How to calculate center of mass & centerline a of a boat?

[appliedF]

Can anyone explain how to calculate the center of mass of a boat? and the centerline of a boat?

Formulas, websites, anything helpful, just to let you know I haven't taken any high level physics classes so i don't know any of the fancy stuff lol. Thanks for the help

 

[RJLiberator]

Are you familiar with this equation: xcm=x1m1+x2m2+.../(m1+m2+...)

(center of mass equation)

 

[Simon Bridge]

Welcome to PF;
Real world objects can be complicated ... we can answer better if we know what you want to know this for.
Basically you work out the com of a boat the same way as for any object.

 

[appliedF]

Are you familiar with this equation: xcm=x1m1+x2m2+.../(m1+m2+...)

(center of mass equation)

I have heard of it but never considered it because I had no idea what it meant lol... what does the eq mean?

Welcome to PF;
Real world objects can be complicated ... we can answer better if we know what you want to know this for.
Basically you work out the com of a boat the same way as for any object.

There's an engineering team in my school, we build a motor boat and basically go to a competition and race at the end of the school year. Anyways, I need to find the center of mass for the boat.

 

[Simon Bridge]

If the idea is to engineer the boat to have a specific location for the center of mass - that is what ballast is for.
What you do is measure the location of the com for your basic hull and add a repositionable weight. The com of the boat + weight is easy to work out.
If you build the boat with port-starboard symmetry, then the center-line is along the line of symmetry.

 

[appliedF]

If the idea is to engineer the boat to have a specific location for the center of mass - that is what ballast is for.
What you do is measure the location of the com for your basic hull and add a repositionable weight. The com of the boat + weight is easy to work out.
If you build the boat with port-starboard symmetry, then the center-line is along the line of symmetry.

Thanks man I appreciate it, I have some questions, what is a port-starboard? and what is a com? and by weight you mean the weight of the boat right? i know i sound stupid lol but seriously help would be appreciated thanks

 

[Simon Bridge]

port-starboard symmetry is left-right symmetry for boats... how boats are normally built.
com = center of mass (lazy way of writing c.o.m.)
weight = the moveable weight you are using to adjust the total com. (in "the com of boat + weight is easy to work out")

By "engineering team at my school" you don't mean part of a college school of engineering do you?

 

[appliedF]

Nah it's a high school team. How does weight affect the com?

 

[Simon Bridge]

If you move it forward, the com moves forward. Move it back and the com moves back.
Have you tried looking up "center of mass"? You can find the maths with a diagram done better than I can describe it here.
http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html

[You (and I) should be careful to distinguish between "weight" which is the force of gravity on a mass, and "a weight" or "the weight": which is a lump of metal used as a standard mass when weighing things.]

 

[appliedF]

If you move it forward, the com moves forward. Move it back and the com moves back.
Have you tried looking up "center of mass"? You can find the maths with a diagram done better than I can describe it here.
http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html

[You (and I) should be careful to distinguish between "weight" which is the force of gravity on a mass, and "a weight" or "the weight": which is a lump of metal used as a standard mass when weighing things.]

Thanks, but what should I do to find the centerline of the boat?

 

[SteamKing]

Thanks, but what should I do to find the centerline of the boat?

The centerline of a boat is a reference plane which is established when the boat is designed and built. It is not determined by calculation in most circumstances. The centerline establishes the location about which the breadths of the vessel are symmetric:

The centerline is indicated by the C and the L superimposed.

 

[Shehbaj singh]

Though there are many ways like integration but an easy way without mathematical calculations is the intersection of axis of symmetry. A simple way applicable for regular bodies of uniform density. If the things in body is to me concluded then take centre of mass of centre of mass of boat and equipment by following formula.
C.M = am1 + bm2 / m1 + m2

 

[Norman Hibberd]

Try to get hold of a book called "Small Boat Design for beginners" by Frank Bailey. It explains all that you need in simple, easy to follow format and gives all necessary calculations with examples. Top book.

 

[anorlunda]

You will also need to consider center of buoyancy (cob) as well as com. Cob is determined by the shape of the hull below the water line.

