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Lucille II
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Lucille II is an exceptionally agile 0.62 kg, 2.5W single-screw inboard-outboard powerboat based on the 52x16x6 Family Yacht hull. A not-so-simple change in overdrive gearing ratio allows her to wrings a good bit more speed out of the same hull, battery, motor, and prop used by the original Lucille.
About this creation
Please feel free to look over the images and skip the verbiage.

See also:
Lucille, the original version of this boat prior to drivetrain optimization.

On this page



Introduction

I usually optimize MOC propulsion systems before posting them, but I got ahead of myself with the original Lucille (below).



The iterative process of optimizing a powerboat for top speed is described here in some detail. The variables to be juggled are (i) total resistance in the target speed range, (ii) battery and IR receiver selection, (iii) motor selection, (iv) prop selection, and last but by no means least, (v) the final overdrive ratio between motor and prop.

If nothing else, the variety of designs found in this Motorized boats and ships folder speaks to the value of keeping an open mind to all the possibilities and trade-offs inherent in the list above.

The juggling act might even be manageable if the listed inputs were independent of each other, but that's not the way powerboats work. Instead, every little thing affects everything else big-time.

Best, then, to maintain one's sanity by (i) settling on an overall boat concept, and (ii) narrowing the choices accordingly before the juggling begins.

For both Lucilles, the 2 factors with the most influence on total resistance -- namely, hull selection and appendage design -- were largely pre-ordained by the desire to try my hand at a highly maneuverable inboard-outboard based on a newly acquired Family Yacht hull. Final operating displacement would then determined mainly by battery and motor selection.



The motor and battery choices were easy. In a hull easily capable of handling the weight of 2 XLs, the need to maximize installed power with a single motor could only mean an XL.

The battery was also a no-brainer, as the 7.4V PF Li polymer rechargeable would maximize sustained power output to the current-hungry XL while minimizing displacement. With those choices made, the IR receiver could only be a high-current V2 (not shown in these photos).

That narrowed the juggling down to prop and overdrive ratio. Though virtually impossible in a moving non-Mindstorms LEGO® boat, measuring shaft speed at full power with a hand-held laser tachometer while holding the boat still in the water, as in a static thrust test, is almost as good. Trident demonstrates a static thrust test in the video below:



Testing quickly ruled out original Lucille's 1:4.63 overdrive ratio (3 stages, 20:12 each), as it resulted in a motor shaft speed ~50% above optimum with a 55 mm prop. That immediately ruled out the only other prop I had (52 mm, same design), as it would have made motor shaft even higher at 1:4.63. It also ruled out the next available ratio of 1:5 (36:12 and 20:12). Hence I went straight to next higher overdrive ratio of 1:8.33 (36:12, 20:12, and 20:12).

It took a lot of beefing-up of the upper part of the stern drive, where the 1st two overdrive stages reside, to realize that 1:8.33 overdrive ratio without gear skipping. Other changes had to be made as well, but shaft speed was thankfully spot-on at 88 RPM with the 55 mm prop -- the first one I tried.

Optimization complete! Hence, Lucille II below, with an updated XL/8.33/55 drive train.





Though ostensibly much like the original Lucille, her optimal 1:8.33 overdrive ratio -- nearly double that of the original -- wrings noticeably more speed out of the same hull, appendages, battery, XL motor, and 55 mm prop.

Whether that performance boost will be enough to beat Earline -- the only other boat I've powered with a single XL motor, but with a very different (and most importantly, much longer) hull -- remains to be seen.






Overview

Like the original Lucille, Lucille II is a 2.5W inboard-outboard monohull powerboat based on the 2nd largest LUH available -- the 56x16x6 LU Family Yacht hull (FYH). And like outboard-driven Earline, both Lucilles excel in maneuverability and seaworthiness.

Though clearly faster than the original Lucille, Lucille II is still a good bit slower than our fastest boat at the time, 4.9W twin-XL Nadine below.



The next 5 photos show Lucille II in her entirety from additional angles.














