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Lucille
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Lucille is a seaworthy and exceptionally maneuverable 0.595 kg, 2.5W inboard-outboard monohull powerboat based on the rare 52x16x6 unitary hull -- the 2nd largest available. A single-XL inboard motor and pivoting stern drive give her decent speed, but her gearing still needs work.
About this creation
Please feel free to look over the images and skip the verbiage.

See also:
Lucille II, the optimized version of this boat.

On this page



Introduction

Shawn Kelly and I have been avidly building, racing, and occasionally sinking Power Functions (PF) remote control (RC) speedboats for over a year now. In fact, it's become something of an obsession for us. To date, we've come up with at least 2 dozen seaworthy no-frills LEGO® powerboats (mostly no-frills speedboats) based on various LEGO® unitary hulls (LUHs). We've also dabbled in LUH-based motorized ship models like Stormin' Norma, 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.



The video above shows Lucille doing some low-speed maneuvering in the tub.




Overview

Lucille is a very seaworthy and exceptionally maneuverable 0.595 kg, 2.5W inboard-outboard monohull powerboat based on the 2nd largest LUH available -- the 56x16x6 LU Family Yacht hull (FYH).









Like her sister Earline (below), Lucille's main strengths are maneuverability and seaworthiness. She's more maneuverable than most of our boats with screw propellers, including Earline, and may even rival Tramontana in that regard.

Though certainly not slow by LEGO® standards, Lucille looks to be slower than Earline and a good bit slower than our fastest boat, Nadine.



Lucille's 2.5W propulsion system consists of (i) a single inboard XL motor powered by a 7.4V PF Li polymer rechargeable battery via a V2 IR receiver, (ii) an efficient pivoting stern drive with 3-stage 1:4.63 overdrive gearing, and (iii) a very efficient third-party 55 mm 3-blade prop.















I should emphasize that Lucille's motor/gearing/prop combination has yet to be optimized. I have 2 somwehat conflicting concerns: (i) Her motor shaft speed may be too far off the ideal 90 RPM at top speed with her current overdrive ratio. (ii) Her 55 mm prop may be overloaded by the high resistance associated with her greater than average breadth, low length-breadth ratio (L/B), and very rough bottom. If so, retreating to a 52 mm prop could well improve her top speed. Only further testing will tell.

The rationale behind the third-party prop is discussed here, and the motor/gearing/prop optimization process, here.

Lucille's newly developed stern drive pivots on a small Technic turntable. Her PF servo steering motor drives the 28-tooth turntable gear via a 36-tooth double-bevel.





Thrust vectoring over a ±115° steering angle range makes Lucille the most maneuverable of all my boats with conventional propellers by a wide margin. The grid below her stern drive at hard to port, dead ahead, and hard to starboard.







Lucille can't match the maneuverability of the Voith-Schneider propeller test boat shown below (MOCpage coming soon) in that she'll never be able to move directly to the side like the VSP boat can, but she comes pretty close otherwise and is much, much faster.








Design goals and issues

I built Lucille for 3 main reasons: (i) To see if I could beat Earline's maneuverability with a pivoting stern drive, (ii) to see if I could make the stern drive lighter and smaller than Earline's outboard by moving the propulsion motor inboard, and (iii) to test the powerboat compatibility of the Family Yacht hull Shawn Kelly loaned me.

She has yet to see open water, but tub trials suggest better than average stability and seakeeping ability, as one would expect from a boat with a generous waterline breadth and high breadth-draft ratio (see her stats below).



Speed

Lucille hasn't been properly clocked or raced yet, but I'm guessing that she does at least 0.75 m/s (Froude number ≥0.40).



She's definitely slower than our fastest 3 boats (above): Long, blue Nadine (0.855 kg, 4.9W, 5.9 W/kg, 0.540 m, 0.99 m/s) in the distance, Laverne (0.545 kg, 4.3W, 7.9 W/kg, 0.345 m, ~0.97 m/s) in the middle, and Trident in the foreground (0.495 kg, 4.3W, 8.7 W/kg, 0.372 m, ~0.95 m/s).

Lucille has lots of reasons to be slower than these boats: (i) For starters, her installed power to displacement ratio (only 4.1 W/kg) is significantly lower. (ii) She's much shorter than Nadine but almost as broad at waterline. (iii) Her waterline length (0.364 m) is comparable to Laverne's (0.345 m) and Trident's (0.374 m), but she's much broader than either of them. (iv) With the lowest waterline length-breadth ratio (3.1) of all our boats, she's also anything but slender. (iv) Her FYH has the roughest bottom to be found on any unitary hull.

Together, these disadvantages suggest higher viscous resistance, wave-making resistance, and total resistance than our 3 fastest boats face.



Control

Like Earline, Lucille's best operated with a dual PF 3-state (full forward, full reverse, off) handset and speed control like the one above (more info on the speed control mod here).





