Specs.Aero.W_S.SLS * 9.81 / 1000, 1 / (Aircraft.Specs.Power.P_W.SLS / 9.81 * 1000), 48, "o", "MarkerEdgeColor", [0, 0.251, 0.478], "MarkerFaceColor", [0, 0.251, 0.478]);
-
-% format the axis sizes
-xlim([0, 8]);
-ylim([0, 0.2]);
-axis square
-
-% turn on gridlines
-grid on
-
-% get the axis object
-A = gca;
-
-% set the grid to be semi-transparent and move it to the top
-A.GridAlpha = 0.5;
-A.Layer = "top";
-
-% add minor gridlines
-A.XMinorGrid = "on";
-A.YMinorGrid = "on";
-
-% increase font size
-set(gca, "FontSize", 28);
-
 
 end

+ConstraintDiagramPkg/+ConstraintSpecsPkg/SUSAN.m

@@ -2,9 +2,14 @@
 %
 % [] = SUSAN()
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 25 sep 2025
+% last updated: 22 jul 2026
 %
-% create a constraint diagram for NASA's SUSAN aircraft.
+% create a constraint diagram for NASA's SUSAN aircraft. information was
+% extracted from the following paper:
+%
+% Chau, T., & Duensing, J. (2024). Conceptual Design of the Hybrid-Electric
+% Subsonic Single Aft Engine (SUSAN) Electrofan Transport Aircraft. In AIAA
+% SciTech 2024 Forum (p. 1326). https://doi.org/10.2514/6.2024-1326
 %
 % INPUTS:
 %     none
@@ -28,7 +33,7 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 % aircraft class
-Aircraft.Specs.TLAR.Class = "Turbofan";
+Aircraft.Specs.TLAR.Class = "Turboprop";
 
 % CFR regulations to certify
 Aircraft.Specs.TLAR.CFRPart = 25;
@@ -41,33 +46,38 @@
 %                            %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-% altitudes
-Aircraft.Specs.Performance.Alts.Crs = UnitConversionPkg.ConvLength(40000, "ft", "m");
-Aircraft.Specs.Performance.Alts.Srv = UnitConversionPkg.ConvLength(42000, "ft", "m");
+% altitudes [cruise from economy mission outlined in 2024 paper; service
+% ceiling estimated]
+Aircraft.Specs.Performance.Alts.Crs = UnitConversionPkg.ConvLength(37000, "ft", "m");
+Aircraft.Specs.Performance.Alts.Srv = UnitConversionPkg.ConvLength(40000, "ft", "m");
 
-% stall speed
+% stall speed [based on wing loading from 2024 paper]
 Aircraft.Specs.Performance.Vels.Stl = sqrt(2 * 634 * 9.81 / 2 / 1.225);
 
-% cruise mach number
+% cruise mach number [2024 paper, Tab. 5]
 Aircraft.Specs.Performance.Vels.Crs = 0.775;
 
-% runway lengths and obstacle clearances
-Aircraft.Specs.Performance.TOFL    = 2750;
-Aircraft.Specs.Performance.LFL     = 2750;
+% runway lengths and obstacle clearances [Boeing 737-800 MAX airport
+% planning manual]
+Aircraft.Specs.Performance.TOFL    = 2040;
+Aircraft.Specs.Performance.LFL     = 1700;
 Aircraft.Specs.Performance.ObstLen = UnitConversionPkg.ConvLength(1000, "ft", "m");
 
 % multiplicative factors for OEI conditions
 Aircraft.Specs.Performance.TempInc = 1.25;
 Aircraft.Specs.Performance.MaxCont = 1 / 0.94;
 
 % design specific excess power loss
-Aircraft.Specs.Performance.PsLoss = 0.7689; % mean for twin-engine aircraft
+% 0.9171 - mean SEP loss for twin-engine aircraft
+% 0.0720 - lose a single distributed propulsor (most outboard)
+% 0.3426 - lose the aft turbofan engine
+Aircraft.Specs.Performance.PsLoss = 0.3426;
 
