# Usage

The calculator offers three input fields. 

- Equations
- Assumptions
- Looking for

Each field accepts one input per line. After entering your inputs, click **Solve** to run the symbolic solver. An example input is shown in the figure below.

```{image} _static/example_input.png
:width: 300px
:alt: Example Inputs
```

---

## Conceptual Overview

Everything Aero does not follow a fixed calculation order.

Instead, it:
1. Collects all known symbols and equations
2. Automatically activates all solvable equation templates
3. Solves the resulting system symbolically
4. Relaxes assumptions if the system is over-constrained

You only need to provide *enough information* - not a specific workflow.

---

## Indexed Variables

All symbols **must be indexed**.

Examples:

```
v0
rho0
F_z_total1
```


Each index represents a separate operating point.

Typical use cases:
- $v_0$, $v_1$: two different speeds
- $\rho_0$, $\rho_1$: different atmospheric conditions
- $F_{z0}$, $F_{z1}$: before / after a setup change

If your problem involves only one condition, simply use index `0` everywhere.

If *any* symbol is missing an index, the solver will not run.

---

## Input Fields

### Equations

This field is used for:

- Known numerical values (e.g. `v0 = 30`)
- Known relationships from the problem statement
- Custom equations not already built into the solver

Examples:
```
v0 = 30
rho0 = 1.225
Re0 = Re1
```

All equations entered here are treated as **hard constraints**.
If the system is inconsistent, no solution will be found.

### Assumptions

Assumptions are **soft constraints** that may override physics. This field is optional.

Example:

```
W_lat0 = 0
```


If assumptions conflict with physical equations, the solver will:
1. Try to preserve equations related to variables in **Looking for**
2. Relax assumption equations if necessary

This mirrors how assumptions are treated in real engineering problems.


### Looking for

This field is optional but strongly recommended.

It serves two purposes:
1. Highlights variables in the LaTeX solution output
2. Tells the solver which equations to prioritize when resolving conflicts


Example:

```
F_z_total_cornering_fl
F_z_total_cornering_fr
```
---

## Solve

Once inputs are entered, click **Solve**.

- Scalar-only problems solve instantly
- Symbolic functions may take a few seconds
- If no solution is found, check indexing first

---

## Custom Equations

You can add custom equations directly in the **Equations** field.
New symbols are allowed.

The example below solves [FS-Quiz Question 366](https://fs-quiz.eu/question/366)  
and correctly finds $v_1 = 86.6666$.

Custom equations used:
```
Re0 = Re1
nu0 = nu1
rho0 = rho1
```

```{image} _static/custom_eq_input.png
:width: 100%
:alt: Custom equation input example, FSQUIZ: ID366
```

---

## Troubleshooting:
If nothing happens after pressing Solve, the most likely cause is that not every symbol has an index currectly appended to it. If this is the case, add the correct index and solve again.