From dd386d58b7def19a0078b3430b714b13847d2c1f Mon Sep 17 00:00:00 2001
From: sroscher <s.roscher@tu-berlin.de>
Date: Wed, 5 Feb 2025 17:36:21 +0100
Subject: [PATCH 1/4] - Made some formatting bug fixes

---
 .../landing_gear_design/design_method.md      | 355 ++++++++++--------
 .../landing_gear_design/getting_started.md    |   6 +-
 .../sizing/landing_gear_design/index.md       |   2 +
 .../run_your_first_design.md                  |  14 +-
 4 files changed, 212 insertions(+), 165 deletions(-)

diff --git a/docs/documentation/sizing/landing_gear_design/design_method.md b/docs/documentation/sizing/landing_gear_design/design_method.md
index d117245..6fe365b 100644
--- a/docs/documentation/sizing/landing_gear_design/design_method.md
+++ b/docs/documentation/sizing/landing_gear_design/design_method.md
@@ -11,7 +11,7 @@
 
 
 ## Initial positions {#initial-positions}
-First, initial x axis positions for the nose $x_{NLG}$ and main landing gear $x_{MLG}$ are estimated. If any of the required values are missing, default values are used, such as a minimum distance of 2 meters between the main landing gear and the aft-most center of gravity.
+First, initial x axis positions for the nose $x_{\text{NLG}}$ and main landing gear $x_{\text{MLG}}$ are estimated. If any of the required values are missing, default values are used, such as a minimum distance of 2 meters between the main landing gear and the aft-most center of gravity.
 
 The nose gear position is determined either from module configuration data or input parameters, such as the front reference point of the payload area or existing landing gear positions. If no relevant data is available, a default starting position, such as 5 meters, is applied.
 
@@ -28,85 +28,93 @@ Default values are assigned if parameters are not explicitly provided.
 
 #### Distance between nose and main landing gear
 The distance between the nose and the main landing gear can be estimated using the following equation:
-$
-  d_{NLG\_MLG} = |x_{MLG} - x_{NLG}|
-$
+$$
+  d_{\text{NLG-MLG}} = |x_{\text{MLG}} - x_{\text{NLG}}|
+$$
+
 In which
-- $ x_{MLG}$ - x position of main landing gear
-- $ x_{NLG}$ - x position of nose landing gear
+
+- $x_{\text{MLG}}$ - x position of main landing gear
+- $x_{\text{NLG}}$ - x position of nose landing gear
 
 #### Distance between nose gear and foremost center of gravity position
 If the foremost center of gravity position is already known, the distance to the nose gear can be determined according to the following formula:
-$
-  d_{NLG\_front\_CG} = |x_{front\_CG} - x_{NLG}|
-$
+$$
+  d_{\text{NLG front CG}} = |x_{\text{front CG}} - x_{\text{NLG}}|
+$$
+
 In which
-- $ x_{front\_CG}$ - x position of foremost center of gravity
 
-Otherwise, $d_{NLG\_front\_CG}$ is determined by using a first estimation:
-$
-  d_{NLG\_front\_CG} = |(x_{MLG} - 2) - x_{NLG}|
-$
+- $x_{\text{front CG}}$ - x position of foremost center of gravity
+
+Otherwise, $d_{\text{NLG front CG}}$ is determined by using a first estimation:
+$$
+  d_{\text{NLG front CG}} = |(x_{\text{MLG}} - 2) - x_{\text{NLG}}|
+$$
 
 #### Distance between nose gear and rearmost center of gravity
 The distance between the nose gear position and the rearmost center of gravity in x direction can be calculated as follows:
-$
-  d_{NLG\_rear\_CG} = |x_{rear\_CG} - x_{NLG}|
-$
+$$
+  d_{\text{NLG rear CG}} = |x_{\text{rear CG}} - x_{\text{NLG}}|
+$$
+
 In which
-- $x_{rear\_CG}$ - x position of rearmost center of gravity
 
-Otherwise, $d_{NLG\_rear\_CG}$ is determined by using a first estimation:
-$
-  d_{NLG\_rear\_CG} = |(x_{MLG} - 1) - x_{NLG}|
-$
+- $x_{\text{rear CG}}$ - x position of rearmost center of gravity
+
+Otherwise, $d_{\text{NLG rear CG}}$ is determined by using a first estimation:
+$$
+  d_{\text{NLG rear CG}} = |(x_{\text{MLG}} - 1) - x_{\text{NLG}}|
+$$
 
 #### Distance between main landing gear and rearmost center of gravity position
-If no distance between the main landing gear and the rearmost center of gravity is available from earlier iterations, it equals `1`.
+If no distance between the main landing gear and the rearmost center of gravity is available from earlier iterations, it equals `1.0`.
 
 ### Vertical distances
 ![](figures/vertical_distances.png)
 
 #### Vertical distance between ground and center of gravity position
-Starting with the second iteration loop, the vertical distance between ground and center of gravity $\Delta h_{GND\_CG}$ is known.
+Starting with the second iteration loop, the vertical distance between ground and center of gravity $\Delta h_{\text{GND-CG}}$ is known.
 
 In the first loop, however, the vertical distance must be calculated as sum of the following heights:
-1. Vertical distance from fuselage center line to center of gravity $\Delta h_{FCL\_CG}$
-2. z position of tail tipping point (equals vertical distance between fuselage center line and tail tipping point) $z_{TP}$
-3. Vertical distance from tail tipping point to ground $\Delta h_{TP\_GND}$
+
+1. Vertical distance from fuselage center line to center of gravity $\Delta h_{\text{FCL-CG}}$
+2. z position of tail tipping point (equals vertical distance between fuselage center line and tail tipping point) $z_{\text{TP}}$
+3. Vertical distance from tail tipping point to ground $\Delta h_{\text{TP-GND}}$
 
 **1. Vertical distance from fuselage center line to center of gravity**<br>
-The distance between global center of gravity in z-direction and the fuselage center line $\Delta h_{FCL\_CG}$ is either estimated by subtracting the z position of the fuselage center line $z_{FCL}$ from the z position of the most aft CG position $z_{rear\_CG}$
-$
-  \Delta h_{FCL\_CG} = |z_{rear\_CG} - z_{FCL}|
-$
+The distance between global center of gravity in z-direction and the fuselage center line $\Delta h_{\text{FCL-CG}}$ is either estimated by subtracting the z position of the fuselage center line $z_{\text{FCL}}$ from the z position of the most aft CG position $z_{\text{rear CG}}$
+$$
+  \Delta h_{\text{FCL-CG}} = |z_{\text{rear CG}} - z_{\text{FCL}}|
+$$
 
 or, if those values are not given, set to `0.5` for single-aisle and `1.0` for wide-body configurations.
 
