Arm Length Fractions

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.

import matplotlib.pyplot as plt
import numpy as np

from pytrebuchet.simulation import Simulation
from pytrebuchet.trebuchet import HingedCounterweightTrebuchet, Arm


# Define range of arm fraction values to test
arm_fractions = np.linspace(
    0.5, 0.8, 100
)  # fraction of total arm length that is projectile arm
total_arm_length = 1.75 + 6.792

# Define result arrays
distances = np.empty_like(arm_fractions, dtype=np.float64)
in_tension = np.empty_like(arm_fractions, dtype=bool)  # Track if sling stays in tension

# Compute distance for each arm fraction
default = HingedCounterweightTrebuchet.default()
for i, arm_fraction in enumerate(arm_fractions):
    # Create trebuchet with specified arm lengths
    projectile_arm_length = arm_fraction * total_arm_length
    counterweight_arm_length = total_arm_length - projectile_arm_length
    trebuchet = HingedCounterweightTrebuchet(
        arm=Arm(
            length_projectile_side=projectile_arm_length,
            length_weight_side=counterweight_arm_length,
            mass=default.arm.mass,
        ),
        weight=default.weight,
        pivot=default.pivot,
        sling_projectile=default.sling_projectile,
        sling_weight=default.sling_weight,
        release_angle=default.release_angle,
        projectile=default.projectile,
    )

    # Simulate
    simulation = Simulation(
        trebuchet, verify_sling_tension=False
    )  # we will check tension manually
    simulation.solve()

    # Record distance and tension status
    distances[i] = simulation.distance_traveled
    in_tension[i] = np.all(simulation.where_sling_in_tension())

# Plot results
fig, ax = plt.subplots()
ax.plot(arm_fractions, distances, label="Distance Traveled")
ax.fill_between(
    arm_fractions,
    0,
    np.max(distances),
    where=in_tension,
    color="green",
    alpha=0.3,
    label="Sling in Tension",
)
ax.fill_between(
    arm_fractions,
    0,
    np.max(distances),
    where=~in_tension,
    color="red",
    alpha=0.3,
    label="Sling Slack",
)
ax.set_xlabel("Projectile Arm Length / Total Arm Length")
ax.set_ylabel("Distance Traveled (m)")
ax.legend()
plt.show()