feat: takeoff performance documentation

* feat: takeoff performance documentation

* initial info for performance calc

* add new advanced guide pages

* review round 1

* advanced guide text added

* add mathjax.js

* add formulas to advanced page

* add runway slope header

* add images

* image updates

* add performance page image

* marketing url redirect

* Apply suggestions from code review

alepouna review

Co-authored-by: alepouna <98479040+alepouna@users.noreply.github.com>

* initial beginner-guide changes

* formatting beginner guide changes

* slein review

* missed review commits

* fix broken links

---------

Co-authored-by: alepouna <98479040+alepouna@users.noreply.github.com>

docs/fbw-a32nx/feature-guides/flypados3/performance.md

@@ -1,12 +1,159 @@
 ---
 title: flyPadOS 3 EFB - Performance
-description: A comprehensive guide covering the descent and landing performance calculators provided by flyPadOS 3 in the FlyByWire A32NX.
+description: A comprehensive guide covering the takeoff, descent, and landing performance calculators provided by flyPadOS 3 in the FlyByWire A32NX.
 ---
 
 <link rel="stylesheet" href="../../../../stylesheets/efb-interactive.css">
 
 # flyPad Performance
 
+## Takeoff Performance Calculator
+
+<div style="position: relative;">
+    <img src="/fbw-a32nx/assets/flypados3/flypad-performance-takeoff.png" style="width: 100%; height: auto;" loading="lazy">
+    <a href="../dashboard/">   <div class="imagemap" style="position: absolute; left: 1.7%; top:  6.9%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Dashboard</span></div></a>
+    <a href="../dispatch/">    <div class="imagemap" style="position: absolute; left: 1.7%; top: 14.1%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Dispatch</span></div></a>
+    <a href="../ground/">      <div class="imagemap" style="position: absolute; left: 1.7%; top: 21.1%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Ground</span></div></a>
+    <a href="../performance/"> <div class="imagemap" style="position: absolute; left: 1.7%; top: 28.3%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Performance</span></div></a>
+    <a href="../charts/">      <div class="imagemap" style="position: absolute; left: 1.7%; top: 35.6%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Navigation & Charts</span></div></a>
+    <a href="../online-atc/">  <div class="imagemap" style="position: absolute; left: 1.7%; top: 43.0%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Online ATC</span></div></a>
+    <a href="../failures/">    <div class="imagemap" style="position: absolute; left: 1.7%; top: 50.1%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Failures</span></div></a>
+    <a href="../checklists/">  <div class="imagemap" style="position: absolute; left: 1.7%; top: 57.3%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Checklists</span></div></a>
+    <a href="../presets/">     <div class="imagemap" style="position: absolute; left: 1.7%; top: 64.7%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Presets</span></div></a>
+    <a href="../settings/">    <div class="imagemap" style="position: absolute; left: 1.7%; top: 85.0%; width: 5.8%; height: 7.0%;"><span class="imagemapname">Settings</span></div></a>
+    <span class="imagesub">Click on the menu icons in this image to see other flyPad pages.</span>
+</div>
+
+This calculator lets the pilots:
+
+1.	Determine if the airplane can take off at the intended takeoff weight from a designated runway at a specified temperature, wind, and QNH setting using a specified airplane configuration and bleed settings (A/I and A/C);
+2.	Determine the Flex temperature if a reduced thrust setting (Flex) can be used; 
+3.	Determine the appropriate takeoff speeds, V1, VR, and V2, for the conditions specified.
+
+!!! tip "Takeoff Performance Examples and Guide"
+    To learn more about how to plan and identify the required information to input into the flyPad takeoff performance calculator, see our guide:
+
+    [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md){ .md-button }
+
+The calculator considers the following potentially limiting conditions:
+
+- Runway Length
+- 2nd Segment Climb Performance
+- Ground Minimum Control Speeds (VMCG)
+- Maximum Brake Energy Speed (VMBE)
+- Maximum Tire Speed
+
+!!! warning ""
+    Takeoff obstacle clearance is not currently covered.
+
+### Usage
+
+All input fields must be filled before the "Calculate" button becomes available. There are two ways in which certain input fields can be automatically filled. If [SimBrief data 
+has been loaded into the EFB](dashboard.md), airport and runway information (including runway bearing, TORA, runway elevation, and runway slope), as well as environmental data 
+(wind, temperature, and QNH), can be automatically filled in by selecting "OFP" in the upper right drop-down selection box and clicking on the **Fill data from**.
+
+This will load the environment data used by your SimBrief flight plan. You can either change/update the environment data or load it from scratch automatically without having
+loaded it from the OFP by ensuring the Airport input field in the calculator is filled, then selecting "METAR" in the upper right drop-down selection box and clicking on **Fill
+data from**.
+
+### Information Required
+
+**Airport**
+
+- Enter the ICAO code for the airport. See the examples in [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md).
+
+**Runway**
+
+- Enter the runway number of the runway being used for takeoff.
+
+**Runway Bearing** 
+
+- This is the direction of the runway referenced to magnetic North. It will be filled automatically after entering the runway number.
+
+**TORA**
+
+- This is the length of the portion of the runway available for takeoff. It will be filled automatically after entering the runway number. Be aware that this information comes 
