From c1f63afb1f8c5cbeb1e6181e5a103ec0ef1edb21 Mon Sep 17 00:00:00 2001
From: Meric Taneri <meric.taneri@tum.de>
Date: Wed, 5 Feb 2025 12:55:12 +0100
Subject: [PATCH 1/6] constraint analysis documentation added
---
docs/documentation/analysis.md | 2 +-
.../analysis/constraint_analysis/index.md | 249 ++++++++++++++++++
2 files changed, 250 insertions(+), 1 deletion(-)
create mode 100644 docs/documentation/analysis/constraint_analysis/index.md
diff --git a/docs/documentation/analysis.md b/docs/documentation/analysis.md
index a2581a3..7db3eaf 100644
--- a/docs/documentation/analysis.md
+++ b/docs/documentation/analysis.md
@@ -61,7 +61,7 @@ The `constraint_analysis` module updates the performance criteria wing loading a
|Module Version|Language|License|Documentation|
|:---:|:---:|:---:|---|
-|1.0.0|:simple-cplusplus: |GPLv3|-|
+|1.0.0|:simple-cplusplus: |GPLv3|[Link](analysis/constraint_analysis/index.md)|
---
diff --git a/docs/documentation/analysis/constraint_analysis/index.md b/docs/documentation/analysis/constraint_analysis/index.md
new file mode 100644
index 0000000..152af7c
--- /dev/null
+++ b/docs/documentation/analysis/constraint_analysis/index.md
@@ -0,0 +1,249 @@
+# Constraint Analysis {#mainpage}
+
+# Aerodynamic and Performance Equations for Constraint Analysis Module
+
+## Function
+
+Adjust the design point based on the point performance requirements.
+
+## Rationale
+
+The end-of-the-loop aircraft’s aerodynamic performance is different to that of the beginning-of-the-loop aircraft. Therefore, it is necessary to size the aircraft based on the most up to date data from the design loop. This way, the design is ensured to have the best fitting characteristics to the mission and performance requirements.
+
+## Logic
+
+Point performance requirements are evaluated as constraints within the T_SL/W_TO – W_TO/S_Ref design space. The point is selected to have the minimum T_SL/W_TO possible value that lies in the feasible space.
+
+## Derivation
+
+1\. Lift Equation (getCL):
+
+L=n\\cdot W=\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot C_L\\cdot S
+
+C_L=\\frac{n}{\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot\\left(W/S\\right)
+
+2\. Drag Equation:
+
+D=\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot C_D\\cdot S,\\emsp\\mathrm{where\\ }C_D=f\\left(C_L\\right)
+
+3\. Thrust-Difference Equation:
+
+T-D=W\\cdot\\frac{d}{dt}\\left(h+\\frac{\\left(M\\cdot a\\right)^2}{2\\cdot g}\\right)
+
+4\. Weight and Thrust Relationships:
+
+W=\\beta\\cdot W_{TO}
+
+T=\\alpha\\cdot T_{SL},\\emsp\\mathrm{where\\ }\\alpha=f\\left(M,h\\right)
+
+5\. Substituted Thrust-Difference Equation:
+
+T-\\left(\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot f\\left(C_L\\right)\\cdot S\\right)=W\\cdot\\frac{d}{dt}\\left(h+\\frac{\\left(M\\cdot a\\right)^2}{2\\cdot g}\\right)
+
+## Final Substituted Equation
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta\\cdot\\frac{d}{dt}\\left(h+\\frac{V^2}{2\\cdot g}\\right)+\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot f\\left(C_L\\right)}{\\alpha\\cdot\\left(W_{TO}/S\\right)}
+
+f\\left(C_L\\right)=C_D\\left(\\frac{\\beta\\cdot n}{\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot\\left(W_{TO}/S\\right)\\right)
+
+## Parameter Meanings
+
+L: Lift (N)
+
+n: Load factor (dimensionless)
+
+W: Weight (N)
+
+ρ: Air density (kg/m^3)
+
+M: Mach number (dimensionless)
+
+a: Speed of sound (m/s)
+
+C_L: Lift coefficient (dimensionless)
+
+C_D: Drag coefficient (dimensionless)
+
+S: Reference area (m^2)
+
+T: Thrust (N)
+
+D: Drag (N)
+
+h: Altitude (m)
+
+g: Gravitational acceleration (9.81 m/s^2)
+
+β: Weight fraction (dimensionless)
+
+W_{TO}: Takeoff weight (N)
+
+α: Thrust fraction (dimensionless), α = f(M, h)
+
+T_{SL}: Sea-level thrust (N)
+
+f(C_L): Functional relationship defining drag coefficient in terms of lift coefficient
+
+## Cases
+
+Equation 1 (constant_altitude_speed_cruise):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(\\frac{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}{\\beta}\\cdot\\frac{1.0}{W/S}\\right)\\cdot C_D
+
+Equation 2 (constant_speed_climb):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(\\frac{C_D}{\\frac{\\beta}{q\\cdot W/S}}+\\frac{1}{u}\\cdot\\frac{dh}{dt}\\right),\\ \\ \\ \\ where:u=M\\cdot a,\\emsp q=0.5\\cdot\\rho\\cdot u^2
+
+Equation 3 (constant_altitude_speed_turn):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(K_1\\cdot n^2\\cdot\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S+\\frac{C_{D0}}{\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S}\\right)
+
+Equation 4 (horizontal_acceleration):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\frac{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}{\\beta}\\cdot\\frac{1.0}{W/S}\\cdot C_D\\cdot\\frac{1}{g_0}\\cdot\\frac{dv}{dt}
+
+Equation 5 (takeoff_ground_roll):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta^2}{\\alpha}\\cdot\\frac{k_{T0}^2}{s_G\\cdot\\rho\\cdot g_0\\cdot C_{L_{\\mathrm{max,\\ TO}}}}\\cdot W/S
+
+Equation 6 (braking_roll):
+
+W/S=\\frac{s_G\\cdot\\rho\\cdot\\ g_0\\cdot\\mathrm{\\ }\\ \\left(C_{D_L}-\\mu_B\\cdot\\ C_{L_L}\\right)}{\\beta\\cdot\\ l\\ n\\left(1+\\frac{C_{D_L}-\\mu_B\\cdot\\ C_{L_L}}{\\frac{\\mu_B\\cdot\\ C_{L_L}}{k_{T0}^2}}\\right)}
+