 **2. z position of tail tipping point**<br>
-If the position of the tail tipping point in z direction is not known, it is assumed to equal $z_{TP} = -0.3 \cdot h_{fuselage}$. The fuselage height $h_{fuselage}$ in meter is known or assumed to be `3.8` for single-aisle and `5.8` for wide-body aircraft.
+If the position of the tail tipping point in z direction is not known, it is assumed to equal $z_{\text{TP}} = -0.3 \cdot h_{\text{fuselage}}$. The fuselage height $h_{\text{fuselage}}$ in meter is known or assumed to be `3.8` for single-aisle and `5.8` for wide-body aircraft.
 
 **3. Vertical distance from tail tipping point to ground**<br>
-The vertical distance from the tail tipping point to the ground $\Delta h_{TP\_GND}$ is estimated in the following way:
+The vertical distance from the tail tipping point to the ground $\Delta h_{\text{TP-GND}}$ is estimated in the following way:
 
-$
-  \Delta h_{TP\_GND} = |\tan(\theta_{LDG}) \cdot d_{MLG\_TP}| - h_{susp}
-$
+$$
+  \Delta h_{\text{TP-GND}} = |\tan(\theta_{\text{LDG}}) \cdot d_{\text{MLG-TP}}| - h_{\text{susp}}
+$$
 
-The vertical distance between the main landing gear and the tail tipping point $d_{MLG\_TP}$ is either known or set to `15` for single-aisle or `25` for wide-body aircraft configurations.
+The vertical distance between the main landing gear and the tail tipping point $d_{\text{MLG-TP}}$ is either known or set to `15.0` for single-aisle or `25.0` for wide-body aircraft configurations.
 
-If a strut suspension system is implemented, the vertical distance between ground and CG decreases by the suspension travel $h_{susp}$ that equals `0` if no suspension system is implemented.
+If a strut suspension system is implemented, the vertical distance between ground and CG decreases by the suspension travel $h_{\text{susp}}$ that equals `0.0` if no suspension system is implemented.
 
 **Vertical distance between ground and center of gravity position**<br>
 Finally, the vertical distance between the ground and the CG position can be calculated by summing up these values:
 $
-  \Delta h_{GND\_CG} = \Delta h_{FCL\_CG} + |z_{TP}| + \Delta h_{TP\_GND}
+  \Delta h_{\text{GND-CG}} = \Delta h_{\text{FCL-CG}} + |z_{\text{TP}}| + \Delta h_{\text{TP-GND}}
 $
 
 ## Load estimation {#loads}
 Subsequently, the loads on the nose and main landing gear are calculated based on Norman S. Currey's work<sup>[1]</sup>, unless explicitly stated otherwise. It considers the static and dynamic loads during takeoff, landing, and taxiing, while ensuring the loads conform to the permissible percentages as per aviation regulations.
 
 The following data is necessary:
+
 - Maximum aft position of nose landing gear
 - Minimum foremost position of nose landing gear
 - Minimum foremost position of main landing gear
@@ -116,166 +124,188 @@ If no values are available, initial values are set.
 
 ### Nose landing gear loads
 **Minimum static nose gear load**
-$
-  L_{NLG,stat,min} = \frac{MRW \cdot (d_{NLG\_MLG} - d_{NLG\_rear\_CG})}{d_{NLG\_MLG}}
-$
+$$
+  L_{\text{NLG,stat,min}} = \frac{MRW \cdot (d_{\text{NLG-MLG}} - d_{\text{NLG rear CG}})}{d_{\text{NLG-MLG}}}
+$$
+
 In which
+
 - $MRW$ - maximum ramp weight
-- $d_{NLG\_MLG}$ - distance between nose and main gear
-- $d_{NLG\_rear\_CG}$ - distance between nose gear and rearmost center of gravity
+- $d_{\text{NLG-MLG}}$ - distance between nose and main gear
+- $d_{\text{NLG rear CG}}$ - distance between nose gear and rearmost center of gravity
 
 **Maximum static nose gear load**
-$
-  L_{NLG,stat,max} = \frac{MRW \cdot (d_{NLG\_MLG} - d_{NLG\_front\_CG})}{d_{NLG\_MLG}}
-$
+$$
+  L_{\text{NLG,stat,max}} = \frac{MRW \cdot (d_{\text{NLG-MLG}} - d_{\text{NLG front CG}})}{d_{\text{NLG-MLG}}}
+$$
+
 In which
+
 - $MRW$ - maximum ramp weight
-- $d_{NLG\_MLG}$ - distance between nose and main gear
-- $d_{NLG\_front\_CG}$ - distance between nose gear and foremost center of gravity
+- $d_{\text{NLG-MLG}}$ - distance between nose and main gear
+- $d_{\text{NLG front CG}}$ - distance between nose gear and foremost center of gravity
 
 **Maximum dynamic nose gear load**
-$
-  L_{NLG,dyn,max} = L_{NLG,stat,max} + \frac{10 \cdot d_{GND\_rear\_CG} \cdot MRW}{32.2 \cdot d_{NLG\_MLG}}
-$
+$$
+  L_{\text{NLG,dyn,max}} = L_{\text{NLG,stat,max}} + \frac{10 \cdot d_{\text{GND rear CG}} \cdot MRW}{32.2 \cdot d_{\text{NLG-MLG}}}
+$$
+
 In which
-- $d_{GND\_rear\_CG}$ - vertical distance between ground and aft center of gravity
+
+- $d_{\text{GND rear CG}}$ - vertical distance between ground and aft center of gravity
 
 The static loads on the nose landing gear should be between 6% and 20% of the maximum ramp weight for all CG positions. These values are absolute limits and must not be exceeded at any time. Ideally, the static loads for the minimum and maximum nose landing gear load should be between 8% and 15%. If the limits are violated, the landing gear positions and/or the empty mass center of gravity must be varied. This leads to a renewed check of the center of gravity movement and the limits to be adhered to (iterative process).
 
