Measuring max weight for boat
 

Hello,
I am going to print a 3D printed rc boat and i want to know if i can measure the maximum weight it can hold. The boat is gonna be a tugboat (allow me to post link or picture for clarification), it will be consisted of ABS material and the total weight of the boat, as measured by fusion 360, is around 600g. Because i will use it for my uni i need to understand the mathematical side also not just a number. The length of the boat is around 550mm, the width around 205mm and the height 250mm

One thing I'm not quite sure of is the height. Is the 250 mm to the water line, top of the pilot house or the top of the mast? I'm not a marine engineer but I do know that you're forgetting a few things that will make a difference:
1) depth of keel to water line
2) shape of the hull below the water line
3) weight of structure and height of that weight above the water line
4) WHERE IS THE CENTER OF GRAVITY????
All of the above is just as important as how much weight the hull can carry. It is a big factor in full sized ships as well. Many ships that were built during the last century were actually overweight above the water line if they had been built as planned. Many had to have the upper structures built from lighter materials to get the ship to be stable, often using aluminum alloys or similar light weight materials to get the CG to an acceptable level.

If you have a mathematical description of the underwater hull shape, no problem.. The difficulty there is that there is no such description. All hulls are different, almost none are a simple enough shape to be amenable to mathematical description, being a combination of constantly changing curves.
An approximation can be arrived at if you have the hull cross sections at known distances.
Break each underwater cross section down to rectangles and triangles or other known shapes. Add these now known areas of two adjacent sections, divide by two, multiply by the separating distance and you have the volume of that section. Start The more cross sections, the nearer the answer will be. at one end, repeat until you get to the other end, add all the volumes f the sections together, convert volume to weight of water displaced, thats your answer, give or take a bit.
Or, use a block co-eficient. Measure the draught, beam and waterline. Work out that volume. Look at the actual shape and guess the percentage of inside to outside that your hull will take, and go from there. For a tug, somewhere between 50 and 70 percent.
Or get the hull built, put it in a test tank, ballast it to waterline, weigh it.
There is a story that Edison, when looking for assistants, asked the prospects to work out the volume of one of his light bulbs. The winner was the guy who suggested filling it with water, and measuring that. Allegedly.

I haven't figured out where the waterline would be but i got some extra info and screenshots for you that maybe can help you. How can i find where is the waterline?
stern keel angle: 17.7 degrees
Bow keel angle: 34.5 degrees
bottom to deck height: 128mm
volume of waterline: ????
Total volume of hull: 2.093E+0.6 mm^3
Go to sirick93.tumblr.com for screenshots
Last screenshot is center of mass!

Is there any practical reason for trying to determine how much weight a model boat would hold using mathematics?
Math can be very useful when no other method is feasible, but in this case, unless you're brushing up on math skills or trying to solve a mental puzzle for the hell of it, the method you chose to find an answer to your question borders on insanity when there are infinitely simpler means of accomplishing this.
Assuming insanity is not in play here, I would suggest trial and error as a method of choice.
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The reason is that the 3D print is gonna cost about 30 € .Also my professor wanna know before hand if the boat gonna handle the weight before he prints it. It is a time wasting procedure.
Considering sellable hulls cost way more, makes this information valuable.

If the level of proficiency in math (at the institution your professor is involved with) is on par with the English grammar and common sense displayed, I'd say you have more than a formidable challenge ahead.

Is this guy for real? Dude if you don’t want to contribute for the answer why do you even bother replying in this thread? To express your toxic behavior? If my level of English will be a challenge, your way of using English will get you nowhere. Back to the point, if there is another way explaining the max weight a boat can hold, I will gladly accept it. I only want to explain it on my thesis!

From a model building hobby perspective, the maximum weight a boat can hold is determined by placing a proposed hull in the water and adding weight to it to the point that the hull reaches the desired depth, commonly referred to as the waterline. One can then check the amount of weight that was added.

I think mfr02 gave you your answer. Your initial question lacked much of the relevant information we needed to even help you out. If I were you, I'd take your design and find a computer program that can model your boat and see where that leads you. Otherwise, you can do as airsteve172 suggests and print your boat and add weight until it sinks.
That said, isn't a thesis supposed to be something researched by the author and not just repeating what you're told by others? I am curious how that works since it took me six weeks to write a term paper on the subject of internet and multimedia addictions for a psychology class back in 2009, using every source I could find starting with combing through several libraries and finishing by interviewing the owner of a treatment facility less than five miles from the headquarters of Microsoft. How ironic is that?