+Equation 7 (service_ceiling):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(K_1\\cdot\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S+K_2+\\frac{C_{D0}}{\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S}+\\frac{1}{M\\cdot a}\\cdot\\mathrm{SEP}\\ \\right)
+
+Equation 8 (takeoff_climb_angle):
+
+\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot(K_1\\cdot\\frac{C_{L_{\\mathrm{max,\\ TO}}}}{k_{T0}^2}+K_2+\\frac{C_{D0}}{\\frac{C_{L_{\\mathrm{max,\\ TO}}}}{k_{T0}^2}}+\\sin\\funcapply\\gamma)
+
+Equation 9 (gust):
+
+W/S=\\frac{C_{L_\\alpha}\\cdot\\rho\\cdot V_{TO_L}\\cdot w_g}{d_{n_G}\\cdot2\\cdot\\beta}
+
+## Building the Cases for Constraint Analysis
+
+Constraint 1: One Engine Inoperative
+
+Inputs are:
+
+W_over_S_data,
+
+CD_vector (taken from the polar or calculated based on quadratic fit),
+
+weight_fraction_TO (taken from the mission analysis results),
+
+alpha_TO (taken from the engine library and modified to account for OEI),
+
+M_TO,
+
+altitude = 0.0,
+
+load_factor = 1.0,
+
+2.4 / 100.0 \* climb_speed;
+
+Climb speed is taken from the aircraft XML file. The OEI climb gradient is 2.4%.
+
+Output is the minimum Thrust to Weight ratio that the aircraft shall have as a vector.
+
+Constraint 2: Service Ceiling (SEP)
+
+Inputs are:
+
+W_over_S_data,
+
+CD_vector (taken from the polar or calculated based on quadratic fit),
+
+weight_fraction_segment (taken from the mission analysis results),
+
+alpha_segment (taken from the engine library),
+
+M_max (taken from the aircraft XML file),
+
+altitude_cruise,
+
+load_factor = 1.0,
+
+climb_gradient = 0.508;
+
+The climb rate is 100 ft/min which corresponds to 0.508 m per second.
+
+Output is the minimum Thrust to Weight ratio that the aircraft shall have as a vector.
+
+Constraint 3: Landing Field Length
+
+Inputs are:
+
+CD_max_L (taken from the polar or calculated based on quadratic fit),
+
+CL_max_L (C_LmaxLanding node of the aircraft XML),
+
+weight_fraction_landing (taken from the mission analysis results),
+
+alpha_landing (taken from the engine library),
+
+M_TO (taken from the aircraft XML file),
+
+altitude = 0.0,
+
+my_B (breaking_coefficient node of the aircraft XML),
+
+s_G_L (takeoff or landing field length)
+
+Output is the maximum Wing Loading value that the aircraft shall have.
+
+Constraint 4: Gust
+
+Inputs are:
+
+CL_alpha (the slope of the linear segment of the CL-AoA polar),
+
+altitude = 0.0,
+
+V_TO_L (taken from the aircraft XML file),
+
+w_g (taken from the gust_speed node of the module config),
+
+dn_G (taken from the gust_load_factor node of the module config),
+
+weight_fraction_TO (taken from the mission analysis results),
+
+## Updating the Design Point
+
+min_finder.find_dominant_curve();
+
+double sf = this->configuration_xml->at("module_configuration_file/program_settings/safety_factor/value");
+
+min_finder.find_design_point(sf);
+
+min_finder.update_design_point();
+
+Steps:
+
+1. Find the dominant curve: Takes the max T/W required at each W/S, hence gets the constraining curve
+2. Read the “safety factor” which adds the desired increment to the minimum T/W for additional safety. (CAN BE VARIED EACH ITERATION FOR FASTER CONVERGENCE)
+3. Find the minimum T/W from the dominant curve, get the W/S value corresponding to this T/W
+ 1. Not an “optimization”, just a sorting algorithm
+ 2. Does not interpolate between points
+4. Update the design point
+
+## Functional Flow
+
+1. Initialize the Aircraft XML, Polar XML, Engine, and the Config XML
+2. Initialize the wing loading vector
+3. For each case:
+ 1. Read the polar that corresponds to the desired Mach number and the flight configuration
+ 2. Get the CL based on the Lift Equation
+ 3. Get the CD that corresponds to the CL by either:
+ 1. Getting the CD directly from the polar or,
+ 2. Calculating the CD based on quadratic fit
+ 4. Evaluate the constraint
+4. Assemble the constraints
+5. Find the dominant curve
+6. Evaluate the feasible area
+7. Find the minimum T/W from the dominant curve and get the W/S that corresponds to this T/W
+8. Update the design point
+9. Plot the results
+10. Save the plots
\ No newline at end of file
--
GitLab
From df5253e54ea512463a6e68d07193f7c4696d188a Mon Sep 17 00:00:00 2001
From: Meric Taneri <meric.taneri@tum.de>
Date: Wed, 5 Feb 2025 14:44:30 +0100
Subject: [PATCH 2/6] documentation modified
---
.../analysis/constraint_analysis/index.md | 256 ++---------------
.../constraint_analysis/principles.md | 270 ++++++++++++++++++
mkdocs.yml | 3 +
3 files changed, 295 insertions(+), 234 deletions(-)
create mode 100644 docs/documentation/analysis/constraint_analysis/principles.md
diff --git a/docs/documentation/analysis/constraint_analysis/index.md b/docs/documentation/analysis/constraint_analysis/index.md
index 152af7c..4d50556 100644
--- a/docs/documentation/analysis/constraint_analysis/index.md
+++ b/docs/documentation/analysis/constraint_analysis/index.md
@@ -1,249 +1,37 @@
# Constraint Analysis {#mainpage}
+One of the essential aspects of aircraft design is to size the aircraft to meet the point performance requirement. This process involves the evaluation of the constraints within the Thrust to Weight and Wing Loading design space. As the tool is "sizing" the aircraft, it requires information about the aerodynamic performanca of the aircraft and the change of weight throughout the mission. Therefore this tool gets executed at the end of each loop to correctly size the aircraft.
