Mar2E Turbine Performance

Overview

What we found, in one page

Our brief is to cut the drag on Magallanes' tidal turbine, so its floating hull tips less and its moorings pull less, without losing much power. Here is the answer to each research question. Click through for the evidence.

Main result

Most of the drag is the rotor's thrust, and thrust falls faster than power when the blades work slightly less hard. Turning the blades a couple of degrees more edge-on is the best-value change we found: about 13% less thrust for 6% less power.

−13%

thrust, blades pitched +2°

−6%

power for that change

5×

lower peak thrust in fast tides with pitch-to-feather control

improvement ideas scored against all three criteria

01 · How does a turbine make power?

Water → rotor → gearbox → generator → cable. About 37% of the water's energy reaches the grid; the rotor is the biggest loss and the part we redesign.

How it works →

02 · Can we cut drag without losing much power?

Yes. Ideal theory says we keep 95% of the power for 84% of the thrust by slowing the water a little less.

Power vs drag →

03 · Which blade changes work best?

Pitching blades +2° (−13% thrust, −6% power) and 20% narrower blades (−9%, −5%). More blades go the wrong way.

Blade model →

04 · What happens in very fast tides?

Pitch-to-feather control keeps peak thrust around 660 kN. Over-speed or stall control lets it reach 3.7 MN at 5 m/s.

Fast tides →

05 · What else could we improve?

24 ideas across drag, power and material. They mostly help each other: less thrust means a lighter structure.

Improvements →

06 · How does Nova Scotia change things?

Tides above 5 m/s, very turbulent, faster near the surface. Worst-case loads and fatigue matter more here than average power.

Nova Scotia →

07 · How do we prove it?

Sweep each rotor's speed in the towing tank, subtract strut drag, repeat 3 times. A 2% speed error becomes a 6% power error.

Tank testing →

08 · What do we do with it next?

11 draft spec lines, 7 morphological chart rows and 8 selection criteria, ready for weeks 9–11.

Next steps →

The brief, in short

Client

Magallanes Renovables (fictional brief)

Floating platform "ATIR": 45 m hull, two 19 m rotors on a strut.

Our site and criterion

Nova Scotia · reduce drag and bending moment

To reduce hull pitching and mooring line loads.

Other criteria (other teams)

Increase power · minimise material

We may look at these, but ours comes first.

What we can change

Blades, nose cone, added structure

Generator, gearboxes and hub come in a kit.

Assessed on

Power · thrust and drag · bending and platform pitch · transmission losses · mass · annual energy

Portfolio weight

55% is predict, test and iterate

Prediction 10% · testing 30% · final iteration 15%.

Who is researching what

Area	Person	Overlap with performance
Company	Seymen	ATIR's real rotor size and rating
Location	Emily	Tide speeds, depth, turbulence (inputs to the performance numbers)
Turbines	Will C	Turbine types; this site covers only their performance effect
Wildlife	Alessandro	Tip speed, cavitation noise
Safety	Jakub	Runaway rotor, braking
Performance	Will B	This site
Cost and market	Jayden	Annual energy feeds cost per MWh

01 · Research question

How does a tidal turbine turn moving water into electricity?

Result

Energy passes along a chain, and each step loses a little. About 37% of the water's energy reaches the grid. The rotor is the biggest loss, and it's the part we redesign. Power rises with flow speed cubed; the push on the rotor rises with speed squared.

37%

water-to-wire efficiency

8×

power when tide speed doubles

1.16 MW

in a 2 m/s tide, 19 m rotor

670 kN

thrust at 2.4 m/s, about 68 tonnes

What this means for our design

Our blade changes act on the rotor's share (\(C_P\)), the biggest single loss in the chain.
Speed matters enormously: a 10% speed error is a 33% power error. Every number we quote must say which tide speed it's at.
On our test rig the generator and gearboxes lose energy too. We must measure the kit's losses once, so they don't hide or fake a rotor improvement.
The rig's electrical load sets the rotor speed. Changing it lets us test each design across a range of speeds.

The energy chain

Flowing waterkinetic energy
100%

Rotorblades capture some
× 0.42

Gearboxslow → fast shaft
× 0.96

Generatorspin → electricity
× 0.95

Electrics, cableto the grid
× 0.97 = 0.37

Power and push at different tide speeds (19 m rotor)

Tide speed	Power in the water	Power captured (C_P 0.42)	Thrust (C_T 0.8)
1 m/s	0.15 MW	0.06 MW	116 kN
2 m/s	1.16 MW	0.49 MW	465 kN
3 m/s	3.92 MW	1.65 MW	1,046 kN
4 m/s	9.30 MW	3.91 MW	1,860 kN
5 m/s	18.2 MW	7.63 MW	2,906 kN

For comparison, a 19 m wind turbine in a strong 12 m/s wind has 0.30 MW available. Water is about 840 times denser than air.

How we worked it out 5 equations, each explained

Power in the water

\[ P_{avail} = \tfrac12 \rho A U^3 \]

\(P_{avail}\)	Power carried by the water passing through the rotor's circle	W
\(\rho\) (rho)	Water density: 1025 seawater, 1000 tank	kg/m³
\(A\)	Area of the circle the blades sweep, \(\pi R^2\) (R = rotor radius)	m²
\(U\)	Tide speed	m/s

Plain EnglishKinetic energy is ½ × mass × speed². The mass of water passing each second is density × area × speed. Multiply them and speed appears three times.

