BUG: EllipticalFins Roll Damping Factor Calculation

[MateusStano]

Pull request type

• Code base additions (bugfix, features)
• Code maintenance (refactoring, formatting, renaming, tests)
• ReadMe, Docs and GitHub maintenance
• Other (please describe):

Pull request checklist

• Tests for the changes have been added
• Docs have been reviewed and added / updated if needed
• Lint (black rocketpy) has passed locally and any fixes were made
• All tests (pytest --runslow) have passed locally

What is the current behavior?

An EllipticalFins object could be defined if it had the span smaller than the rocket radius, as stated in Issue #390. This was due to the expression used to evaluate the roll_damping_interference_factor that wasn't defined at that domain.

What is the new behavior?

With a whole bunch of calculus, I got the correct expressions for when the span is bigger to the rocket radius and for when the span is equal to the radius.

The new expressions have been added to the documentation and added to the code accordingly

Does this introduce a breaking change?

• Yes
• No

[Gui-FernandesBR]

Well done!!

To confirm the correct behavior, I've tested different sets of fins, just to confirm that the roll damping coefficient has a continuous behavior when varied against the span.

To illustrate:

from rocketpy import EllipticalFins
import matplotlib.pyplot as plt


def test_elliptical_fins(rc, span, rr):
    fins = EllipticalFins(
        n=4,
        root_chord=rc,
        span=span,
        rocket_radius=rr,
        cant_angle=0,
        airfoil=None,
        name="Fins",
    )
    return fins.roll_damping_interference_factor


span = range(1, 500, 10)
span = [s / 1000 for s in span]
damping = [] * len(span)

for s in span:
    damping.append(test_elliptical_fins(rc=0.2, span=s, rr=0.1))
plt.scatter(span, damping)
plt.plot(span, damping)
plt.xlabel("Span [m]")
plt.ylabel("Roll Damping Interference Factor")
plt.title("Roll Damping Interference Factor vs Span")
plt.xlim(0, 0.5)
plt.show()

As you can see, the point where S==r is the x=0.2, and the roll damping coefficient seems to have an expected behavior (no gaps in the curve)