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Trident
A fast, seaworthy, outside-the-box 0.495 kg, 4.3W no-frills power trimaran centered around the very slender 48x6x5 LU Speedboat hull. A top speed of 0.95 m/s makes her our 3rd fastest boat after Nadine and Laverne.
About this creation
Please feel free to look over the images and skip the verbiage.

Shawn Kelly and I have been avidly building, racing, and occasionally sinking Power Functions (PF) remote control (RC) speedboats for 2 years now. To date, we've come up with dozens of seaworthy LEGO® powerboats (mostly no-frills speedboats) based on various LEGO® unitary hulls (LUHs).

Shawn's boat Radio Flyer below even took 1st place in the boat drag races at BrickWorld 2015!



We've also dabbled in LUH-based motorized ship models like Stormin' Norma II, a marine geology research vessel.



The comments below come out of that experience and a very deep plunge into naval architecture -- the engineering discipline devoted to the design, testing, and construction of boats and ships of all kinds.



Of all our boats, Trident is easily the farthest outside the box. She may look like a cross between a duck and a space ship, but she's our lightest and 3rd fastest boat to date. She's part trimaran, part submersible, and all business. Every design detail serves seaworthiness, speed, or both.



On this page:


Overview

Trident is a 0.495 kg twin-screw power trimaran with a highly optimized 4.3W powerplant consisting of (i) twin L motors powered by a PF Li polymer rechargeable battery via a V2 IR receiver, (ii) efficient twin inverted-V outdrives with 2-stage 1:5 overdrive gearing, and (iii) very efficient third-party 55 mm 3-blade counter-rotating props.









Her small side hulls nicely stabilize the long, narrow 48x6x5 LU Speedboat hull in between and add some needed buoyancy as well. Watertight hulls and excellent stability make Trident seaworthy enough for the chop typical of a very busy swimming pool -- the LEGO® equivalent of a heavy storm sea.



A top speed of ~0.95 m/s (Froude number ~0.50) makes her our 3rd fastest no-frills LEGO® speedboat to date after big blue Nadine in the distance and Laverne in the middle. If the LEGO® powerboats seen on YouTube are any indication, that's pretty darned fast.

Granted, a hobby-shop RC boat costing half as much could easily beat Trident's top speed, but the goal here was an unconventional speedboat competitive in the LEGO® realm. Designing and building her with the fewest non-LEGO® components possible was much of the fun.

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Design goals
Trident grew out of a self-imposed challenge to build a small, fast trimaran around a single 48x6x5 LU Speedboat hull (SBH, from the 2003 set of the same name). The side hulls would have to cover buoyancy and stability deficits left by the long, narrow, low-volume SBH center hull with a minimum of added resistance.

In our experience, all-SBH multihulls excel in stability and structural stiffness but are slower than expected for reasons I'm still trying to sort out.



The all-SBH base of the 0.92 kg trimaran airboat above strongly resists wave- and thrust-induced flexure and attitude changes.

As a twin-screw speedboat, however, the same trimaran base was ~10% slower than Dubble°°Bubble, the 0.72 kg all-SBH catamaran below. Dubble°°Bubble, in turn, is ~15% slower than Trident.



Smaller side hulls were clearly in order.



A sealed Technic air tank on each side turned out to add just the right amount of buoyancy and roll stability. Axle holes in each end of the tank allow secure and hydrodynamically clean mounting with a minimum of structural plastic in the water.

The conical forward fairings earn their keep by improving flow around the side hulls and increasing effective sidehull length and slenderness -- all of which reduce total side hull drag. In Trident's current configuration, the side hulls account for 7% of her displacement volume at rest.



Both boats use similar 4.3W twin-L propulsion systems, but Dubble°°Bubble (right) dwarfs Trident in overall size, displacement, and wetted surface area.

Trident's much greater installed power to displacement ratio (8.7 vs. 6.0 W/kg) certainly contributes to the current 15% difference in speed, but the gap was only 6% prior to Trident's most recent side hull rearrangement. Hence, a full 9% goes directly to hull interference reduction on Trident's part.