Example19 m rotor (A = 283.5 m²), 2 m/s: ½ × 1025 × 283.5 × 2³ = 1.16 MW.

Power coefficient

\[ C_P = \frac{P}{\tfrac12 \rho A U^3} \]

\(C_P\)	Fraction of the water's power the rotor captures	–
\(P\)	Power the rotor actually makes at its shaft	W

Plain English"What we got ÷ what was there." It removes size and speed, so a 0.3 m model and a 19 m rotor can be compared directly.

Example490 kW from 1.16 MW available: C_P = 0.42.

Thrust (our "drag")

\[ T = \tfrac12 \rho A U^2 \, C_T \]

\(T\)	Push of the water on the rotor, in the flow direction	N
\(\tfrac12\rho U^2\)	Dynamic pressure: the pressure if the flow were stopped dead	Pa
\(C_T\)	Thrust coefficient: how much of that full force the rotor feels	–

Plain EnglishForce = pressure × area × a shape factor. Speed is squared, so double the speed means four times the push.

Example2.4 m/s, C_T = 0.8: ½ × 1025 × 2.4² × 283.5 × 0.8 = 670 kN.

Water-to-wire efficiency

\[ \eta_{total} = C_P \times \eta_{gear} \times \eta_{gen} \times \eta_{elec} \]

\(\eta\) (eta)

Efficiency of each part: output ÷ input

–

Plain EnglishLosses multiply: each stage passes on a fraction of what it receives.

Example0.42 × 0.96 × 0.95 × 0.97 = 0.37.

Electrical power on the rig

\[ P_e = V I = \frac{V^2}{R_{load}} \]

\(V, I\)	Voltage and current measured at the load	V, A
\(R_{load}\)	Resistance we connect. A lower resistance draws more current, which brakes the rotor harder.	Ω

Plain EnglishPower = voltage × current. Changing the resistor changes how fast the rotor spins.

Example6 V across 10 Ω: 0.6 A, so 3.6 W.

02 · Research question

Can we cut drag without losing much power?

Result

Yes. To take energy from water you have to slow it, and slowing it causes thrust, so the two are linked. But near the best-power point, power barely changes while thrust keeps rising. A rotor that slows the water slightly less keeps 95% of its power for 84% of the thrust.

59.3%

the most any open rotor can capture (Betz limit)

−16%

thrust…

−5%

…for this much power (ideal theory)

a ≈ 0.25

target slow-down, instead of 0.33

What this means for our design

Design the blades to slow the water by about 20–25% at the rotor, not the textbook 33%.
This is the reason our blade changes in tab 03 (pitch, narrower blades) work.
Avoid ducts (funnels round the rotor): they raise power per rotor area, but add a large drag force.

Power and thrust against how hard the rotor slows the water

Teal: power coefficient. Amber: thrust coefficient. Horizontal axis: a, the fraction by which the rotor slows the water. Power peaks at a = 1/3 and is flat near the top. Thrust keeps climbing.

Slow-down a	C_P	C_T	Power kept	Thrust kept
0.333 (best power)	0.593	0.889	100%	100%
0.30	0.588	0.840	99%	94%
0.25	0.562	0.750	95%	84%
0.20	0.512	0.640	86%	72%

How we worked it out the "actuator disc" model, step by step

Replace the rotor with a thin leaky disc that slows the water. Follow a tube of water through it: as the water slows, the tube widens, because the same mass passes every point each second.

Speeds

\[ U_{rotor} = U(1-a), \qquad U_{wake} = U(1-2a) \]

\(a\)

Fraction of speed lost by the time the water reaches the rotor (axial induction factor)

–

Example3 m/s tide, a = 1/3: 2 m/s at the rotor, 1 m/s far behind.

Step 1: thrust = change in momentum per second (Newton's 2nd law)

\[ T = \underbrace{\rho A U(1-a)}_{\text{kg of water per second}} \times \underbrace{2aU}_{\text{speed each kg loses}} = 2\rho A U^2 a(1-a) \]

Plain EnglishA known mass of water loses a known amount of speed every second. The force needed to do that is the thrust.

Step 2: the two coefficients

\[ C_T = 4a(1-a), \qquad C_P = 4a(1-a)^2 \]

Plain EnglishDivide the thrust by \(\tfrac12\rho A U^2\) to get C_T. Power is thrust × speed at the rotor; divide it by \(\tfrac12\rho A U^3\) to get C_P. Both depend only on a.

Examplea = 0.25: C_T = 0.75, C_P = 0.5625.

Step 3: the best possible rotor

\[ \frac{\mathrm dC_P}{\mathrm da} = 4(1-a)(1-3a) = 0 \;\Rightarrow\; a = \tfrac13,\quad C_{P,\max} = \tfrac{16}{27} = 0.593 \]

Plain English\(\mathrm dC_P/\mathrm da\) is the slope of the power curve. At the top of a hill the slope is zero. Slow the water too little and you catch little; too much and it goes round the rotor instead.

The key ratio

\[ \frac{C_P}{C_T} = 1 - a \]

Plain EnglishThe less the rotor slows the water, the more power you get per unit of thrust.

03 · Research question

Which blade changes cut thrust most for the least power?

Result

Turning the blades a couple of degrees more edge-on ("pitch towards feather") is the best value: +2° gives 13% less thrust for 6% less power. Narrower blades come second. Spinning the same rotor slower is poor value, and adding blades goes the wrong way.