The 3-state on the right is good for full-throttle starts, emergency braking, and abrupt hard to port and hard to starboard turns. The attached speed control on the left allows more nuanced operation but response lags at the receiving end are noticeably longer, as usual.

The speed control on the left provides 15-step adjustment of prop power from full forward (+7) to full reverse (-7) and 15-step adjustment of steering angle in ~16° increments. The resulting steering angle range of ±115° is more than enough to make Lucille our most maneuverable boat with screw propellers.

Steering servo return-to-center accuracy is excellent, as usual, but that of the stern drive is less than perfect, as explained in the next section.



Having steering and propulsion on the same IR channel allows me to switch back and forth between handsets for either steering or propulsion while underway. I generally prefer this more flexible single-channel mode, but it does have some drawbacks.

Earline's dual receivers give the operator the ability to defer the decision to run in single- or dual-channel mode until launch time. (The current-hungry propulsion motor always goes on her V2 receiver.) The same could be done for Lucille.





Steering issues

Lucille loses a bit of return-to-center accuracy -- an absolute must for play value and controllability (hence seaworthiness) in single-screw boats -- to the backlash and half-tooth misalignment problem inherent in all gear-based steering mechanisms. Linkage-based steering mechanisms like Earline's (below) eliminate these problems, but initial stabs at steering linkages for Lucille ran afoul of FYH-related fore-aft balance and stern drive mounting issues.

The half-tooth misalignment issue deserves some explanation. First, some observations: (i) With the exception of the old 14-tooth single-bevel, all LEGO® gear tooth counts (8, 12, 16, 20, 24, 28, 36, 40, 48, 56) are whole-number multiples of four. (ii) Each of the 4 splines on a cross-axle aligns with a tooth. (iii) Turntable gears are also aligned with teeth at 0°, 90°, 180°, and 270° to available mounts.

As a consequence, when the steering servo returns to center, the 36-tooth gear on its shaft has 2 teeth in the hull's centerline plane -- one pointing forward and the other aft. Since this gear meshes with the 28-tooth gear on the small turntable serving as the stern drive's pivot bearing, it follows that the stepper motor and stern drive can't be aligned with the centerline plane at the same time.

Hence, centering the stepper motor leaves the stern drive off-center by half a tooth on the 28-tooth turtable gear -- i.e., by (360° / 28) / 2 = 6.4°, as shown in the photo below. A stern drive pivot made from a large turnable (56 teeth) would cut that error in half, but all of mine were tied up elsewhere.



I have yet to find an easy fix for this gotcha. Compensating by steering one click in the opposite direction with a speed control handset was out, as Lucille's steering angle steps are ~16° apart. Continuous steering angle adjustment could be had by replacing her steering servo with a regular motor, but I knew from experience that steering accuracy and reliability would suffer tremendously, as it's virtually impossible to go right to a specific steering angle, even with a steering worm drive and lots of practice. Cancelling the error by inserting a 28-tooth idler between the 36-tooth gear and the turntable would be difficult for a host of practical reasons, but the added backlash turned out to be the deal-killer there, as not only return-to-center reliability but steering reliability in general would then go right out the window. Finally, an EV3-based solution comes to mind, but I doubt that the FYH could support the added displacement gracefully.




More photos



Lucille could easily be the poster-child for shaft reinforcement. Long drive shafts are generally to be avoided in high-torque settings like this one, but load balance requirements left me little choice here.

Building up a propulsion drive shaft from 180° angle connectors and supporting it at mid-span kept power losses due to shaft sag and torsion to a minimum. Two shaft supports would probably have been better.



Her Family Yacht hull has the same unfavorable bottom texture as the Cargo Carrier and Fishing Boat hulls. There's just a heck of lot more of it in the water.



Add that large, complex bottom recess at the stern (a sure recipe for premature flow separation), and you've got the dirtiest bottom on any LEGO® unitary hull by a wide margin.

Together, the large wetted surface area, extensive bottom roughness, and early flow separation add up to a lot of viscous resistance for a propulsion system to overcome. It would take a lot of patience to fair all those hydrodynamic flaws with electrician's tape, but if you're stuck on an FYH-based speedboat, it might be worth the effort.

The FYH's open stern, also unique among unitary hulls, has its pros and cons. On the positive side, inboard propulsion motors could potentially be located closer their props and lower in the hull. Neither of these potential advantages panned out in Lucille's case, but the former would reduce shaft losses and the mass of propulsion system supports, and the latter would would improve stability by lowering the boat's center of gravity.







On the downside, the FYH's open stern has a sill 2 bricks high on the inside. Hence, the opening provides an easy path for water entry, while the sill traps it onboard. (One of the main attractions of a well-designed open stern is that one can bail a lot of water with a simple punch of the throttle.) The FYH's stern sill is high enough to trap dangerous volumes of water onboard.

