Pivot Point

[Paul Elliott]

In space, or on a real-world boat you can always combine the thrust vectors from two or more sources (props / rudders) into a virtual single thrust vector. The location of this virtual thrust vector depends on the location of the individual vectors.

In space, with zero drag, the center of rotation will be the center of mass, whether the force is momentary or continuous. There will usually be a directional vector to the motion, but the rotation will be around C.O.M.

On the water you *must* take the drag and other sources of resistance (rudders, keels, chines, etc), into account. For example, my single-screw power boat, with virtually no keel, has a point of rotation up near the bow. This is a long distance from the center of mass.

[LIboater]

This is still an ongoing discussion with my scientists friends. They insist it is the CoM (excluding other factors such as the drag). One even asked another friend of his who is physics prof at Princeton University.

I will have to relate some of the thought/comments many of you made to my friends. I know they can be obstinate "know it all's" at times

The shopping cart analogy is a good one and I'd like to run that by them.

I am not sure if I previously mentioned this, I know I did to my friends, but what about the haul out points on a boat. My 34ft is marked with 2 points that indicate where to place the slings when hauling the boat out of water. The mid-way point between the slings, one would suppose, should be the CoM. If it were not the boat might unbalanced in the slings. However, I can state with certainty that the Pivot Point is considerable aft of that sling mid-point.

[Bigggwilly]

I feel this is going to devolve into a "plane on a conveyor belt" scenario, but here it goes...

Firstly, I feel in your mental model of the boat, you're not disregarding the drag of the propeller pods.

Anyways - if we imagine a completely ideal body, with a mass, but no drag, and two equal but opposite forces (thrusts) acting parallel to each other, some distance apart, what we have is a simple force couple, also known as a moment, a torque, or a twisting force.

For minute, consider this object to be massless. This torque, acting on a vertical axis will of course rotate the object if it is not fixed in place. Since this object is assumed to be frictionless and not fixed, there are in fact infinite solutions on where this object will rotate, it is mathematically insolvable.

But let's reintroduce the mass, and remember two of Newtons laws. One of them is that a force exerted on an object is proportional to its mass multiplied by its acceleration, and another is that ever action has an equal and opposite reaction.

So how do these laws contribute to the model? Well, consider two scenarios: one, the object is rotating around the center of mass, and two, the object is not rotating around its center of mass.

Scenario one first. If the object is rotating around its center of mass, the center of mass is staying in one place. So - no action for there to be a reaction to, so no forces and everything will be in equilibrium.

Scenario two: the objects is rotation at a point other than the center of mass. Therefore the center of mass is moving ( in a circle). As it's moving in a circle, it's constantly being accelerated to keep it on its circular path. The acceleration, multiplied by the mass, gives a force. But where is the force coming from? Especially if it needs an opposite and equal reaction force - but there are no external reaction forces. So the answer must be that this force doesn't exist.

And therefore, the object must be rotating around the center of mass. In a real boat, the center of mass and center of drag would proportionally combine to define the real point of rotation.

If your friends are real engineers, I wouldn't trust anything they're engineering.


Sent from my iPhone using Cruisers Sailing Forum

[StuM]

I'm a bit late coming to this discussion. But:

Consider the case where one engine is in forward and one is in reverse with the same thrust in both directions. What you have is a "simple couple"

A couple consists of two parallel forces that are equal in magnitude, opposite in sense and do not share a line of action. It does not produce any translation, only rotation.

More importantly: " A couple may be moved anywhere in its plane or a parallel plane without changing its external effect. The magnitude of the couple is independent of the reference point and its tendency to create a rotation will remain constant.

So, critically, it doesn't matter where the engines actually are in respect to the centre of mass. For the same effort, the boat will still rotate the same amount around the CofM.

In an extreme case, think of a frypan sitting on an ice rink with two strings attached to the handle. Start to pull the strings in opposite directions and the pan will start to spin around it's centre, not around the handle. The couple exerts a rotation on the body!

Ask you engineer mates to explain it in terms of couples.

(Note: we are talking here about the initial turning moment. Don't get confused by thinking about pulling the strings continuously in one direction. In the situation under consideration, the direct of thrust varies immediately the boat/frypan starts to rotate)

[ranger58sb]

Originally Posted by LIboater

I am not sure if I previously mentioned this, I know I did to my friends, but what about the haul out points on a boat. My 34ft is marked with 2 points that indicate where to place the slings when hauling the boat out of water. The mid-way point between the slings, one would suppose, should be the CoM. If it were not the boat might unbalanced in the slings. However, I can state with certainty that the Pivot Point is considerable aft of that sling mid-point.

1) Sling points are often slightly adjusted slightly fore and aft to clear machinery... so while center of mass would indeed be between sling points, I doubt you can assume it's dead center between the two.

2) I think our forward sling point is approximately at our real-world pivot point, when I'm spinning the boat (mostly) in place using forward/aft gears only. (I'll try to remember to check that.)

3) I suspect a "real-world" pivot point (as above) and a theoretical pivot point can differ... in the real world.

-Chris

[CaptTom]

oooo, now we're getting somewhere!

Skipping over the stuff a layman like me can't comprehend, I'm perplexed by the frying pan on ice analogy.

Tie one string to the side of the ice rink and pull the other one.

I'd stake a lot on the prediction that the pan will rotate away from the fixed string, on a pivot point in line with the fixed string.