 #### Dynamic nose gear loads for takeoff and landing condition
 The calculation of the dynamic nose gear loads for takeoff and landing conditions is in accordance with CS 25.733 (b)(2) and (b)(3)<sup>[2]</sup>.
 
-**Maximum static nose gear landing load**
-In order to calculate the maximum static nose gear load at landing, the maximum static nose gear landing load $ L_{NLG,stat,max,LDG}$ has to be estimated first.
+**Maximum static nose gear landing load**<br>
+In order to calculate the maximum static nose gear load at landing, the maximum static nose gear landing load $ L_{\text{NLG,stat,max,LDG}}$ has to be estimated first.
+
+$$
+  L_{\text{NLG,stat,max,LDG}} = \frac{MLM \cdot g \cdot (d_{\text{NLG-MLG}} - d_{\text{NLG front CG}})}{d_{\text{NLG-MLG}}}
+$$
 
-$
-  L_{NLG,stat,max,LDG} = \frac{MLM \cdot g \cdot (d_{NLG\_MLG} - d_{NLG\_front\_CG})}{d_{NLG\_MLG}}
-$
 In which
+
 - $MLM$ - maximum landing mass
 - $ g$ - gravitational acceleration
-- $d_{NLG\_MLG}$ - distance between nose and main gear
-- $d_{NLG\_front\_CG}$ - distance between nose gear and foremost center of gravity
+- $d_{\text{NLG-MLG}}$ - distance between nose and main gear
+- $d_{\text{NLG front CG}}$ - distance between nose gear and foremost center of gravity
 
-!!! note 
-  If no maximum landing mass exists, 90% of the maximum ramp weight are initially assumed for the calculation.
+!!! note
+    If no maximum landing mass exists, 90% of the maximum ramp weight are initially assumed for the calculation.
 
-Subsequently, the maximum dynamic load at landing $ L_{NLG,dyn,max,LDG} $ can be calculated based on CS 25.733 (b)(2):
-$
-  L_{NLG,dyn,max,LDG} = L_{NLG,stat,max,LDG} + 0.31 \cdot L_{NLG,stat,max,LDG}
-$
+Subsequently, the maximum dynamic load at landing $ L_{\text{NLG,dyn,max,LDG}} $ can be calculated based on CS 25.733 (b)(2):
+$$
+  L_{\text{NLG,dyn,max,LDG}} = L_{\text{NLG,stat,max,LDG}} + 0.31 \cdot L_{\text{NLG,stat,max,LDG}}
+$$
 
-**Maximum dynamic nose gear takeoff load**
+**Maximum dynamic nose gear takeoff load**<br>
 The maximum dynamic nose gear load at takeoff can be calculated in accordance with CS 52.733 (b)(3):
-$
-  L_{NLG,dyn,max,TO} = L_{NLG,stat,max} + 0.2 \cdot L_{NLG,stat,max}
-$
+$$
+  L_{\text{NLG,dyn,max,TO}} = L_{\text{NLG,stat,max}} + 0.2 \cdot L_{\text{NLG,stat,max}}
+$$
 
 ### Main landing gear loads
 The total main gear load can be estimated using the following equation:
-$
-  L_{MLG,max} = \frac{100 - L_{NLG,stat,min}}{100} \cdot MRW
-$
+$$
+  L_{\text{MLG,max}} = \frac{100 - L_{\text{NLG,stat,min}}}{100} \cdot MRW
+$$
+
 In which
-- $L_{NLG,stat,min}$ - minimum static nose gear load **in percent**
+
+- $L_{\text{NLG,stat,min}}$ - minimum static nose gear load **in percent**
 
 ### Nose landing gear position
 The maximum possible foremost and aft position of the nose landing gear can be determined based on the loads.
 
 #### Foremost nose landing gear position
-A maximum of 20 percent of the maximum ramp weight is allowed as the maximum static nose gear load $ L_{NLG,stat,max,possible}$:
-$
-  L_{NLG,stat,max,possible} = 0.06 \cdot MRW
-$
+A maximum of 20 percent of the maximum ramp weight is allowed as the maximum static nose gear load $L_{\text{NLG,stat,max,possible}}$:
+$$
+  L_{\text{NLG,stat,max,possible}} = 0.06 \cdot MRW
+$$
 
 The foremost nose landing gear position therefore results in:
-$
-  d_{NLG\_front\_CG\_min} = \frac{MRW \cdot d_{NLG\_MLG} - L_{NLG,stat,max,possible} \cdot d_{NLG\_MLG}}{MRW}
-$
+$$
+  d_{\text{NLG front CG min}} = \frac{MRW \cdot d_{\text{NLG-MLG}} - L_{\text{NLG,stat,max,possible}} \cdot d_{\text{NLG-MLG}}}{MRW}
+$$
+
 In which
+
 - $MRW$ - maximum ramp weight
-- $d_{NLG\_MLG}$ - distance between nose and main gear
+- $d_{\text{NLG-MLG}}$ - distance between nose and main gear
 
 #### Aft nose landing gear position
-A minimum of 6 percent of the maximum ramp weight is allowed as the minimum static nose gear load $ L_{NLG,stat,min,possible}$:
-$
-  L_{NLG,stat,min,possible} = 0.2 \cdot MRW
-$
+A minimum of 6 percent of the maximum ramp weight is allowed as the minimum static nose gear load $L_{\text{NLG,stat,min,possible}}$:
+$$
+  L_{\text{NLG,stat,min,possible}} = 0.2 \cdot MRW
+$$
 
 The aft nose landing gear position therefore results in:
-$
-  d_{NLG\_aft\_CG\_max} = \frac{MRW \cdot d_{NLG\_MLG} - L_{NLG,stat,min,possible} \cdot d_{NLG\_MLG}}{MRW}
-$
+$$
+  d_{\text{NLG aft CG max}} = \frac{MRW \cdot d_{\text{NLG-MLG}} - L_{\text{NLG,stat,min,possible}} \cdot d_{\text{NLG-MLG}}}{MRW}
+$$
 
 ## Tires {#tires}
 Tire selection in accordance to CS 25.733<sup>[2]</sup> und EASA ETSO tire list<sup>[3]</sup>, bridgestone aircraft tires<sup>[4]</sup>  from landing gear lib (see [getting started](getting_started.md) page for more information).
  
