Da Vinci's Paddleboat Read online

  Da Vinci’s Paddleboat

  Historical Notes and Illustrated Guide for a Scale Model

  Dean A Beeman

  Copyright 2014-2017 Dean A. Beeman

  All Rights Reserved

  No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise without the signed permission from the author. Excerpts made be used for review and promotional purposes.

  Limit of Liability/ Disclaimer of Warranty. As the author points out in the text, the instructions in this book involve the use of sharp and otherwise dangerous tools and other items. The author makes no representation that injury will not occur. The author does not guarantee that the results obtained will be acceptable to any person undertaking this or any related project. The instructions and images may not be suitable for any given situation. The author shall not be liable for any errors or omissions, loss of any amount of money including lost profit or any other personal or commercial damages, including but not limited to special, incidental, consequential, personal injury or any other damages.

  Table of Contents

  Preface

  Background

  Layout

  The Math

  Tools and Materials

  The Template

  The Model

  Preface

  So far, we’ve explored men, the sea, and America. In my opinion those subjects are worthy things to explore. Trying to fully understand any one of them is a fool’s game.

  And until now our boats has been, in one way or another, successful. The philosophy of each one has been clear, and the designers, builders and sponsors were successful. Perhaps the sailors weren’t so lucky, but that’s a sailor’s life.

  This time I’m going to build a power boat that was designed by a landlubber. As a boat, it was a total failure. As a matter of fact it’s famous, but never existed. Which is just as well since, as designed, it couldn’t float or even operate. It’s interesting because those characteristics aren’t the point.

  At the dawn of machines (the 15th century or so), it was common for what we now call engineers to create a rendering of a final product without revealing the mysteries of how it worked, or for that matter, that it worked at all. (If you think that anything has changed since then, consider how many fortunes have been made in Silicon Valley on precisely the same premise and evidence.)

  To demonstrate 21st century thinking I’m sticking with hype and hope but throwing practicality out the window.

  So, we’re going to build a power boat as an object of 15th century entrepreneurship and its 21st century legacy, but not as a power boat. Or even a boat, for that matter.

  In case you’ve been following the construction of ships that aren’t really ships and boats that aren’t really boats, I’m on my way to the extreme. (A sailor’s sense of humor is something we should have addressed before now.)

  And since I’m a Buonarroti fan I tried to somehow fit a gravy boat into this whole subject. No luck. So, we’re stuck with Da Vinci.

  Background

  Sometime in the early 15th century an Italian engineer by the name of Mariano di Jacopo detto il Taccola (Taccola) rendered his concept of a boat powered by rotary paddles. That boat, as drawn, was powered (more or less) by what we now know as a winch.

  Much later in that century a young man named Leonardo Da Vinci theorized that such a simple mechanical device could be improved if its driving mechanism could be replaced by a machine- in other words, moving parts that acted together to perform the same function. Enter the whole subject of gears.

  Improvements and documentation on the basic theory of the gear and the screw date back at least to Archimedes. (And while the ancient Chinese, Greeks and Egyptians knew (and in many cases documented) most of what was found in Da Vinci's notebooks, they didn't paint the Mona Lisa, so they've been screwed out of the credit for things like the helicopter and the armored tank. As a matter of fact, prehistoric humans who observed a frog, a dragonfly or a beetle stand unacknowledged, too.)

  But single details in a mural or charcoal image on the wall of a cave just aren’t the same as thousands of pages of detailed art.

  We’ve discussed the value of works-in-progress, and the enforcement of fair play associated with the whole concept of copyright. Since it’s unlikely that any human will ever match the volumes of such work recorded by Da Vinci, civilized people have a responsibility to preserve them.

  The original sketches that make up the Codex Atlanticus reside in the Bibliotheca Ambrosiana, Milan, Italy. I’m going to have some light fun with one of those sketches (and a few others), but that doesn’t mean that you and I shouldn’t contribute to their preservation by recognizing the value of whatever copyright resides with that library.

  My references for Da Vinci’s sketches can be found online, or in various texts. I own a copy of “Leonardo’s Machines- Da Vinci’s Inventions Revealed”, C. David & Charles Limited 2006, originally published by Guinti Editore, C. 2005, Florence-Milan. While the images are enlightening, the text is often one gear short of a workable machine.

  The authors note that none of Da Vinci’s machines was built during his lifetime. I doubt that. I’ve concluded that some models were built, and the model-makers and I reached the same conclusions.

  Anyway, in folio 945r in the Codex Atlanticus, Da Vinci presents a sketch of what appears to be a boat and its mechanism. The probable details of its mechanism could, according to some authors, be found in folio 30v and perhaps folio 24r.

