```html Solar Yacht Comfort • Naval Architecture Guide
☀︎
SOLAR YACHT
Naval Architect Edition
MOTION COMFORT GUIDE

Why Solar Yachts
Roll More — And
How To Fix It

A practical naval architecture primer for designers of slow, sail-less, solar-powered vessels. Explains resonance, damping, metacentric height, natural roll period, RAD comfort, and more.

● Sailboats
● Powerboats
● Solar Displacement Craft
SECTION 1
Why Different Boats Roll Differently
SECTION 2
Center of Gravity (KG)
Metacentric Height (GM)
Natural Roll Period
Resonance & RAOs
Damping
Waterplane Area & BM
RAD Comfort Index
Underwater Foils & Stabilizers
DESIGN RECOMMENDATIONS FOR SOLAR YACHTS
All formulas use SI units.
g = 9.81 m/s²

Content written for novice naval architects working on solar vessels.

1. Why Different Boats Roll Differently

⛵

Sailboats roll less — even at zero speed

The primary reason is aerodynamic roll damping from the sails and rig. When a boat rolls, the apparent wind angle changes across the sail plan. This creates a restoring force that opposes the roll — essentially a giant air brake.

Typical roll damping coefficient with sails up can be 3–5× higher than a bare rig. The keel also provides hydrodynamic damping, but the sails dominate at low speeds.

Quantified: A 12m monohull with full sail might have a roll decay time (to 50% amplitude) of ~25 seconds. Without sails it can exceed 90 seconds.

⚡

Powerboats roll less because they go fast

At speed, two effects dominate:

  1. Encounter frequency averaging: A fast vessel crosses many wave crests per minute. The instantaneous wave surface under the boat averages toward mean sea level.
  2. Hydrodynamic damping increases with velocity. Lift on underwater appendages and hull shape creates strong restoring moments.

A 15-knot trawler in a 1.5 m significant wave height sea may experience only 40% of the roll amplitude of the same hull at 4 knots.

☀︎

Solar boats are the worst combination

They typically:

  • Move at hull speed or below (Fn < 0.3)
  • Have no sails for aerodynamic damping
  • Often carry heavy solar arrays high up → raised center of gravity
  • Use light, beamy hulls for stability and panel area

Result: High roll amplitudes, uncomfortable motion, and crew fatigue.

2. Key Naval Architecture Concepts

📍 Center of Gravity (KG) and Metacentric Height (GM)

KG is the height of the center of gravity above the keel.

KM is the height of the metacenter above the keel.

GM = KM − KG

GM is the single most important number for initial stability. Typical values:

  • Monohull sailboat: GM = 0.8 – 2.0 m
  • Catamaran: GM = 3 – 8 m (much stiffer)
  • Comfortable solar yacht target: GM ≈ 0.6 – 1.2 m (tender but safe)
M (Metacenter)
G (CG)
Righting Arm = GM × sin(θ)

Higher GM = stiffer, quicker roll. Lower GM = slower, more comfortable roll (until it becomes dangerous).

Natural Roll Period (Tr)

$$ T_r = 2\pi \frac{k}{\sqrt{g \cdot GM}} $$

where k = roll radius of gyration ≈ 0.35 × Beam for monohulls, 0.45 × Beam for cats.

GM = 0.8 m, Beam = 5 m
9.2 s
Comfortable monohull
GM = 2.5 m, Beam = 5 m
5.1 s
Snappy, uncomfortable
GM = 0.6 m, Beam = 7 m (solar cat)
13.8 s
Very tender — may need damping

Target roll period for liveaboard comfort: 8–12 seconds. Below 6 s feels violent. Above 14 s can cause motion sickness from slow, lingering leans.

Resonance

When the wave encounter period matches the boat’s natural roll period, roll amplitudes can increase dramatically (the “parametric rolling” or simple forced resonance phenomenon). This is why many solar boats feel awful in specific sea states.

Encounter period Te = Tw / (1 − (V·cosμ)/C)
When Te ≈ Tr → Very bad

Roll Damping

Damping is the “friction” that reduces roll amplitude. Without it, even a well-designed GM will oscillate for a long time.

Sources of damping:
  • 1 Hull skin friction & eddy making (bilge keels add a lot)
  • 2 Sails & rigging (aerodynamic damping — often >50% of total)
  • 3 Active fins or gyro stabilizers
  • 4 Underwater foils at speed
Typical non-dimensional damping coefficient (ζ):

Bare monohull: 0.05 – 0.12
With bilge keels: 0.15 – 0.25
With sails: 0.25 – 0.45
With active stabilizers: >0.6

Waterplane Area & BM

BM (metacentric radius) = I / ∇
where I is the second moment of area of the waterplane.

A beamy solar catamaran has enormous I → very large BM → high GM even with high KG from solar panels.

RAD Comfort Index

The Ride Acceleration & Duration (RAD) comfort index is a weighted metric combining:

  • Roll RMS acceleration (m/s²)< 0.2 good
  • Vertical acceleration at bow< 0.15g good
  • Roll angle (peak)< 8° good
  • Duration of exposure
ISO 2631 and BS 6841 standards are commonly used. A RAD score > 80 is considered excellent for long passages.

Underwater Foils & Stabilizers

Fixed bilge keels, passive paravanes, active fins, and gyros are all tools in the solar designer’s kit. Active fins are power-hungry (typically 2–8 kW), which matters on solar vessels.

Passive
Bilge keels
Fixed fins
Paravane stabilizers
Active
Gyro stabilizers (low power when spinning)
Active fins (highest power draw)
Rotating sail-drogue systems

Quantitative Comparison

Vessel Type Typical GM Roll Period Damping Factor RAD Comfort (est.)
Sailing Monohull (12m) 1.4 m 8.1 s 0.38 78
Fast Powerboat (15 kn) 1.1 m 6.9 s 0.55 85
Solar Catamaran (slow) 4.2 m 11.4 s 0.09 42
Optimized Solar Monohull (with fins) 0.9 m 10.8 s 0.31 81

Design Recommendations for Solar Yachts

How to make a slow solar boat comfortable:

  1. 1
    Target a natural roll period of 9–11 seconds. This usually means a relatively low GM (0.7–1.1 m for monohulls). Use ballast low in the hull or lifting keels.
  2. 2
    Add significant passive damping. Large bilge keels (or “ roll-damping bulbs”), fixed underwater foils, or even cleverly shaped hull chines.
  3. 3
    Consider a compromise catamaran with narrow hulls and high tunnel clearance — this reduces slamming while maintaining high waterplane inertia.
  4. 4
    Keep solar panels as low and central as possible. Every 10 cm you raise the CG costs you valuable GM.
  5. 5
    Use a small active stabilizer only when solar production is high, or investigate low-power gyro systems (e.g. 24 VDC units under 1 kW average).

FINAL RULE OF THUMB

“Make it tender enough to be comfortable,
but damped enough to stop rolling.”

— Every successful liveaboard solar yacht designer

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