As a center hull, the SBH has at least 6 outstanding attributes that should add up to a fast trimaran if properly exploited:
  • Exceptional slenderness, as evidenced by a waterline length-breadth ratio (L/B) nearly twice that of any other LEGO® unitary hull (LUH).
  • Second greatest waterline length available with an LUH at Trident's freeboard.
  • A very clean bottom hydrodynamically.
  • An easily sealed weather deck.
  • Less capacity for trapping water above decks than any other LUH by a wide margin.
  • The most secure cross-structure attachment points (in the form of pin holes) on any LUH, also by a good margin.





Length and slenderness at waterline (high L/B) reduce wave-making resistance -- by far the greatest impediment to higher top speeds in all our speedboats. Unmatched water-shedding ability makes a properly sealed SBH quite seaworthy at near-zero freeboard (think submarine cruising at the surface).

To make up for SBH's modest waterline length (372 mm at near-zero freeboard) and low below-deck volume, I'd have to
  • Choose and position the side hulls very carefully
  • Keep displacement (total mass) to a minimum
  • Maximize installed power
  • Maximize powertrain, propeller, and structural efficiency
  • Minimize water resistance in all its forms
  • Maintain an adequate margin of safety for bathtub and open-water trials along the way.
In practice, these goals are fundamentally contradictory and completely intertwined -- especially in such a small package. Everything would depend on everything else, and the trade-offs would have to be played just so.

The only workable approach to such an involuted design problem is the naval architect's design spiral -- a process of systematic iterative refinement that eventually converges on a well-optimized boat -- that is, if the initial premises are valid.

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Built for speed
The most important factors behind Trident's speed are
  • Extremely high installed power (PI) to displacement (Δ) ratio of 8.7 W/kg -- probably close to the maximum possible in a seaworthy LEGO® powerboat given available powerboat-compatible hulls (PCHs). A whopping 51% of Trident's displacement goes to propulsion.

  • Second longest load waterline length (LWL) possible with a LEGO® unitary hull (LUH) to minimize center hull wave-making resistance at speed.

  • Side hull configuration optimized to induce negative (i.e., beneficial) hull interference.

  • Low total wetted surface area to minimize viscous resistance at all speeds

  • Highly efficient third-party props -- her only non-LEGO® parts -- to make full use of the shaft power produced by her motors.

  • No-frills outfit to keep displacement down -- with the added benefit of maximizing freeboard and hence water clearance for her electricals.

  • Very little plastic in the water aside from the hulls to minimize appendage drag.



The rationale behind the twin inverted-V outdrives and third-party props is discussed here.

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Drivetrain optimization
Trident's "L/5/55" drivetrain (L motors, 1:5 overdrive, and 55 mm props) came out of a methodical and rather tedious motor/gearing/prop (MGP) optimization process. As seen here, many of my speedboats end up with L/1:5/55 drivetrains via MGP optimization, but L/1:5/52 and XL/1:8.33/55 drivetrains also find use.

Replacing Trident's twin L motors with twin XLs would add 0.6W of installed power and 0.054 kg of motor mass. However, she'd then need a stronger cross-structure and much larger side hulls to support it all. Given available side hull alternatives, a marked increase in total resistance would be unavoidable.

To keep the same installed power to displacement ratio, the added cross-structure and side hull mass would have to come in under 0.012 kg -- a clear impossibility given available side hull alternatives. Hence, she'd end up with a lower installed power to displacement ratio and a lot more resistance to contend with.

Granted, that combination works for much longer Nadine below, but I don't see a faster SBH-based trimaran coming out of it.



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Tub and pool trial videos

The 3 videos below show Trident in bathtub and swimming pool trials prior to her most recent hull reconfiguration. The side hulls are currently more aft and outboard than seen here, and the cross-structure was revised accordingly. The version in the videos was otherwise identical to the current one shown in the photos.

Trident's top speed in the videos was ≥ 0.84 m/s (center hull Froude number ≥ 0.43). Particularly noteworthy in these tests are (i) her near-zero freeboard at all speeds; (ii) her slightly positive (bow-up) trim and wet decks aft at speed; (iii) excellent stability and controllability in both calm water and bathtub chop; and (iv) her rather prominent wave wake -- especially the high transverse waves astern.



Pool trial: The odd stops and starts are all due to Power Functions IR remote control failures. (Don't get me started.)



Tub trial: Trident's outdrive struts are just long enough to keep her props from ventillating (sucking air) in forward motion, but they ventillate a lot in reverse. The latter cuts into maneuverability when a motor has to be reversed, but keeping the struts as short as possible without ventillation maximizes thrust and reduces positive trim at speed, thereby improving top speed.