+from the MSFS 2020 runway length data and may not always be accurate. We recommend checking the TORA distance with the airport 10-9 (or 10-9A) chart as shown in the examples in [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md), especially if you plan an intersection departure. You should also reduce the TORA if you start on the runway, as MSFS 2020 typically places the airplane well forward of the beginning of the TORA.
+- If you enter a TORA that is less than the MSFS 2020 runway length, the difference will be shown as a TO Shift (takeoff shift) value in the replica of the MCDU performance 
+  page on the right side of the calculator. 
+
+!!! warning "TO Shift - Not Yet Implemented"
+    This is for information only at this point since the TO Shift entry in the MCDU Takeoff Perf Page is not yet implemented.
+
+**Entry Angle** 
+
+- This is the angle of the taxiway to the runway. An input is needed to allow the calculator to reduce the TORA distance by the distance used to align the airplane on 
+the runway for takeoff (since the runway behind the airplane should not be used to calculate takeoff performance). The entry angle can be determined from the airport 10-9 (or 10-9A) chart as shown in the examples in [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md).
+
+**Runway Elevation** 
+
+- This is the elevation of the runway at the beginning of the TORA. It will be automatically filled after entering the runway number. It can also be determined or checked from
+  the airport 10-9 chart, as shown in the following examples in [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md).
+
+**Runway Slope** 
+
+- This is the gradient of the runway in the direction of takeoff. It will be automatically entered after entering the runway number. It can also be determined or checked from 
+the airport 10-9 chart, but requires a little calculation from the data present on Jeppesen charts, as shown in the examples in [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md). A negative slope is downhill, while a positive slope is uphill.
+
+**Runway Condition** 
+
+- This allows input of runway conditions, including dry, wet, and numerous types of runway contamination. It defaults to a dry runway. Although the calculations are provided 
+for other runway conditions, be aware that MSFS 2020 currently does not simulate these surface conditions properly.
+
+**Wind** 
+
+- The wind can be input simply as the headwind component (a single positive number) or tailwind component (a single negative number), or it can be input in the form degrees/kts. 
+It can be automatically entered from either the OFP or the METAR as described above. If you enter the wind yourself, be sure you are entering the wind in terms of a magnetic 
+  direction rather than the true direction. ATIS winds will be provided in terms of a magnetic direction, but METAR winds are in terms of true direction. If you enter the winds 
+  from METAR, consult the airport 10-9 (or 10-9A) chart to determine the magnetic variation and convert the direction to magnetic, as shown in the following examples in [Advanced Takeoff Calculator Guide](../../../pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md). If you choose to enter the winds automatically from the 
+  METAR, this conversion will be done automatically.
+
+- If the wind direction is given as variable, enter the wind direction into the takeoff performance calculator as a tailwind. If the wind direction varies between 2 values, 
+enter the wind direction that will result in the largest tailwind (if the direction includes a tailwind direction) or the smallest headwind. If the wind speed includes a gust value, enter only the steady wind value. 
+
+**Temperature** 
+
+- This is simply the outside air temperature. It can be automatically entered from either the OFP or the METAR as described above. It can also be entered manually based on 
+either the active ATIS or METAR.
+
+**QNH** 
+
+- This is the sea-level atmospheric pressure at the airport. It can be automatically filled from either the OFP or the METAR as described above. It can also be entered manually 
+based on either the active ATIS or METAR.
+
+**Takeoff Weight**
+
+- This is the weight at which the airplane starts the takeoff (after taxiing to the runway). It can either be automatically entered from the OFP as described above or entered 
+manually.
+
+**CG Position** 
+
+- This is the takeoff CG position. The standard CG position is the default entry. Select the forward CG position if the takeoff CG is forward of (less than) 27% MAC. (The 
+standard CG envelope’s forward limit for takeoff is 25% MAC. However, considering the accuracy of loading calculations and to allow a tolerance, the extended forward CG takeoff performance should be used anytime the takeoff CG position is forward of 27% MAC.)
+
+**Configuration**
+
+- This is the flap/slat position to be used for takeoff. It is defaulted to CONF 1+F.
+- Other choices are: 
+    - Optimum (which will provide the highest Flex temperature, or if the Flex temperatures are the same, the lowest takeoff speeds); 
+    - CONF 2, or 
+    - CONF 3.
+
+**Thrust**
+
+- This is the thrust rating that will be used for takeoff. Flex (a reduced thrust) is the default, but TOGA can be selected. If Flex is selected but TOGA must be used, the 
+calculator will inform you and perform the calculation with TOGA thrust.
+
+**Anti-Ice** 
+
+- This refers to the setting of the anti-ice bleeds. It defaults to off. Select engine or engine + wing anti-ice if anti-ice will be used for takeoff. Using anti-ice will 
+reduce the takeoff thrust.
+
+**Packs** 
+
+- This refers to whether the air conditioning packs will be on for takeoff. It defaults to on, but can be changed to off if the air conditioning packs will 
+be off for takeoff. Turning the air conditioning packs off allows the engines to produce more takeoff thrust.
+
 ## Top of Descent Calculator
 