 If a maximum takeoff stall speed exists, the maximum design speed **(in miles per hour)** corresponds to the greater of the two values maximum approach speed or maximum takeoff stall speed*1.3:
-$
-  v_{max\_des} = max(v_{app,max},v_{s,TO} \cdot 1.3)
-$
+$$
+  v_{\text{max,des}} = max(v_{\text{app,max}},v_{\text{s,TO}} \cdot 1.3)
+$$
+
 In which
-- $v_{app,max}$ - maximum approach speed (in mph)
-- $v_{s,TO}$ - takeoff stall speed (in mph)
+
+- $v_{\text{app,max}}$ - maximum approach speed (in mph)
+- $v_{\text{s,TO}}$ - takeoff stall speed (in mph)
 
 Otherwise, the following applies:
-$
-  v_{max\_des} = v_{app,max}
-$
+$$
+  v_{\text{max,des}} = v_{\text{app,max}}
+$$
 
 ### Nose gear
-For both, the number of nose gear struts $n_{NLG\_struts}$ as well as the number of nose gear tires per strut $n_{NLG\_tires\_per\_strut}$, the user can define specific values. These values are checked for compliance and parameters, e.g., the number of axis, are set accordingly. If no values are given, default values are used.
+For both, the number of nose gear struts $n_{\text{NLG struts}}$ as well as the number of nose gear tires per strut $n_{\text{NLG tires per strut}}$, the user can define specific values. These values are checked for compliance and parameters, e.g., the number of axis, are set accordingly. If no values are given, default values are used.
 
 #### Design load estimation
-The **single tire design load** $v_{NLG\_tire\_des}$ is calculated according to CS 25.733 (b)(1):
-$
-  v_{NLG\_tire\_des} = \frac{\frac{L_{NLG,stat,max}}{g} \cdot 2.2}{n_{NLG\_tires\_per\_strut} \cdot n_{NLG\_struts}}
-$
+The **single tire design load** $v_{\text{NLG,tire,des}}$ is calculated according to CS 25.733 (b)(1):
+$$
+  v_{\text{NLG,tire,des}} = \frac{\frac{L_{\text{NLG,stat,max}}}{g} \cdot 2.2}{n_{\text{NLG tires per strut}} \cdot n_{\text{NLG struts}}}
+$$
+
 In which
-- $ L_{NLG,stat,max}$ - maximum static nose gear load
-- $ g$ - gravitational acceleration
 
-Subsequently, the **single tire dynamic landing load** $v_{NLG\_tire\_LDG}$ is estimated based on CS 25.733 (b)(2):
-$
-  v_{NLG\_tire\_LDG} = \frac{\frac{L_{NLG,dyn,max,LDG}}{g} \cdot 2.2}{n_{NLG\_tires\_per\_strut} \cdot n_{NLG\_struts}}
-$
+- $L_{\text{NLG,stat,max}}$ - maximum static nose gear load
+- $g$ - gravitational acceleration
+
+Subsequently, the **single tire dynamic landing load** $v_{\text{NLG tire LDG}}$ is estimated based on CS 25.733 (b)(2):
+$$
+  v_{\text{NLG tire LDG}} = \frac{\frac{L_{\text{NLG,dyn,max,LDG}}}{g} \cdot 2.2}{n_{\text{NLG tires per strut}} \cdot n_{\text{NLG struts}}}
+$$
+
 In which
-- $ L_{NLG,dyn,max,LDG}$ - maximum dynamic load at landing
 
-Afterwards, the calculation of the **single tire dynamic takeoff load** $v_{NLG\_tire\_TO}$ for nose gear tires is in accordance to CS 25.733 (b)(3):
-$
-  v_{NLG\_tire\_TO} = \frac{\frac{L_{NLG,dyn,max,TO}}{g} \cdot 2.2}{n_{NLG\_tires\_per\_strut} \cdot n_{NLG\_struts}}
-$
+- $L_{\text{NLG,dyn,max,LDG}}$ - maximum dynamic load at landing
+
+Afterwards, the calculation of the **single tire dynamic takeoff load** $v_{\text{NLG tire TO}}$ for nose gear tires is in accordance to CS 25.733 (b)(3):
+$$
+  v_{\text{NLG tire TO}} = \frac{\frac{L_{\text{NLG,dyn,max,TO}}}{g} \cdot 2.2}{n_{\text{NLG tires per strut}} \cdot n_{\text{NLG struts}}}
+$$
+
 In which
-- $ L_{NLG,dyn,max,TO}$ - maximum dynamic load at takeoff
+
+- $L_{\text{NLG,dyn,max,TO}}$ - maximum dynamic load at takeoff
 
 #### Tire selection
 Knowing the design speed and loads, a suitable tire is selected from the database.
 
 ### Main gear tire selection
-Similar to the nose landing gear, the number of main gear struts $n_{MLG\_struts}$ as well as the number of main gear tires per strut $n_{MLG\_tires\_per\_strut}$ can be defined by the user. These values are checked for compliance and parameters, e.g., the number of axis, are set accordingly. If no values are given, default values are used.
+Similar to the nose landing gear, the number of main gear struts $n_{\text{MLG struts}}$ as well as the number of main gear tires per strut $n_{\text{MLG tires per strut}}$ can be defined by the user. These values are checked for compliance and parameters, e.g., the number of axis, are set accordingly. If no values are given, default values are used.
 