  Let’s start with the finished drawing from folio 30v (this machine is reportedly similar to a set of drawings by Francesco di Giorgio). Some writers have implied that this winch is the basis for the power that later appeared on Da Vinci’s paddleboat.

  In Da Vinci’s formal schematic, an opposing pair of internal, saw-toothed gears are driven by a pair of opposing pawls. If the drive shaft is turned in one direction (by a lever in this case), the first drive pawl catches a gear tooth and moves that gear in one direction, while the other pawl rides over its saw-tooth. Move the lever in the other direction and the second (riding) pawl now drives its gear in the opposite direction of the first while the first pawl rides.

  Unfortunately, for two fixed gears on a single drive shaft to drive a third gear forward you need a fourth gear to reverse one of the first two. Or split the drive shaft, resulting in the same, but more dramatic, outcome.

  If you doubt that, find a copy of the drawing (folio 30v) and draw arrows associated with the lever direction on the finished figure to the right of the exploded view. The drive gears will continuously move in opposite directions, but the weight on the pulley isn’t going anywhere.

  But to his credit, Da Vinci sketched his theory in great detail.

  On to the paddleboat, folio (page) 945r.

  As best I can recall, my grades in Art as a grammar school subject were not discussed with my parents. (There were equally-depressing grades in other subjects that I keenly recall.)

  So, my rendering of folio 945r is right up there with a stick figure drawing of a cloud. But I’m providing it so you’ll get a feeling for the image that you might want to study on the web:

  There is roughly a 4:1 speed advantage by having a large drum (in the foreground) drive a smaller gear on the paddle’s drive axle (at the top). That might be OK if the smaller gears were hardened steel, but given the resistance (water) on the very large paddles these wooden gears would have shredded in short order, even with a fourth gear.

  If the resistance could be managed by lowering the water resistance (smaller paddles, less depth, etc.), we’re still stuck with the machine. Step down on one peddle and the dr
ive gears go forward, driven by the rotation of the drive drum, Step down on the other peddle and the drive drum reverses and, like the winch, the drive gears reverse, too. The saw tooth gears are very similar to the previous drawing. So, this boat isn’t going anywhere, either.

  You will discover that there are many models and drawings available that attempt to resolve this dilemma. Most simply leave off a gear or two, so something can rotate. Others add a seesaw set of drive pedals or eliminate the belt and pedals altogether. If you wander through several online images and study the meshing of gears you’ll soon get the gist of these excuses.

  Frankly I think we can solve the engineering problem with some minor slight-of-hand. We’ll see how that goes.

  A more practical design than the one I’ve chosen can be found in folio 1063 and elsewhere. In that case the machine gears are replaced by direct drive crank handles. That version might work on a very small boat (the size that people pedal around resort ponds), but not on the Arno.

  And as presented in yet another example, these cranks drive large iron flywheels that in turn power the paddle wheels. That inertial version might work a little better, but it isn’t nearly as much fun to build.

  I wouldn’t call any of the other boats in this series a work of art. But in this case, we don’t have much choice since it wasn’t a boat to begin with. So, I’m going to build it for the sole purpose of enjoying how a bunch of wooden pieces (mostly scrap from other models) can be assembled into a very pleasant but fatal contribution to the subject of power boats. And the timeless nature of well-intentioned ideas.

  I also considered (given those subjects), John Fitch’s Perserverance. But since we’ve already given him credit (in the Steamboat) for the same contribution, it’s time to move on.

  I’ve also decided to have some fun with dangling participles.

  Before I leave the weighty subjects that we’ve been considering, it occurred to me that Da Vinci would have been much more successful if he had the benefit of some 20th century communications tools. You are all familiar (or at least have imagined) the dreaded Conference or Board room exercises in bloviated logic.

  I happen to believe that 15th century nobles, like their modern counterparts, would have been much more supportive of Da Vinci if he had been able to create a PowerPoint request for funding:

  Layout

  The most difficult part of recreating any of Da Vinci’s machine concepts is the studded wheel (external gear). Sooner or later, a studded gear drives a cage gear (the small gears in the drawings). These all require more-or-less perfect circles and spacing of teeth. Or you're stuck with a very bumpy machine.

  While most of his designs consist of large (main) gears with teeth that are spaced at a simple and easy-to-draw 10 degrees (more or less), in those designs you still must install 36 teeth in an inner circle and another 36 on the outer rim of the same circle. We’ve been through the tolerances of wood, and that many teeth on a 6’ wheel might be one thing, but getting that many onto a one-inch wheel will be a squeeze.

  But any size difference in the gears results in differing angles due to the meshing of their teeth with the teeth of the main gear, and any radius that is not a multiple of 10 degrees will eventually cause a set of gears to jam, even with wide tolerances (spacing). And I intend to power the paddles.