-# Aerodynamic and Performance Equations for Constraint Analysis Module
+# Baseline Implementation
+The constraint analysis tool is established with an energy based approach which is coming from Jack D. Mattingly's Aircraft Engine Design book.
-## Function
+# Module Configuration
+The module can be configured to meet specific user needs by selecting desired parameters within the program_settings section of the module config file.
+A summary of possible selections can be found below:
+- `method`: This defines the method of constraint analysis
+ - Energy_Based
-Adjust the design point based on the point performance requirements.
+- `aero_method`: This defines the method of getting information about the aerodynamic characteristics of the aircraft
+ - Calculate_Polar: Calculates the aerodynamic performance based on simple quadratic fit
+ - Read_Polar: Reads the polar infomration from the output of aerodynamic_analysis
-## Rationale
+- `Mach_TO`: The mach number at takeoff
-The end-of-the-loop aircraft’s aerodynamic performance is different to that of the beginning-of-the-loop aircraft. Therefore, it is necessary to size the aircraft based on the most up to date data from the design loop. This way, the design is ensured to have the best fitting characteristics to the mission and performance requirements.
+- `takeoff_climb_anlge`: The takeoff climb angle for which the constraint shall be evaluated
-## Logic
+- `gust_speed`: The gust speed at takeoff for which the constraint shall be evaluated
-Point performance requirements are evaluated as constraints within the T_SL/W_TO – W_TO/S_Ref design space. The point is selected to have the minimum T_SL/W_TO possible value that lies in the feasible space.
+- `gust_load_factor`: The additional gust load factor for which the constraint shall be evaluated
-## Derivation
+- `Oswald_factor`: The Oswald factor for calculating the polar, effective only if the aero_method is selected to be Calculate_Polar
-1\. Lift Equation (getCL):
+- `climb_gradient_OEI`: The minimum climb rate required for which the constraint shall be evaluated, CS25 defines this parameter to be 2.4% for the second climb segment
-L=n\\cdot W=\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot C_L\\cdot S
+- `minimum_climb_rate`: The minimum climb rate required at the service ceiling, CS25 defines this parameter to be 100 ft/min which is equal to 0.508 m/s
-C_L=\\frac{n}{\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot\\left(W/S\\right)
+# Module Output
-2\. Drag Equation:
+- `Updated Design Point`: An updated Thrust to Weight and Wing Loading pair
-D=\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot C_D\\cdot S,\\emsp\\mathrm{where\\ }C_D=f\\left(C_L\\right)
+- `Constraint Plot`: The constraint plot if plotting is enabled
-3\. Thrust-Difference Equation:
-
-T-D=W\\cdot\\frac{d}{dt}\\left(h+\\frac{\\left(M\\cdot a\\right)^2}{2\\cdot g}\\right)
-
-4\. Weight and Thrust Relationships:
-
-W=\\beta\\cdot W_{TO}
-
-T=\\alpha\\cdot T_{SL},\\emsp\\mathrm{where\\ }\\alpha=f\\left(M,h\\right)
-
-5\. Substituted Thrust-Difference Equation:
-
-T-\\left(\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot f\\left(C_L\\right)\\cdot S\\right)=W\\cdot\\frac{d}{dt}\\left(h+\\frac{\\left(M\\cdot a\\right)^2}{2\\cdot g}\\right)
-
-## Final Substituted Equation
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta\\cdot\\frac{d}{dt}\\left(h+\\frac{V^2}{2\\cdot g}\\right)+\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot f\\left(C_L\\right)}{\\alpha\\cdot\\left(W_{TO}/S\\right)}
-
-f\\left(C_L\\right)=C_D\\left(\\frac{\\beta\\cdot n}{\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot\\left(W_{TO}/S\\right)\\right)
-
-## Parameter Meanings
-
-L: Lift (N)
-
-n: Load factor (dimensionless)
-
-W: Weight (N)
-
-ρ: Air density (kg/m^3)
-
-M: Mach number (dimensionless)
-
-a: Speed of sound (m/s)
-
-C_L: Lift coefficient (dimensionless)
-
-C_D: Drag coefficient (dimensionless)
-
-S: Reference area (m^2)
-
-T: Thrust (N)
-
-D: Drag (N)
-
-h: Altitude (m)
-
-g: Gravitational acceleration (9.81 m/s^2)
-
-β: Weight fraction (dimensionless)
-
-W_{TO}: Takeoff weight (N)
-
-α: Thrust fraction (dimensionless), α = f(M, h)
-
-T_{SL}: Sea-level thrust (N)
-
-f(C_L): Functional relationship defining drag coefficient in terms of lift coefficient
-
-## Cases
-
-Equation 1 (constant_altitude_speed_cruise):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(\\frac{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}{\\beta}\\cdot\\frac{1.0}{W/S}\\right)\\cdot C_D
-
-Equation 2 (constant_speed_climb):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(\\frac{C_D}{\\frac{\\beta}{q\\cdot W/S}}+\\frac{1}{u}\\cdot\\frac{dh}{dt}\\right),\\ \\ \\ \\ where:u=M\\cdot a,\\emsp q=0.5\\cdot\\rho\\cdot u^2
-
-Equation 3 (constant_altitude_speed_turn):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(K_1\\cdot n^2\\cdot\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S+\\frac{C_{D0}}{\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S}\\right)
-
-Equation 4 (horizontal_acceleration):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\frac{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}{\\beta}\\cdot\\frac{1.0}{W/S}\\cdot C_D\\cdot\\frac{1}{g_0}\\cdot\\frac{dv}{dt}