 #### Design load estimation
 The **single tire design load** is calculated according to CS 25.733 (a)(1):
-$
-  v_{MLG\_tire\_des} = \frac{\frac{L_{MLG,max}}{g} \cdot 2.2}{n_{MLG\_tires\_per\_outer\_strut} \cdot n_{MLG\_outer\_struts} + n_{MLG\_tires\_per\_inner\_strut} \cdot n_{MLG\_inner\_struts}} \cdot f_{safety}
-$
+$$
+  v_{\text{MLG tire des}} = \frac{\frac{L_{\text{MLG,max}}}{g} \cdot 2.2}{n_{\text{MLG tires per outer strut}} \cdot n_{\text{MLG outer struts}} + n_{\text{MLG tires per inner strut}} \cdot n_{\text{MLG inner struts}}} \cdot f_{\text{safety}}
+$$
+
 In which
-- $L_{MLG,max}$ - maximum main gear load
+
+- $L_{\text{MLG,max}}$ - maximum main gear load
 - $g$ - gravitational acceleration
-- $n_{MLG\_tires\_per\_outer\_strut}$ - number of tires per outer strut
-- $n_{MLG\_outer\_struts}$ - number of outer struts
-- $n_{MLG\_tires\_per\_inner\_strut}$ - number of tires per inner strut
-- $n_{MLG\_inner\_struts}$ - number of inner struts
-- $f_{safety}$ - safety factor
+- $n_{\text{MLG tires per outer strut}}$ - number of tires per outer strut
+- $n_{\text{MLG outer struts}}$ - number of outer struts
+- $n_{\text{MLG tires per inner strut}}$ - number of tires per inner strut
+- $n_{\text{MLG inner struts}}$ - number of inner struts
+- $f_{\text{safety}}$ - safety factor
 
-If only one main gear tyre is mounted to one main landing gear strut, $f_{safety} = 1$. If more than one tire is mounted to one main landing gear strut, an additional safety load margin according to CS 25.733 (c)(1) is required that results in $f_{safety} = 1.07$.
+If only one main gear tyre is mounted to one main landing gear strut, $f_{\text{safety}} = 1$. If more than one tire is mounted to one main landing gear strut, an additional safety load margin according to CS 25.733 (c)(1) is required that results in $f_{\text{safety}} = 1.07$.
 
 #### Tire selection
 Knowing the design speed and loads, a suitable tire is selected from the database.
 
 ## Limitations {#limitations}
-Estimation of ground strike limitations in accordance to Sforza<sup>[5]</sup> and CS-25<sup>[2]</sup>
+Estimation of ground strike limitations in accordance to Sforza<sup>[5]</sup> and CS-25<sup>[2]</sup>.
 
 The safest and highest permissible rotation angle during takeoff, considering both landing constraints and tail tipping risks, is calculated, considering different constraints and configurations.
 
@@ -292,42 +322,49 @@ With the known values, the landing gear placement and dimensions are estimated m
 Ground clearance angles for nacelles and wing tips are calculated and verified in accordance to Torenbeek<sup>[6]</sup> and CS-25<sup>[2]</sup>.
 
 ### Nacelle clearance
-The ground clearance $c_{nacelle}$ for each nacelle is given as:
-$
-  c_{nacelle} = d_{GND\_to\_FCL} - |z_{nacelle}| - |h_{nacelle}|
-$
+The ground clearance $c_{\text{nacelle}}$ for each nacelle is given as:
+$$
+  c_{\text{nacelle}} = d_{\text{GND to FCL}} - |z_{\text{nacelle}}| - |h_{\text{nacelle}}|
+$$
+
 In which
-- $d_{GND\_to\_FCL}$ - vertical distance between ground and fuselage center line
-- $z_{nacelle}$ - z position of nacelle
-- $h_{nacelle}$ - height of nacelle
+
+- $d_{\text{GND to FCL}}$ - vertical distance between ground and fuselage center line
+- $z_{\text{nacelle}}$ - z position of nacelle
+- $h_{\text{nacelle}}$ - height of nacelle
 
 The nacelle clearance angle can then be determined:
-$
-    \theta_{nacelle} = \arctan\left(\frac{c_{nacelle}}{|y_{nacelle}| - y_{MLG\_outer\_strut}}\right) \cdot \frac{180}{\pi}
-$
+$$
+  \theta_{\text{nacelle}} = \arctan\left(\frac{c_{\text{nacelle}}}{|y_{\text{nacelle}}| - y_{\text{MLG outer strut}}}\right) \cdot \frac{180}{\pi}
+$$
 
 In which:
-- $y_{nacelle}$ - y position of nacelle
-- $y_{MLG\_outer\_strut}$ - y position of outer main landing gear strut
+
+- $y_{\text{nacelle}}$ - y position of nacelle
+- $y_{\text{MLG outer strut}}$ - y position of outer main landing gear strut
 
 This value is then checked regarding the minimum required clearance angle of 5 degree, defined by CS 25.149, and the user-specified nacelle clearance angle.
 
 ### Wing tip clearance
-The wing tip ground clearance $c_{wing\_tip}$ is known from the positions of the wing tip section.
-$
-  c_{wing\_tip} = d_{GND\_to\_FCL} - z_{wing\_tip}
-$
+The wing tip ground clearance $c_{\text{wing tip}}$ is known from the positions of the wing tip section.
+$$
+  c_{\text{wing tip}} = d_{\text{GND to FCL}} - z_{\text{wing tip}}
+$$
+
 In which
-- $d_{GND\_to\_FCL}$ - vertical distance between ground and fuselage center line
-- $z_{wing\_tip}$ - z position of wing tip
+
+- $d_{\text{GND to FCL}}$ - vertical distance between ground and fuselage center line
+- $z_{\text{wing tip}}$ - z position of wing tip
 
 The wing tip clearance angle is calculated using the wing tip's position relative to the main gear outer strut:
-$
-    \theta_{wing\_tip} = \arctan\left(\frac{c_{wing\_tip}}{|y_{wing\_tip}| - y_{MLG\_outer\_strut}}\right) \cdot \frac{180}{\pi}
-$
+$$
+    \theta_{\text{wing tip}} = \arctan\left(\frac{c_{\text{wing tip}}}{|y_{\text{wing tip}}| - y_{\text{MLG outer strut}}}\right) \cdot \frac{180}{\pi}
+$$
+
 In which:
-- $y_{wing\_tip}$ - y position of wing tip
-- $y_{MLG\_outer\_strut}$ - y position of outer main landing gear strut
+
+- $y_{\text{wing tip}}$ - y position of wing tip
+- $y_{\text{MLG outer strut}}$ - y position of outer main landing gear strut
 
 This value is then validated against the minimum required clearance angle of 5 degree, defined by CS 25.149, and the user-specified wing tip clearance angle.
 