−13.4%

thrust at +2° pitch

−5.6%

power at +2° pitch

−9.4%

thrust with 20% narrower blades (−5% power)

+16%

thrust with 4 blades instead of 3

What this means for our design

Shortlist two concepts: a pitch offset (print the blade root a few degrees round) and narrower blades, or both together.
We can partly win the power back with a lower-drag foil shape (tab 05, More power).
These results are from a demonstration rotor in our own Python model. Rerun it with the baseline blade when it's released.

Every change we tested in the model

Compared with the starting blade at its best-power point. "Thrust saved per 1% power": bigger is better for us.

Design change	Power change	Thrust change	Thrust saved per 1% power
Pitch +2° towards feather	−5.6%	−13.4%	2.4
Pitch +4°	−13.6%	−25.8%	1.9
Blades 20% narrower	−5.0%	−9.4%	1.9
Pitch +6°	−22.8%	−36.6%	1.6
Blades 40% narrower	−14.4%	−23.3%	1.6
2 blades instead of 3	−15.6%	−20.2%	1.3
Same blade, spun slower	−22.5%	−21.3%	0.9
4 blades instead of 3	+6.9%	+16.0%	wrong way

Power and thrust curves for four pitch settings

Darkest line 0°, then +2°, +4°, +6° (lightest). Left: power coefficient. Right: thrust coefficient. Horizontal axis: tip speed ratio, meaning how fast the blade tips move compared with the tide. Dots mark each setting's best-power point.

The trade-off in one chart

Power (up) against thrust (right) for each pitch setting as rotor speed changes. Dashed: the perfect rotor from tab 02. We want designs high and to the left.

Limits: the model uses placeholder foil data, and can't capture 3D flow near the hub, the tank walls, or a 3D-printed surface. Computer models can be badly off, so the tank test is the judge and the model tells us what to test.

How we worked it out what a blade feels, and how the model works

Each blade is a twisted underwater wing. A slice of blade moves sideways while water arrives from upstream, so it feels the water coming at a slant, like running through vertical rain. Lift on the slice is split: part turns the rotor (power), and part pushes it backwards (thrust).

Tip speed ratio

\[ \lambda = \frac{\Omega R}{U} \]

\(\lambda\) (lambda)	How many times faster the blade tip moves than the tide	–
\(\Omega\) (omega)	Rotor spin speed: rpm × 2π ÷ 60	rad/s
\(R\)	Rotor radius	m

Plain EnglishThe rotor's "gear". Too low and the blades stall; too high and the rotor acts like a wall. Best is usually 4–6.

Example19 m rotor at 12 rpm in 2.4 m/s: Ω = 1.26 rad/s, tip speed 11.9 m/s, λ = 5.0.

The angles a blade slice sees

\[ \tan\varphi = \frac{U(1-a)}{\Omega r(1+a')}, \qquad \alpha = \varphi - \theta \]

\(\varphi\) (phi)	Angle the flow arrives at, measured from the plane the rotor spins in	°
\(r\)	Radius of this slice	m
\(a'\)	Small extra from the wake's swirl (usually below 0.05)	–
\(\theta\) (theta)	Angle the blade is set at here: built-in twist plus pitch	°
\(\alpha\) (alpha)	Angle of attack: what the foil actually sees. Best around 5–8°; stalls above about 10–14°.	°

Plain EnglishNear the hub the blade moves slowly, so the flow arrives steeply. Near the tip it arrives nearly flat. That's why blades are twisted. Pitching towards feather raises θ everywhere, which lowers α, so less lift and less thrust.

ExampleSlice at 70% radius: Ωr = 8.36 m/s, water 1.6 m/s, so φ = 10.8°. Blade set at 4° gives α = 6.8°.

Splitting lift and drag into thrust and turning force

\[ \Delta T = B(L\cos\varphi + D\sin\varphi), \qquad \Delta F_{turn} = B(L\sin\varphi - D\cos\varphi) \]

\(L, D\)	Lift and drag on one slice: \(\tfrac12\rho W^2 c\,C_L\,\Delta r\) and the same with \(C_D\)	N
\(W\)	Speed of the flow the slice feels	m/s
\(c\)	Chord: blade width at this radius	m
\(C_L, C_D\)	Lift and drag coefficients of the foil shape, from foil data	–
\(B\)	Number of blades	–

Plain EnglishThe forces lean at angle φ, so sin and cos split them. Drag subtracts from the turning force, so a low-drag foil makes more power. Near the tip φ is small, so almost all the lift becomes thrust.

ExampleAt φ = 10.8°: 98% of the lift is thrust and 19% turns the rotor.

How the model (BEM) works

Plain EnglishBlade element momentum (BEM): cut each blade into thin slices. For each slice, find the slow-down a at which the momentum result (tab 02) and the foil forces (above) agree. Then add up all the slices.

Steps1) Guess a = 0.3. 2) Work out φ and α, look up C_L and C_D. 3) Calculate a new a from the forces, and repeat until it stops changing. 4) Add up thrust and torque over all slices; power = torque × spin speed. 5) Repeat at many tip speed ratios to draw the curves. Code: bem_performance_model.py, plus a tip-loss correction (water leaking round the blade tip) and a high-loading correction.

04 · Research question

What happens to thrust when the tide is faster than the turbine needs?

