Question:

On many Sikorsky rotorheads they have stops installed that limit flapping in a static or low rotational speed and droop stops that limit the downward travel of the blades when they are at rest. These stops are mechanically linked to the rotorhead so that when the rotorhead is spinning the stop assemblies rotate with it. However the stops are free to move outward in a radial direction and as the speed builds the anti cone (flap) stops will move outward against a spring. This frees the blades to cone with applied collective pitch. Once the blades come off the droop stops they too will also move outward against a spring load. As the blades slow down after landing the droop stops will move inward thus limiting the downward movement of the blade and shortly thereafter the anti cone (flap) stops will be drawn inward limiting the ability of the blade to sail at low speed. The inward movement is effected by a spring(s)

Here is the question: What force causes these stops to move outward against the springs?

Would anyone disagree with the following thought process?

1. I lie on the floor, on the equator, which is part of the Earth's surface rotating at impressive speed about the Earth's axis (and in a multitude of other directions through space but lets ignore that!)
2. Luckily gravity sucks me towards the centre of Earths mass (actually towards all the individual components of its mass)and in fact I attract the Earth with exactly the same force. If it were not for this mutual attraction I would disappear from the Earth's surface in a direction tangential to the rotation of the Earth's surface at this point (Rather like some of these threads!).
3. Gravity is providing a force on my body, towards the centre of the Earth, rather greater than the centripetal force required to accelerate me in a circular path along with the surface of the earth. This extra force can be felt, while I am lying here I can feel sharp stones pressing into me (Of course they are not, I am pressing onto them and I feel the REACTION to that).
4. The extra force is rather useful, it means that if I jump over a fence I return to earth the other side and if an engineer drops a spanner he is likely to find it at the bottom of the engine bay or on the floor.
5. Now let's carry out an experiment of the mind - Let's, in a major mining exercise remove a vast quantity of the Earth's mass and send it off into space where it will not have a significant gravitational effect on us. As the Earth's mass reduces our mutual attraction reduces until at some point the gravitational force is exactly that required to maintain the centripetal force. I am now IN ORBIT on the Earth's surface, I feel weightless and if I jump up I will leave Earth's atmosphere.
6. At this point there is only one force acting on me - gravity - it is acting on my body, towards the centre of mass of the earth, this is centripetal force.
7. Where does centrifugal force come into this? My belief is that centrifugal force is the REACTION to centripetal force and is the force that I exert on the earth, attracting it to me. If you measure very accurately you will find that I am causing the Earth to 'wobble' on it's axis, even though I still feel weightless.

Thats it for now, I would be interested in your thoughts on this, I'm off for a lie down!

[ 18 December 2001: Message edited by: TeeS ]

Lu
As the rotor head starts to rotate the springs provide the centripetal force to accelerate the weights towards the centre. As the rpm increases more force is required by the springs and so they stretch. The weights themselves are just trying to do there own thing and travel in a straight line.

To: TeeS

Remove the springs from the stops. The weights will be accelerated in a circular path and as a result will still fly outward and the only restraint is their attachment to the rotorhead. Now this could be the same as one of the definitions of centripetal force in that it is the force exerted in order to move a body through a circular path. In another definition it states that it is the inward force exerted in order to restrain a body that is moving in a circular path from flying outward.

I know it is not just me that finds this concept difficult to absorb although I have, thanks to the many posts on this and other threads but non educated individuals like myself find it difficult to view the restraining action of the rotorhead as a force tending to move the blade inward when there is no inward movement.

I think the best non-engineering explanation is that the centripetal force is opposing centrifugal force. That way, both forces are recognized.

Lu

Take the springs away and gravity on it's own does the job. I suspect that if you put your rotor head into a gravity free, frictionless environment (I know it's getting silly now!) then as soon as you rotate the shaft the balls will extend to the horizontal. Not because they are being 'thrown out' but because that is the closest to a straight path that they can travel in. The only thing stopping them traveling in their desired path (a straight line)is the centripetal force applied by the shaft.

Lu,
I request you go back to my logic chain and discuss the point at which you lose understanding. Otherwise, we will continue to go around and around (absolutely no pun)with your latest example. I chose David & Goliath because that was the example you first asked about, then I mentioned the car after the second series you asked about. We then explained the alcohol pump in the FAA questionnnaire to you, and the marble on the merry go round.

Instead of introducing yet another example by trying to answer your questions on droop stops, shouldn't we nut out the principle so they can be applied to all of your examples?
Please?