@@ -343,17 +380,19 @@ The undercarriage masses are calculated in accordance to Torenbeek<sup>[6]</sup>
 
 Under the use of these coefficients, the mass for the nose as well as the main landing gear can be calculated using the following equation:
 
-$
-  m = c_{wing} \cdot \left( A + B \cdot MTOM^{0.75} + C \cdot MTOM + D \cdot MTOM^{1.5} \right) \cdot f_{corr}
-$
+$$
+  m = c_{\text{wing}} \cdot \left( A + B \cdot MTOM^{0.75} + C \cdot MTOM + D \cdot MTOM^{1.5} \right) \cdot f_{\text{corr}}
+$$
+
 In which:
-- $c_{wing}$ - wing position coefficient (`1.0`for low or mid wing position, `1.8`for high wing position)
+
+- $c_{\text{wing}}$ - wing position coefficient (`1.0`for low or mid wing position, `1.8`for high wing position)
 - $MTOM$ - maximum takeoff mass
-- $f_{corr}$ - landing gear correction factor (taken from user specification)
+- $f_{\text{corr}}$ - landing gear correction factor (taken from user specification)
 - $ A,B,C,D$ - coefficients from above table
 
 !!! note 
-  If the maximum takeoff mass is not available, it is calculated by dividing the maximum ramp weight by the gravitational acceleration.
+    If the maximum takeoff mass is not available, it is calculated by dividing the maximum ramp weight by the gravitational acceleration.
 
 The total nose/main landing gear mass divided by the number of struts per nose/main landing gear results in the per-strut mass.
 
@@ -362,8 +401,8 @@ The calculation is based on the COMFAA Tool developed by the Federal Aviation Ad
 Detailed information can be taken from the website:
 
 !!! note 
-  By clicking on the following link, you will leave the UNICADO website. Please note that we are not responsible for the content of the linked website and do not assume any liability.<br>
-  https://www.airporttech.tc.faa.gov/Products/Airport-Safety-Papers-Publications/Airport-Safety-Detail/comfaa-30
+    By clicking on the following link, you will leave the UNICADO website. Please note that we are not responsible for the content of the linked website and do not assume any liability.<br>
+    [External link to FAA COMFAA 3.0](https://www.airporttech.tc.faa.gov/Products/Airport-Safety-Papers-Publications/Airport-Safety-Detail/comfaa-30)
 
 The Aircraft Classification Number (ACN) is a standardized measure that describes the load a particular aircraft imposes on the surface of a runway or taxiway. It is defined by the International Civil Aviation Organization (ICAO) in Annex 14<sup>[7]</sup> and is used to assess whether an aircraft is compatible with a specific pavement's structural capacity, expressed as the Pavement Classification Number (PCN).
 The subsequent section provides some information on the method.
@@ -377,7 +416,7 @@ The subsequent section provides some information on the method.
     - Rigid pavements: Concrete surfaces with a stiff structure.
     - Flexible pavements: Asphalt or other elastic materials.
     !!! note 
-      Currently only flexible pavement implemented. 
+        Currently only flexible pavement implemented. 
   - Subgrade strength (the strength of the ground beneath the pavement) is divided into four categories: High (H), Medium (M), Low (L), Very Low (VL).
 3. Standardization
   - The ACN is normalized to a reference Single Wheel Load (SWL) of 10 tons.
diff --git a/docs/documentation/sizing/landing_gear_design/getting_started.md b/docs/documentation/sizing/landing_gear_design/getting_started.md
index 6bdeea4..2567908 100644
--- a/docs/documentation/sizing/landing_gear_design/getting_started.md
+++ b/docs/documentation/sizing/landing_gear_design/getting_started.md
@@ -11,6 +11,7 @@ This section will guide you through the necessary steps to get the _landing\_gea
     It is assumed that you have the `UNICADO package` installed including the executables and UNICADO libraries.
 
 Generally, we use two files to set or configure modules in UNICADO:
+
 - The aircraft exchange file (or _acXML_) includes
     - data related inputs (e.g., configuration type) and
     - data related outputs (e.g., component design data).
@@ -42,6 +43,7 @@ _landing\_gear\_design_ can be single executed without the execution of any othe
 - ... -->
 
 The following data should be available in the _acXML_ (2. and 3. are optional):
+
 1. Requirements and specifications
     - Design specification
         - Configuration information
@@ -97,6 +99,7 @@ The following data should be available in the _acXML_ (2. and 3. are optional):
 The _configXML_ is structured into two blocks: the control and program settings.
 
 The control settings are standardized in UNICADO and will not be described in detail here. But to get started, you have to change at least
+
 - the `aircraft_exchange_file_name` and `aircraft_exchange_file_directory` to your respective settings,
 - the `console_output` at least to `mode_1`, and
 - the `plot_output` to false (or define `inkscape_path` and `gnuplot_path`).
@@ -166,6 +169,7 @@ The landing gear library contains files that are necessary to generate a valid l
 
 #### Tire list
 The EASA ETSO (European Technical Standard Order) tire list (`EASA_ETSO_tire_list_2022.xml`) contains data on several nose and main landing gear tires. The following values are provided:
+
 - Tire size
 - Diameters
 - Rated pressure, speed, load, and ply
@@ -174,7 +178,7 @@ The EASA ETSO (European Technical Standard Order) tire list (`EASA_ETSO_tire_lis
 The data is used to find matching tires for the main and nose gear.
 
 #### Bridgestone manuals
-Valuable information on the tire selection can be found in the Bridgestone manuals. There you can find information on cut depths, lengths limits and useful terminology, as well as tire specifications.
+Valuable information on the tire selection can be found in the Bridgestone manuals. There you can find information on cut depths, lengths limits, and useful terminology, as well as tire specifications.
 