Result

Above its maximum power (here about 2.4 m/s), a turbine has to throw energy away. How it does that decides the worst-case thrust. Turning the blades edge-on ("pitch to feather") keeps peak thrust around 660 kN. Letting the rotor over-speed or stall lets it reach about 3.7 MN at 5 m/s, more than five times as much.

2.4 m/s

rated speed in our 750 kW example

660 kN

peak thrust, pitch to feather

3.7 MN

thrust at 5 m/s, over-speed or stall

5+ m/s

Nova Scotia peak tides

What this means for our design

For the full-size turbine, argue for pitch-to-feather control. ATIR's blades can already pitch, so it fits the existing machine.
Add a spec line: peak thrust in the fastest tide must not exceed the thrust at rated speed.
A flexible blade that twists edge-on by itself under load ("passive pitch") is a good concept to sketch.

Power and thrust against tide speed (19 m rotor, 750 kW)

Left: power is capped at 750 kW above about 2.4 m/s; dashed is what it would be with no cap. Right: thrust for each way of capping power. Simplified estimates.

Way of capping power	What it does	Thrust	Notes
Pitch to feather	Turn blades edge-on, so less lift	falls	Needs a pitch mechanism (ATIR has one). Lower blade loads in published comparisons.
Pitch to stall	Turn blades the other way until they stall	stays high	Stalled blades still push hard.
Over-speed	Spin faster so less is captured	rises	Simplest. Highest thrust; faster tips raise cavitation and wildlife risk.
Under-speed (stall)	Brake it so the blades stall	lower	Hard to control; heavy on the gearbox.
Passive pitch	Flexible blade twists itself edge-on	capped	No motor. Hard to tune.

The tide reverses about every six hours. ATIR turns its blades round to face the other way; a blade that can't turn needs a symmetric foil, which is less efficient.

05 · Research question

What else could we improve, and what does each change cost?

Result

We found 24 improvement ideas across the brief's three criteria. They mostly support each other: less thrust means a lighter blade, strut and moorings, and a more level hull keeps the rotor facing the flow. Best for drag: pitch and lighter loading. Best for power: a clean, low-drag foil. Best for material: designing the rotor to spin faster.

−13%

thrust: pitch +2°

+5%

power: lower-drag foil

−15 to −50%

power lost to fouled blades

−58%

blade material, designed to spin faster (−4.6% power)

Result: where the drag and bending come from, and how to cut them

Bending = force × distance. The rotor hangs well below the hull, so its thrust makes a big tipping effect. Example: 670 kN at 10 m gives 6.7 million N·m.
Three ways in: less rotor thrust, a lower-drag strut, or a shorter strut.
A streamlined strut has about 10× less drag than a round one, but must cope with the tide reversing. Seal-whisker-shaped struts work from any direction.

Idea (best first)	Why it works	Power	Thrust	Can we print it?
Pitch a few degrees towards feather	Blades slow the water less	small loss	big cut	Yes
Lighter loading (slow-down 0.2–0.25)	Narrower blades or lower design lift	small loss	big cut	Yes
Unload the tip	The outer blade makes most thrust and bending	small loss	cut	Yes
Lower-drag foil	Wins back power lost elsewhere	gain	neutral	Yes
Passive pitch	Flexible blade caps thrust in fast tides	small loss	caps peak	Partly
Bumpy leading edge (whale flipper)	Keeps flow attached past stall; smoother loads	gain	smoother	Yes
Streamlined nose cone	Less hub drag	neutral	small cut	Yes
Streamlined or whisker strut	Lower strut drag	neutral	cut	Yes
2 blades	Less blade area	bigger loss	cut	Yes
Ducts, more blades, wider blades	Make the rotor work harder	gain	rise	Avoid

How we worked it out bending moment and strut drag

Bending moment about the hull

\[ M = T\,h_{hub} + \sum \Delta D_{strut}\, z \]

\(M\)	Bending moment, which tips the hull nose-down	N·m
\(T\)	Rotor thrust	N
\(h_{hub}\)	Distance from the hull down to the rotor (the lever arm)	m
\(\Delta D_{strut},\ z\)	Drag on one slice of strut, and that slice's depth below the hull	N, m

Plain EnglishLike a spanner: a push further from the bolt turns it more. Add the rotor's push × strut length to each strut slice's push × its depth.

Example670 kN × 10 m = 6.7 million N·m. 20% less thrust gives 20% less moment.

Strut drag

\[ D_{strut} = \tfrac12 \rho U^2\, C_{D,s}\, t\, L \]

\(C_{D,s}\)	Drag coefficient of the strut shape: round ≈ 1.0, streamlined ≈ 0.1	–
\(t, L\)	Strut thickness facing the flow, and length in the water	m

Example50 mm model strut at 1 m/s: round 25 N per metre; streamlined 2.5 N per metre.

Result: the biggest power levers

Keep the blades clean: fouling (barnacles, weed) can cut power by 15–50%.
Use a lower-drag foil: about +5% power.
Variable-speed control: about +2.4% energy a year, by keeping the rotor at its best speed as the tide changes.
Point into the flow: 10° off-line loses 4.5% of power; 20° loses 17%.
Generator size changes yearly energy by tens of percent (a cost question for Jayden).

