Stability trend is not consistent

[javedalikhanpatan18]

@elcf @caterpillar85

I am currently a student exploring the openplaning framework to better understand the dynamic stability characteristics of planing hulls. In a specific case at a fixed Froude number (or speed), my expectation—based on theoretical understanding—is that increasing the deadrise angle should improve dynamic stability. Specifically, I anticipated that the system’s eigenvalues would shift further into the left-half of the complex plane, indicating increased damping and improved stability.

However, in all my simulations—despite testing across a range of hull design parameters—I consistently observe the opposite: eigenvalues tend to shift toward the right, and in some cases, the system appears to become unstable as deadrise increases.

I have attached both a screenshot of the results and the Python script used to call openplaning. I would be very grateful if you could help me understand whether I may be missing something conceptually, or if this observed trend is in fact expected under certain conditions.

Thank you very much in advance for your time and guidance.

code is here:
from openplaning import PlaningBoat
import numpy as np
#from control import *
from scipy import signal
import matplotlib.pyplot as plt

cdelta = 0.608
beam = np.array([9,9,9])0.0254
length = beam5
mass = cdelta1025.87beam**3
g = 9.8066
weight = mass*g
lcg = np.array([1-0.605,1-0.59,1-0.595])length #m, long. center of gravity
vcg=1beam
r_g = np.array([0.248,0.26,0.25])*length
betaRange=np.array([30,20,10])
frRange = np.array([1.1898])
#frRange=np.arange(0.1,1.3,0.1)
#Propulsion
epsilon = 0 #deg, thrust angle w.r.t. keel
vT = vcg #m, thrust vertical distance
lT = lcg #m, thrust horizontal distance

#Options
wetted_lengths_type = 3
roughness_penalty_type = 1

tauData=[]
tauData2=[]
settldata=[]
eigVals=[]
criticaltrim=[]
criticaltrimData=[]
lcpOffsetData=[]
lcpOffsetData2=[] # full across all beta

Create boat object

for i, beta in enumerate(betaRange):
tauData = []
criticaltrim = []
lcpOffsetData = []

for fr in frRange:
    speed = fr*(g*length[i])**0.5 #m/s

    boat = PlaningBoat(speed, weight[i], beam[i], lcg[i], vcg[i], r_g[i],
                       beta, epsilon, vT[i], lT[i], length[i],
                       wetted_lengths_type=wetted_lengths_type,
                       roughness_penalty_type=roughness_penalty_type)

    boat.get_steady_trim()
    offset = boat.lcp - boat.lcg  # NEW LINE
    lcpOffsetData.append(offset) # NEW LINE
    tauData.append(boat.tau)
    boat.print_description()     # KEPT AS YOU WROTE
    eigVals.append(boat.eigenVal)
    print(boat.eigenVal)         # KEPT AS YOU WROTE
    settldata.append(boat.settletime)
    criticaltrim.append(boat.critical)

tauData2.append(tauData)
criticaltrimData.append(criticaltrim)
lcpOffsetData2.append(lcpOffsetData)  # NEW LINE

=== Eigenvalue Plot on Complex Plane ===

plt.figure(figsize=(10,6))
for i, beta in enumerate(betaRange):
eigs = eigVals[i] # List of eigenvalues for this beta
eigs = np.array(eigs).flatten()
plt.plot(np.real(eigs), np.imag(eigs), '.', label=f'β = {beta:.2f}°', markersize=10)

plt.axhline(0, color='gray', linestyle='--', linewidth=0.8)
plt.axvline(0, color='gray', linestyle='--', linewidth=0.8)
plt.xlabel('Real')
plt.ylabel('Imaginary')
plt.title('Eigenvalues of System vs Deadrise Angle β')
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()

[elcf]

Hello, I'm glad that you've been able to find the code useful for exploration.

I've yet to run your specific case, but I do know from my previous studies that increasing deadrise will typically increase running trim angle at a fixed speed--which will typically place you closer to instability. If that's what is happening in your case, you can confirm by fixing trim angle in your runs (easiest would be to force it by removing the stability search, or alternatively do a center of gravity search for having the same trim angle for varying deadrises). With fixed running trim, you can check the eigen values behavior with varying deadrise.

Let me know if this helps.

[javedalikhanpatan18]

Hello,

Thank you very much for your response. I did perform the free-trim analysis versus deadrise angle (β), and the results I obtained seem consistent with expectations in terms of trim angle variation.

However, what’s puzzling is that I expected the system to also become more stable as β increases. Instead, I’m observing the opposite—the eigenvalues tend to shift toward the right in the complex plane with increasing β, which suggests reduced damping or even potential instability.

I wasn’t entirely sure what you meant by “fixing the trim,” since in my current setup the trim angle is being solved based on the condition of net moment equilibrium. If you could guide me further on how to correctly assess the stability behavior in this context, or clarify what might be going wrong in my interpretation, it would be a huge help.

Thanks again for your time and support.

[javedalikhanpatan18]

I tested the system by fixing the trim angle across all deadrise angles and evaluated the eigenvalues at two trim settings: 3° and 6°.

At a fixed trim of 3°, I observed that higher deadrise still results in a less stable system, with eigenvalues shifting toward the right—this contradicts the expected trend.

However, at a fixed trim of 6°, the behavior aligns with expectations: the higher deadrise (β = 30°) case appears more stable than the lower deadrise case. This could be because, for β = 10°, a 6° trim might already be close to its critical or marginally stable trim angle, while for β = 30°, 6° is still within a safer, more stable regime.

What I am ultimately trying to validate is this:
Even in the free-trim configuration, I would expect higher deadrise hulls to exhibit more stable eigenvalues than lower deadrise one yet this is not what I observe. Please help me out for this case.

[elcf]

Porpoising depends on the coupling of pitch and heave dynamics, and deadrise affects both. What reference are you referring to when you say that increasing deadrise increases stability?

If you're basing it on Savitsky's porpoising regimes figure, something we can safely conclude from it is that as you increase deadrise, the vessel needs a larger running trim to porpoise--not that increasing deadrise will generally increase stability.

Because there is so much interplay with trim and heave, in some cases counterintuitive things can happen. One is that you might increase calm water efficiency if you increase deadrise (this might happen if the vessel with a low deadrise is running with very low trim, and increasing deadrise increases trim to a more efficient attitude.

If you want to isolate the effects of deadrise alone, you have to fix heave and trim.

But another thing to have in mind is that the program is a semi-empirical code, and Faltinsen's approach to get the linear coefficients does make a few assumptions. So any results you get with the exploration, are results that you would have to find/get experimental data to confirm.

A sanity check would be to replicate Savitsky's stability regimes for different deadrises, and see if the behavior is the same. It's been some years since I read Faltinsen's papers on the coefficients, but if I recall correctly he did compare both methods. But doing that exercise with OpenPlaning would be a good sanity check. I would consider a red flag if we can't replicate Savitsky's figure when using a vessel similar to the vessels used to get that figure.

Let me know if this makes sense.