I’m a junior in high school and in my physics class we are designed to build a cardboard boat to float you and your partner in a nearby lake for a race. For the assignment we were asked to show the watermark but i have no idea how to find the mark and neither does my partner… any help would be appreciated! thank you!
In my high school physics class we are told to determine the waterline for our cardboard boat. Our boat is 9ft long, 4 feet wide and 2 feet tall. I weigh 130 lbs and my partner is about 150 lbs. How do i find the waterline?
Just do one about 2/3 up the hull. A true watermark depends
on how much weight is in the boat. Like ballast, cargo ect.
Have fun.
Each hull shape has its own variance on the formula. . . ie: pontoons, catamaran hulls, and cylinders are calculated using pie (pie = 3. 14 x diameter).
Assuming we are not dealing with pontoon or catamaran hulls. . . this will do it for you. . . enough so, that you can figure out the rest on your own.
1. first calculate the “volume” of your boat’s hull.
this is done by simple ” length x width x height ”
remember here, that you are dealing with “cubic” feet
and not square feet.
2. once you determine the number of “cubic feet” in your hull,
You need to know your vessels weight. . .
use your boats “normal operating weight”
I always use the weight of all my materials
to build the boat, plus the weight of all the
mechanics, machinery, appliances, pumps,
motors, water, fuel, batteries, gear etc. and all
things stationary on the boat,
as well as 350 lbs (my own estimate of two
passengers’ weight)
Once you have the cubic feet in your hull, and your estimate of the boats weight. . . the rest is easy.
Just remember this “old boat-builders” saying:
“8 pints, 8 pounds, the world around. . . ”
That will help you remember:
8 pints weighs 8 pounds
8 pints in a gallon = 8 pounds in a gallon
8 gallons in 1 cubic foot. . .
and 8 lbs in one gallon. . .
thus: 8 gallons x 8 lbs each = 64 pounds in one cubic foot.
Whala! 64 lbs. . . Wouldn’t you know this just happens to be the weight of 1 cubic foot of seawater. . . (fresh water of course is slightly less – 62) but I always use 64 no matter what. The difference is insignificant.
So now take the cubic feet in your hull x 64
then divide that number by the number of inches in the height of your hull. . . so this will give you the answer as to how much weight will sink your vessel 1 inch into the water. . .
So take that weight and divided into the “total weight” of your vessel with all its gear, etc. . . and you will have your waterline.
I build boats all the time. . . I have always used this formula to determine bouyancy. . . and to estimate waterline. . . and thus draft & freeboard. . . I always paint 3 inch waterline strips. . . between my bottom paint and topside hull paint. . . and I have never had to re-paint a waterline yet
I always round up to the nearest cubic foot. . . and I never worry about figuring in small space between close quartered, sharp, or tapered bows.
example if your boat is: 2 ft wide x 7 ft long x 1ft tall = 14 cu ft
14 cu ft x 64 lbs = 896 lbs
896 divided by 12 inch tall = 74. 6 lbs
weight of boat & 1 crew & equipment = 300 lbs
300 divided by 74. 6 = 4. 02 inches
draft = 4. 02 inches
freeboard = 7. 98 inches
Note: if your boat has a flat, or “slight” round or “slight” V shape, these calculations will be close enough. . . believe me. . . (ie: the slight difference in volume measured is actually a gain in floation. . . which, ironically is neutrized by the lower centered concentrated weight created by the shape).
If however your boat has a “deep” V then you will need to make 2 calculations. . . one measuring just the V from its bottom to is union with the hull. . . to figure the cu ft double the width, calculate your cu ft and divide the result in half.
and then add this cu ft measurement to the cu ft from the top of the V to the top side of your hull
Your vessel will float at the point where its weight has pushed aside (displaced) a volume of water weighing the same as itself (including payload). So . . .
1/ Specify your vessel’s displacement, say 150kg¹.
2/ Find what the volume of this displaced water is, in cubic meters:
(Volume = Mass ÷ Density and density of saltwater = 1025 kg per cubic meter)
therefore the volume of water displaced will be:
150kg ÷ 1025 kg ⁄ m³ = 0. 15m³.
So your vessel will float at the point where it has pushed away 0. 15m³ of water.
3/ Find this waterline (your answer) at the height (h) up the vessel (from the bottom) at which this volume is obtained, given that:
Volume = Beam × Length × Height – which is to say:
0. 15m³ = 1. 22m × 2. 74m × h
Put this the other way around (‘transpose’ it) so you can start with the unknown you wish to find (height) thus:
h = 0. 15m³ ÷ (1. 22 × 2. 74)m
Do the little sum in the brackets, which tidies it up to:
h = 0. 15m³ ÷ 3. 34m
Finally, just do this main sum to obtain your waterline, thus:
h = 0. 04m.
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[ Just to prove it for your own satisfaction and to check, along the original lines of Beam × Length × Height : (0. 04* × 1. 22 × 2. 74)m = 0. 15m³
*I've rounded the answer here down to two decimal places. To get the answer correct, only do this at the end. Your calculator should give 0. 044910 . . . etc . . . at this point! ]
I now convert you back to inches:
0. 04m = 1. 57 inches!
So, LWL² = 1. 57 inches up from base.
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Notes: I have assumed a fairly uniform ‘box’ shape, or ’section’, from top to bottom, with flat bottom. And be sure to leave plenty of freeboard without exceeding this displacement specification.
¹ My conversions to SI system units from your specified dimensions (for easier calculations!) are as follows:
Length 9 feet [2. 74m]
Beam 4 feet [1. 22m]
Displacement:
You, 130 pounds (US)
Partner, 150 pounds (US)
Vessel, (estimate) 50 pounds (US)
Displacement = 330 pounds (US) [150kg]
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² BTW, ‘watermark’ is what you get in bank notes and fancy stationery. In boat design, the mark at which a vessel floats is indeed referred to as ‘its marks’ but more correctly, the waterline or ‘load waterline’: LWL.
For freshwater it’s even easier! Density of fresh water = 1000 kg per cubic meter.
(I’m not convinced the ‘cardboard’ is a goer though!
)
Good luck.
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