Idea	How it helps	How much	Catch
Clean, smooth blades	Roughness adds drag and causes early stall	Fouling: −15% to −50%	Anti-fouling coatings; cleaning (ATIR's rotors can be raised)
Lower-drag foil	Foil drag eats into the turning force	≈ +5%	Slightly more thrust
Right twist and width	Every slice at its best angle	a few %	Twist is hard to print accurately
Tip shape (winglets)	Less water leaking round the tip	≈ 1–3%	Adds thrust
4 blades	More lifting surface	+6.7%	+16% thrust: against our criterion
Bigger rotor	Power grows with diameter squared	+10% size: +21%	+21% thrust; depth limits
Variable speed	Holds the best tip speed ratio as the tide changes	+2.4% a year	Needs power electronics
Generator size	500 kW → 2,940 MWh/yr · 750 → 4,030 · 1,000 → 4,900 · 1,500 → 6,240	large	Bigger costs more (Jayden)
Face the flow	Power falls as cos³ of the angle off-line	10°: −4.5%	Floating platforms swing to face it naturally
Sit in faster water	Water near the surface is faster	+5% speed: +16%	Closer to waves and cavitation
Keep the hull level	A tipped hull tilts the rotor off the flow	links to our criterion
Higher cable voltage	Less current, so less cable heating	690 V → 11 kV: ≈250× less loss	Needs transformers

How we worked it out cable losses and misalignment

Cable losses

\[ I = \frac{P}{\sqrt3\,V}, \qquad P_{loss} = I^2 R_{cable} \]

\(I\)	Current in the cable	A
\(V\)	Cable voltage; √3 because the grid uses three-phase AC	V
\(R_{cable}\)	Cable resistance	Ω

Example1.5 MW at 690 V: 1,255 A. At 11 kV: 79 A. Loss goes with current squared, so about 250× less.

Pointing off the flow

\[ P_\gamma \approx P_0 \cos^3\gamma \]

\(\gamma\) (gamma)

Angle between the rotor axis and the tide direction

Examplecos³(10°) = 0.955, so 4.5% lost.

Result: same energy, less material

Design the rotor to spin faster (tip speed ratio 6.5 instead of 5): 58% less blade material for 4.6% less power. The blades get much narrower.
A higher-lift foil: 47% less material for 2.4% less power.
Less thrust = less material. Pitch +2° cuts root bending by 15%, so the blade, strut and moorings can all be lighter.
Catches: narrower blades are more highly stressed and need a thicker root. Faster tips raise cavitation and wildlife risk.

Teal: best power. Amber: blade material. Both are shown as a % of a blade designed for tip speed ratio 5.

Change (our model)	Power	Thrust	Root bending	Blade material
Designed to spin faster (6.5, not 5)	−4.6%	−0.7%	0%	−58%
Higher-lift foil (C_L 1.1, not 0.8)	−2.4%	+2.1%	+4.7%	−47%
Blades 20% narrower	−5.1%	−9.5%	−8.7%	−36%
Pitch +2°	−5.7%	−13.5%	−14.9%	0% (could then be thinner)
2 blades	−15.6%	−20.2%	+21% per blade	−33%
4 blades	+6.7%	+16%	−13% per blade	+33%

Size for repeated loads

Each spin passes through faster and slower water, around 100 million load cycles in 20 years. Smoother loads mean lighter blades.

Choose materials by index

For light, stiff blades, compare \(\sqrt{E}/\rho\) (stiffness, density). Carbon and glass composites win, and they don't rust.

Neutral buoyancy

A blade that weighs the same as the water it displaces has no up-down gravity load each spin.

On our model

Printed mass depends on infill, which says little about a full-size composite blade. Report volume instead.

How we worked it out bending stress

Bending stress at the blade root

\[ \sigma_b = \frac{M}{Z}, \qquad Z \propto c^2 t \]

\(\sigma_b\)	Bending stress: what tries to snap the blade	Pa
\(M\)	Bending moment at the root	N·m
\(Z\)	Section modulus: how good the cross-section is at resisting bending	m³
\(c, t\)	Chord and thickness of the root. "∝" means "proportional to".	m

Plain EnglishA thin ruler bends more easily than a thick one. Narrower blades save material, but need a thicker root or a stronger material.

Result: every idea against every criterion

+ helps · − hurts · 0 little effect. Use it as the starting point for the morphological chart and the Pugh matrix.

Idea	Power	Drag / bending	Material	Yearly energy	Tank-testable?
Pitch a few degrees towards feather	−	+ +	+	0	Yes
Lighter loading	−	+ +	+	0	Yes
Design to spin faster	−	0	+ +	0	Yes
Higher-lift foil	0	0	+ +	0	Yes
Lower-drag foil	+	0	0	+	Yes
Unload the tip	−	+	+	0	Yes
Winglets	+	−	0	+	Yes, fragile
Bumpy leading edge	+	+	+	0	Yes
Passive pitch (flexible blades)	0	+ +	+	0	Partly
Two blades	− −	+	+	−	Yes
Four blades	+	−	−	+	Yes
Bigger rotor	+ +	− −	−	+ +	Limited
Streamlined nose cone	+	+	0	+	Yes
Streamlined or whisker strut	+	+ +	0	0	Yes
Shorter strut	+	+ +	+	+	Partly
Duct	+	− −	− −	+	Wrong way for us
Second rotor, opposite spin	+	−	−	+	No
Pitch-to-feather control	0	+ +	+	0	Argue in report
Variable speed	+	0	0	+	Vary the load
Anti-fouling, smooth finish	+ +	0	0	+ +	Sanding only
Composite, neutrally buoyant blades	0	0	+ +	+	No
Direct drive (no gearbox)	+	0	−	+	No
Higher cable voltage	0	0	+	+	No
Swing to face the flow	+	0	0	+	No