  And one inch is about the right size for, say, a tree ornament.

  Since Da Vinci and his peers either didn’t know or didn’t care about scale, I see no reason why I should. But gears require consistency of angle and, if you get into the subject, about a dozen other characteristics.

  Let’s start with all the important components:

  Looking at the circle (lower right), I’m starting with a gear that has a diameter of 1”. That particular circle has been carved up into 10-degree radii. I have extended these so you can use a compass and create the same pattern at whatever size you choose.

  Now if you doubt that 10 degrees was a staple of Da Vinci’s sketches, here is that same circle overlaid on Vitruvius (the Vitruvian Man):

  (This sketch has been copied, edited and otherwise reproduced so many times that copyright protection is another fool's game.)

  Back to business, the smaller circle in my schematic is ¼ the size of the larger, and the red lines on that circle are drawn at 40 degrees.

  So, any set of teeth on one wheel should (will) mesh with the gear teeth on the other.

  The paddle is a paddle. If you don't like mine, have at it.

  The Math

  If you locate an original drawing and simply count and extrapolate what can be seen in Da Vinci’s sketch, the gear count is as follows:

  Main drive gear: 36 spindles, 18 teeth

  Intermediate Drive Gear

  Interior18 teeth

  Outer12 teeth

  Cage (small) gear6 spindles

  The diameter of the main drive gear is 77% (roughly) of the diameter of the intermediate gear. This is to compensate for the meshing of the main gear with the interior gears of the intermediate gear. Once the intermediate gear is turned by the main gear the tooth count on the outer and cage gear must be multiples of each other, but could be any number that is evenly divided by 360. Da Vinci apparently chose 6 and 12. The ratio of the intermediate gear to the diameter of the small cage gear is about 4:1.

  Keep in mind that he was still a young man who was educating himself (probably through the discipline of his sketches), so numerical uniformity was not high on his list of interesting subjects. And given the ratios, his paddleboat was capable of reaching a speed (by my math) of at least 30mph (if the components didn’t disintegrate, the paddles moved in the right direction and he had added a gear or two).

  So, while some optimists have given him (very) dubious credit for inventing the automobile, I think he was closer to the first F1 power boat. (Getting back to Guy Lombardo, he might have been whacky enough about boats to try it.)

  Tools and Materials

  Every model-building text starts with a tool description. I built my first scratch model using a machinist’s rule, a razor blade and scraps of sandpaper. That model took a while, and I’ve only added tools that fit what I needed. My advice is to read the text, figure out what tools might be handy, and buy them only if you feel you need them. What comes next is the result of many, many models, including the ones in this series.

  While I started this series of books with a description of a set of tools for each model, the sets began to look very similar, so here are most of the things I use every day. (In order left to right, top to bottom.)

  Scrap Bins- one for short and one for long scraps. Indispensable.

  Cord Box. In this assortment, I have rigging cords that start at .008 all the way up through sewing thread, button thread and 48-pound hemp.

  Clamp Box. In here you’ll find wooden clothespins, adjustable bar clamps, bulldog clamps and paper clamps. Almost hidden in front of that are a couple of ship model planking clamps- I have many more, and they are very handy.

  Sanding Wands. I’ll describe these later. There are also some emery boards, a round, small wand and one scrap of many scraps of sandpaper.

  Micro files. Sharp and broken-off round, plus the normal assortment. Very handy.

  Fences. These are metal rulers, a machinist’s rule and a machinist’s square. All stainless steel, to stand up to the knife blades.

  Loupe. Only handy if your eyesight is as bad as mine and the work is tiny. (It will be tiny as we go along.)

  Glues. CA gel, craft and wood glue. Mandatory.

  Template Bin and wire. All small templates, subassemblies and small parts I’m working with on a given model go in here or they’ll get lost. We won’t be using that much wire or brass rod.

  Pin Board. This once was a piece of foam craft board that now has hat pins and various other pins that I use for marking, gluing, clamping and other things that I forget until I need a specific pin. Stuck into the side are sewing needles of various sizes- there is no logic to explai
n how they got there.

  Scissors. Any sharp pair will do.

  Step gauge. You can’t see this too well, but this homemade gauge is cut (stepped off) in 1mm increments from 1-5mm. I have another one stepped off in 1/32nds. As you’ll see when we stab-mark and cut thin strips of basswood these make the job simple and repeatable. If I know I’ll be working in large increments like these, this is also how I measure and cut at the same time.

  Tweezers. Large and small, and sooner or later you’ll be filing the tips because they just don’t work right until you do. The tape on a couple of these is to disable the locking feature- sometimes that feature is good, but the spring-loaded pair on the right is usually better.

  Masking tape and Q-tips.