 ## Next steps {#next-steps}
 The next step is to [run the _landing\_gear\_design_ module](run_your_first_design.md).
\ No newline at end of file
diff --git a/docs/documentation/sizing/landing_gear_design/index.md b/docs/documentation/sizing/landing_gear_design/index.md
index 8eab731..7e9913d 100644
--- a/docs/documentation/sizing/landing_gear_design/index.md
+++ b/docs/documentation/sizing/landing_gear_design/index.md
@@ -13,10 +13,12 @@ Body-mounted                 | ...              | ...       | ...       | under
 ## A user's guide to landing gear design
 The _landing\_gear\_design_ tool is your key to designing the aircraft's landing gear. In this user documentation, you’ll find all the information you need to understand the tool, as well as the necessary inputs and configurations to run a landing gear design from the ground up.
 The following sections will walk you through the process:
+
 - [Getting started](getting_started.md)
 - [Run your first landing gear design](run_your_first_design.md)
 
 For a comprehensive understanding of the tool’s functionality, the documentation is structured into two distinct sections:
+
 - A [method description](design_method.md) and
 - a [software architecture](software_architecture.md)
 section.
diff --git a/docs/documentation/sizing/landing_gear_design/run_your_first_design.md b/docs/documentation/sizing/landing_gear_design/run_your_first_design.md
index aa5198a..785d01b 100644
--- a/docs/documentation/sizing/landing_gear_design/run_your_first_design.md
+++ b/docs/documentation/sizing/landing_gear_design/run_your_first_design.md
@@ -3,6 +3,7 @@ Let's dive into the fun part and design a landing gear!
 
 ## Tool single execution
 The tool can be executed from the console directly if all paths are set. The following will happen:
+
 - [Console output](#console-output)
 - [Generation of reports and plots](#reporting)
 - [Writing output to aircraft exchange file](#acxml)
@@ -98,9 +99,10 @@ Finally, you receive information about the reports and plots created (depending
 