 <div style="position: relative;">
@@ -220,3 +367,7 @@ Be aware that there might be other restrictions that prohibit landing of an A320
 This runway can't be used for landing in the given circumstances. It is similar to Example 2 but has a higher weight and therefore higher approach speed.
 
 ![flyPad Performance Calculator Landing](../../../fbw-a32nx/assets/flypados3/performance-landing-notok.png "flyPad Performance Calculator Landing"){loading=lazy}
+
+*[TORA]: Take-Off Run Available
+*[QNH]: sea level atmospheric pressure
+*[OFP]: Operational Flight Plan

docs/javascripts/mathjax.js

@@ -0,0 +1,19 @@
+window.MathJax = {
+  tex: {
+    inlineMath: [["\\(", "\\)"]],
+    displayMath: [["\\[", "\\]"]],
+    processEscapes: true,
+    processEnvironments: true
+  },
+  options: {
+    ignoreHtmlClass: ".*|",
+    processHtmlClass: "arithmatex"
+  }
+};
+
+document$.subscribe(() => {
+  MathJax.startup.output.clearCache()
+  MathJax.typesetClear()
+  MathJax.texReset()
+  MathJax.typesetPromise()
+})

docs/pilots-corner/advanced-guides/flight-planning/.pages

@@ -6,6 +6,7 @@
 title: Flight Planning
 nav:
 #    - Overview: overview.md
+    - Takeoff Performance: takeoff-perf-calc.md
     - fixinfo.md
     - leg-types.md
     - disco.md