Cob position relative to com determines if the boat sits level in the water or leans in some direction. It is also critical to stability as the picture shows. An unstable boat will capsize.

As Simon Bridge said, you can add ballast to adjust com. You can also shift position of the engine to achieve balance.

Calculating cob is not easy. It might be easier for you to measure it by experiment, perhaps using a small scale model.

 

[Merlin3189]

Nah it's a high school team... we build a motor boat and basically go to a competition and race at the end of the school year. Anyways, I need to find the center of mass for the boat.

On that basis etc, I assume it is a model boat. In which case it would not be too difficult to locate the CoG by measuring weights when the boat is supported by two or more supports, then calculating moments. I have used this method on a real boat (14' about 200kg) to locate the fore & aft location, but the vertical dimension is hard to handle because boats don't lie stably on their beam.

Simon asked why you need to find the CoM and that still seems a pertinent question.

 

[appliedF]

On that basis etc, I assume it is a model boat. In which case it would not be too difficult to locate the CoG by measuring weights when the boat is supported by two or more supports, then calculating moments. I have used this method on a real boat (14' about 200kg) to locate the fore & aft location, but the vertical dimension is hard to handle because boats don't lie stably on their beam.

Simon asked why you need to find the CoM and that still seems a pertinent question.

Thx i used your method and calculated it on our boat (it's a real boat) thanks man

 

[Simon Bridge]

Boats are usually built so the port side a the mirror image of the starboard side - it's normally obvious, just from looking at one, where the mirror plane is. The centerline is in the mirror plane ... use the definition of the center line to work it out.

 

[appliedF]

Boats are usually built so the port side a the mirror image of the starboard side - it's normally obvious, just from looking at one, where the mirror plane is. The centerline is in the mirror plane ... use the definition of the center line to work it out.

Our boat was not exactly symmetrical, and plus it had a few extrs nails on one side. We found exact centerline or else compton high would beat us lol like they did a few years ago. If we assume our boat is symmetrical then we will calculate our centerline wrong and our boat will bot go straight forward

 

[Simon Bridge]

So "a few extra nails" was enough to throw the centerline off significantly?!
That is a detail I didn't have - same with the boat not being symmetrical.
When asking a question you should provide the important information... especially when asked.

You can usually aide steering with a rudder or fins ... the effect depends on things like how fast you are going. You can adjust the tiller in tests.
The symmetry could be adjusted back by adding a few extra nails to the other side... sure it makes the boat heavier but you said it is full size: variations in the weather on the race day will have a bigger effect.

But if it really is so sensitive to the assumed centerline, then you'll have to measure it.

 

[SteamKing]

Our boat was not exactly symmetrical, and plus it had a few extrs nails on one side. We found exact centerline or else compton high would beat us lol like they did a few years ago. If we assume our boat is symmetrical then we will calculate our centerline wrong and our boat will bot go straight forward

The centerline of a boat is still the reference plane about which the breadths of the vessel are geometrically symmetric. That the construction of the vessel has left it with a center of gravity which is offset to one side of the centerline is immaterial.

There are ways of correcting such an imbalance which do not involve fiddling with the location of the centerline.

What's to keep you from putting some additional nails on the side opposite of the extra nails which caused the original imbalance? Some vessels require the use of extra weights in the form of fixed ballast in order to obtain proper sinkage, trim, or heel.

 

[Merlin3189]

And what happens when the crew is aboard?
When I’m on my boat, the CG must move significantly as I move about. Can the exact position of CG be that important? Can the crew simply move slightly to ensure the boat runs true? In a sailing dinghy that's what you do , among other adjustments like sail balance.

 

[Simon Bridge]

... good question since the boat is full-sized. I was picturing a radio-controlled boat.

 

[sophiecentaur]

If the boat is strong enough and not too heavy. I suggest hanging it up by a single rope / string and taking a photograph of it. The COM will lie on the line of the rope. Take several photos from different angles and with different points of suspension, so the boat is pointing roughly along three (xyz) axes (hanging from its bow, from the side and from the top or keel). The lines on all the pictures will (should) all pass through the COM of the boat. This would be possible for anything up to the size of a dinghy.
http://www.antonine-education.co.uk/Pages/Physics_GCSE/Unit_3/Triple_06_Centre_of_mass/Triple_06.htmwhich shows how to do it for a flat (2D) object and extend the idea for a 3D one.