-
-Equation 5 (takeoff_ground_roll):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta^2}{\\alpha}\\cdot\\frac{k_{T0}^2}{s_G\\cdot\\rho\\cdot g_0\\cdot C_{L_{\\mathrm{max,\\ TO}}}}\\cdot W/S
-
-Equation 6 (braking_roll):
-
-W/S=\\frac{s_G\\cdot\\rho\\cdot\\ g_0\\cdot\\mathrm{\\ }\\ \\left(C_{D_L}-\\mu_B\\cdot\\ C_{L_L}\\right)}{\\beta\\cdot\\ l\\ n\\left(1+\\frac{C_{D_L}-\\mu_B\\cdot\\ C_{L_L}}{\\frac{\\mu_B\\cdot\\ C_{L_L}}{k_{T0}^2}}\\right)}
-
-Equation 7 (service_ceiling):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(K_1\\cdot\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S+K_2+\\frac{C_{D0}}{\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S}+\\frac{1}{M\\cdot a}\\cdot\\mathrm{SEP}\\ \\right)
-
-Equation 8 (takeoff_climb_angle):
-
-\\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot(K_1\\cdot\\frac{C_{L_{\\mathrm{max,\\ TO}}}}{k_{T0}^2}+K_2+\\frac{C_{D0}}{\\frac{C_{L_{\\mathrm{max,\\ TO}}}}{k_{T0}^2}}+\\sin\\funcapply\\gamma)
-
-Equation 9 (gust):
-
-W/S=\\frac{C_{L_\\alpha}\\cdot\\rho\\cdot V_{TO_L}\\cdot w_g}{d_{n_G}\\cdot2\\cdot\\beta}
-
-## Building the Cases for Constraint Analysis
-
-Constraint 1: One Engine Inoperative
-
-Inputs are:
-
-W_over_S_data,
-
-CD_vector (taken from the polar or calculated based on quadratic fit),
-
-weight_fraction_TO (taken from the mission analysis results),
-
-alpha_TO (taken from the engine library and modified to account for OEI),
-
-M_TO,
-
-altitude = 0.0,
-
-load_factor = 1.0,
-
-2.4 / 100.0 \* climb_speed;
-
-Climb speed is taken from the aircraft XML file. The OEI climb gradient is 2.4%.
-
-Output is the minimum Thrust to Weight ratio that the aircraft shall have as a vector.
-
-Constraint 2: Service Ceiling (SEP)
-
-Inputs are:
-
-W_over_S_data,
-
-CD_vector (taken from the polar or calculated based on quadratic fit),
-
-weight_fraction_segment (taken from the mission analysis results),
-
-alpha_segment (taken from the engine library),
-
-M_max (taken from the aircraft XML file),
-
-altitude_cruise,
-
-load_factor = 1.0,
-
-climb_gradient = 0.508;
-
-The climb rate is 100 ft/min which corresponds to 0.508 m per second.
-
-Output is the minimum Thrust to Weight ratio that the aircraft shall have as a vector.
-
-Constraint 3: Landing Field Length
-
-Inputs are:
-
-CD_max_L (taken from the polar or calculated based on quadratic fit),
-
-CL_max_L (C_LmaxLanding node of the aircraft XML),
-
-weight_fraction_landing (taken from the mission analysis results),
-
-alpha_landing (taken from the engine library),
-
-M_TO (taken from the aircraft XML file),
-
-altitude = 0.0,
-
-my_B (breaking_coefficient node of the aircraft XML),
-
-s_G_L (takeoff or landing field length)
-
-Output is the maximum Wing Loading value that the aircraft shall have.
-
-Constraint 4: Gust
-
-Inputs are:
-
-CL_alpha (the slope of the linear segment of the CL-AoA polar),
-
-altitude = 0.0,
-
-V_TO_L (taken from the aircraft XML file),
-
-w_g (taken from the gust_speed node of the module config),
-
-dn_G (taken from the gust_load_factor node of the module config),
-
-weight_fraction_TO (taken from the mission analysis results),
-
-## Updating the Design Point
-
-min_finder.find_dominant_curve();
-
-double sf = this->configuration_xml->at("module_configuration_file/program_settings/safety_factor/value");
-
-min_finder.find_design_point(sf);
-
-min_finder.update_design_point();
-
-Steps:
-
-1. Find the dominant curve: Takes the max T/W required at each W/S, hence gets the constraining curve
-2. Read the “safety factor” which adds the desired increment to the minimum T/W for additional safety. (CAN BE VARIED EACH ITERATION FOR FASTER CONVERGENCE)
-3. Find the minimum T/W from the dominant curve, get the W/S value corresponding to this T/W
- 1. Not an “optimization”, just a sorting algorithm
- 2. Does not interpolate between points
-4. Update the design point
-
-## Functional Flow
-
-1. Initialize the Aircraft XML, Polar XML, Engine, and the Config XML
-2. Initialize the wing loading vector
-3. For each case:
- 1. Read the polar that corresponds to the desired Mach number and the flight configuration
- 2. Get the CL based on the Lift Equation
- 3. Get the CD that corresponds to the CL by either:
- 1. Getting the CD directly from the polar or,
- 2. Calculating the CD based on quadratic fit
- 4. Evaluate the constraint
-4. Assemble the constraints
-5. Find the dominant curve
-6. Evaluate the feasible area
-7. Find the minimum T/W from the dominant curve and get the W/S that corresponds to this T/W
-8. Update the design point
-9. Plot the results
-10. Save the plots
\ No newline at end of file
+- `Design Points`: The list of design points throughout the loop, to check for convergence performance
\ No newline at end of file
diff --git a/docs/documentation/analysis/constraint_analysis/principles.md b/docs/documentation/analysis/constraint_analysis/principles.md
new file mode 100644
index 0000000..7c271ac
--- /dev/null
+++ b/docs/documentation/analysis/constraint_analysis/principles.md
@@ -0,0 +1,270 @@
+# Constraint Analysis
+
+# Aerodynamic and Performance Equations for Constraint Analysis Module
+
+## Function
+
+Adjust the design point based on the point performance requirements.