What changed

Lucille II displaces 0.620 kg now, up 0.025 kg from the original Lucille. Most of the added mass went into the beefed-up axle support needed to handle the higher shaft loads associated with the new 1:8.33 overdrive ratio. A new PF extension cable needed to move the IR receiver forward to counterbalance the new stern drive's added mass accounts for rest of the displacement increase.











Before and after: The upper photo below shows the first 2 stages of the original Lucille's lighter and more compact 1:4.63 overdrive transmission. The lower photo shows the extra axle support needed to eliminate gear skipping in a 1:8.33 overdrive transmission connecting the same XL motor and 55 mm prop. The 3rd overdrive stage is on the prop shaft in both cases.





To accommodate a 36-tooth gear in the stern drive, I had to raise the inboard XL motor and drive shaft by 1 LU relative to the hull. To compensate for the new stern drive's greater and somewhat differently distributed mass, I had to move the XL motor 3 LU forward, the IR receiver tower 2 LU forward and starboard, and the battery 1 LU forward. This rebalancing resulted in a slightly more level keel and a little more resting freeboard astern.





The 6x8 studded base used to adapt the stern drive to the hull's open stern is completely above waterline at rest and full forward speed now but still gets immersed by overtaking waves and when running astern.



To slow the rate at which water percolates through the base, I reduced its porosity by plugging the half-pins seen here with Lucille II's only modified parts other than her prop hub -- pieces of 3 mm bar cut from antennas.










What was retained

Both Lucilles use a 2.5W propulsion system consisting 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 overdrive gearing, and (iii) the same efficient third-party 55 mm 3-blade prop.

Functionally, they differ only in their overdrive ratios between motor and prop: 1.8.33 for Lucille II vs. 1:4.63 for the original.

The lower part of the stern drive hasn't changed. As before, the stern drive pivots on a small Technic turntable driven by a PF servo steering motor drives via a 36-tooth double-bevel. The return-to-center accuracy issue resulting from this gear-driven steering mechanism remains.





The rationale behind the third-party prop is discussed here.

Lucille II still has the original's ±115° steering angle range. With the possible exception of Tramontana, this range makes the 2 Lucilles the most maneuverable of all my boats with screw propellers. The sequence below shows the original Lucille's stern drive at hard to port, dead ahead, and hard to starboard.







NB: For additional details, including info about hull resistance and more on coping with the open stern, see original Lucille's MOCpage.




Specifications

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:0.620 kg (1.4 lb)
Displacement volume:6.2 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:4.0 W/kg
Top speed:~0.80 m/s (conservative estimate)
Critical speed:0.76 m/s
Froude number at top speed:~0.42
Reynolds number at top speed:~2.9 x 105
Static thrust:[] N m at motor shaft speed of 89 RPM (49% no-load speed)




Design features
Construction:
Studded and studless
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 1:8.33 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, plugs for half-pins in stern drive base
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

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 
  August 17, 2017
Quoting Seaman SPb Excellent!
Thanks, Seaman!
 I like it 
  August 17, 2017
Excellent!
 I made it 
  January 9, 2015
Quoting Nerds forprez Wonderful job Jeremy! As always, your attention to functionality and detail is superior. Your write-ups of findings is second to no one. Very informative.
Nerds forpres, Comments like that make the time spent on the write-up worthwhile, but I have to admit they have a selfish motivation as well: Nothing makes it clearer that I really don't understand something as well as I thought than when I try to explain it in writing.
 I made it 
  January 9, 2015
Quoting Yann (XY EZ) Awesome moc! This is true engineering. Thanks for the documentation as well ! 5/5
Yann, thanks for your continued encouragement. It's greatly appreciated.
 I made it 
  January 9, 2015
Quoting Walter Lee awesome write up and photos. Thanks for sharing this!
Thanks, Walter.
 I like it 
  January 8, 2015
Wonderful job Jeremy! As always, your attention to functionality and detail is superior. Your write-ups of findings is second to no one. Very informative.
 I like it 
  January 5, 2015
Awesome moc! This is true engineering. Thanks for the documentation as well ! 5/5
 I like it 
  January 5, 2015
awesome write up and photos. Thanks for sharing this!
 
By Jeremy McCreary
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