-% landing weight as a fraction of MTOW (computed from baseline)
+% landing weight as a fraction of MTOW (computed from FAST simulations)
 Aircraft.Specs.Performance.Wland_MTOW = 0.8411;
 
 % requirement type (0 = Roskam; 1 = Mattingly, 2 = de Vries et al.)
-Aircraft.Specs.TLAR.ReqType = 0;
+Aircraft.Specs.TLAR.ReqType = 2;
 
 % constraints to use
 Aircraft.Specs.Performance.ConstraintFuns = ["Jet25_111"; "Jet25_119"; "Jet25_121a"; "Jet25_121b"; "Jet25_121c"; "Jet25_121d"; "JetCrs"; "JetLFL"; "JetTOFL"];
@@ -83,18 +93,19 @@
 %                            %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-% wing loading
+% wing loading [2024 paper]
 Aircraft.Specs.Aero.W_S.SLS = 634;
 
-% wing properties
-Aircraft.Specs.Aero.AR = 11.22091;
+% wing properties [2024 paper]
+Aircraft.Specs.Aero.AR = 9.44;
 
-% lift coefficients (from Chau & Duensing and FINCH)
-Aircraft.Specs.Aero.CL.Crs = 0.61;
-Aircraft.Specs.Aero.CL.Tko = 2.0;
-Aircraft.Specs.Aero.CL.Lnd = 3.5;
+% lift coefficients [cruise lift coefficient from 2024 paper, others are
+% estimated based DEP tech. improvements]
+Aircraft.Specs.Aero.CL.Crs = 1.0; % given as 0.61 in 2024 paper, but need maximum CL for the constraint diagram
+Aircraft.Specs.Aero.CL.Tko = 2.5;
+Aircraft.Specs.Aero.CL.Lnd = 3.0;
 
-% parasite drag coefficients (computed)
+% parasite drag coefficients (computed from Raymer)
 Aircraft.Specs.Aero.CD0.Crs = 0.0176;
 Aircraft.Specs.Aero.CD0.Tko = 0.0626; % cruise CD0 + 0.045
 Aircraft.Specs.Aero.CD0.Lnd = 0.1076; % cruise CD0 + 0.090
@@ -112,7 +123,7 @@
 %                            %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-% MTOW
+% MTOW [2024 paper]
 Aircraft.Specs.Weight.MTOW = UnitConversionPkg.ConvMass(190890, "lbm", "kg");
 
 % ----------------------------------------------------------
@@ -124,12 +135,19 @@
 %                            %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-% thrust-weight ratio
+% thrust-weight ratio [2024 paper]
 Aircraft.Specs.Propulsion.T_W.SLS = 0.298;
 
-% number of engines
+% number of engines [for appropriate FARs]
 Aircraft.Specs.Propulsion.NumEngines = 2;
 
+% lapse rate [estimated]
+Aircraft.Specs.Propulsion.LapseRate.Crs = 0.35;
+
+% alternatively, a power-weight ratio [assumed takoeff airspeed as the
+% "characteristic speed" to avoid singularities]
+Aircraft.Specs.Power.P_W.SLS = (Aircraft.Specs.Propulsion.T_W.SLS * 1.21 * Aircraft.Specs.Performance.Vels.Stl) * 9.81 / 1000;
+
 
 %% RUN THE CONSTRAINT ANALYSIS %%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -142,6 +160,6 @@
 