+
+## Rationale
+
+The end-of-the-loop aircraft’s aerodynamic performance is different to that of the beginning-of-the-loop aircraft. Therefore, it is necessary to size the aircraft based on the most up to date data from the design loop. This way, the design is ensured to have the best fitting characteristics to the mission and performance requirements.
+
+## Logic
+
+Point performance requirements are evaluated as constraints within the T_SL/W_TO – W_TO/S_Ref design space. The point is selected to have the minimum T_SL/W_TO possible value that lies in the feasible space.
+
+## Derivation
+
+1\. Lift Equation (getCL):
+
+$ L=n\\cdot W=\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot C_L\\cdot S $
+
+$ C_L=\\frac{n}{\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot\\left(W/S\\right) $
+
+2\. Drag Equation:
+
+$ D=\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot C_D\\cdot S $
+
+where:
+
+$ C_D=f\\left(C_L\\right) $
+
+3\. Thrust-Difference Equation:
+
+$ T-D=W\\cdot\\frac{d}{dt}\\left(h+\\frac{\\left(M\\cdot a\\right)^2}{2\\cdot g}\\right) $
+
+4\. Weight and Thrust Relationships:
+
+$ W=\\beta\\cdot W_{TO} $
+
+$ T=\\alpha\\cdot T_{SL} $
+
+where:
+
+$ \\alpha=f\\left(M,h\\right) $
+
+5\. Substituted Thrust-Difference Equation:
+
+$ T-\\left(\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot f\\left(C_L\\right)\\cdot S\\right)=W\\cdot\\frac{d}{dt}\\left(h+\\frac{\\left(M\\cdot a\\right)^2}{2\\cdot g}\\right) $
+
+## Final Substituted Equation
+
+$ \\frac{T_{SL}}{W_{TO}}=\\frac{\\beta\\cdot\\frac{d}{dt}\\left(h+\\frac{V^2}{2\\cdot g}\\right)+\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2\\cdot f\\left(C_L\\right)}{\\alpha\\cdot\\left(W_{TO}/S\\right)} $
+
+$ f\\left(C_L\\right)=C_D\\left(\\frac{\\beta\\cdot n}{\\frac{1}{2}\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot\\left(W_{TO}/S\\right)\\right) $
+
+## Parameter Meanings
+
+L: Lift (N)
+
+n: Load factor (dimensionless)
+
+W: Weight (N)
+
+ρ: Air density (kg/m^3)
+
+M: Mach number (dimensionless)
+
+a: Speed of sound (m/s)
+
+$C_L$: Lift coefficient (dimensionless)
+
+$C_D$: Drag coefficient (dimensionless)
+
+S: Reference area (m^2)
+
+T: Thrust (N)
+
+D: Drag (N)
+
+h: Altitude (m)
+
+g: Gravitational acceleration (9.81 m/s^2)
+
+β: Weight fraction (dimensionless)
+
+$W_{TO}$: Takeoff weight (N)
+
+α: Thrust fraction (dimensionless), α = f(M, h)
+
+$T_{SL}$: Sea-level thrust (N)
+
+$f(C_L)$: Functional relationship defining drag coefficient in terms of lift coefficient
+
+## Cases
+
+Equation 1 (constant_altitude_speed_cruise):
+
+$ \\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(\\frac{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}{\\beta}\\cdot\\frac{1.0}{W/S}\\right)\\cdot C_D $
+
+Equation 2 (constant_speed_climb):
+
+$ \\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(\\frac{C_D}{\\frac{\\beta}{q\\cdot W/S}}+\\frac{1}{u}\\cdot\\frac{dh}{dt}\\right) $
+
+where:
+
+$ u=M\\cdot a $
+
+$ q=0.5\\cdot\\rho\\cdot u^2 $
+
+Equation 3 (constant_altitude_speed_turn):
+
+$ \\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(K_1\\cdot n^2\\cdot\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S+\\frac{C_{D0}}{\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S}\\right) $
+
+Equation 4 (horizontal_acceleration):
+
+$ \\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\frac{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}{\\beta}\\cdot\\frac{1.0}{W/S}\\cdot C_D\\cdot\\frac{1}{g_0}\\cdot\\frac{dv}{dt} $
+
+Equation 5 (takeoff_ground_roll):
+
+$ \\frac{T_{SL}}{W_{TO}} = \\frac{\\beta^2}{\\alpha} \\cdot \\frac{k_{T0}^2}{s_G \\cdot \\rho \\cdot g_0 \\cdot C_{L_{max,TO}}} \\cdot W/S $
+
+Equation 6 (braking_roll):
+
+$ W/S=\\frac{s_G\\cdot\\rho\\cdot\\ g_0\\cdot\\mathrm{\\ }\\ \\left(C_{D_L}-\\mu_B\\cdot\\ C_{L_L}\\right)}{\\beta\\cdot\\ l\\ n\\left(1+\\frac{C_{D_L}-\\mu_B\\cdot\\ C_{L_L}}{\\frac{\\mu_B\\cdot\\ C_{L_L}}{k_{T0}^2}}\\right)} $
+
+Equation 7 (service_ceiling):
+
+$ \\frac{T_{SL}}{W_{TO}}=\\frac{\\beta}{\\alpha}\\cdot\\left(K_1\\cdot\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S+K_2+\\frac{C_{D0}}{\\frac{\\beta}{0.5\\cdot\\rho\\cdot\\left(M\\cdot a\\right)^2}\\cdot W/S}+\\frac{1}{M\\cdot a}\\cdot\\mathrm{SEP}\\ \\right) $
+
+Equation 8 (takeoff_climb_angle):
+
+$ \\frac{T_{SL}}{W_{TO}}=
