I am going to build another Pert now that I have an idea of what to do and I have started that quest by buying two more motors at $10 each from Princess Auto in London ON. As I said earlier these only come as a Left Hand model and have to be disassembled and rotated to become a RH model. To do that I removed the four screws on the worm gear shaft end and screwed it onto the other side. They have identical screw hole locations but are mirror images of each other. I also replaced the through screws with longer ones in order to attach the motor to a bracket which in turn will be attached to the ship. I had a peek at the brush end and discovered it has a nice little circuit (snubber) to prevent arcing and Radio Frequency Interference (RFI). However that seems to play badly with the 2kHz signal from the ESC. More work to do there. The brushes and commutator appear to be brand new. Of course, I had to remove the armature to spring the brushes back onto the commutator. To put the electrical connector in a more accessible position I rotated the body through 180 degrees but had to remove a resin keying pip with a hacksaw and knife..

I had mentioned that the archives had an incorrect description of one of the drawings. Here is the original description and is a caution that sometimes things just get misfiled .... stuff happens ... and that when researching we should keep an open mind to the possibilities that we may have missed something in spite of our best efforts. Since ordering this print the description has been deleted and, once again, the prints are gorgeous:

DHL delivered my National Marine Museum Thronycroft prints/drawings (a Christmas present to myself) this morning and they are crisp on elegant paper ... works of art I must say.
0. less than two weeks from order to delivery and at Christmas time too.
1. solid tube packaging
2. rolled, no creases
3. crisp photography and printing and coloured!!
I had to compete for room on the dining room table!

Pert has independent paddle drive and can therefore spin on a dime (penny?). But getting her to go straight requires balancing her two motors to give roughly equal thrust on each side. It is much simpler to change direction by a limited amount of rudder input than messing with the motor control, be it both motors on one stick or one motor on each stick. Side-wheelers were very appealing to the navy as they could maneuver large aircraft carriers into position, pushing and tugging with great dexterity. They were only replaced when technological changes in design were developed eg. electric drives, bow thrusters and steerable Kort nozzles. Furthermore, every competitive sailor knows that the rudder acts as a Great Big Brake costing seconds to the finish line. That is not a problem here as the only thing on the pond to avoid are those really fast and cheap things in the hands of immat .... OK Rob, cut the Rant! Be nice. 😂

Pert's rudder uses a miniature servo tucked into her stern, very close to the bell crank. Because there is no propeller shaft and the rudder shaft tube exits above the water line and the hull is solid polystyrene then there is no leakage to worry about.

I put up some more information about the motors on the original post but there are several requests for more, specifically, how fast.
How fast is fast? I run my S7 (1/43) trains at scale speeds. I don't like tearing around the layout flat out. It annoys me and damages the loco.
The motor runs at 180rpm on 12 Vdc. It behaves relatively linearly running at 90 rpm on 6Vdc. I have not altered the gearing. I use Radiolink ESCs, CL9030, one on each motor. I believe that the graph below may be for this motor. I have some work to do on the Radiolink ESC-Motor combination. It goes into an awful noise resonance due to the ESC 2kHz pulse width modulation (PWM) which may be cured with a simple snubber network at the motor terminals. I have to experiment on this. I will scope the ESC tomorrow and report back.
The combination of this motor and my simple paddle throws too much water at 12Vdc and I trust that a lower voltage will produce a much more rewarding pond experience. We will see. Unfortunately the weather is most inclement at this time of the year in Southern Ontario, resembling at best, gale conditions on the south coast of the IOW. The wind rips across Lake Erie tearing off roof shingles from my house, burying Buffalo in 4 ft snowdrifts and creating a 4ft seiche. The summers are very satisfying though, much better than Lee-on-the-Solent. I have not yet sailed the boat on the pond but if we get a nice sunny day I will shoot a video.
Can somebody please tell me how to reply to questions and comments which appear below these posts? I don't see a reply button.
Edits:
1. Snubber
A snubber is a filter circuit which reduces ringing or arcing in an inductive circuit. In its simplest form it is a capacitor soldered across the terminals of a motor. More effective snubbers will use a network of passive devices (resistors, capacitors and inductors).
The most effective snubbers use an elaborate combination of both passive and active devices (eg. specialised diodes)
A few minutes visiting the site below (electronics.stackexchange.com) would be rewarding.
2. Battery voltage choice
I went with a 12V lead acid battery because:
a. it is cheaper
b. it is well understood
c. it is heavy and adds to the ship's low point ballast (metacentric height and all that)
d. I did not know what to expect as I went along on the electrics so this gave me options (I have never used ESCs before, at the most only three servos for my sailboats)
e. the Radiolink ESCs have a BEC
3. About The photo of myself in the Lab at the college: Note the whiteboard: It has the first student experiment+theory on filters 🤔🙄😁 ... great stuff ... fun to teach.