Reverse which string is tied, and which is pulled, and you get the same result; a pivot point in line with the fixed string. in either case, the CoM has nothing to do with where the pivot point is.

Repeat the experiment with neither string tied to the side of the rink. Pull on both with the same force. How can the pivot point NOT be between the strings? If the CoM is the pivot point, then one string has to move farther than the other, or put another way, one requires a lot of force to pull, while the other requires little or none.

Am I wrong?

[LIboater]

Bigggwilly, I think you are agreeing with my friends.....or they agree with you. Initially I felt, albeit intuitively, that the boat did not pivot on the CoM, but after much discussion with both friends and this forum I have to go along with the PP being CoM.

[LIboater]

StuM

The frying pan example is a good analogy.

[StuM]

Originally Posted by CaptTom

oooo, now we're getting somewhere!

Skipping over the stuff a layman like me can't comprehend, I'm perplexed by the frying pan on ice analogy.

Tie one string to the side of the ice rink and pull the other one.

I'd stake a lot on the prediction that the pan will rotate away from the fixed string, on a pivot point in line with the fixed string.

...
If the CoM is the pivot point, then one string has to move farther than the other, or put another way, one requires a lot of force to pull, while the other requires little or none.

Am I wrong?

Looks like you didn't real the whole post:

(Note: we are talking here about the initial turning moment. Don't get confused by thinking about pulling the strings continuously in one direction. In the situation under consideration, the direct of thrust varies immediately the boat/frypan starts to rotate)

That should of course be "direction", not "direct"

[CaptTom]

Originally Posted by StuM

Looks like you didn't real the whole post:
[B]
(Note: we are talking here about the initial turning moment. Don't get confused by thinking about pulling the strings continuously in one direction. In the situation under consideration, the direct of thrust varies immediately the boat/frypan starts to rotate)

Yes, that explains it. I certainly agree that if we set the frying pan spinning with just a brief tug on the two strings, it'll end up pivoting around its CoM.

I thought we were talking about sustained, directed thrust from two props, with the clutches split. It would appear there are several different scenarios, with different parameters, being discussed here. No wonder we are all coming to different conclusions!

[StuM]

Originally Posted by CaptTom

Yes, that explains it. I certainly agree that if we set the frying pan spinning with just a brief tug on the two strings, it'll end up pivoting around its CoM.

I thought we were talking about sustained, directed thrust from two props, with the clutches split. It would appear there are several different scenarios, with different parameters, being discussed here. No wonder we are all coming to different conclusions!

We are, but you have to realise that with the rudders centered, the sustained, directed thrust is constantly changing direction as the boat rotates. The best way to think about the frypan version is a series of tugs on the two strings, always at right angles to the handle as it rotates.

[Lepke]

I have handled many twin screw vessels from destroyers (3000 tons, 60,000hp, 9' props) to PBR patrol craft (20 ton?, 400hp jet drives) and lots of others in between. I have never tried to pivot w/o the effect of the rudder(s) and don't see why you would want to. All vessels pivoted somewhere near the vessel center depending on the hull shape, number of rudders, etc.
I've never had a bow thruster to use. My current boat pivots easily and with opposite rudder will walk the stern sideways.

[ranger58sb]

Originally Posted by Lepke

I have never tried to pivot w/o the effect of the rudder(s) and don't see why you would want to.

For me, its just a matter of convenience. When docking stern-to in a four-way tie up, usually rudders aren't necessary to turn 90° in the fairway and back into the slip... so I don't usually fool with rudder angle, just center the rudders at the start of the exercise, dock, done.

Assuming wind, tide, current, cooperate -- of course.

-Chris

[Lodesman]

Originally Posted by CaptTom

I'm going to fall back on an old trick I use for teaching twin-screw handling: Imagine you're holding a stationary shopping cart, both hands on the handle, near the outer edges. Push one and pull the other. Where is the pivot point?

That's not how a boat handles. If you oppose your engines, the bow doesn't swing around with the screws at the centre of the circle - the stern swings an arc and the pivot point would be somewhere just forward of the longitudinal midpoint. I would assume it's close to the centre of the cross-sectional area forward of the screws.

[Lodesman]

Originally Posted by LIboater

I have been having a lengthy "discussion" with some friends about the pivot point of a twin engine cruiser. We discussed v-drives and stern drives. To normalize the comparison we assumed that the stern drive uses only forward/reverse thrust to pivot.

Ignoring drag of any sort on hull, wind, current or other external factors we wanted to know the PP. There were three "opinions"

1) Between the props. Thus, no matter where the props were, under boat, off back of transom or even (for purposes of theory) 20 ft behind the transom one of us insisted the pivot is between the spinning props

2) At the point that the force/thrust is delivered to the hull. In this argument it says very simply that the force developed by the props is sent through a shaft to a trans (either a v-drive, a stern drive trans or if you like direct to engine if that is setup) and that the point of connection is the pivot point. Thus, in a v-drive the PP is essentially right at the v-drive.

3) The third opinion was that the PP will always be at the Center of Mass of the boat. It does not matter where the props are or how the driving force is delivered to the boat.

Which is correct?

Thanks!!!

I can't believe this is still being discussed. You got your answer in post 14. The pivot point is not fixed - at rest it's near (and usually just forward of) the longitudinal centre of the boat, and moves forward or aft from that point as the boat increases speed going forward or astern respectively. It varies with the hull shape.