Static thrust demo: The props ventillated slightly when producing forward thrust here only because I was holding them too close to the surface.

Trident owes her current ~0.95 m/s top speed to a subsequent relocation of each side hull by 3 LU aft and 3 LU outboard. Considering that her displacement, hulls, and propulsion system stayed the same, that's a pretty impressive gain, and it's entirely due to a marked reduction in wave-making resistance, aka wave drag.

Wave-making resistance limits top speed more than all other factors combined in all our speedboats. Hull interference, an important component of wave-making resistance in multihulls, is a lot less important in Trident these days.





The new side hull rearrangement reduces hull interference by promoting destructive interference among the wave wakes coming off each hull -- especially between hulls.

In the videos above, Trident's total water resistance and wave-making resistance were dominated by the power lost to transverse waves, so named because their crests are roughly normal to the direction of motion. The most conspicuous transverse waves occur behind Trident in the pool trial. Their longer wavelengths make the transverse waves look lower than the divergent waves angling away from her bows, but the opposite is true.

With the transverse waves now largely gone, total and wave-making resistance are dominated by the power lost to the less power-hungry divergent waves.

Also critical to Trident's performance and seaworthiness are watertight hulls with no capacity to trap water onboard below decks and negligible capacity to trap it above (e.g., in a deck well). In fact, Trident's steeply cambered (sloped) center and side hulls hurry water overboard as fast as it comes aboard.

Trident owes her ability to operate safely at near-zero freeboard to such hulls (think submarine cruising at the surface). Without them, she would have had to rely on ample freeboard to keep water out (as the vast majority of boats do), and a 50% allocation of displacement to propulsion would have been impossible. Top speed would have suffered accordingly.

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More photos





Side hull mounting and fairing details. The conical fairings reduce more drag than they create.



No other unmodified powerboat-compatible hull has a bottom this clean.



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Comparison with other fast boats

The group shots below show our 3 fastest boats together for comparison purposes. With the possible exception of my yet to be raced CHL-based outboard Earline (not shown), these 3 leave our other boats far behind.



The fastest boat here, by a small margin, is long blue Nadine, also based on the CLH. Next fastest, again by a small margin, is Laverne, based on a black 51x12x6 LU Police boat hull (PBH).

The top speeds represented here range from ~0.95 m/s for Trident to ≥0.99 m/s for Nadine -- a spread of ~5%. By LEGO® powerboat standards, all are quite high.

All 3 of the boats gathered here use similar twin outdrives with the following optimized drivetrains: XL/8.33/55 for Nadine, and L/5/55 for Trident and Laverne.



Nadine's overall length far exceeds Trident's and Laverne's, as does her water line length (LWL). Trident's center hull is shortest in overall length, but Laverne has the shortest LWL here.



Each boat reaches her top speed in her own way. Nadine's biggest advantage is her great length, but her 4.9W of twin-XL installed power (PI) certainly help. As configured here, XL motors are too heavy for Laverne and Trident, but their twin-L PI of 4.3W is still quite potent.

Trident succeeds by combining an extreme installed power to displacement (PI / Δ) ratio (8.7 to Nadine's 5.7) with much lower total resistance (RT) than Nadine encounters at comparable speeds. Laverne edges out Trident by confronting an even lower RT with the same PI and lower but comparable PI / Δ (8.3).

Nadine's LWL of 0.540 m and top speed Umax of ≥0.99 m s-1 correspond to maximum Froude number (Frmax) of at least 0.43.

For Laverne, LWL = 0.345 m, Umax ≈ 0.97 m/s, and Frmax ≈ 0.53.

For Trident, LWL = 0.372 m at her center hull, Umax ≈ 0.95 m/s, and Frmax ≈ 0.50, respectively.

The significance of these Froude numbers will soon become apparent.

Compared to Trident's center hull, Nadine's hull is 45% longer at waterline, displaces 73% more water, and has almost twice the total wetted surface area (S).

Nadine's length is a huge advantage WRT to wave-making resistance (RW), the overwhelmingly dominant component of total resistance at these Froude numbers. That more than offsets the disadvantage of having the largest S, which is proportional to viscous resistance (RV). Laverne has the smallest S of all.