Specification headings, from a performance angle

Heading	Performance angle	Owner of the rest
Performance	Power and thrust curves, cut-in and rated speed, works both ways, yearly energy	Will B
Environment	Fastest tides, turbulence, waves, fouling	Emily, Alessandro
Materials	Stiffness, fatigue, erosion, smooth finish	Modelling element (iii)
Manufacture	Accurate shape and twist, identical blades	Team
Maintenance	Performance drops as blades foul; access to clean	Jakub, team
Life in service	Fatigue life; performance kept over 20+ years	Team
Safety and testing	Runaway if the load is lost; braking; tank procedure	Jakub
Standards	IEC TS 62600-200 (power curves); DNV tidal turbine standard (loads)	Team
Cost and market	Cost per MWh = yearly cost ÷ yearly energy	Jayden

06 · Research question

How does our site change the performance picture?

Result

The Minas Passage is fast (above 5 m/s), very turbulent, and faster near the surface. That makes worst-case thrust and repeated (fatigue) loads more important here than average power, which strengthens the case for pitch-to-feather control and lighter blade loading.

5+ m/s

peak tide speed

4.4×

thrust at 5 m/s vs 2.4 m/s if nothing limits it

+16%

speed at the top of the rotor vs the bottom

≈4,000 MWh

per rotor per year (rough example)

What this means for our design

Design for the fastest tide, not the average. Our spec should state peak-thrust limits.
Turbulence and speed differences across the rotor make the thrust flicker every turn, so smoother-loading ideas (pitch, bumpy leading edge, flexible blades) score extra here.
A thrust-cutting design loses power only below rated speed, so its yearly energy loss is smaller than its peak power loss.
Emily owns the site data. These numbers get updated when she shares tide speeds and depth.

Very fast tides

Thrust goes with speed squared: (5 ÷ 2.4)² ≈ 4.4× the thrust at rated speed. The worst case sizes the moorings.

Very turbulent

Swirling flow makes thrust flicker, which means fatigue. It differs between incoming and outgoing tides. Our tank is calm, so it only shows averages.

Faster near the surface

The top of a 19 m rotor sees about 16% more speed than the bottom, so each blade feels about a third more push at the top of each turn.

Power is sensitive to speed

Power goes with speed cubed, so every spec number must say which speed it's at.

How we worked it out yearly energy

Annual energy production (AEP)

\[ \text{AEP} = 8760 \times \sum_i P(U_i)\, f(U_i), \qquad \text{capacity factor} = \frac{\text{AEP}}{8760 \times P_{rated}} \]

8760	Hours in a year	h
\(U_i\)	One band of tide speed, e.g. 2.0–2.2 m/s	m/s
\(P(U_i)\)	Power the turbine makes at that speed	W
\(f(U_i)\)	Fraction of the year spent at that speed (site data)	–
\(\sum_i\)	Add up over all speed bands

Plain EnglishPower at each speed × how often it happens, all added up. Capacity factor = how full the turbine runs on average.

Example750 kW rotor, tide peaking at 4.5 m/s: about 4,000 MWh a year, capacity factor ≈ 0.6.

07 · Research question

How do we prove our design is better in the towing tank?

Result

Tow each rotor at a steady speed and change the electrical load to sweep its speed. Subtract the strut's own drag, then convert the readings into C_P and C_T. Repeat every run three times. Speed accuracy is the big risk: a 2% speed error becomes a 6% power error, which is as big as the improvement we're trying to show.

test steps

±6.8%

example uncertainty in C_P

68,000

model Reynolds number (real: 10 million)

×3

repeats per test point

The test plan

Strut only, no rotor: measures strut drag to subtract later, and gives our baseline for any strut fairing.
Baseline rotor: step through the electrical loads, from free-spinning to stalled.
Our design: the same sweep, same speed, same kit if possible (kits differ).
A second towing speed: if C_P changes with speed, that's the small-model effect, and we say so.
Three repeats of everything: report the average and the spread.

Model vs real turbine

	Real (ATIR-like)	Our model
Diameter	19 m	≈ 0.3 m (to confirm)
Tide or towing speed	2–5 m/s	≈ 0.5–1.5 m/s
Reynolds number	≈ 10,000,000	≈ 68,000

A small, slow model feels the water as relatively "sticky" (low Reynolds number), so its foils work less well. We compare our design against the baseline tested the same way, not against real-world numbers.

Tank walls

In a narrow tank water can't flow round the rotor freely, which inflates results. Correct both rotors the same way if the rotor fills more than about 5% of the tank's cross-section.

Smooth surface

Print layer lines act as roughness, which matters a lot on small blades. Sand both rotors the same way.

Check the twist

A 2° printing error is as big as the pitch change we're testing. Print an angle template.

Fit and balance

Check the hub fit for our kit and balance the rotor.

