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Laverne
A fast, seaworthy 0.52 kg, 4.3W no-frills speedboat based on the very hydrodynamic 51x12x6 LU Police Boat hull. With a top speed of ~0.97 m/s, she runs neck-and-neck with Celine and only a tad behind our 2nd fastest boat, Nadine.
About this creation
Please feel free to look over the images and skip the verbiage.

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Introduction

Laverne is a fast, seaworthy 0.52 kg twin-screw monohull speedboat based on the 51x12x6 LU Police Boat hull (PBH) -- the smallest powerboat-compatible hull (PCH) capable of carrying our standard 0.35 kg speedboat load in a monohull boat.

I built her to get a feel for the then-unfamiliar PBH. I had reservations about its stability, but the easily sealed weather deck provided a comfortable margin for error for tub trials. 1



Her slender appearance in silhouette is deceiving, as her bow overhangs her waterline quite a bit. Under her speedboat load, waterline length is only 345 mm -- almost 30 mm less than Trident's and 200 mm less than Nadine's. Her L/B ratio of only 3.9 is slightly higher than Nadine's (3.8) but far below Trident's (7.8).



To make up for her modest length and slenderness at waterline, where it counts, I'd have to
  • 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 completely intertwined and largely at odds with one another -- especially in such a small package. Everything would depend on everything else, and the trade-offs would have to be played just so.




Overview

Laverne is the quintessential no-frills speedboat. Every design detail serves seaworthiness, speed, or both.







The only video I have of her is the tub trial shown below.



The other boat in the video is a simple test platform for LEGOŽ ducted propellers. As you can see, the ducted props are much slower than Laverne's third-party props.




Seaworthiness

Laverne's initial stability (stability near 0° roll angle) is less than Nadine's and Trident's. However, her ample angle of vanishing stability exceeds her angle of deck edge submersion, and she's proven herself seaworthy in heavy swimming pool chop.



As usual, I sealed her weather deck with black electrician's tape to keep water from going below decks -- an essential rough-water safety measure given that the large PBH deck well can trap 0.36 kg of water above decks.

That alone would be more than enough to send Laverne to the bottom. Water hiding below decks would cut into the reserve buoyancy needed to recover her when the deck well gets too wet for comfort.

As on most PCHs with weather decks, the tape across the bow and around the stern corners needs frequent maintenance but sticks well everywhere else.



While I had the tape out, I also covered the PBH's only significant hydrodynamic flaw -- the long keel tunnel housing mounts for submersible motors and weights. Fairing the tunnel left her with the cleanest PCH available.




Propulsion system

Laverne's highly optimized 4.3W powerplant consists of (i) twin L motors powered by a PF Li polymer rechargeable battery via a V2 IR receiver, (ii) efficient twin inverted-V stern drives with 2-stage 1:5 overdrive gearing, and (iii) very efficient third-party 55 mm 3-blade counter-rotating props.





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



A top speed of ~0.97 m/s (Froude number ~0.53) makes Laverne our 2nd fastest no-frills LEGOŽ speedboat to date after big blue Nadine in the distance (0.99 m/s). She just edges out Trident in the foreground (~0.95 m/s). If the LEGOŽ powerboats seen on YouTube are any indication, those speeds are pretty fast.

Granted, a hobby-shop RC boat costing half as much could easily beat Laverne's top speed, but designing and building boats like this with the fewest non-LEGOŽ components possible is at least half the fun.



Built for speed
The most important factors behind Laverne's speed are

Drivetrain optimization







Laverne's twin "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.




More photos



Laverne's no-frills outfit keeps her displacement down and installed power to displacement ratio as high as possible. It also serves seaworthiness, in that it maximizes freeboard.

With a deck well this large, freeboard is the only real defense against deck wetness and flooding. It also adds water clearance for her electricals should she swamp. Laverne's 22 mm of freeboard at midships is modest but adequate in heavy swimming pool chop.










Comparison with other fast boats

The group shots below show our 3 of our 5 fastest boats together for comparison purposes. (Celine, not shown, has the same top speed as Laverne.) With the possible exception of my yet-to-be-raced CLH-based outboard Earline (also not shown), these 3 boats, Celine, and especially Triton leave all our other boats far behind.



