UQ Projectile Example

Location: examples/rappture2/uq_projectile/

A multi-input physics example with UQ support. Demonstrates how uncertainty in launch parameters (velocity, angle, gravity) propagates to trajectory predictions.

tool.xml

<?xml version="1.0"?>
<run xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
     xsi:noNamespaceSchemaLocation="../../../rappture2web/contract.xsd">
<tool>
  <title>Projectile Motion with UQ (rappture2web)</title>
  <about>Classic projectile motion example with Uncertainty Quantification.

Set any of the numeric inputs to a uniform or gaussian distribution
to explore how parameter uncertainty propagates through the simulation.
The 'Number of time steps' input has UQ disabled — it always uses an
exact value.</about>
  <command>python3 @tool/uq_projectile.py @driver</command>
  <uq>true</uq>
  <contract>
    <input>
      <number id="height">
        <about>
          <label>Initial Height</label>
          <description>The initial height of the projectile above the ground.</description>
        </about>
        <units>m</units>
        <min>0m</min>
        <max>1000m</max>
        <default>0</default>
      </number>
      <number id="velocity">
        <about>
          <label>Initial Velocity</label>
          <description>The initial speed of the projectile.</description>
        </about>
        <units>m/s</units>
        <min>10m/s</min>
        <max>1000m/s</max>
        <default>100</default>
      </number>
      <number id="angle">
        <about>
          <label>Launch Angle</label>
          <description>The angle (in degrees) at which the projectile is launched.</description>
        </about>
        <min>5</min>
        <max>85</max>
        <default>45</default>
      </number>
      <number id="g">
        <about>
          <label>Gravity (g)</label>
          <description>Gravitational acceleration. Standard gravity is 9.80665 m/s^2.</description>
        </about>
        <units>m/s2</units>
        <min>9.7639m/s2</min>
        <max>9.8337m/s2</max>
        <default>9.80665</default>
      </number>
      <integer id="npts">
        <about>
          <label>Number of time steps</label>
          <description>How many points to use when plotting the trajectory.</description>
        </about>
        <min>20</min>
        <max>2000</max>
        <default>200</default>
      </integer>
    </input>
    <output>
      <curve id="path">
        <about>
          <label>Trajectory</label>
          <description>Distance vs. height of the projectile.</description>
        </about>
        <xaxis><label>Distance</label><units>m</units></xaxis>
        <yaxis><label>Height</label><units>m</units></yaxis>
      </curve>
      <curve id="height_vs_time">
        <about>
          <label>Height vs Time</label>
          <description>Height of the projectile as a function of time.</description>
        </about>
        <xaxis><label>Time</label><units>s</units></xaxis>
        <yaxis><label>Height</label><units>m</units></yaxis>
      </curve>
      <number id="distance">
        <about>
          <label>Total Distance</label>
          <description>Horizontal distance the projectile travels.</description>
        </about>
        <units>m</units>
      </number>
      <number id="maxheight">
        <about>
          <label>Maximum Height</label>
          <description>Peak height reached by the projectile.</description>
        </about>
        <units>m</units>
      </number>
    </output>
  </contract>
</tool>
<input>
  <number id="height">
    <about>
      <label>Initial Height</label>
      <description>The initial height of the projectile above the ground.</description>
    </about>
    <default>0</default>
    <units>m</units>
    <min>0m</min>
    <max>1000m</max>
  </number>
  <number id="velocity">
    <about>
      <label>Initial Velocity</label>
      <description>The initial speed of the projectile.</description>
    </about>
    <default>100</default>
    <units>m/s</units>
    <min>10m/s</min>
    <max>1000m/s</max>
  </number>
  <number id="angle">
    <about>
      <label>Launch Angle</label>
      <description>The angle (in degrees) at which the projectile is launched.</description>
    </about>
    <default>45</default>
    <min>5</min>
    <max>85</max>
  </number>
  <number id="g">
    <about>
      <label>Gravity (g)</label>
      <description>Gravitational acceleration.  Standard gravity is 9.80665 m/s^2.</description>
    </about>
    <default>9.80665</default>
    <units>m/s2</units>
    <min>9.7639m/s2</min>
    <max>9.8337m/s2</max>
  </number>
  <integer id="npts">
    <about>
      <label>Number of time steps</label>
      <description>How many points to use when plotting the trajectory.</description>
    </about>
    <uq>false</uq>
    <default>200</default>
    <min>20</min>
    <max>2000</max>
  </integer>
</input>
<output>
  <curve id="path">
    <about>
      <label>Trajectory</label>
      <description>Distance vs. height of the projectile.</description>
    </about>
    <xaxis><label>Distance</label><units>m</units></xaxis>
    <yaxis><label>Height</label><units>m</units></yaxis>
  </curve>
  <curve id="height_vs_time">
    <about>
      <label>Height vs Time</label>
      <description>Height of the projectile as a function of time.</description>
    </about>
    <xaxis><label>Time</label><units>s</units></xaxis>
    <yaxis><label>Height</label><units>m</units></yaxis>
  </curve>
  <number id="distance">
    <about>
      <label>Total Distance</label>
      <description>Horizontal distance the projectile travels.</description>
    </about>
    <units>m</units>
  </number>
  <number id="maxheight">
    <about>
      <label>Maximum Height</label>
      <description>Peak height reached by the projectile.</description>
    </about>
    <units>m</units>
  </number>
</output>
</run>

Running

rappture2web examples/rappture2/uq_projectile/

Inputs

All inputs support UQ except “Number of time steps”:

Input

UQ

Description

Initial Height (m)

Yes

Starting height above ground

Initial Velocity (m/s)

Yes

Launch speed

Launch Angle (degrees)

Yes

Angle above horizontal

Gravity (m/s^2)

Yes

Gravitational acceleration

Number of time steps

No

Points for plotting (<uq>false</uq>)

Try this

  1. Set Initial Velocity to gaussian, mean=100, std=10

  2. Set Launch Angle to uniform, min=40, max=50

  3. Leave other inputs as exact values

  4. Click Simulate

The UQ analysis will show:

  • How the trajectory uncertainty band widens over time

  • Which parameter (velocity or angle) has more influence on the range

  • The PDF of the total distance traveled

Key pattern: multi-output UQ

The script writes both curve and number outputs:

# Curves: trajectory and height-vs-time
rx['output.curve(path).component.xy'] = (distance, height)
rx['output.curve(height_vs_time).component.xy'] = (time, height)

# Scalars: PUQ fits response surfaces for these
rx['output.number(distance).current'] = f'{total_distance:.2f}m'
rx['output.number(maxheight).current'] = f'{max_height:.2f}m'

PUQ generates PDFs for the scalar outputs and probability bands for the curve outputs automatically.