Fix/wb workshop

Update to the documentation according to the workshop discussions: MLM, MRM, loading diagram, modes description, inertia calculation Raymer

docs/documentation/analysis/weight_and_balance_analysis/basic-concepts.md

@@ -50,20 +50,16 @@ Let us start defining the different masses calculated by the tool and how they a
 
 With the knowledge about the OEM, the design payload mass and the design fuel masses at different points during flight, the total design masses of the aircraft at specific times can be calculated: 
 
-  - ***design mass mission*** (the mass of the aircraft in the parking position before the start):
+  - **Maximum Ramp Mass (MRM)** is the mass of the aircraft in the parking position before the start:
   
-    $$ design\_mass\_mission = OEM + design\_fuel\_mass\_mission + design\_payload\_mass. $$
+    $$ MRM = OEM + design\_fuel\_mass\_mission + design\_payload\_mass. $$
 
   - ***design mass at take-off*** (equal with the MTOM and to the ***design mass*** written in the acxml)
   - ***design mass at midflight*** 
   - ***design mass at landing***
 
 The **Maximum Landing Mass (MLM)** is the maximum mass at which the pilot of the aircraft is allowed to attempt to land due to structural or other limits. 
-Two calculation modes are available:
-
-  - based on the mission information and the consumed fuel during flight (`default method`):
-
-    $$ MLM = OEM + design\_fuel\_mass\_landing + design\_payload\_mass $$
+The following calculation mode is available:
         
   - via the `RWTH regression method`: This calculation uses different formulas depending on whether the maximum takeoff mass exceeds a threshold value of 15,000 kg.
   
@@ -134,10 +130,7 @@ Below is a detailed breakdown of idealized key loading processes and their effec
   - High-Wing Aircraft:
     - Fuel is consumed in the reverse order: central or fuselage tanks → inner tank → outer tank.
 
-!!! note 
-    For the moment only the loading case 3 - 1 - 2 - 4 is implemented. The different selection of the loading scenarios can be made in the _weight\_and\_balance\_analysis\_conf.xml_ file.
-
-Finally, the **most forward and most aft _x_-CG positions** and the corresponding masses are depicted from the resulting diagramm.  
+The sequence between the different loading scenarios can be made in the _weight\_and\_balance\_analysis\_conf.xml_ file. The shift in CG due to the different loading scenarios is considered only for the longitudinal axis, as it is assumed that the aircraft is loaded symmetrically. Finally, the **most forward and most aft _x_-CG positions** and the corresponding masses are depicted from the resulting diagramm.  
 
 ---
 ## Mass Moments of Inertia {#inertia}
@@ -170,13 +163,19 @@ Where:
 - $f_{xx}$ and $f_{yy}$: Technology factors set to $1.25$ respectively $1.15$   
 - $ R_x, R_y, R_z $: Nondimensional radii of gyration. The following values are implemented:
 
-| **Aircraft Configuration**                      | $ R_x $ | $ R_y $ | $ R_z $ |
-|-----------------------------------------|-----------|-----------|-----------|
-| Fuselage-mounted engines                | 0.24      | 0.34      | 0.42      |
-| 2 wing-mounted engines                  | 0.23      | 0.33      | 0.45      |
-| 4 wing-mounted engines                  | 0.24      | 0.36      | 0.44      |
-| Blended wing body                       | 0.28      | 0.40      | 0.46      |
+| **Aircraft Configuration**                    | $ R_x $ | $ R_y $ | $ R_z $ |
+|---------------------------------------------|-----------|-----------|-----------|
+| Single prop engine                          | 0.25      | 0.38      | 0.39      |
+| Twin prop engine                            | 0.30      | 0.40      | 0.44      |
+| 2 fuselage-mounted jet engines              | 0.24      | 0.34      | 0.42      |
+| 2 wing-mounted jet engines                  | 0.23      | 0.33      | 0.45      |
+| 4 wing-mounted jet engines                  | 0.24      | 0.36      | 0.44      |
+| Blended wing body                           | 0.28      | 0.40      | 0.46      |
+
+The aircraft configuration is determined based on the data from the TLARs. For this, the information about the possible propulsion types, mounting positions and number of engines are used.
 
+!!! note 
+    If no matching radii of gyration are found, a critical message is shown and the values for the radii are set to the ones for a jet with two wing mounted engines to keep the workflow running. It is the user's responsability to check the validity of the chosen calculation methods and the results.
 
 #### 2. Using the LTH Tables (*Luftfahrttechnisches Handbuch*) 
 The LTH provides tabulated values and empirical methods specific to various aircraft configurations. These tables account for typical mass distributions and structural layouts. They are more accurate than Raymer’s approach but require knowledge of the specific aircraft class and design. The `calculate_inertia_by_lth_method` function is tailored specifically for conventional tube-and-wing configurations. This method uses aircraft mass properties like the OEM, the payload mass ($m_{payload}$) and the fuel mass ($m_{fuel}$) and geometric dimensions such as wing span $b$ and fuselage length $l$. All cross-product terms ($I_{xy}$, $I_{xz}$, etc.) are set to $0$, assuming symmetry.