Assuming that you have a dimensioned drawing of the intended item, follow the procedure that I offered earlier. Create yourself a spreadsheet to put the numbers into and let the formulas that you insert into the cells do the hard work.
The waterline is where you determine it is going to be. Look at pictures of tugboats to get an idea.
The center of gravity is where whatever you load it with puts it, both vertically, fore and aft and crosswise horizontally. The most influential item is usually the battery, but tug models often require ballast low down both for stability and trim. It might be a good idea while searching the internet to look up things like "center of buoyancy" and "metacenter".

One other way for a model - look for real manufaturers information involving hulls that closely resemble yours. Work out from their information what scale yours could be considered as being to, scale their information to fit. More maths, but you will learn about cube roots, which should please your professor.

You are right had to search for material before i post. I just ask for guidance. Anyway one last thing. Searching the internet i found out about archimedes principle which states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. So finding that mass of the displaced water will tell us if an object will float, correct? So multiplying the total length, width and height to deck of the boat, we get the volume of the displaced water. Mine is 13200 cm^3. Converting this to mass of water (Weight of 13200 cubic centimeters of seawater) we get 13.52 kg. My boat along with the load weights 2.9 kg. So does that mean the buoyant force will push out of the water the boat until it's weight is equal to the boat's weight?

You're on the right track, but forgetting one thing. As mfr2 said, the shape of your boat isn't a rectangle so the shape will affect your computations. Otherwise, you will be correct. Since the hull is rounded, the depth and width are not consistent, meaning the volume will vary from frame to frame. This must be accounted for or your computation will be meaningless. If you were computing from a specific size of piece of lumber, your numbers would be correct. Now, let's start cutting away material from the outside of that piece of lumber. Since it's size has now changed, the water it displaces will now be less. With the more wood you remove, the displacement will get proportionally smaller. This is where you need to start, not at the 13200 cubic centimeters derived from that squared piece of lumber.
Now, let's throw in another variable. You have your external shape, so we now need to remove material from the inside to make room for the drive and control systems. You are again removing material, reducing the displacement. Now, add in motors, speed controllers, rudder and linkages, battery packs, receiver and servo. These will all have different weights, densities and effects on the buoyancy of your hull. Your superstructure will also add weight but, at the same time, can cause your boat to be unstable due to a high CG. This will require ballasting of both the proper weight and location(s) in the boat to keep the CG where it is needed for stability As you have probably surmised by now, this isn't an easy thing to figure out through a mathematical equasion

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Yes Archimedes did know what he was talking about. Once you know the underwater volume of the boat, you know the total weight it can be.
Unless you intend to sink the boat down to the deck level, NO.
The submerged volume is the waterline length times waterlin beam times draught (waterline to lowest point). This figure is true only if the hull is shaped like a brick. The shape of the hull will reduce the volume considerably (go back to what I said about block coefficients). For a tug, probably about 50% - 60%.
Another word to google - freeboard. This is the height of the hull above water up to the deck. The volume of this height contributes to the weight, but does nothing for buoyant force. Probably about 15% of the hull volume, in your case 13.52 X15%, giving 11.5Kg underwater. Except, that is the brick shape, not a boat shape. Allowing for a typical hull shape for a tug, nearer 5.75Kg. This will be the total weight of the boat in sailing trim. Hull, deck, superstructure, running gear, battery and ballast. And any payload. Any extra weight will cause the hull to sit lower in the water until such time as the water gets above deck level. Then it sinks.
At 2.9Kg, it would sit on, rather than in, the water. It might not be very stable until it gets the extra 2.8Kg, preferably low down, to take it down to its waterline. Having it float is an important consideration. Having it float upright is also important. Where the weight is is important for ensuring this.

Ok understood what you both said that for now i have roughly estimations. The information of your posts will help me balance the boat when i get it. I also have enough knowledge now to somehow justify the flotation and the waterline level (shape, density, volume all taking part). Thank you all for your time and help!