The fastest boat here, by a small margin, is long blue Nadine, also based on the CLH. The slowest -- though not by much -- is Trident, the trimaran with the red 48x6x5 LU Speedboat hull (SBH) for a center hull.

The top speeds represented here range from ~0.95 m/s for Trident to ≥0.99 m/s for Nadine (a spread of <5%), with Laverne and Celine splitting the difference at ~0.97 m/s. By LEGOŽ powerboat standards, all are quite fast. All 3 use similar twin stern drives with the following optimized twin drivetrains: XL/8.33/55 for Nadine, and L/5/55 for Trident and Laverne.



Despite some bow overhang, Nadine's waterline length (LWL) far exceeds Trident's and Laverne's. Trident's center hull is the shortest of the 3 in overall length, but she makes full use of it at operating freeboard. Laverne's long bow overhang at operating freeboard leaves her with the shortest LWL here.

Hull slenderness at waterline reduces both viscous and wave-making resistance. The length-breadth ratio at waterline (hereafter, simply L/B) is a good measure of slenderness.

Laverne's so-so L/B of 3.9 is a bit higher than Nadine's (4.9) but much lower than Trident's center hull L/B of 7.8. Trident's side hulls are much less slender (L/B = 3.5) than her center hull but small enough that the impact on total resistance is probably small.



To each her own
Each boat reaches her top speed in her own way. Nadine's biggest advantages are her great length and massive installed power (PI) of 4.9W delivered twin XL motors.

XL motors are too heavy for Laverne and Trident, but these much lighter boats get much higher installed power to displacement (PI / Δ) ratios out of their 4.3W twin-L PI powerplants.



Trident runs with the top dogs by combining an extreme PI / Δ (8.7 W/kg 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 -- in part, due to the absence of side hulls -- with the same PI and slightly lower PI / Δ (8.3 W/kg).



Froude numbers
The Froude number (Fr) is a length-adjusted dimensionless index of speed defined 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), and LWL is the load waterline length. (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 to characterize speed when trying to make sense (and use) of the relationships linking power, resistance, speed, and hull dimensions -- especially the all-important waterline length.

Because the Froude number's a dimensionless quantity (units in numerator and denominator cancel), the resistance-Froude number relationship takes on a universal character independent of waterline length. The relationship between effective power and Froude number -- the ultimate limit on top speed in our boats -- does the same.

Nadine's LWL of 0.540 m and top speed Umax of ≥0.99 m s-1 correspond to a 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.



Froude number and wave-making resistance
Laverne's PBH emulates a planing hull, but she can't get up on plane with LEGOŽ motors and batteries. Hence, she's still a displacement craft for all intents and purposes. As such, reaching a Froude number of ~0.53 -- the highest among our boats -- is quite impressive.



Fast displacement ships like modern destroyers (above) and many large motor yachts seldom get much past Fr ≈ 0.40. For boats with appropriately designed hulls and gobs of installed power, hydrodynamic lift and planing behavior start kicking in at Fr > 0.6. Froude numbers in excess of 1.0 are required for full planing (skimming over the water with minimal draft). LEGOŽ unitary hulls have no chance of reaching planing speeds with LEGOŽ motors and batteries.

Two boats with displacement hulls and identical Froude numbers encounter the same relative proportions of wave-making resistance (RW) and viscous resistance (RV), the two main components of total resistance (RT). This hydrodynamic similarity holds for any combination of absolute speed and length yielding the same Froude number.

The variation of total resistance growth rate with speed will also be the same -- even if one boat is a hundred times longer than the other.

This variation gives the specific resistance (total resistance / weight) vs. Froude number curve for monohull boats a characteristic shape independent of boat size and largely independent of hull form. (Trimarans with small side hulls like Trident follow a very similar curve.) Hence, the curve has the same features at the same Froude numbers for 400 meter supertankers and LEGOŽ boats alike.

Viscous resistance is proportional to the square of speed at all speeds. At Fr < 0.30, total resistance follows a similar quadratic trend, but it rises well above that trend at supercritical speeds corresponding to 0.40 < Fr < 0.59.