Hull slenderness at waterline reduces RW and RV. The length-breadth ratio at waterline (hereafter, simply L/B) is a good measure of slenderness.

Trident's center hull L/B of 7.8 dwarfs Nadine's (3.8) and Laverne's (3.9). Her side hulls are much less slender (L/B = 3.5) but small enough that the impact on RT is probably negligible.

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Power, resistance, and Froude number Fr

As explained here on Nadine's page in more detail, the Froude number (Fr) is a very useful length-adjusted index of speed given by

Fr = U / √(g LWL)

where U is boat speed relative to the water, and g is the acceleration of gravity (~9.81 m s-2). For trimarans with small side hulls like Trident, LWL is taken at the center hull.

Since Fr is proportional to speed, one can speak of speed and Froude number interchangeably. However, the Froude number is a much better way of gauging speed when trying to make sense (and use) of the relationships linking power, resistance, speed, and hull dimensions -- especially waterline length.

Because the Froude number's a dimensionless quantity (units in numerator and denominator cancel), the specific resistance-Froude number relationship takes on a universal character independent of waterline length. (Specific resistance is just total resistance divided by displacement.)

The effective power-Froude number relationship -- the ultimate limit on top speed -- shares this useful property.

For reasons explained shortly, the critical Froude number (Frcrit) is defined by

Frcrit ≡ 0.40

A boat of waterline length LWL is said to be at critical speed (Ucrit) when its absolute speed Ucorresponds to its critical Froude number. Hence,

Ucrit = Frcrit √(g LWL

Total resistance grows dramatically at supercritical speeds -- i.e., when U > Ucrit. Once in the supercritical regime, hull form has only a minor effect on total resistance, but some hull forms have a harder time getting there than others. Nadine's tanker-like hull form comes to mind.

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Power vs. resistance
Effective power (PE) is defined as the mechanical power needed to tow a boat at steady speed U against the total resistance RT encountered at that speed. The relationship is deceptively simple:

PE = RT U

Due to various power losses between the motors and the water processed by the props, the installed power PI needed to reach a target speed U always exceeds the PE associated with that speed but follows a similar upward trend with increasing U. Mathematically, installed and effective power are related by the total propulsive efficiency (ηT) given by

ηTPE / PI

Like all efficiencies, ηT is a dimensionless number between 0 and 1. In LEGO® powerboats, it subsumes (i) all the electrical power losses associated with the batteries, RC receivers, and motors; (ii) all the mechanical losses associated with powertrain mounts, bearings, shafts, and gears (including those inside the motors); and (iii) all hydrodynamic losses associated with the props.

In the real world, ηT is generally on the order of 50-60% for well-designed displacement monohulls with efficient props and often a bit less for multihulls.

Our efficiencies are probably in the 50-60% range as well -- but only when we run size-optimized third-party props like Trident's. With LEGO® props, we'd be lucky to get 20%, as explained here.

The bottom-line equation below expresses target speed U in terms of installed power PI, propulsive efficiency ηT, and total resistance RT:

U = ηT PI / RT

This equation is worth remembering, as it clearly identifies installed power, propulsive efficiency, and total resistance as limiting factors of equal importance when it comes to (i) maximizing either top speed or battery life or (ii) minimizing the installed power needed for a particular operating speed.

You'd need some way of measuring or estimating ηT and RT at speed to use it quantitatively, but that's not the point.

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Resistance vs. Froude number
A boat moving dead ahead at steady speed U -- or equivalently, Froude number Fr -- is opposed by a speed-dependent total resistance force (RT) acting on its hull in the opposite direction from its forward motion. (Speed and direction here are relative to the water.)

RT is the sum of several physically distinct components, the most important of which are viscous resistance (RT) and wave-making resistance (RW).

NB: The links supplied in the last paragraph lead to more detailed discussions of resistances than I'll give here. The comments below are most accurate for monohulls like Nadine and Laverne but fit well enough for trimarans with small side hulls like Trident. They apply only to displacement craft -- i.e., boats supported by buoyancy alone with no significant help from hydrodynamic lift at the speeds of interest, regardless of size or hull type.

Displacement craft include all LEGO® powerboats at all conceivable speeds, all merchant vessels, and all surface warships larger than patrol boats. Excluded are all real semi-planing, planing, and hydrofoil-supported craft once going fast enough for lift to kick in and all hovercraft.

