How to Calculate a Boats Waterline - Archimedes Principle

[@RachelSindlinger]

Extremely helpful! I used these calculations for a cardboard boat project, and the waterline was exact!

[@PatriotContraptions]

Thanks 👍

[@jasondoherty2784]

Thank you! Im building a boat to cross a river with some friends and this was just what I needed! Should only be a few inches below the waterline of this shallow river.

[@PatriotContraptions]

Sounds like a fun project 😁 Should check out my Barrel raft build with a paddle wheel its what we use in shallow water.

[@bart4549]

Hands down the easiest video for the topic to follow

[@PatriotContraptions]

Thanks 👍

[@estebanleon7637]

Thank you very much. It is very simple and helpful.

[@PatriotContraptions]

Thanks, glad you enjoyed the video :-)

[@logancarlo5]

Amazing video keep up the great work but how would you calculate water line on a boat with a non flat bottom

[@PatriotContraptions]

That gets really complicated as you have to use equations with variables and then solve for them ...it's hard to explain and depends allot on the individual boat design. Basically you segment the boat up even more a using custom equations for value with a variable for hight you then add them all together and set it equal to the volume of displaced water like I do in video but more complex... hmmm

[@logancarlo5]

@@PatriotContraptions thanks I love the videos you do an amazing job

[@mattfuchs7626]

Great and simple, good work

[@PatriotContraptions]

Thanks 👍

[@allanmarks2150]

Greetings from Guatemala. Thank you for posting this excellent video. I am getting ready to build my first boat. It will be a very simple and very light weight catamaran, built for carrying one person - me - about 150 pounds. I plan to power the boat with something like a number of lithium ion batteries, and I am trying to calculate the combined power of the batteries I will need. I am not trying to build a speed boat. A catamaran that move at 5 knots per hour on the lake near my house would be fine. For my initial testing I do not need batteries that last more than an hour, before I paddle back to shore, and recharge the batteries for the next day of testing. I have started studying and learning about catamarans, batteries, motors, and boat drag. The boat, and everything in the boat, including myself, will probably weigh less than 250 pounds, and I will probably have enough foam in the pontoons to float maybe 1000 pounds. If my understanding of Archimedes principle is correct (?), for each boat length it moves, the boat will need enough power to displace its weight of water. Does this mean that my catamaran will have almost no drag, since the boat will have so much foam flotation and so little weight of water to displace? Note - I am learning how to shape the pontoons to be, for a reasonable cost, as hydrodynamic as possible, and I will get 2 excellent propellers.

[@PatriotContraptions]

Catamarans are indeed very good at going through the water with very low drag if done correctly...I have never built a catamaran so I don't have any field testing to go on.. that said I have seen sail catamarans in action and they out run the same size sailboat with about three times the speed(I tried to race one once...I lost bad.. ). The one issue they don't do well on is turning as with two hulls its basically like have two dagger boards. The trick I think for you will be figuring out you length to width on the hulls if you go to narrow it may force you to stay in the center of your boat as going to onside would put all your weight on only one hull. Archimedes' principle is for a boat not in motion just sitting in the water. As soon as the boat starts moving other factors start to effect how much drag you have on the boat. For example if you have seen any race boats or fast speed boats they are almost completely out of the water when moving at speed. This is because the shape of the hull is adding extra downward force to the water do to allot of complex physics and forces that act on the boat and water so as to lift the boat our of its natural Archimedes state when it is still at the dock. You can also have a worse drag for example a sub on the surface may have waves coming over the front of it trying to keep it down deeper in the water than its normal state. I would suggest the main things to keep in mind would be where is the safe center of weight for me on my boat(where can I sit without it flipping over). on a catamaran this is normal a square in the center as both individual hulls can support the weight of the person but going to the tip on the font of one or the back would cause the weight on that hull to be forward of its center of gravity(I do have a video on boat stability that sorta covers this). I also highly recommend build a scale floating model first I do this with all my boats(normally I do either 1in or 2in equals a 1ft as scale). BTW You made my day knowing people from other countries watch my videos :-)

[@allanmarks2150]

@@PatriotContraptions - Thank you for your interesting reply to my comment. Yogi Berra - In theory there is no difference between theory and practice. In practice there is. Me - For the last several weeks I have been learning a lot of diy boat building theory from YT videos. I have zero practice. The below ideas are some of the ideas I have gathered from watching YT videos. They look to me like they should work. But someone like myself, who has no practice, can easily miss something. This will not only be my first boat, and my first significant diy project, it will also be my first electrical project. I am planning to wire batteries to a motor. The motor will have a propeller attached to its motor shaft. In the videos I have seen, some combination of gears, fan belts, and shafts is almost always used to get power to the propellers. But I have seen at least one good YT video of someone wiring up batteries to a motor that is underwater and directly attached to a propeller. The wiring is done in a waterproof way, which I will probably also do, but I don't know if this is necessary since I will probably use a 775 motor that is made to be used in water. I plan to use 2 propellers, each with their own speed controller, and probably add some mechanism to control the direction of the propellers. With that kind of setup I do not think I will have any problem making whatever turns might be needed on the lake. After all, my first catamaran will be moving relatively slowly (maybe about 2 to 5 knots per hour), and I should be able to put 1 propeller in reverse, since the power is electrical. In fact, I really don't see why the catamaran should need a rudder, and I have no plans to have a rudder. In the future, I might replace the relatively small number of low-capacity cheap batteries that I use on my initial tests, with a much more powerful marine battery, and then I expect that the boat would go very fast. My catamaran is going to be really light weight. I believe I have figured out how to make the pontoons, the center board, and the propulsion system very light weight. And that is about all that will be needed to floated besides myself (about 150 lbs). The pontoons can be made structurally strong by using light weight packing tape. I have a good YT video of one professional small boat builder in Thailand, using packing tape to wrap around foam pontoons. Over the packing tape will likely be some kind of fiberglass. For some kinds of fiberglassing, I will probably hire someone to do that part of the build. I plan to use 2 sheets of expanded polystyrene (EPS) foam (8ft*4ft*2in) to fill the pontoons. That should provide over 1200 pounds of flotation. With that ratio of provided flotation (over 1200 lbs) to needed flotation (something less than 250 pounds), the pontoons should be largely above the water line, and have very little drag.