How we worked it out converting readings, accuracy, scaling

Turning readings into results

\[ \lambda = \frac{2\pi N R}{60\,U}, \qquad C_P = \frac{P_e / (\eta_{gen}\eta_{gear})}{\tfrac12 \rho A U^3}, \qquad C_T = \frac{F_x - F_{strut}}{\tfrac12 \rho A U^2} \]

\(N\)	Rotor speed in rpm	rpm
\(U\)	Towing speed	m/s
\(P_e\)	Electrical power measured (V × I)	W
\(\eta_{gen}\eta_{gear}\)	Kit efficiencies, measured separately	–
\(F_x,\ F_{strut}\)	Total drag measured, and strut-only drag	N

Example0.3 m rotor at 1 m/s, 290 rpm, 9 W, kit efficiency 0.72: λ = 4.6, C_P = 12.5 W ÷ 35.3 W = 0.35.

How accurate is C_P?

\[ \frac{\delta C_P}{C_P} \approx \sqrt{\left(\frac{\delta P}{P}\right)^2 + \left(3\frac{\delta U}{U}\right)^2 + \left(2\frac{\delta D}{D}\right)^2} \]

\(\delta\) (delta)	Possible error in a measurement; δU/U is that error as a fraction	–
3, 2	Speed is cubed in C_P, so its error counts 3×. Diameter is squared, so 2×.	–

Example3% power, 2% speed, 0.5% diameter errors: √(3² + 6² + 1²) ≈ 6.8%.

Scaling

\[ C_P = f(\lambda,\ Re), \qquad Re = \frac{W c}{\nu} \]

\(f(\ldots)\)	"Depends only on": for the same shape, C_P depends on tip speed ratio and Reynolds number
\(Re\)	Reynolds number: momentum vs stickiness of the flow	–
\(\nu\) (nu)	Water's kinematic viscosity, 1.0 × 10⁻⁶	m²/s

Plain EnglishMatch the tip speed ratio and the model behaves like the real rotor, apart from the Reynolds effect. Matching Re too would need the model about 60× faster than the tide, which is impossible.

08 · Research question

What do we do with this in weeks 9–11?

Result

Ready for the team to agree: 11 draft specification lines (week 9), 7 morphological chart rows (week 10) and 8 weighted selection criteria (week 11). The baseline rotor is a ready-made datum for a Pugh matrix.

spec lines

morphological chart rows

selection criteria

open questions to chase

Week 9 · Draft specification lines (performance)

Written as measurable requirements, not solutions. X, Y, Z and W get set once the baseline data arrives.

#	Requirement	How we check it
P1	Thrust coefficient at best power at least X% below the baseline	Tank sweep, strut drag subtracted
P2	Best power coefficient at least Y% of the baseline (suggest 90)	Tank sweep
P3	Bending at the strut root at least Z% below the baseline	Force × lever arm
P4	Full size: thrust in the fastest tide (5.5 m/s) no more than at rated speed	Prediction
P5	Generates both ways, each within N% of the other	Prediction
P6	Starts generating at or below the baseline's speed	Slow tow
P7	No cavitation at the fastest tide and shallowest tip	Cavitation check
P8	Blade material no more than the baseline unless justified	CAD volume
P9	Yearly energy at least W% of the baseline	Power curve × site data
P10	Kit losses measured and reported separately	Drive the shaft, compare in and out
P11	Every result averaged over 3 repeats, with uncertainty	Test log

Week 10 · Morphological chart rows

Job	Options
Capture energy	2 / 3 / 4 blades · full or light loading · thin, cambered or symmetric foil
Limit thrust in fast tides	Fixed pitch offset · motor pitch · flexible blade · stall at low speed
Work both tide directions	Turn blades 180° · symmetric foil · turn the whole rotor
Use less material	Spin faster · higher-lift foil · hollow blade with spar · neutral buoyancy
Hub shape	Hemisphere · ellipsoid · long pointed nose and tail
Low-drag support	Round · streamlined · swinging fairing · whisker-style · shorter
Keep performing	Anti-fouling · cleanable surface · tough leading edge

Ideas from nature for the write-up: humpback whale flippers (bumpy leading edge), seal whiskers (strut), fish fins (flexible blades).

Week 11 · Selection criteria

Start with a Pugh matrix against the baseline (better +1, same S, worse −1), then weight the best few.

Criterion	Weight (1–5)	Evidence
Thrust and bending reduction	5	Model ΔC_T
Power kept	4	Model ΔC_P
Thrust in fast tides	4	Tab 04
Printable and fits the kit	4	Workshop check
Material used	3	CAD volume
Yearly energy	3	Power curve × site data
Works both directions	3	Foil and pitch choice
Can we measure the benefit?	3	Effect vs test error

Open questions

Blackboard (not released yet): baseline blade shape, power and thrust curves, CAD, equations sheet, site data.
Tank and workshop staff: does the towing post measure drag? Tank size? Speed accuracy? Kit efficiency?
Emily: tide speeds over time, depth, rotor depth.
Will C and Seymen: confirmed ATIR rotor size, power, rated speed, pitch range.
Team: how much power loss is "significant"? Where do we measure bending?

09 · Reference

Glossary: every word and symbol

Units in brackets; "–" means no units (a ratio).