Viscous and wave-making resistance vary with length and speed, each in its own way, and each generally responds to different countermeasures. Since their relative importance also varies with length and speed, it's important to know which one happens to be dominating RT at the moment.

Conveniently, the Froude number encapsulates the combined influence of length and speed in a single scale-independent quantity.

The most important change in the make-up of total resistance occurs at Fr ≈ 0.30. Viscous resistance dominates in the low-speed regime defined by Fr < 0.30. At Fr < 0.20, RW becomes negligible.

Wave-making resistance takes over as the main component of total resistance in the high-speed regime defined by Fr > 0.30. Waterline length has its greatest and most favorable impact on performance in this regime.

Beyond the critical Froude number at Frcrit ≡ 0.40, the dominance of wave-making resistance becomes overwhelming. Viscous resistance is still alive and well and worth addressing at supercritical speeds, but it's small change compared to RW. Total resistance pretty much follows RW in the supercritical regime.

The dominance of wave-making resistance peaks at Fr ≈ 0.54 and ends at Fr ≈ 0.59. At higher speeds, RW and RV are comparable.

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Humps, hollows, and the wave wall
Total resistance generally grows with the square of speed or Froude number. Dependencies of this kind are said to be quadratic or parabolic.

For RT, the overall trend is one of ever-steepening increase with increasing speed or Froude number, but it's a bit more complicated than that in detail, and the details matter.

At certain length-dependent speeds of great relevance to most boats, LEGO® powerboats included, RT deviates above or below the background quadratic trend.

On plots of RT vs. Fr, deviations from the quadratic growth of RT show up humps (local maxima) and hollows (local minima) superimposed on the overall quadratic trend. The humps and hollows are primarily due to variations in the growth of RW with speed.

It's helpful to know where a boat stands WRT these humps and hollows, as some have important implications for top speed and fuel consumption or battery life. The Froude number shines as a length-adjusted index of speed because the humps and hollows occur at similar Froude numbers for all displacement monohulls, regardless of size and with little dependence on hull type -- i.e., for Nadine, Laverne, and real supertankers alike.

The humps and hollows found in trimarans with small side hulls like Trident follow a very similar pattern when Froude number is calculated using center hull LWL, as I do here.

It takes less PE -- hence, less fuel consumption or slower battery discharge -- to maintain an Fr at the bottom of a hollow than it does to run at a slightly lower (or higher) Fr within the same hollow.

Long-haul merchant vessels are optimized to cross entire oceans at the bottom of a single well-chosen low-speed hollow (i.e., one below Fr ≈ 0.30) so as to maximize their fuel consumption to payload ratio.

That would also be an excellent way to run a heavy model ship with difficult battery access like Stormin' Norma.

Conversely, it takes more PE to maintain an Fr at the top of a hump than it does to run at slightly higher (or lower) Fr on the same hump. Merchant vessel designers and operators avoid humps like the plague.

Like our speedboats, fast modern warships like destroyers, cruisers, and aircraft carriers top out at speeds on the main hump (the largest hump of all) at 0.40 < Fr < 0.59, and for all the same reasons. However, such warships make a point of cruising in the hollows whenever possible to conserve fuel and thereby maximize tactical range.

The main hump peaks at Fr ≈ 0.54, where Laverne tops out. Trident tops out short of the peak Fr ≈ 0.50. Seeing as how the current crop of US Navy destroyers and cruisers top out at Fr ≈ 0.41, I'm rather proud of those performances.

The main hump's very steep upswing between the critical Froude number (0.40) and its peak at Fr ≈ 0.54 marks an explosive growth of RW and hence RT with increasing speed.

All our monohull speedboats other than Laverne top out against this aptly named wave wall. Most, like Nadine, give up near the bottom.

Trident and Laverne prove that the wave wall's not a physical barrier. All that's needed to climb it is a huge installed power to displacement ratio and a cavalier attitude toward fuel consumption or battery life. The fact that massive Nadine beats both in a race (though not by much) proves that increased length is also an effective path to high speed.

Since length appears in the denominator of the Froude number formula, it pushes the wave wall out to higher absolute speeds, thereby reducing the wave-making resistance associated with lesser absolute speeds. Since RW is the dominant form of resistance at Fr > 0.30, waterline length has a major impact on RW at such speeds -- especially in the supercritical regime.

