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    "# Arm Length Fractions\n",
    "\n",
    "This notebook performs a parameter study of the projectile and counterweight arm lengths of a hinged counterweight trebuchet. It fixes the total arm length and varies the fraction projectile_arm_length/total_arm_length. For some values of this fraction, the projectile sling is not in tension for the full duration of the launch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from pytrebuchet.simulation import Simulation\n",
    "from pytrebuchet.trebuchet import HingedCounterweightTrebuchet, Arm\n",
    "\n",
    "\n",
    "# Define range of arm fraction values to test\n",
    "arm_fractions = np.linspace(\n",
    "    0.5, 0.8, 100\n",
    ")  # fraction of total arm length that is projectile arm\n",
    "total_arm_length = 1.75 + 6.792\n",
    "\n",
    "# Define result arrays\n",
    "distances = np.empty_like(arm_fractions, dtype=np.float64)\n",
    "in_tension = np.empty_like(arm_fractions, dtype=bool)  # Track if sling stays in tension\n",
    "\n",
    "# Compute distance for each arm fraction\n",
    "default = HingedCounterweightTrebuchet.default()\n",
    "for i, arm_fraction in enumerate(arm_fractions):\n",
    "    # Create trebuchet with specified arm lengths\n",
    "    projectile_arm_length = arm_fraction * total_arm_length\n",
    "    counterweight_arm_length = total_arm_length - projectile_arm_length\n",
    "    trebuchet = HingedCounterweightTrebuchet(\n",
    "        arm=Arm(\n",
    "            length_projectile_side=projectile_arm_length,\n",
    "            length_weight_side=counterweight_arm_length,\n",
    "            mass=default.arm.mass,\n",
    "        ),\n",
    "        weight=default.weight,\n",
    "        pivot=default.pivot,\n",
    "        sling_projectile=default.sling_projectile,\n",
    "        sling_weight=default.sling_weight,\n",
    "        release_angle=default.release_angle,\n",
    "        projectile=default.projectile,\n",
    "    )\n",
    "\n",
    "    # Simulate\n",
    "    simulation = Simulation(\n",
    "        trebuchet, verify_sling_tension=False\n",
    "    )  # we will check tension manually\n",
    "    simulation.solve()\n",
    "\n",
    "    # Record distance and tension status\n",
    "    distances[i] = simulation.distance_traveled\n",
    "    in_tension[i] = np.all(simulation.where_sling_in_tension())\n",
    "\n",
    "# Plot results\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(arm_fractions, distances, label=\"Distance Traveled\")\n",
    "ax.fill_between(\n",
    "    arm_fractions,\n",
    "    0,\n",
    "    np.max(distances),\n",
    "    where=in_tension,\n",
    "    color=\"green\",\n",
    "    alpha=0.3,\n",
    "    label=\"Sling in Tension\",\n",
    ")\n",
    "ax.fill_between(\n",
    "    arm_fractions,\n",
    "    0,\n",
    "    np.max(distances),\n",
    "    where=~in_tension,\n",
    "    color=\"red\",\n",
    "    alpha=0.3,\n",
    "    label=\"Sling Slack\",\n",
    ")\n",
    "ax.set_xlabel(\"Projectile Arm Length / Total Arm Length\")\n",
    "ax.set_ylabel(\"Distance Traveled (m)\")\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  }
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