The good news: (i) The 6x8 base used to mount the stern drive in the open stern effectively raises the sill another 25 mm or so. (ii) Water percolates the base very slowly when the base is properly seated. (iii) The waterline recedes from the sill as the trough of the first stern transverse wave deepens with forward speed in calm water.

The bad news: (i) The open stern increases the likelihood of taking on green water astern in a following sea. (ii) You can easily create the equivalent of an overtaking wave in calm water by running full astern or cutting power abruptly at full ahead.



Best, then, to keep an eye out for flooding in any FYH-based boat. The 20 cc curved-tip syringe shown above -- the best bailer I've found to date -- is especially good at removing water from corners and between studs.




Comparison with Earline

The photos below show Lucille alongside her bigger sister Earline. Lucille seems slower than Earline in the tub. Granted, that really only means that Earline's faster off the line, but I have every reason to believe that a long course over open water will only make the speed gap more apparent.





Having a breadth, draft, and breadth-draft ratio comparable to Earline's suggests comparable roll stability, but lesser freeboard makes Lucille a little more susceptible to deck wetness and hence a bit less seaworthy in very rough water.



Earline's outboard hangs a lot more mass over the stern than Lucille's FYH can tolerate.

Displacements -- 0.595 kg for Lucille, 0.915 kg for Earline -- differ substantially. As mentioned earlier, there are also substantial differences in waterline length, slenderness, and bottom roughness -- all of which work in Earline's favor WRT top speed.

If both boats were to run at Lucille's top speed, I'd expect Lucille to encounter more total resistance. They should be comparable WRT appendage drag, but Lucille should see more viscous resistance and much more wave-making resistance -- the last due to Lucille's much shorter length and lack of slenderness. Her greater installed power to displacement ratio (4.1 W/kg to Earline's 2.8) doesn't seem to be able to offset that added burden.




Tables of features and stats



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


Overall dimensions:
420 x 126 x 140 mm (LxWxH, excluding stern drive)

Displacement:
0.595 kg (1.3 lb)

Displacement volume:
6.0 x 10 -4 m3

Depth:
48 mm

Waterline length:
364 mm

Waterline breadth:
116 mm

Draft at keel:
16 mm (midships)

Freeboard:
32 mm (midships)

Wetted surface area:
n/a2

Midship section area:
1.8 x 10 -3 m2

Waterplane area:
3.8 x 10 -2 m2

Block coefficient:
0.88

Prismatic coefficient:
0.88

Midship coefficient:
~0.99

Waterplane area coefficient:
0.90

Length-breadth ratio:
3.1

Breadth-draft ratio:
7.3

Length-displacement ratio:
4.3




Performance measures

Installed power:
2.5W

Installed power to displacement ratio:
4.1 W/kg

Top speed:
~0.75 m/s (conservative estimate)

Critical speed:
0.76 m/s

Froude number at top speed:
~0.40

Reynolds number at top speed:
~2.7 x 105

Static thrust:
[] N m at [] motor shaft RPM ([]% of no-load speed)




Design features

Construction:

Mostly studded

Hull:

Unitary 52x16x5 LU Family Yacht hull (Set 5848)

Propulsion:
Inboard-outboard with pivoting stern drive

Motors:
2 -- inboard XL for propulsion; outboard PF servo for steering

Propeller:
55 mm 3-blade (non-LEGO®)

Gearing:
3-stage 1:4.63 overdrive

Steering:
Stern drive thrust vectoring via PF servo motor

Steering angle range:
±115°

Electrical power supply:

Power Functions 7.4V Li polymer rechargeable battery

IR receivers:
V2

IR receiver connections:
2, 1 for each motor

Modified LEGO® parts:

Prop hub

Non-LEGO® parts:
Prop

Credits:

Entirely original MOC





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

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

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 
  January 5, 2015
Thanks to all for the kind words. Matt R.: Yeah, the VSPs are fascinating. I'll be posting that VSP boat in the next week or so. You'd probably get a kick out of the Voith Water Tractor (VWT) simulator app called iVSP for iPhone and Android. (Published by Voith, but I got it from Google Play.) A VWT is a tractor tug propelled by a pair of VSPs near the bow. iVSP has an inset that shows how the blades adjust their angle of attack as you steer the tug. Very cool.
Jeremy McCreary
 I like it 
matt rowntRee
  January 4, 2015
That VSP system is truly strange, like someone with a ton of money got to looking at an egg beater. Can't wait to see her at work, looks stable and amazingly maneuverable. Lucille looked like she might be faster being an inboard but it would seem that everything effects everything again. Oh well, still looks fun. Sweet!
Jeremy McCreary
 I like it 
Matt Bace
  January 1, 2015
Wow! This look like a major science project in the works.
 I like it 
  January 1, 2015
awesome :)
 
By Jeremy McCreary
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