docs/pilots-corner/advanced-guides/flight-planning/takeoff-perf-calc.md

@@ -0,0 +1,80 @@
+# Calculating Takeoff Performance
+
+This is an advanced guide on how to calculate takeoff performance in the A32NX. This is meant to supplement information the provided in our flyPadOS 3 documentation and usage guide.
+
+[flyPad Performance Calculator Page](../../../fbw-a32nx/feature-guides/flypados3/performance.md){ .md-button }
+
+Clicking on the calculate button after all the input fields are filled properly will either result in takeoff speeds and Flex temperature (if Flex was selected and can be used) 
+being displayed in the replica of the MCDU Takeoff Perf Pages provided on the right side of the calculator unless the takeoff weight exceeds the maximum takeoff weight for the 
+input conditions or if any of the input conditions exceed any airplane limitations. If any of these conditions occur, a suitable error message will pop up.
+
+## Examples
+
+Information that can be obtained from Airport 10-9 (or 10-9A) charts
+
+### EGLL
+
+![egll-to.png](..%2F..%2Fassets%2Fadvanced-guides%2Ftakeoff-perf%2Fegll-to.png){loading=lazy}
+
+- Item 1 is the elevation for a takeoff from Runway 09L. 
+- Item 2 shows an example of a relatively rare zero-degree turn-on angle from the taxiway to the runway. This is denoted by the gray taxiway extending far enough after the turn 
+  to align the airplane with the runway direction before it gets to the beginning of the runway (indicated by the beginning of the black runway diagram). 
+- Item 3 is the elevation for a takeoff from Runway 27R. 
+- Item 4 shows a common 90-degree entry from the taxiway to the runway, which requires a portion of the runway to align the airplane in the direction of the runway for takeoff.
+
+Since the elevations of both ends of the runway are the same, the slope for takeoffs from both Runway 09L and 27R is zero. 
+
+!!! info "Unmarked In Above Example"
+    The magnetic variation for this airport is shown by the arrow on the lower-right side of the chart. 
+
+The magnetic variation at EGLL is 0 degrees, so there is no difference between a true heading and a magnetic heading. No conversion is needed for the METAR wind direction when 
+the wind is input manually for this airport.
+
+![eggl-10-9a.png](..%2F..%2Fassets%2Fadvanced-guides%2Ftakeoff-perf%2Feggl-10-9a.png){loading=lazy}
+
+For a large airport like EGLL, there is not enough space to add the additional runway information on the 10-9 chart. In this case, TORA distance for each runway and for 
+intersection takeoffs is provided on the 10-9A chart. For a Runway 09L full-length takeoff, the TORA is 12,799 feet, or 3901 meters.
+
+### SBRF
+
+Be aware that some runways for which the airport 10-9 chart shows a zero-degree runway entry angle, MSFS 2020 has the taxiway aligned such that a 90-degree entry angle is 
+required. One example of this is SBRF/Recife, Brazil. The marked area in the airport 10-9 chart below shows that the airplane can be aligned in the direction of takeoff before 
+entering the black runway area. In MSFS 2020, however, the taxiway meets the runway end at a 90-degree angle.
+
+![sbrf-to.png](..%2F..%2Fassets%2Fadvanced-guides%2Ftakeoff-perf%2Fsbrf-to.png){loading=lazy width=75%}
+
+The magnetic variation for SBRF is 21 degrees West. For a magnetic variation in the West direction, add the magnetic variation to the true wind direction referenced to 
+true North number to get the magnetic wind direction referenced to true North. For example, if the winds are 240/10 from the METAR, then input 261/10 into the takeoff calculator (240+21).  
+
+!!! info "Rounding"
+    You can also round this off to the nearest ten degrees, 260/10, which will probably be what ATIS would give you.
+
+### LOWI
+
+![lowi.png](..%2F..%2Fassets%2Fadvanced-guides%2Ftakeoff-perf%2Flowi.png){loading=lazy}
+
+This airport’s 10-9 chart has all the information on one chart. This is an example where both runways have a 180-degree entry angle; that is, the airplane must use the runway 
+to taxi to the runway end and then turn around to use the full runway length for takeoff. TORA values for the full runway length as well as from the taxiway 
+intersections (where a 90-degree entry angle would apply) are listed in the Additional Runway Information section.
+
+#### Calculating Runway Slope
+
+The runway elevation for each runway is different, so each runway will have a slope value. Use the following equation to calculate the slope value:
+
+!!! info "Slope Equation"
+    $$\frac{Elevation\,at\,end\,of\,TORA - Elevation\,at\,beginning\,of\,TORA}{TORA} * 100$$ 
+
+    \[ with\,all\,units\,being\,the\,same.\]
+
+!!! info "Runway 08 Example"
+    To calculate the runway slope for Runway 08 the equation with units included would look like the following:
+
+    $$\frac{1894 - 1907}{6562} * 100 = -0.20\%$$
+
+For LOWI, the magnetic variation is 4 degrees East. When the magnetic variation is to the East, subtract the variation from the true wind value to determine winds referenced to the 
+magnetic North. If the winds are 240/10 true from the METAR, adjust it to 236/10 when entering it into the takeoff performance calculator. 
+
+Since the magnetic variation is only 4 degrees and winds are normally rounded to the nearest ten degrees, you can also just skip converting the wind reference from true North 
+to magnetic North for LOWI.
+
+*[TORA]: Take-Off Run Available