d4t_formulas/lib/defaults/formulas.d4rt

[

{
  "name": "Temperature converter",
  "description": "Example of simple formula, just unit conversion",
  "input": [
    {"name": "Input", "unit": "Kelvin" }
  ],
  "output": {"name": "Output", "unit": "Kelvin" },
  "d4rtCode": "Output = Input;",
  "tags": ["converter", "temperature" ]
},
  // Free fall distance (vertical)
  {
    "name": "Free Fall Distance",
    "description": r"""
Calculates vertical displacement under constant gravity

$$h = \\frac{1}{2}gt^2$$

Where:
- $g$: Gravitational acceleration ($9.81\\ \\mathrm{m/s^2}$ on Earth)
- $t$: Time in free fall (seconds)

![Free Fall Diagram](https://altcalculator.com/wp-content/uploads/2023/08/Free-Fall.png)""",
    "input": [
      {"name": "t", "unit": "second"},  // Time in seconds
      {"name": "g", "unit": "meters per second"}  // Gravitational acceleration
    ],
    "output": {"name": "h", "unit": "meter"},  // Height in meters
    "d4rtCode": "h = 0.5 * g * pow(t, 2);",
    "tags": ["physics", "kinematics"]
  },
  
  // Newton's Law of Universal Gravitation
  {
    "name": "Gravitational Force",
    "description": r'''
Newton's law of universal gravitation

\(F = G\\frac{m_1m_2}{r^2}\)

Where:
- $G$: Gravitational constant ($6.674\\times 10^{-11}\\ \\mathrm{N\\cdot m^2/kg^2}$)
- $m_1, m_2$: Masses of two objects
- $r$: Distance between centers of masses

![Gravitation](https://upload.wikimedia.org/wikipedia/commons/thumb/3/33/NewtonsLawOfUniversalGravitation.svg/1200px-NewtonsLawOfUniversalGravitation.svg.png)''',
    "input": [
      {"name": "m1", "unit": "kilogram"},  // Mass 1
      {"name": "m2", "unit": "kilogram"},  // Mass 2
      {"name": "r", "unit": "meter"}     // Distance between masses
    ],
    "output": {"name": "F", "unit": "newton"},  // Force in newtons
    "d4rtCode": "F = (6.67430e-11 * m1 * m2) / pow(r, 2);",
    "tags": ["physics", "astronomy", "gravity"]
  },
  
  // Kinetic Energy
  {
    "name": "Kinetic Energy",
    "description": r'''
Energy possessed by a moving object

$$KE = \\frac{1}{2}mv^2$$

Where:
- $m$: Mass of object
- $v$: Velocity of object

![Kinetic Energy](https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Kinetic_energy.svg/1200px-Kinetic_energy.svg.png)''',
    "input": [
      {"name": "m", "unit": "kilogram"},  // Mass
      {"name": "v", "unit": "meters per second"}  // Velocity
    ],
    "output": {"name": "KE", "unit": "joule"},  // Energy in joules
    "d4rtCode": "KE = 0.5 * m * pow(v, 2);",
    "tags": ["physics", "energy", "mechanics"]
  },
  
  // Projectile Motion Range
  {
    "name": "Projectile Range",
    "description": r"""Calculates horizontal distance of projectile motion
                 $$R = \\frac{v^2 \\sin(2\\theta)}{g}$$
                 Where:
                 - $v$: Initial velocity
                 - $\\theta$: Launch angle
                 - $g$: Gravitational acceleration
                 ![Projectile Motion](https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Projectile_motion_diagram.png/800px-Projectile_motion_diagram.png)""",
    "input": [
      {"name": "v", "unit": "meters per second"},  // Initial velocity
      {"name": "a", "unit": "degree"}   // Launch angle
    ],
    "output": {"name": "R", "unit": "meter"},  // Horizontal distance
    "d4rtCode": """
       var radians = a * (pi / 180);
       R = (pow(v, 2) * sin(2 * radians)) / 9.80665;
    """,
    "tags": ["physics", "kinematics", "projectile"]
  },

  {
    "name": "Newton's Second Law",
    "description": r'''
Force equals mass times acceleration

$$F = m \\cdot a$$

Where:
- $m$: Mass of object ($\\mathrm{kg}$)
- $a$: Acceleration ($\\mathrm{m/s^2}$)

![Newton's Second Law](https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Newtonslawsofmotion.jpg/800px-Newtonslawsofmotion.jpg)''',
    "input": [
      {"name": "m", "unit": "kilogram"},  // Mass
      {"name": "a", "unit": "meters per square second"} // Acceleration
    ],
    "output": {"name": "F", "unit": "newton"},  // Force in newtons
    "d4rtCode": "F = m * a;",
    "tags": ["physics", "mechanics", "newton"]
  },

  // Apgar Score
  {
    "name": "Apgar Score",
    "description": "Newborn health assessment scoring system\n\nScores 0-2 for:\n1. Heart rate\n2. Breathing\n3. Muscle tone\n4. Reflexes\n5. Skin color\nTotal score 0-10",
    "input": [
      {"name": "HeartRate", "values": ["hr1", "hr2", "hr3"] },
      {"name": "Breathing", "values": ["hr1", "hr2", "hr3"] },
      {"name": "MuscleTone", "values": ["hr1", "hr2", "hr3"] },
      {"name": "Reflexes", "values": ["hr1", "hr2", "hr3"] },
      {"name": "SkinColor", "values": ["hr1", "hr2", "hr3"] }
    ],
    "output": {"name": "Result", "unit": "scalar"},
    "d4rtCode": """
      var total = HeartRate + Breathing + MuscleTone + Reflexes + SkinColor;
      var interpretation = switch (total) {
        >= 7 => 'Normal',
        4-6 => 'Requires attention',
        _ => 'Emergency care needed'
      };
      Result = 'Score: \$total - \$interpretation';
    """,
    "tags": ["medical", "pediatrics", "assessment"]
  }
]