+\\frac{\\beta}{\\alpha} \\cdot
+\\left(
+K_1 \\cdot \\frac{C_{L_{max,TO}}}{k_{T0}^2}
++ K_2
++ \\frac{C_{D0}}{\\frac{C_{L_{max,TO}}}{k_{T0}^2}}
++ \\sin \\gamma
+\\right) $
+
+Equation 9 (gust):
+
+$ W/S=\\frac{C_{L_\\alpha}\\cdot\\rho\\cdot V_{TO_L}\\cdot w_g}{d_{n_G}\\cdot2\\cdot\\beta} $
+
+## Building the Cases for Constraint Analysis
+
+Constraint 1: One Engine Inoperative
+
+Inputs are:
+
+W_over_S_data,
+
+CD_vector (taken from the polar or calculated based on quadratic fit),
+
+weight_fraction_TO (taken from the mission analysis results),
+
+alpha_TO (taken from the engine library and modified to account for OEI),
+
+M_TO,
+
+altitude = 0.0,
+
+load_factor = 1.0,
+
+2.4 / 100.0 \* climb_speed;
+
+Climb speed is taken from the aircraft XML file. The OEI climb gradient is 2.4%.
+
+Output is the minimum Thrust to Weight ratio that the aircraft shall have as a vector.
+
+Constraint 2: Service Ceiling (SEP)
+
+Inputs are:
+
+W_over_S_data,
+
+CD_vector (taken from the polar or calculated based on quadratic fit),
+
+weight_fraction_segment (taken from the mission analysis results),
+
+alpha_segment (taken from the engine library),
+
+M_max (taken from the aircraft XML file),
+
+altitude_cruise,
+
+load_factor = 1.0,
+
+climb_gradient = 0.508;
+
+The climb rate is 100 ft/min which corresponds to 0.508 m per second.
+
+Output is the minimum Thrust to Weight ratio that the aircraft shall have as a vector.
+
+Constraint 3: Landing Field Length
+
+Inputs are:
+
+CD_max_L (taken from the polar or calculated based on quadratic fit),
+
+CL_max_L (C_LmaxLanding node of the aircraft XML),
+
+weight_fraction_landing (taken from the mission analysis results),
+
+alpha_landing (taken from the engine library),
+
+M_TO (taken from the aircraft XML file),
+
+altitude = 0.0,
+
+my_B (breaking_coefficient node of the aircraft XML),
+
+s_G_L (takeoff or landing field length)
+
+Output is the maximum Wing Loading value that the aircraft shall have.
+
+Constraint 4: Gust
+
+Inputs are:
+
+CL_alpha (the slope of the linear segment of the CL-AoA polar),
+
+altitude = 0.0,
+
+V_TO_L (taken from the aircraft XML file),
+
+w_g (taken from the gust_speed node of the module config),
+
+dn_G (taken from the gust_load_factor node of the module config),
+
+weight_fraction_TO (taken from the mission analysis results),
+
+## Updating the Design Point
+
+min_finder.find_dominant_curve();
+
+double sf = this->configuration_xml->at("module_configuration_file/program_settings/safety_factor/value");
+
+min_finder.find_design_point(sf);
+
+min_finder.update_design_point();
+
+Steps:
+
+1. Find the dominant curve: Takes the max T/W required at each W/S, hence gets the constraining curve
+2. Read the “safety factor” which adds the desired increment to the minimum T/W for additional safety. (CAN BE VARIED EACH ITERATION FOR FASTER CONVERGENCE)
+3. Find the minimum T/W from the dominant curve, get the W/S value corresponding to this T/W
+ 1. Not an “optimization”, just a sorting algorithm
+ 2. Does not interpolate between points
+4. Update the design point
+
+## Functional Flow
+
+1. Initialize the Aircraft XML, Polar XML, Engine, and the Config XML
+2. Initialize the wing loading vector
+3. For each case:
+ 1. Read the polar that corresponds to the desired Mach number and the flight configuration
+ 2. Get the CL based on the Lift Equation
+ 3. Get the CD that corresponds to the CL by either:
+ 1. Getting the CD directly from the polar or,
+ 2. Calculating the CD based on quadratic fit
+ 4. Evaluate the constraint
+4. Assemble the constraints
+5. Find the dominant curve
+6. Evaluate the feasible area
+7. Find the minimum T/W from the dominant curve and get the W/S that corresponds to this T/W
+8. Update the design point
+9. Plot the results
+10. Save the plots
\ No newline at end of file
diff --git a/mkdocs.yml b/mkdocs.yml
index 08d43de..02c068c 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -303,6 +303,9 @@ nav: # Customizes the main navigation struc
- ecological_assessment/namespaces.md
- ecological_assessment/files.md
- ecological_assessment/functions.md
+ - Constraint Analysis:
+ - Introduction: documentation/analysis/constraint_analysis/index.md
+ - Principles: documentation/analysis/constraint_analysis/principles.md
- Libraries:
- Overview: documentation/libraries.md # Link to libraries overview.