 % add the existing sizing point
 hold on
-scatter(Aircraft.Specs.Aero.W_S.SLS, Aircraft.Specs.Propulsion.T_W.SLS, 48, "o", "MarkerEdgeColor", "red", "MarkerFaceColor", "red");
+scatter(Aircraft.Specs.Aero.W_S.SLS * 9.81 / 1000, 1 / (Aircraft.Specs.Power.P_W.SLS / 9.81 * 1000), 48, "o", "MarkerEdgeColor", "red", "MarkerFaceColor", "red");
 
 end

+ConstraintDiagramPkg/Jet25_111.m

@@ -2,7 +2,7 @@
 %
 % [FAR] = Jet25_111(W_S, T_W, Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 30 mar 2026
+% last updated: 11 jul 2026
 %
 % derive the constraints for takeoff climb with one engine inoperative.
 %
@@ -72,6 +72,11 @@
     % compute the climb gradient from a sigmoid curve
     G = ConstraintDiagramPkg.Sigmoid(Aircraft, 0.5026, -42.54, 0.7925, 1.198);
 
+elseif (Type == 2)
+
+    % extrapolate for any aircraft with more than 4 engines
+    G = 0.005 + 0.003 * NumEng;
+
 else
 
     % throw an error

+ConstraintDiagramPkg/Jet25_119.m

@@ -2,7 +2,7 @@
 %
 % [FAR] = Jet25_119(W_S, T_W, Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 04 dec 2025
+% last updated: 11 jul 2026
 %
 % derive the constraints for a balked landing climb with all engines
 % operative.
@@ -61,6 +61,12 @@
     % compute the climb gradient from a sigmoid curve
     G = ConstraintDiagramPkg.Sigmoid(Aircraft, 0, 0, 0, 3.2);
 
+elseif (Type == 2)
+
+    % extrapolate for any aircraft with more than 4 engines, but it will
+    % always remain the same here
+    G = 0.032;
+
 else
 
     % throw an error

+ConstraintDiagramPkg/Jet25_121a.m

@@ -2,7 +2,7 @@
 %
 % [FAR] = Jet25_121a(W_S, T_W, Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 30 mar 2026
+% last updated: 11 jul 2026
 %
 % derive the constraints for the transition segment climb.
 %
@@ -72,6 +72,13 @@
     % compute the climb gradient from a sigmoid curve
     G = ConstraintDiagramPkg.Sigmoid(Aircraft, 0.4999, -151.22, 0.7855, 0.001);
 
+elseif (Type == 2)
+
+    % extrapolate for any aircraft with more than 4 engines (only applies
+    % for >4 engines, but taking the maximum in case an aircraft with <=4
+    % engines is being designed
+    G = max(0, -0.007 + 0.003 * NumEng);
+
 else
 
     % throw an error

+ConstraintDiagramPkg/Jet25_121b.m

@@ -2,7 +2,7 @@
 %
 % [FAR] = Jet25_121b(W_S, T_W, Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 30 mar 2026
+% last updated: 11 jul 2026
 %
 % derive the constraints for the second segment climb.
 %
@@ -72,6 +72,11 @@
     % compute the climb gradient from a sigmoid curve
     G = ConstraintDiagramPkg.Sigmoid(Aircraft, 0.6024, -42.00, 0.7829, 2.398);
 
+elseif (Type == 2)
+
+    % extrapolate for any aircraft with more than 4 engines
+    G = 0.018 + 0.003 * NumEng;
+
 else
 
     % throw an error

+ConstraintDiagramPkg/Jet25_121c.m

@@ -2,7 +2,7 @@
 %
 % [FAR] = Jet25_121c(W_S, T_W, Aircraft)
 % written by Paul Mokotoff, prmoko@umich.edu
-% last updated: 30 mar 2026
+% last updated: 11 jul 2026
 %
 % derive the constraints for the enroute climb.
 %
@@ -73,6 +73,11 @@
     % compute the climb gradient from a sigmoid curve
     G = ConstraintDiagramPkg.Sigmoid(Aircraft, 0.5026, -42.54, 0.7925, 1.198);
 
+elseif (Type == 2)
+
+    % extrapolate for any aircraft with more than 4 engines
+    G = 0.005 + 0.003 * NumEng;
+
 else
 
     % throw an error