The next largest hump -- prismatic hump centered at Fr ≈ 0.30 -- pales in comparison to the main hump but is still worth avoiding when operating below top speed. From there, the humps and hollows get progressively smaller with decreasing Froude number.

There are no humps or hollows to speak of beyond Fr ≈ 0.59, meaning that RT remains quadratic WRT speed from there on out. I doubt that LEGO® powerboats can reach such speeds with LEGO® motors and batteries, but I keep trying.

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Hull interference

Compared to monohulls of the same displacement, power multihulls tend to have 20-30% more wetted surface area AW. The skin drag component of viscous resistance (RV) increases by the same amount, but the impact on total resistance (RT) is partially offset by the main multihull advantage -- i.e., great stability despite the use of very slender hulls.

Hull slenderness reduces the form drag component of RV. Its effect on wave-making resistance (RW) due to each individual hull is even more favorable.

The great inherent stability of the trimaran configuration allows extremely slender center and side hulls (L/B ratios of 15-20), at which point form drag all but disappears. Such hulls could never be used in catamarans, much less alone.

However, the hulls in a multihull interact via the waves they generate, and that interaction leads to a significant wave-making resistance component not found in monohulls. This component, called hull interference, depends primarily on speed, hull length, and relative hull position, but in very complex way.

Trimaran hull interference is greatly complicated by the interaction of 3 hulls with 3 bow and stern transverse wave systems and 3 bow and stern divergent wave systems.

When the net effect is an overall increase in constructive interference among these wave systems, the mean wave amplitude rises, and so does wave-making resistance, which grows with the square of mean wave amplitude. When the net effect is an overall increase in destructive interference, as in Trident's present situation, the mean wave amplitude declines, and wave-making resistance follows suit.

In a well-designed multihull, the net effect is generally a small to moderate increase in RT relative to equal-displacement monohulls at most speeds. This penalty diminishes with increasing separation -- i.e., the transverse distance(s) between hull centerlines.

At certain combinations of speed and separation, however, hull interference can go negative, meaning that total resistance actually falls below the sum of the total resistances the individual hulls would experience in isolation at the same speed, draft, and trim.

If it goes negative enough at supercritical speeds, where wave-making resistance overwhelms viscous resistance, total resistance can fall below that of an equal-displacement monohull. Trident may well be there now.

The large separations needed to induce negative hull interference in catamarans aren't always practical due to the high cross-structure stresses involved. Trimarans, however, offer two additional hull arrangement variables that can be juggled to induce large negative hull interferences at practical hull separations.

These trimaran-only adjustments are side hull vertical position (draft) and stagger -- i.e., longitudinal side hull position relative to the center hull. Stagger, the more important of the two, is often given as the longitudinal offset between center and side hull bows, but other definitions are still in use.

Stagger and separation are typically expressed in dimensionless form by dividing them by center hull waterline length. (Trident's bow-to-bow separation and stagger in these terms are 28% and 57%, respectively.) Trident's large negative hull interference was achieved by fine-tuning stagger and separation.

I adjusted the vertical position of Trident's side hulls to maximize their contribution to roll stability -- something her center hull sorely lacks due to its high L/B of 7.75 and very low breadth-draft (B/T) ratio of 1.33.

That led to more side hull wetted surface area than I would have liked on resistance grounds but had the added advantage of increasing center hull freeboard slightly and motor and battery water clearance along with it.

Further Trimaran complications arise from the great disparity in center and side hull Froude numbers occurring when the side hulls are much shorter than the center hull, as in Trident's case.

For example, when Trident's at her current top speed, her center and side hull Froude numbers are 0.50 and 0.80, respectively. In isolation, her side hulls would be well past the main hump in the divergent wave-only regime at Fr > 0.59, while her center hull would be burdened with near-maximum transverse wave constructive interference at the main hump peak at Fr ≈ 0.54.

[]

Power trimaran research is still in its infancy, but simple hull interference prediction tools and hull positioning aids are unlikely to appear. However, I managed to dig up several very helpful design studies on fast trimaran ferries and warships -- mostly theses -- based on extensive model testing and sophisticated hydrodynamic simulations.