- AircraftGeometry2:
--
GitLab
From b8fa51714e5f4599e232f0cab7adcc9980f9e154 Mon Sep 17 00:00:00 2001
From: Meric Taneri <meric.taneri@tum.de>
Date: Thu, 6 Feb 2025 08:46:59 +0100
Subject: [PATCH 3/6] Apply 1 suggestion(s) to 1 file(s)
Co-authored-by: Kristina Mazur <kristina.mazur@tum.de>
---
docs/documentation/analysis/constraint_analysis/index.md | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/docs/documentation/analysis/constraint_analysis/index.md b/docs/documentation/analysis/constraint_analysis/index.md
index 4d50556..90c97db 100644
--- a/docs/documentation/analysis/constraint_analysis/index.md
+++ b/docs/documentation/analysis/constraint_analysis/index.md
@@ -1,5 +1,5 @@
# Constraint Analysis {#mainpage}
-One of the essential aspects of aircraft design is to size the aircraft to meet the point performance requirement. This process involves the evaluation of the constraints within the Thrust to Weight and Wing Loading design space. As the tool is "sizing" the aircraft, it requires information about the aerodynamic performanca of the aircraft and the change of weight throughout the mission. Therefore this tool gets executed at the end of each loop to correctly size the aircraft.
+One of the essential aspects of aircraft design is to size the aircraft to meet the point performance requirement. This process involves the evaluation of the constraints within the Thrust to Weight and Wing Loading design space. As the tool is "sizing" the aircraft, it requires information about the aerodynamic performance of the aircraft and the change of weight throughout the mission. Therefore this tool gets executed at the end of each loop to correctly size the aircraft.
# Baseline Implementation
The constraint analysis tool is established with an energy based approach which is coming from Jack D. Mattingly's Aircraft Engine Design book.
--
GitLab
From 16f88a20a917fe7ce00705dde3857ae60bb1ef17 Mon Sep 17 00:00:00 2001
From: Meric Taneri <meric.taneri@tum.de>
Date: Thu, 6 Feb 2025 08:47:17 +0100
Subject: [PATCH 4/6] Apply 1 suggestion(s) to 1 file(s)
Co-authored-by: Kristina Mazur <kristina.mazur@tum.de>
---
docs/documentation/analysis/constraint_analysis/index.md | 1 +
1 file changed, 1 insertion(+)
diff --git a/docs/documentation/analysis/constraint_analysis/index.md b/docs/documentation/analysis/constraint_analysis/index.md
index 90c97db..6606d55 100644
--- a/docs/documentation/analysis/constraint_analysis/index.md
+++ b/docs/documentation/analysis/constraint_analysis/index.md
@@ -7,6 +7,7 @@ The constraint analysis tool is established with an energy based approach which
# Module Configuration
The module can be configured to meet specific user needs by selecting desired parameters within the program_settings section of the module config file.
A summary of possible selections can be found below:
+
- `method`: This defines the method of constraint analysis
- Energy_Based
--
GitLab
From 9df27ded40acdd80501cc3d553f81ac7c1e00142 Mon Sep 17 00:00:00 2001
From: Meric Taneri <meric.taneri@tum.de>
Date: Thu, 6 Feb 2025 08:48:50 +0100
Subject: [PATCH 5/6] Apply 3 suggestion(s) to 2 file(s)
Co-authored-by: Kristina Mazur <kristina.mazur@tum.de>
---
docs/documentation/analysis/constraint_analysis/index.md | 4 ++--
docs/documentation/analysis/constraint_analysis/principles.md | 2 +-
2 files changed, 3 insertions(+), 3 deletions(-)
diff --git a/docs/documentation/analysis/constraint_analysis/index.md b/docs/documentation/analysis/constraint_analysis/index.md
index 6606d55..c093eeb 100644
--- a/docs/documentation/analysis/constraint_analysis/index.md
+++ b/docs/documentation/analysis/constraint_analysis/index.md
@@ -17,13 +17,13 @@ A summary of possible selections can be found below:
- `Mach_TO`: The mach number at takeoff
-- `takeoff_climb_anlge`: The takeoff climb angle for which the constraint shall be evaluated
+- `takeoff_climb_angle`: The takeoff climb angle for which the constraint shall be evaluated
- `gust_speed`: The gust speed at takeoff for which the constraint shall be evaluated
- `gust_load_factor`: The additional gust load factor for which the constraint shall be evaluated
-- `Oswald_factor`: The Oswald factor for calculating the polar, effective only if the aero_method is selected to be Calculate_Polar
+- `oswald_factor`: The Oswald factor for calculating the polar, effective only if the aero_method is selected to be Calculate_Polar
- `climb_gradient_OEI`: The minimum climb rate required for which the constraint shall be evaluated, CS25 defines this parameter to be 2.4% for the second climb segment
diff --git a/docs/documentation/analysis/constraint_analysis/principles.md b/docs/documentation/analysis/constraint_analysis/principles.md
index 7c271ac..13c2bd2 100644
--- a/docs/documentation/analysis/constraint_analysis/principles.md
+++ b/docs/documentation/analysis/constraint_analysis/principles.md
@@ -12,7 +12,7 @@ The end-of-the-loop aircraft’s aerodynamic performance is different to that of
## Logic
-Point performance requirements are evaluated as constraints within the T_SL/W_TO – W_TO/S_Ref design space. The point is selected to have the minimum T_SL/W_TO possible value that lies in the feasible space.
+Point performance requirements are evaluated as constraints within the $T_{SL}/W_{TO}$ – $W_{TO}/S_{Ref}$ design space. The point is selected to have the minimum $T_{SL}/W_{TO}$ possible value that lies in the feasible space.