Naval architects refer to this interval of exceptionally high specific resistance as the main hump in reference to its appearance on the specific resistance vs. Froude number curve.

The main hump reflects a dramatic growth of wave-making resistance with speed. On its steep ascending limb at 0.40 < Fr < 0.54 (sometimes called the wave wall), RW varies more like the fourth power of speed. Since RW overwhelms RV at these speeds, RT follows this explosive growth in RW.

It takes a very large installed power to displacement ratio and lower than average viscous resistance to climb the wave wall to the peak of the main hump at Fr ≈ 0.54.

Laverne comes very close to doing just that. Though a little faster in absolute terms, Nadine's still at the foot her wave wall when she gives up at Fr = 0.43.



The importance of being long



The magic of greater waterline length lies in that last paragraph. Since LWL appears in the denominator of the Froude number formula, a longer boat reaches higher absolute speeds before hitting its own wave wall. Meanwhile, the shorter boats running along side it are stuggling climb theirs.




Specifications


Dimensions and hull form coefficients
All measurements taken at rest in fresh water (density 1,000 kg m-3).

Overall dimensions:412 x 88 x 54 mm (LxWxH, excluding props)
Displacement:0.518 kg
Displacement volume:5.2 x 10 -4 m3
Depth:44 mm (midships)
Waterline length:345 mm
Waterline breadth:88 mm
Draft at keel:21 mm (midships)
Freeboard:23 mm (midships)
Wetted surface area:n/a
Midship section area:~2.2 x 10 -3 m2
Waterplane area:~2.8 x 10 -2 m2
Block coefficient:0.86
Prismatic coefficient:0.87
Midship coefficient:~0.98
Waterplane area coefficient:~0.93
Length-breadth ratio:3.9
Breadth-draft ratio:3.8
Length-displacement ratio:4.3
Form factor:0.53




Performance measures

Installed power:4.3W
Installed power to displacement ratio:8.3 W/kg
Critical speed:0.74 m/s
Top speed:~0.97 m/s
Froude number at top speed:≥0.53
Reynolds number at top speed:≥3.3 x 10 5
High speed index:0.93




Design features

Construction:Studded and studless
Hull:51x12x6 LU "Police Boat" (54100c02, 54100c01)
Propulsion:Twin inverted-V stern drives
Motors:2, 1 L on each prop
Propellers:55 mm 3-blade counter-rotating pair (non-LEGOŽ)
Gearing:2-stage 1:5 overdrive
Propeller separation:168 mm on center
Steering:Differential power to props
Electrical power supply:Power Functions 7.4V rechargeable Li polymer battery box
IR receiver:V2
IR receiver connections:2, 1 for each motor
Modified LEGOŽ parts:Prop hubs
Non-LEGOŽ parts:Props and electrician's tape (weather deck seal and keel tunnel fairing)
Credits:Original MOC




Footnotes

1 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 LEGOŽ powerboats (mostly no-frills speedboats) based on various LEGOŽ unitary hulls (LUHs).

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



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

The comments above 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.




References
All 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

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

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-field 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

