ENH: Add simplified opening shock force estimation

CHANGELOG.md

@@ -32,6 +32,7 @@ Attention: The newest changes should be on top -->
 
 ### Added
 
+- ENH: Add simplified opening shock force estimation [#1092](https://github.com/RocketPy-Team/RocketPy/pull/1092)
 - ENH: Support for Meteomatics API in the `Environment` class [#1079](https://github.com/RocketPy-Team/RocketPy/pull/1079)
 - ENH: update master with develop [#1081](https://github.com/RocketPy-Team/RocketPy/pull/1081)
 

rocketpy/utilities.py

@@ -780,3 +780,47 @@ def load_from_rpy(filename: str, resimulate=False):
         simulation = json.dumps(data["simulation"])
         flight = json.loads(simulation, cls=RocketPyDecoder, resimulate=resimulate)
     return flight
+
+
+def calculate_simplified_opening_shock_force(
+    cd_s, air_density, velocity, opening_shock_coefficient=1.5
+):
+    """Estimates the peak transient force experienced by the recovery
+    hardware during parachute inflation (the "opening shock").
+
+    The estimate follows the simplified model described in Knacke's
+    "Parachute Recovery Systems Design Manual" (1992, Section 5.5):
+
+    .. math::
+
+        F_0 = C_x \\cdot C_{d} S \\cdot q
+
+    where :math:`C_x` is the ``opening_shock_coefficient``,
+    :math:`C_{d} S` is the parachute's ``cd_s``, and :math:`q` is the
+    dynamic pressure (:math:`q = \\tfrac{1}{2} \\rho V^2`) at the instant
+    the canopy begins to inflate.
+
+    Parameters
+    ----------
+    cd_s : float
+        Drag coefficient times reference area of the parachute.
+    air_density : float
+        Freestream air density, in kg/m^3, at the moment of parachute
+        deployment.
+    velocity : float
+        Freestream velocity relative to the rocket, in m/s, at the moment
+        of parachute deployment.
+    opening_shock_coefficient : float, optional
+        Empirical coefficient (commonly noted Cx) used to estimate the
+        peak transient force experienced during parachute inflation via
+        :meth:`calculate_opening_shock_force`. Typical values range from
+        1.2 to 2.0 depending on the deployment method and canopy type.
+        Default value is 1.5.
+
+    Returns
+    -------
+    float
+        Estimated peak opening shock force, in Newtons.
+    """
+    dynamic_pressure = 0.5 * air_density * velocity**2
+    return opening_shock_coefficient * cd_s * dynamic_pressure

tests/unit/test_utilities.py

@@ -348,6 +348,41 @@ def test_load_from_rpy(mock_show):  # pylint: disable=unused-argument
     assert loaded_flight.all_info() is None
 
 
+def test_opening_shock_coefficient_default_is_1_5():
+    """Default opening_shock_coefficient must be 1.5."""
+    force_default = utilities.calculate_simplified_opening_shock_force(10.0, 1.225, 10)
+    force_1_5 = utilities.calculate_simplified_opening_shock_force(10.0, 1.225, 10, 1.5)
+    assert force_default == force_1_5
+
+
+def test_calculate_simplified_opening_shock_force_matches_formula():
+    """calculate_simplified_opening_shock_force must return
+    Cx * cd_s * 0.5 * rho * V^2."""
+    cd_s = 10.0
+    cx = 1.6
+    air_density = 1.225
+    velocity = 50.0
+
+    expected_force = cx * cd_s * 0.5 * air_density * velocity**2
+    assert utilities.calculate_simplified_opening_shock_force(
+        cd_s, air_density, velocity, cx
+    ) == pytest.approx(expected_force, rel=1e-9)
+
+
+def test_calculate_simplified_opening_shock_force_scales_with_velocity_squared():
+    """Doubling velocity must quadruple the opening shock force."""
+    force_v = utilities.calculate_simplified_opening_shock_force(10.0, 1.225, 40.0)
+    force_2v = utilities.calculate_simplified_opening_shock_force(10.0, 1.225, 80.0)
+    assert force_2v == pytest.approx(4 * force_v, rel=1e-9)
+
+
+def test_calculate_simplified_opening_shock_force_zero_velocity_is_zero():
+    """No dynamic pressure means no opening shock force."""
+    assert utilities.calculate_simplified_opening_shock_force(
+        10.0, 1.225, 0.0
+    ) == pytest.approx(0.0)
+
+
 # --- Logging (rocketpy.utilities.enable_logging) ------------------------------