## Derivation
--
GitLab
From db27b7ed522f4cb47065af1c428fe0c08726a7a6 Mon Sep 17 00:00:00 2001
From: Meric Taneri <meric.taneri@tum.de>
Date: Thu, 6 Feb 2025 09:17:18 +0100
Subject: [PATCH 6/6] changes made based on remarks
---
.../figures/constraint_plot.png | 3 +
.../figures/constraint_plot.svg | 1840 +++++++++++++++++
.../analysis/constraint_analysis/index.md | 5 +-
.../constraint_analysis/principles.md | 24 +-
4 files changed, 1856 insertions(+), 16 deletions(-)
create mode 100644 docs/documentation/analysis/constraint_analysis/figures/constraint_plot.png
create mode 100644 docs/documentation/analysis/constraint_analysis/figures/constraint_plot.svg
diff --git a/docs/documentation/analysis/constraint_analysis/figures/constraint_plot.png b/docs/documentation/analysis/constraint_analysis/figures/constraint_plot.png
new file mode 100644
index 0000000..fad6579
--- /dev/null
+++ b/docs/documentation/analysis/constraint_analysis/figures/constraint_plot.png
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+version https://git-lfs.github.com/spec/v1
+oid sha256:f501cef1872a29aaf3dd543f5887c60f8cc1bf75320a4b49f8e51f0bc73b4333
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diff --git a/docs/documentation/analysis/constraint_analysis/figures/constraint_plot.svg b/docs/documentation/analysis/constraint_analysis/figures/constraint_plot.svg
new file mode 100644
index 0000000..8374871
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+ dy="-9"
+ id="tspan158">2</tspan><tspan
+ font-family="Sans"
+ font-size="18px"
+ dy="9"
+ id="tspan159">]</tspan></text>
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diff --git a/docs/documentation/analysis/constraint_analysis/index.md b/docs/documentation/analysis/constraint_analysis/index.md
index c093eeb..2bad387 100644
--- a/docs/documentation/analysis/constraint_analysis/index.md
+++ b/docs/documentation/analysis/constraint_analysis/index.md
@@ -1,9 +1,6 @@
# Constraint Analysis {#mainpage}
One of the essential aspects of aircraft design is to size the aircraft to meet the point performance requirement. This process involves the evaluation of the constraints within the Thrust to Weight and Wing Loading design space. As the tool is "sizing" the aircraft, it requires information about the aerodynamic performance of the aircraft and the change of weight throughout the mission. Therefore this tool gets executed at the end of each loop to correctly size the aircraft.
-# Baseline Implementation
-The constraint analysis tool is established with an energy based approach which is coming from Jack D. Mattingly's Aircraft Engine Design book.
-
# Module Configuration
The module can be configured to meet specific user needs by selecting desired parameters within the program_settings section of the module config file.
A summary of possible selections can be found below:
@@ -29,6 +26,8 @@ A summary of possible selections can be found below:
- `minimum_climb_rate`: The minimum climb rate required at the service ceiling, CS25 defines this parameter to be 100 ft/min which is equal to 0.508 m/s
+- `safety_factor`: The additional percentage increment that is added to the Thrust to Weight ratio
+
# Module Output
- `Updated Design Point`: An updated Thrust to Weight and Wing Loading pair
diff --git a/docs/documentation/analysis/constraint_analysis/principles.md b/docs/documentation/analysis/constraint_analysis/principles.md
index 13c2bd2..db95518 100644
--- a/docs/documentation/analysis/constraint_analysis/principles.md
+++ b/docs/documentation/analysis/constraint_analysis/principles.md
@@ -14,6 +14,9 @@ The end-of-the-loop aircraft’s aerodynamic performance is different to that of
Point performance requirements are evaluated as constraints within the $T_{SL}/W_{TO}$ – $W_{TO}/S_{Ref}$ design space. The point is selected to have the minimum $T_{SL}/W_{TO}$ possible value that lies in the feasible space.
+# Baseline Implementation
+The constraint analysis tool is established with an energy based approach which is coming from Jack D. Mattingly's Aircraft Engine Design book.
+
## Derivation
1\. Lift Equation (getCL):
@@ -233,19 +236,11 @@ weight_fraction_TO (taken from the mission analysis results),
## Updating the Design Point
-min_finder.find_dominant_curve();
-
-double sf = this->configuration_xml->at("module_configuration_file/program_settings/safety_factor/value");
-
-min_finder.find_design_point(sf);
-
-min_finder.update_design_point();
-
Steps:
-1. Find the dominant curve: Takes the max T/W required at each W/S, hence gets the constraining curve
-2. Read the “safety factor” which adds the desired increment to the minimum T/W for additional safety. (CAN BE VARIED EACH ITERATION FOR FASTER CONVERGENCE)
-3. Find the minimum T/W from the dominant curve, get the W/S value corresponding to this T/W
+1. Find the dominant curve: Takes the max $T_{SL}/W_{TO}$ required at each $W_{TO}/S_{Ref}$, hence gets the constraining curve
+2. Read the “safety factor” which adds the desired increment to the minimum $T_{SL}/W_{TO}$ for additional safety.
+3. Find the minimum $T_{SL}/W_{TO}$ from the dominant curve, get the $W_{TO}/S_{Ref}$ value corresponding to this $T_{SL}/W_{TO}$
1. Not an “optimization”, just a sorting algorithm
2. Does not interpolate between points
4. Update the design point
@@ -264,7 +259,10 @@ Steps:
4. Assemble the constraints
5. Find the dominant curve
6. Evaluate the feasible area
-7. Find the minimum T/W from the dominant curve and get the W/S that corresponds to this T/W
+7. Find the minimum $T_{SL}/W_{TO}$ from the dominant curve and get the W/S that corresponds to this $T_{SL}/W_{TO}$
8. Update the design point
9. Plot the results
-10. Save the plots
\ No newline at end of file
+10. Save the plots
+
+## Example Output
+
\ No newline at end of file
--
GitLab