WRT minimizing total resistance at speed, all of these sources recommend (i) minimizing side hull displacement given competing stability requirements, and (ii) maximizing side hull separation and stagger given competing demands surrounding maneuverability and handling in rough water. The latter recommendation comes with the proviso that the side hulls should probably not extend behind the center hull stern.

These studies also confirmed that it's valid to design around center hull Froude numbers when combined side hull displacement volume comes to less than 10% or so of the total, as with Trident (7%).

I took that advice with Trident and couldn't be more pleased with the results.



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Specifications
All measurements taken at rest in fresh water (density 1,000 kg m-3).

Overall dimensions and design features
Overall dimensions:384 x 236 x 104 mm (LxWxH) excl props
Displacement:0.495 kg (1.1 lb)
Displacement volume:4.95e-4 m3 (1.1 lb)
Wetted surface area:n/a
Construction:Mostly studless
Center hull:Unitary 48x6x5 LU Speedboat hull (Set 7244, 2003)
Side hulls:Sealed 4x4x8 LU Technic air tanks with bow fairings
Propulsion:Twin inverted-V outdrives
Motors:2, 1 L on each prop
Propellers:55 mm 3-blade counter-rotating pair (non-LEGO®)
Gearing:2-stage 1:5 overdrive
Propeller separation:156 mm on center
Steering:Differential power to props (no rudder)
Electrical power supply:Power Functions 7.4V rechargeable Li polymer battery box
IR receiver:V2
IR receiver connections:2, 1 for each motor
Modified LEGO® parts:Prop hubs
Non-LEGO® parts:Props and electrician's tape (to seal hull)
Credits:Original MOC


Performance measures
Installed power:4.3W
Installed power to displacement ratio:8.7 W/kg
Critical speed:0.76 m/s
Top speed:~0.95 m/s
Froude number at top speed:≥0.50 (center hull)
Reynolds number at top speed:≥3.5 x 105 (center hull)
Static thrust:[] N m at [] motor shaft RPM ([]% of no-load speed)


Center hull
Displacement share:93%
Displacement volume:4.59e-4 m3
Waterline length:372 mm
Waterline breadth:48 mm
Length/breadth ratio at waterline:8.0
Breadth/draft ratio:1.33
Freeboard:8/4/0 mm (foreward/mean/aft)
Draft:0/27/38 mm (foreward/mean/aft)
Block coefficient:0.66
Prismatic coefficient:0.80
Midship coefficient:0.83
Waterplane area coefficient:0.84
Slenderness (length-displacement ratio):4.82
Speed-length ratio:1.73
Froude number at top speed:0.50


Side hulls
Separation:104 mm (28% of LWL) on center
Stagger:212 mm (57% of LWL) from center to side hull bow
Displacement share:3.6% each
Displacement volume:1.80e-5 m3 each
Waterline length:112 mm
Waterline breadth:32 mm
Length/breadth ratio at waterline:3.5
Breadth/draft ratio:2.0
Freeboard:16 mm
Draft:16 mm
Block coefficient:0.36
Prismatic coefficient:0.20
Midship coefficient:0.90
Waterplane coefficient:0.0.59
Slenderness (length-displacement) coefficient:3.53
Speed-length ratio:2.79
Froude number:0.80

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References
Most of the titles below are free online for the digging.

Abramovitch, D., 2005, The Outrigger: A Prehistoric Feedback Mechanism, IEEE Control Systems Magazine, August, 2005

Anonymous, 2011, Basic Principles of Ship Propulsion, MAN Diesel & Turbo, Copenhagen, Denmark

Barrass, C.B., 2004, Ship Design and Performance for Masters and Mates, Elsevier Butterworth-Heinemann

Barrass, C.B., and Derrett, D.R., 2006, Ship Stability for Masters and Mates, 6th ed., Butterworth-Heinemann

Bertram, V., 2000, Practical Ship Hydrodynamics, Butterworth-Heinemann

Biran, A.B., 2003, Ship Hydrostatics and Stability, 1st ed., Butterworth-Heinemann

Blount, D.L., 2014, Performance by Design (self-published book)

Carlton, J.S., 2007, Marine Propellers and Propulsion, 2nd ed., Butterworth-Heinemann

Carr, B., and Dvorak, R., 2007, Investigation of Trimaran Interference Effects, unpublished Bachelors thesis, Webb Institute, Glen Cove, NY