 ### Reporting {#reporting}
 In the following, a short overview is given on the generated reports:
+
 - A `landing_gear_design.log` file is written within the directory of the executable
 - Depending on your settings, the following output is generated and saved in the `reporting` folder, located in the directory of the aircraft exchange file:
-    - an HTML report in the `report_html` folder (not implemented yet)
+    - an HTML report in the `report_html` folder
     - a TeX report in the `report_tex` folder (not implemented yet)
     - an XML file with additional output data in the `report_xml` folder
     - plots in the `plots` folder
@@ -115,16 +117,14 @@ Aircraft exchange file
 |- Component design
 |  |- Landing gear
 |  |  |- Position*
-|  |  |- Mass properties
-|  |  |  |- ...
+|  |  |- Mass properties**
 |  |  |- Aircraft classification number
 |  |  |- Specific
 |  |  |  |- Geometry
 |  |  |  |  |- Landing gear assembly (ID="0")
 |  |  |  |  |  |- Name
 |  |  |  |  |  |- Position*
-|  |  |  |  |  |- Mass properties
-|  |  |  |  |  |  |- ...
+|  |  |  |  |  |- Mass properties**
 |  |  |  |  |  |- Assembly components
 |  |  |  |  |  |  |- Strut diameter
 |  |  |  |  |  |  |- Strut length
@@ -134,7 +134,9 @@ Aircraft exchange file
 |  |  |  |  |  |  |  |- Tire diameter
 |  |  |  |  |  |  |  |- Tire section width
 ```
-<sup>*</sup> Node contains the following sub-nodes: x, y, z
+<sup>*</sup> Node has been shortened. It contains the following sub-nodes: x, y, z
+
+<sup>*</sup> Node has been shortened. It contains sub-nodes with information on the mass, inertia, and center of gravity.
 
 ### Generation of geometry file {#existing-geometry-file}
 The calculated geometry data is written to the `existing_landing_gear_geometry.xml` file and can then be used if the `use_existing_geometry` flag is set to `true`.
-- 
GitLab


From b74d46705e02f9fbfcfe0fa1e9de4f877af9f50b Mon Sep 17 00:00:00 2001
From: AndiGob <andreas.gobbbin@hotmail.de>
Date: Thu, 6 Feb 2025 17:20:01 +0100
Subject: [PATCH 2/4] landing_gear_design_documentation: - update section
 nacelle clearance

---
 .../landing_gear_design/design_method.md      | 24 +++----------------
 1 file changed, 3 insertions(+), 21 deletions(-)

diff --git a/docs/documentation/sizing/landing_gear_design/design_method.md b/docs/documentation/sizing/landing_gear_design/design_method.md
index 6fe365b..6387782 100644
--- a/docs/documentation/sizing/landing_gear_design/design_method.md
+++ b/docs/documentation/sizing/landing_gear_design/design_method.md
@@ -322,28 +322,10 @@ With the known values, the landing gear placement and dimensions are estimated m
 Ground clearance angles for nacelles and wing tips are calculated and verified in accordance to Torenbeek<sup>[6]</sup> and CS-25<sup>[2]</sup>.
 
 ### Nacelle clearance
-The ground clearance $c_{\text{nacelle}}$ for each nacelle is given as:
-$$
-  c_{\text{nacelle}} = d_{\text{GND to FCL}} - |z_{\text{nacelle}}| - |h_{\text{nacelle}}|
-$$
-
-In which
-
-- $d_{\text{GND to FCL}}$ - vertical distance between ground and fuselage center line
-- $z_{\text{nacelle}}$ - z position of nacelle
-- $h_{\text{nacelle}}$ - height of nacelle
-
-The nacelle clearance angle can then be determined:
-$$
-  \theta_{\text{nacelle}} = \arctan\left(\frac{c_{\text{nacelle}}}{|y_{\text{nacelle}}| - y_{\text{MLG outer strut}}}\right) \cdot \frac{180}{\pi}
-$$
-
-In which:
-
-- $y_{\text{nacelle}}$ - y position of nacelle
-- $y_{\text{MLG outer strut}}$ - y position of outer main landing gear strut
+The ground clearance $c_{nacelle}$ for each nacelle can be specified via the module configuration file. A value of 0.45 meters is set by default. 
+This value is usually used by the manufacturers as the nacelle safety clearance; a specification by certification regulations is not given.
 
-This value is then checked regarding the minimum required clearance angle of 5 degree, defined by CS 25.149, and the user-specified nacelle clearance angle.
+The implemented method checks for each existing propulsor whether it is mounted on the wing and if the nacelle used complies with the required safety distance. If the check fails, the necessary delta length of the main landing gear struts is calculated and the dimensioning of these is restarted. The repositioning in the direction of the span resulting due to the change in length is also performed. If there is a collision with the innermost propulsor mounted on to the wing, an error message is displayed and repositioning is terminated.
 
 ### Wing tip clearance
 The wing tip ground clearance $c_{\text{wing tip}}$ is known from the positions of the wing tip section.
-- 
GitLab


From 54eb663e055588786d3a984a74d2686b1b97913a Mon Sep 17 00:00:00 2001
From: sroscher <s.roscher@tu-berlin.de>
Date: Thu, 6 Feb 2025 18:18:34 +0100
Subject: [PATCH 3/4] - Put index 'nacelle' as text (no italic index)

---
 docs/documentation/sizing/landing_gear_design/design_method.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/documentation/sizing/landing_gear_design/design_method.md b/docs/documentation/sizing/landing_gear_design/design_method.md
index 6387782..1a97547 100644
--- a/docs/documentation/sizing/landing_gear_design/design_method.md
+++ b/docs/documentation/sizing/landing_gear_design/design_method.md
@@ -322,7 +322,7 @@ With the known values, the landing gear placement and dimensions are estimated m
 Ground clearance angles for nacelles and wing tips are calculated and verified in accordance to Torenbeek<sup>[6]</sup> and CS-25<sup>[2]</sup>.
 
 ### Nacelle clearance
-The ground clearance $c_{nacelle}$ for each nacelle can be specified via the module configuration file. A value of 0.45 meters is set by default. 
+The ground clearance $c_\text{nacelle}$ for each nacelle can be specified via the module configuration file. A value of 0.45 meters is set by default. 
 This value is usually used by the manufacturers as the nacelle safety clearance; a specification by certification regulations is not given.
 
 The implemented method checks for each existing propulsor whether it is mounted on the wing and if the nacelle used complies with the required safety distance. If the check fails, the necessary delta length of the main landing gear struts is calculated and the dimensioning of these is restarted. The repositioning in the direction of the span resulting due to the change in length is also performed. If there is a collision with the innermost propulsor mounted on to the wing, an error message is displayed and repositioning is terminated.
-- 
GitLab


From 8a30274095053faa56678158ba59e4d7da84103c Mon Sep 17 00:00:00 2001
From: AndiGob <andreas.gobbbin@hotmail.de>
Date: Sun, 9 Feb 2025 20:16:20 +0100
Subject: [PATCH 4/4] landing_gear_design_documentation: - Add missing turn
 over discription

---
 .../sizing/landing_gear_design/design_method.md     | 13 +++++++++++++
 .../sizing/landing_gear_design/getting_started.md   |  8 ++++----
 2 files changed, 17 insertions(+), 4 deletions(-)

diff --git a/docs/documentation/sizing/landing_gear_design/design_method.md b/docs/documentation/sizing/landing_gear_design/design_method.md
index 1a97547..a4dfa74 100644
--- a/docs/documentation/sizing/landing_gear_design/design_method.md
+++ b/docs/documentation/sizing/landing_gear_design/design_method.md
@@ -316,6 +316,19 @@ If this value is not provided, it defaults to using only the given tail strike l
 **Maximum Tail Tipping Angle**<br>
 The calculated maximum rotation angle at landing is compared with the maximum rotation angle during takeoff. The larger of these values is taken as the maximum tail tipping angle.
 
+**Turn over Angle**<br>
+The turnover angle defines how much an aircraft can tilt before it loses lateral stability and tips over. It depends on the center of gravity height and the landing gear track width. A higher center of gravity or a narrower landing gear stance reduces the turnover angle, making the aircraft more prone to tipping during sharp turns, braking, or uneven ground contact.
+For **commercial aircraft**, a turnover angle between 40–60° is generally required to ensure stability during taxiing, ground handling, and takeoff/landing rollouts. This ensures that lateral forces from crosswinds, asymmetric thrust, or sharp turns do not cause the aircraft to tip. If the turnover angle is too small (e.g., below 30°), the aircraft becomes unstable, increasing the risk of accidents on the ground.
+The turnover angle (\theta) is calculated using the formula:
+$$
+  \theta = \tan^{-1} \left( \frac{h}{\frac{T}{2}} \right)
+$$
+In which
+
+- $h$ - height of the center of gravity (CG) above the ground
+- $T$ - track width (distance between main landing gear contact points)
+- $\theta$ - turnover angle (in degrees)
+
 With the known values, the landing gear placement and dimensions are estimated meeting constraints like stability, retractability, turnover limits, and tail strike prevention. If the criteria aren't met, the design is refined in an iterative process.
 
 ## Clearances {#clearances}
diff --git a/docs/documentation/sizing/landing_gear_design/getting_started.md b/docs/documentation/sizing/landing_gear_design/getting_started.md
index 2567908..9877fbe 100644
--- a/docs/documentation/sizing/landing_gear_design/getting_started.md
+++ b/docs/documentation/sizing/landing_gear_design/getting_started.md
@@ -111,16 +111,16 @@ The program settings are structured like this (descriptions can be found in the
 
 ```plaintext
 Program Settings
+|- program_mode
+|  |- Setting use existing geometry
+|  |  |- Path to existing geometry file
+|  |  |- Use as starting point
 |- Configuration (ID="wing_mounted")
 |  |- Fidelity name
 |  |- Method name
 |  |- Fidelity (ID="empirical")
 |  |  |- Landing gear design tu berlin
 |  |  |  |- General
-|  |  |  |  |- Sizing mode
-|  |  |  |  |  |- Setting use existing landing gear
-|  |  |  |  |  |  |- Name of existing geometry file
-|  |  |  |  |  |  |- Use as starting point
 |  |  |  |  |- Ground strike limitations
 |  |  |  |  |  |- Tail strike limit
 |  |  |  |  |  |- Turnover limit
-- 
GitLab