[@PatriotContraptions]

@@allanmarks2150 That sounds like a solid plan to me :-) I still defiantly recommend building several small models first as its always helped me. I even at one point I did a full scale model of a boat(none floating of course) just to visualize fully the idea... I found out the front on my paper design was incorrect in practice do to spacing issues as a result. As far as steering using the motor is fine although if consider adding a sail to design to extend range and save battery. you will probably want twin rudders one on each hull from what I can tell is best... Also two other ideas have you checked out one sheet plywood boats as two strapped together would be a quick catamaran or even two canoes strapped together. Another thing to look at are "mouse boats" they are made from foam and you can probably pick up some good ideas on assembly. As far as motors I can't give much advice as I don't run any on my builds...Manly do to registration laws in my area I don't want to deal with at the moment... Over all looks like you have a solid plan and I hope you post a video when its finished I would love to see how it turns out :-)

[@funkblack]

How do I calculate this in fresh water vs salt water?

[@PatriotContraptions]

You just need to search for the weight of one cubic ft salt water and use same formula... honestly results will be super super close... almost not worth effort unless the water is as thick as say the Dead sea...

[@jacobmills7824]

Super helpful, thanks!

[@danadane1517]

Thanks a bunch man🤙!!!

[@PatriotContraptions]

Welcome 😄

[@Rachie-nj3oi]

What if the liquid isn't water how do we find out what 1 cubic ft of that liquid would weigh?

[@PatriotContraptions]

You would need to Google it after that equation is the same. For example oil is like 55 lb.

[@Rachie-nj3oi]

@@PatriotContraptions I tried lol OK not worries thanks for the reply 👍😊 Great video BTW 👌

[@corrupticecubes418]

If I am understanding this correctly, you want the height of the walls to be taller than the water line right?

[@PatriotContraptions]

Yes, the walls will need to be taller than waterline or the boat will probably sink in short order...If you are building for cardboard boat racing I have a video on how to build a cardboard boat that goes into other factors to consider in wall high as well such as height of rower, waves extra...

[@NA-su3jk]

The cubic feet number needed more expanation.... it "comes out of nowhere" in terms of video progression as well as notes under video.

[@PatriotContraptions]

Thanks for the feedback all be sure to fix it if I do a fallow up on this topic :-)

[@s1mp176]

Thank you!!!!

[@isdosnuk9157]

The boats bottom have a V shape I guess your calculations are for a straight bottom shape Your video helped me a lot but im still quite confuse bc of the V shape. The more sharp will be the more inches it will sink

[@PatriotContraptions]

Yes my calculations are for flat bottom boats as that's what most cardboard boats are and I wanted to make the calculation as simple as possible for kids to use. If you want to calculate the waterline of a none flat bottom boat I have done this before as well, but it is a really pain. You have to figure out the cubic feet of the inside of the boat that will be equivalent to the weight of the water you need to displace. However since you have v shaped side that value will change so you will need to use variables to determine how much extra water is moved aside from the v shape... It's really annoying calculus stuff. Basically what I foundwhen I compared my calculus result to the calculation shown this video. Using my red v shaped boat. Was the difference in the water line was maybe like .3 in as a result of all my work so it wasn't really worth it... That said if you want to get a good estimate and account for some of the v shape I would get a rough water line using my videos calculation (say it's like comes to 3 in)? Then I would figure out what the area of the bottom of your boat would look like if it was at the halfway mark of that measurement (so 1.5 in up the side). In other words the midpoint area of the v shape that we expected to be under water. Then I would use this area in the videos calculations and that should put you really close as taking the halfway the belowwill displace less water but it will be countered by the v above displacing more water thus giving you a very close estimate for a v shape side.

[@inmyopinion6836]

Your math indicates that ALL sides of the boat are perpendicular to the bottom, the very flat bottom. How would you calculate the water line of a canoe? I empty the canoe, place it in the water, then add the number of gallon jugs of water that it takes to equal my projected load. Water is 8.2 lbs. per gallon. Just take a waterproof marker and go around the boat. It is automatically self-leveling. There is your paint break line. From there you have your reference line.

[@PatriotContraptions]

Yes, my math is based on all sides being perpendicular to the bottom for this example. While it is possible to calculate the exact water line for any boat its almost impossible to explain each case do to the formula having to be custom to each design. The basis is that you have to create a formula that adjusts for the curves and set that equal to the wait of water required to be displaced. This is not easy to do as you will ne variable's to account for change in with to high and so on ... For my cardboard boats which have curved sides I normally just ignore the curves and pretend the sides are perpendicular. Then I just figure the actual water line will be just a little bit higher...in past its only made me off about .5in if that... you can get water line easiest by getting in the boat fully loaded and just marking the side where the water hits or filling the boat with the equivalent weight of water to the gear you plan to put in and mark the outside that way(this may not account for boat weight and wall thickness though)...The main reason to use water line calculation is to design a better boat as once boat is built its easier to just get in and see where its at :-)

[@daveengstrom9250]

Archimedes was a rookie.

[@Tagan672]

metric pllleeaassseee

[@PatriotContraptions]

Use the Same Equation just use the metric equivalents...

[@teefor2846]

Dude, don't quit your day job...