Elcin, Z., 2003, Making Resistance Characteristics of Trimaran Hulls, unpublished master's thesis, Naval Postgraduate School, Monterey, CA

Faltinsen, O.M., 2005, Hydrodynamics of High-speed Vehicles, Cambridge University Press

Hlavin, J., 2010, Hydrostatic and Hydrodynamic Analysis of a Lengthened DDG-51 Destroyer Modified Repeat, unpublished master's thesis, Naval Postgraduate School, Monterey, CA

Moisy, F., and Rabaud, M., 2014, Mach-like capillary-gravity wakes, Physical Review E, v.90, 023009, p.1-12

Moisy, F., and Rabaud, M., 2014, Scaling of far- eld wake angle of non-axisymmetric pressure disturbance, arXiv: 1404.2049v2 [physics.flu-dyn] 6 Jun 2014

Molland, A.F., Turnock, S.R., and Hudson, D.A., 2011, Ship Resistance and Propulsion: Practical Estimation of Ship Propulsive Power, Cambridge University Press

Noblesse, F., He, J., Zhu, Y., et al., 2014, Why can ship wakes appear narrower than Kelvin’s angle? European Journal of Mechanics B/Fluids, v.46, p.164–171

Rawson, K.J., and Tupper, E.C., 2001, Basic Ship Theory, vol. 2: Ship Dynamics and Design, 5th ed., Butterworth-Heinemann

Royce, R.A., Mouravieff, A., and Zuzick, A., 2011, Trimaran Resistance Artificial Neural Network, 11th International Conference on Fast Sea Transportation, FAST 2011, Honolulu, Hawaii, USA, September 2011

Schneekluth, H., and Bertram, V., 1998, Ship Design for Efficiency and Economy, 2nd ed., Butterworth-Heinemann

Tupper, E.C., 1996, Introduction to Naval Architecture, 3rd ed., Butterworth-Heinemann

Zhang, J., 1997, Design and Hydrodynamic Performance of Trimaran Displacement Ships, unpublished doctoral dissertation, University College London, London

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Comments

 I made it 
  August 6, 2017
Quoting Justin Li Wow, this is awesome! Love the combination of form and function on this one.
Very kind, Justin! The form/function trade-off has resulted in some pretty ugly boats in my hands, but the form side of the equation worked out better than expected in this case.
 I made it 
  August 6, 2017
Quoting Seaman SPb Excellent fleet!
Thanks, Seaman!
  August 6, 2017
Wow, this is awesome! Love the combination of form and function on this one.
 I like it 
  August 6, 2017
Excellent fleet!
 I made it 
  October 31, 2015
Quoting Franciscus van der Maat That is an impressive amount of information, thanks for that. Lovely builds you have there, don't recall ever seeing a powered boat go as fast as yours. I really need to get my hands on some of those custom props. Been thinking about making a powered LEGO boat for long time :).
Thanks, Franciscus! Would love to see what you come up with. You can find the custom props on ebay by searching for "RC boat props" and the like. Stick with 4.8 mm or 3/16 inch shaft holes to simplify adapting them to Technic axles and pins. For a twin-screw boat, be sure to get a counter-rotating pair with one left-handed and one right-handed prop.
 I like it 
  October 31, 2015
That is an impressive amount of information, thanks for that. Lovely builds you have there, don't recall ever seeing a powered boat go as fast as yours. I really need to get my hands on some of those custom props. Been thinking about making a powered LEGO boat for long time :).
 I made it 
  December 20, 2014
Quoting matt rowntRee Love how odd this one is, reminds me of how we'd end up building rockets by just gluing fins to an engine. Bare essentials, no frills. Kind of amazed at how it stays afloat with that much weight with that little displacement. Awesome!
Thanks, Matt! Trident's always been my favorite boat -- partly because space ducks are just so darned irresistible, but mostly because she doesn't look the least bit fast or seaworthy. She used to give me the willies every time I put her in the water, but she's only let me down once in dozens of pool trials and races. That once involved an unsuspected slow leak in the tape sealing her center hull. As you might imagine, she doesn't do well with a center hull half full of water.
 I like it 
  December 20, 2014
Love how odd this one is, reminds me of how we'd end up building rockets by just gluing fins to an engine. Bare essentials, no frills. Kind of amazed at how it stays afloat with that much weight with that little displacement. Awesome!
 
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