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



Comments

 I made it 
  July 30, 2017
Quoting Builder Allan Wow! A lot of thought and research has gone into this. An interesting read and a very exciting idea :-)
Very kind, Allan! I did a deep dive into naval architecture when I starting building LEGO powerboats, and it paid royally in both safety and performance. I also enjoyed it a great deal, as you can tell. The problem with boat design at any scale: The air-water interface is a perverse medium to travel, and everything in the boat depends exquisitely on everything else.
 I made it 
  July 30, 2017
Quoting James Y. We need to get your boats down to Brickfair Alabama... you'd run circles around some of the competition with these. (Annual Lego boat race in the pool.)
Thanks, James! If the organizers allow non-LEGO props, I'd probably do quite well. Otherwise, a differential-drive paddle-wheeler with SBrick remote control would be a better choice -- but only if the steering's easy to control. Paddles designed to take small bites of water at a high rate are the most effective. A friend and I won the boat drag races at BrickWorld 2015 with a differential drive twin-screw boat running LEGO props, but that was the year before they allowed SBricks, and we won as much on control as we did on raw speed. At BrickWorld 2016, I took 2nd with a rather different triple-screw boat also running LEGO props. That time I lost to a paddle-wheeler of the kind just described.
 I like it 
  July 30, 2017
Wow! A lot of thought and research has gone into this. An interesting read and a very exciting idea :-)
 I like it 
  July 30, 2017
We need to get your boats down to Brickfair Alabama... you'd run circles around some of the competition with these. (Annual Lego boat race in the pool.)
 I like it 
  December 21, 2014
Good stuff, love how you give stats like the critical speed and Froude number, also the water tests, i wish i could do that, however i don't have a large enough water body that i can access...
 I made it 
  December 21, 2014
Quoting matt rowntRee Looking at all three, I would have put money on this one to be the fastest. Wouldn't be the first time I lost a bet, in fact, I rarely win bets. Maybe I should stop betting. XD I like the sleek look of this one, the bow angle has a beautiful steep angle. I have to wonder if a direct inboard drive would be the fastest for a monohull given the water interference of essentially two outboards, but I suppose they are far enough apart to not factor much. Excellent!
Matt, thanks for the kind words. As you well know, everything affects everything else in any well-optimized machine. In my LEGO experience, powerboats are the worst of all in that regard. A year ago I would have bet on Laverne, too, but I've since discovered that all our speedboats top out at speeds where waterline length and slenderness count more than displacement and a lot more than other aspects of hull form. Your point WRT twin stern drive (TSD) appendage drag is well taken. If there were a way to get a prop shaft through a unitary hull without drilling and leakage around the shaft, a single-screw inboard would =definitely= be worth a try. However, to keep up with the TSD boats I've posted, the inboard would have to be comparable WRT (i) installed power, (ii) propulsive efficiency, and (iii) total resistance, not just appendage drag (probably less than 25% of the total). Comparable propulsive efficiency would require a larger single prop but would otherwise be fairly easy to arrange. To get in the ballpark WRT installed power, you'd need to couple 2 L or XL motors to the (single) inboard prop shaft. (Earline clearly shows that it takes more than 1 PF motor to convert available PF battery power into thrust at the required rate.) Problem is, the inboard's displacement would be comparable to that of a finished TSD boat after the necessary overdrive/coupling transmission. A twin-screw inboard would probably be done at that point as well, but a single-screw inboard would need a dedicated steering system -- including a 3rd motor for steering, a rudder, a rudder mechanism, and all the mounts involved. Several speed penalties would come with the added steering load: (i) A monohull inboard would need a City Lines hull (CLH) to carry the necessary propulsion and steering loads. Hence, Nadine would be the comparable TSD boat. (ii) Final inboard displacement would exceed Nadine's by at least 15% at the same waterline length and slenderness -- hence, more hull drag. (iii) Since you can't top Nadine's installed power with PF motors and batteries, the inboard's power/displacement ratio would be that much lower. (iv) Draft would exceed Nadine's, and wetted surface area and bare-hull resistance would increase accordingly. And after all that, appendage drag would still be an issue. To steer a CLH effectively at low speeds and in waves, the rudder would have to be fairly large. Clearance for the large prop would entail a long prop shaft with suitably rigid supports ultimately tied to the deck, as the CLH bottom offers no attachment points aft of midships. Between all that and the large rudder, the inboard could easily end up with a lot more non-hull plastic in the water than Nadine -- hence more appendage drag as well. Even if the inboard ended up with less appendage drag, it's hard to see how that could offset the other penalties. Similar issues have plagued every TSD alternative we've tried, including outboards. Hence, we keep coming back to TSDs as the least of the available evils. All that said, theory goes only so far with boats. You'd have to build such an inboard and put it up against Nadine to be sure.
Jeremy McCreary
 I like it 
matt rowntRee
  December 20, 2014
Looking at all three, I would have put money on this one to be the fastest. Wouldn't be the first time I lost a bet, in fact, I rarely win bets. Maybe I should stop betting. XD I like the sleek look of this one, the bow angle has a beautiful steep angle. I have to wonder if a direct inboard drive would be the fastest for a monohull given the water interference of essentially two outboards, but I suppose they are far enough apart to not factor much. Excellent!
 
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