To stop Pert from bouncing around like a cork I will have more stuff to say about metacentric height and moment of inertia decisions in my next post ... standby one mike-bravo ...

I have decided to build a more accurate and robust model of HMS Pert thus I ordered a set of four Admiralty drawings from the National Maritime Museum at the Royal Museums Greenwich (rmg). These are scaled at 1/4" = 1 ft. that is, 1/48 such that a large surface is required to lay them out flat. The total cost of the set was 239.00GBP plus 20.00GBP shipping. Ouch. Note that on the attached photos the drawings are not on line except for four blurry thumbnails, one of which was included on my original post of HMS Pert. Clicking on the thumbnail image gives you more information ... and the price. Ugh.
As for why this particular ship, Pert, was selected for printing, I have no idea. But there she is (lucky me) and I did not have to travel 5,000 miles to see them since they are in the Caird Reading Room and none of that material is on line. Are there more drawings? Who knows. Until I ordered a set, the description of the drawing at the museum's website described a 17th century sailing brig. That has since changed. Research can be such a frustrating paper chase. And expensive.
Furthermore, the thumbnails are not at the rmg. website but rather at a print website:

https://prints.rmg.co.uk/search?q=pert&type=product

Pert was a Robust Class Royal Navy tug that served in both World Wars in several ports along England's southern coast and flew the Blue Ensign. She was constructed by J Thornycroft and commissioned in 1916 then broken up in 1962. During both wars she carried a Navy QF HA 12 pounder gun which was promptly removed at the end of hostilities both times. Her paddles were independent, driven by two double acting steam engines generating 1000 ihp each. She was 178 feet overall, 36 foot beam, 56 feet across paddle boxes, drew 12 ft of water and displaced 1023 tons.

My scratch built pond model of Pert was started in September this year. She is 47 inches loa, displaces 40 lbs, is "stand-off scale" at 1:48 and is radio controlled. Her hull was assembled from one inch thick polystyrene in the bread and butter method then carved and "rasped" to shape. The finished hull was sheathed in grocery store flyers and a water based varnish then painted with ordinary indoor/outdoor paint. Most of the deck is glued up or soldered from cardstock, foamcore, spruce and brass wire. The paddle drive motors were purchased from an auto surplus store and were initially designed for window openers . They turn at 180 rpm and draw 2Amps when loaded. Although I own two Spectrum transmitters, Spectrum does not sell a an ESC capable of driving a 12Vdc brushed motor so I elected to buy from a newish RC manufacturer, Radiolink which had the system and parts at a reasonable cost. We shall see how that turns out. The paddles themselves are the simplest design I could build and for that I make no apologies since only a vary narrow part of the paddle is visible when in operation. As I said, stand-off scale 😊

Resources were mainly a precious few photos but I chanced on four thumbnails at the National Maritime museum in Greenwich and these have proved invaluable. Additional information is apparently available in the reading room but this requires either personal, or hired researcher, attendance. At present she rests on a drydock module on my Scale 7 (7mm to the foot) model railway but once spring is here I will trim her out at the pond. After a three month build, and almost finished on the build, I broke down and bought the four plans sheets from the museum print service. Cost me more than the entire build! But I have decided to build her again, this time more accurately and build those paddles out of brass.

1. (The paddle motors are in stock (2024Dec29) $10 each at Princess Auto, London, Ontario SKU:9102179) The photo below shows a number of 12Vdc geared surplus motors and other goodies like 12Vdc windshield pump motors for draining our ship's bilge.
2. (The paddle motors are surplus stock intended for auto side widows but are only one hand, as in left and right. Flipping it over to drive the other paddle would cause the gear box to to be high. I had to disassemble one of them to make it right handed or LH depending on your POV and had to remove a plastic keying notch)
3.(The motor gearbox has a long steel square threaded shaft protruding about 4 inches on which it was easy to mount a 2inch length of wood dowel)
4.( The complexity of the paddle is fake ... so many projects so little time. The Westbury Feathering Paddle Wheel from Model Engineer is so appealing but it's a hobby in it's own right. I copied the illustration by JDW and pasted it to my paddles ... sketchy, eh? 😎)
5.The motors are intended for a duty cycle of about 50% which is 5 minutes on, 5 minutes off. After 30 minutes of running they get quite warm, not enough to boil water but a little uncomfortable to hold. All the same, I get easily bored after 30 minutes driving around the pond.