Symbol or word	Name	Meaning	Units	Typical value
\(U\)	Tide speed	How fast the water moves, upstream of the turbine	m/s	1–5 sea; ≈1 tank
\(\rho\) (rho)	Density	Mass of a cubic metre of water	kg/m³	1025 sea, 1000 tank
\(D, R\)	Diameter, radius	Rotor size; R is centre to tip	m	19 m real, 0.3 m model
\(A\)	Swept area	Circle the blades sweep, πR²	m²	283.5 m²
\(P\)	Power	Energy per second	W
\(T\)	Thrust	Push of the water on the rotor ("drag")	N	≈670 kN
\(C_P\)	Power coefficient	Fraction of the water's power captured	–	0.35–0.48
\(C_T\)	Thrust coefficient	How hard the rotor pushes back, as a fraction	–	0.6–0.9
\(a\)	Axial induction factor	Fraction by which the rotor slows the water	–	0.2–0.33
\(\Omega\) (omega)	Spin speed	rpm × 2π ÷ 60	rad/s	≈1.3 real
\(\lambda\) (lambda)	Tip speed ratio	Tip speed ÷ tide speed	–	4–6
\(r\)	Local radius	Distance from centre to a slice of blade	m
\(c\)	Chord	Blade width at one radius	m	≈1 m real, 20 mm model
\(B\)	Number of blades		–	3
Foil	Hydrofoil	The wing-shaped cross-section of a blade
\(\alpha\) (alpha)	Angle of attack	Angle between the oncoming water and the foil	°	5–8° best
\(\varphi\) (phi)	Inflow angle	Angle the flow arrives at, measured from the spin plane	°
\(\theta\) (theta)	Blade setting angle	Twist plus pitch at a given radius	°
Lift, \(C_L\)	Lift	Force at right angles to the oncoming water; turns the rotor	N, –	C_L 0.8–1.2
Drag, \(C_D\)	Foil drag	Force along the oncoming water; wastes energy	N, –	C_D 0.01–0.03
Stall		Angle too steep: flow breaks away, lift drops		above 10–14°
Pitch, feather		Pitch: rotating a blade about its long axis. Feather: turning it edge-on to the flow.	°
\(\sigma\) (sigma)	Solidity	Fraction of a ring that is blade, Bc ÷ 2πr	–
\(Re\)	Reynolds number	Momentum vs stickiness; shows whether a model behaves like the real thing	–	10⁷ real, 7×10⁴ model
\(\nu\) (nu)	Kinematic viscosity	How runny the water is	m²/s	1.0×10⁻⁶
Cavitation		Water boiling at low pressure on a fast blade; bubbles erode and make noise
\(M\)	Bending moment	Force × distance; tips the hull, bends the strut	N·m
\(\sigma_b\)	Bending stress	Stress from bending (a different σ from solidity)	Pa
\(\eta\) (eta)	Efficiency	Output ÷ input for one part	–	0.93–0.98
Rated speed / power		Tide speed at which the generator reaches maximum power	m/s, W	2.4 m/s, 750 kW
AEP	Annual energy production	Energy delivered in a year	MWh
BEM	Blade element momentum	Our method and Python code for predicting power and thrust

10 · Reference

Sources and files

FEEG1204 Group Project Brief: Maritime 2026-27; Maritime Project Allocation 26-27; Week 7 Intro slides; portfolio template and marking scheme (Blackboard, read 12 Nov 2026).
Bahaj, A.S., Molland, A.F., Chaplin, J.R., Batten, W.M.J. (2007). Power and thrust measurements of marine current turbines in a cavitation tunnel and a towing tank. Renewable Energy 32, 407–426. eprints.soton.ac.uk/188933
Burton, Jenkins, Sharpe, Bossanyi. Wind Energy Handbook, Wiley. Actuator disc, BEM, tip loss.
Manwell, McGowan, Rogers. Wind Energy Explained, Wiley. BEM step by step.
Buhl, M.L. (2005). High-loading correction for BEM. NREL/TP-500-36834.
Viterna, L.A., Corrigan, R.D. (1982). Post-stall foil behaviour. NASA.
Whitby, B., Ugalde-Loo, C.E. (2014). Performance of pitch and stall regulated tidal stream turbines. IEEE Trans. Sustainable Energy. Cardiff ORCA
Gambuzza, S. et al. (2023). Over/under-speed control and thrust of tidal turbines. Tethys
Shi, W., Atlar, M. et al. (2016). Tidal turbine with leading-edge tubercles. Ocean Engineering 117. Strathprints
Hanke, W. et al. (2010). Harbor seal whisker shape suppresses vortex-induced vibrations. J. Exp. Biol. 213, 2665–2672.
Walker, J.M. et al. (2014). Blade roughness and fouling on marine current turbine performance. Renewable Energy 66, 257–267.
Garrett, C., Cummins, P. (2007). The efficiency of a turbine in a tidal channel. J. Fluid Mech. 588, 243–251.
Hay, A. (2014). Turbulence and bottom stress in Grand Passage and Minas Passage. OERA. FORCE
FORCE, Fundy Ocean Research Centre for Energy. fundyforce.ca
Magallanes Renovables / ATIR. Overview
Ashby, M.F. Materials Selection in Mechanical Design.
IEC TS 62600-200 (power performance of tidal converters); IEC TS 62600-2 and DNV-ST-0164 (design loads).

Model files

The numbers in tabs 03 and 05 come from two Python scripts in the team project folder: bem_performance_model.py (the rotor model) and performance_studies.py (foil, fouling, blade count, material and control studies). They run a demonstration rotor with placeholder foil data, so treat the numbers as trends until they're rerun with the baseline blade.

Mar2E · FEEG1204 Group Design Project · University of Southampton, 2026–27. Research by Will B. Numbers are illustrative until the baseline data is released.