 

[sophiecentaur]

When I’m on my boat, the CG must move significantly as I move about.

You'll have to lay off the pies, my boy. (I have had the same problem myself)

 

[appliedF]

The centerline of a boat is still the reference plane about which the breadths of the vessel are geometrically symmetric. That the construction of the vessel has left it with a center of gravity which is offset to one side of the centerline is immaterial.

There are ways of correcting such an imbalance which do not involve fiddling with the location of the centerline.

What's to keep you from putting some additional nails on the side opposite of the extra nails which caused the original imbalance? Some vessels require the use of extra weights in the form of fixed ballast in order to obtain proper sinkage, trim, or heel.

Well there are a few reasons of why we don't add more nails or balance out the weight, we ran out of funding because the paint costs a lot of money. And besides, it's not just the nails, our wood might be heavier on one side etc

 

[SteamKing]

Well there are a few reasons of why we don't add more nails or balance out the weight, we ran out of funding because the paint costs a lot of money. And besides, it's not just the nails, our wood might be heavier on one side etc

Rocks are cheap. They're lying around on the ground. They were used for centuries as ballast for ships and boats. Scrap steel can be used if you don't want to go looking for rocks. Lead shot, bricks, concrete, yadda, yadda. The point is, there are a multitude of things which can be used. You just have to use your imagination first.

And why did you spend a lot of money on paint? You've got a boat you're going to race maybe one time. You want to spend your time and effort to make the boat float properly in the water. That's how you win races, not slopping expensive paint allover the place.

 

[gatopardos]

In real boats they used to add cement to stabilze them. Is the center of bouyancy the sum of all the infinitesimal hull forces on the z axis let's say? Wouldn't that require a computer model to calculate? Wouldn't drawing the hull shape and the infinitesimal force vectors in xy, zx , zy planes on paper and placing one on top of each other give you an estimation of where the "cob" is? If the underwater hull height is small the pressure variation should be negligible.

 

[SteamKing]

In real boats they used to add cement to stabilze them. Is the center of bouyancy the sum of all the infinitesimal hull forces on the z axis let's say? Wouldn't that require a computer model to calculate? Wouldn't drawing the hull shape and the infinitesimal force vectors in xy, zx , zy planes on paper and placing one on top of each other give you an estimation of where the "cob" is? If the underwater hull height is small the pressure variation should be negligible.

Trying to arrange ballast in a boat by computer modeling helps, but you cannot possibly model every variation in the boat's hull introduced during construction.

You must take the boat as completed and then physically arrange the various pieces of fixed ballast in the boat until it floats properly.

 

[sophiecentaur]

There are still a few unanswered questions about the actual project. Why do you need to know the position of the COM? Is it so that the boat appears to float level? Is it to get the trim (fore and aft) right. And what are the actual dimensions and weight of it? Any worthwhile answers to your questions will hang on knowing the scale of things. You talk about putting "nails" in, to alter the COM. How big are these nails?
If it's a motor boat, does it 'plane' or is it just a ;displacement craft'? If it does, then the trim can be critical.

 

[appliedF]

There are still a few unanswered questions about the actual project. Why do you need to know the position of the COM? Is it so that the boat appears to float level? Is it to get the trim (fore and aft) right. And what are the actual dimensions and weight of it? Any worthwhile answers to your questions will hang on knowing the scale of things. You talk about putting "nails" in, to alter the COM. How big are these nails?
If it's a motor boat, does it 'plane' or is it just a ;displacement craft'? If it does, then the trim can be critical.

Well we already finished finding the centerline and we placed our motor accordingly. We raced in the competition but we got 38th place :(
We need to know the position of the COM so that we can place our batteries and resistor etc in the right position. The boat is 16 ft long, and 3 feet wide enough to fit one person. The nails are standard nails 1cm long.

 

[Simon Bridge]

The answer to this is the same as the previous answers.
Please reread the above thread.