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

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1. Jan 10, 2016

### 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

2. Jan 10, 2016

### RJLiberator

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

(center of mass equation)

3. Jan 10, 2016

### 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.

4. Jan 10, 2016

### appliedF

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

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.

5. Jan 10, 2016

### 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.

6. Jan 11, 2016

### appliedF

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

7. Jan 11, 2016

### 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?

8. Jan 11, 2016

### appliedF

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

9. Jan 11, 2016

### 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.]

10. Jan 16, 2016

### appliedF

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

11. Jan 16, 2016

### SteamKing

Staff Emeritus
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.

12. Jan 16, 2016

### 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

13. Jan 16, 2016

### 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.

14. Jan 16, 2016

### Staff: Mentor

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.

15. Jan 16, 2016

### Merlin3189

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.

16. Jan 17, 2016

### appliedF

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

17. Jan 17, 2016

### 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.

18. Jan 18, 2016

### appliedF

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

19. Jan 18, 2016

### 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.

20. Jan 18, 2016

### SteamKing

Staff Emeritus
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.

21. Jan 18, 2016

### 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.

22. Jan 18, 2016

### Simon Bridge

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

23. Jan 18, 2016

### 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.
Look at this link, which shows how to do it for a flat (2D) object and extend the idea for a 3D one.

24. Jan 18, 2016

### sophiecentaur

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

25. Jan 19, 2016

### appliedF

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