Again: I request you go back to my logic chain and discuss the point at which you lose understanding.

TeeS, you're bang on except for the part about centrifugal force. Centrifugal force is what we call the force that we feel when we're rotating. We feel it, it is apparent, it is not real.

Lu, you said, "...[some] find it difficult to view the restraining action of the rotorhead as a force tending to move the blade inward when there is no inward movement."

In fact there is inward movement. The "natural" movement is a straight line. To move in a circle, you must move from the straight line towards the center...inward movement.

You seem to consider all the diagrams to be stationary. When you do this, you are in a rotating (non-inertial) reference frame. In that frame, only a centrifugal force appears to be acting. Describing the droop stops as being moved by a centrifugal force is accurate when you're confined to that reference frame. That doesn't mean it's a real force.

If you think of the two as equal and opposite forces, then you end up with a net force of zero. In a rotating frame a net force of zero means you feel nothing. In an inertial frame a net force of zero means the object's path doesn't curve.

[ 19 December 2001: Message edited by: heedm ]

An addition to TeeS' post. Rather than imagining you're in orbit at the surface of the Earth, think of geosynchronous satellites. If there were any such thing as Centrifugal force, they'd be charging off across the Solar System with great abandon. These beats are doing around 7000mph, the only thing holding them in orbit is the Centripetal force of Gravity. To quote Marshall Brain's HowStuffWorks site on Satellites:
"Without gravity, the satellite's inertia would carry it off into space. Even with gravity, if the intended satellite goes too fast, it will eventually fly away. On the other hand, if the satellite goes too slowly, gravity will pull it back to Earth. At the correct orbital velocity, gravity exactly balances the satellite's inertia, pulling down toward Earth's center just enough to keep the path of the satellite curving like Earth's curved surface, rather than flying off in a straight line."
Note the use of the word "inertia". Another point: "Centrifugal Force", if it existes, operates in line with, but opposite to the Centripetal force holding an object in a circle; take away the Centripetal force (David's sling breaks, you let go of the dumb-bell, the Earth disappears) and the object would fly off radially - in the direction of the "Centrifugal Force". It actually flies off tangentially, in the direction its inertia takes it.

a tractor hooks a chain on to a spike wich is driven into a stump. the ground is boggy and the tractor slips on the surface not able to move the stump. some say a force would be pulling the tractor backwards, i say it is a reaction that the tractor stops when it has'nt got the force to pull the stump out. the stump needs a curtain amount of force to remove it. now the tractor turns to drive perpendicular to the stump, the chain spinning on the spike. the tractor gets faster and faster around the stump using its weight more efficiently. eventualy the stump comes out.
some say a force pulling the tractor to the stump causing a direction change is what causes the stump removal. i say that the centrifugal force acoplished by the tractor over comes the force the stump needs to be moved. you could easily say the stump had centripital force holding the tractor, but when the tractor wasnt spinning around the stump what would this be called?

vorticey:
If you dont mind, I will use the logic chain as per our last discussion on the other thread, to answer your question/statement.

If you go to step 3 & 4 re the fact that changing direction requires an acceleration, and thus a force. The the tractor is (like Davids rock in the sling, the car turning a corner, the girl on the merry go round, the alcohol in the pump, the marble on the circular plate, and the droop stops of a rotor system) changing direction because it is going around a circle. Thus, in accordance with step 5 & 6 it requires a force to keep changing it's direction. No change to the logic chain thus far.

What seems to confuse the issue here is that the thrust is coming from the tractor at the edge of the circle, not from the center such as Davids hand in the rock throwing exercise. But what force is the tractor doing? I assume here that the tractor is attempting to create tension on the chain, therefore it cannot be turning around the stump because the chain would then be limp, i.e. it must be trying to go straight ahead. To get it to change direction and go around and around, we need to apply an acceleration (as per above).

We recall from step 3 & 4 that you depict an acceleration as acting in the direction you are accelerating to, such that if you accelerated in a straight line, you would depict that acceleration as toward the front of the tractor. But this tractor has an acceleration causing it to go around and around toward the center of the stump. Therefore the force is acting TOWARD the stump, i.e. centripetal. Thus the fact that the tractor is providing the thrust does not change the direction the force is acting. Indeed the only difference between the car turning and the tractor is that the centripetal is being provided by the tyres on the car, and the chain/stump for the tractor.

The next confusing thing is that the stump gets pulled out of the ground, and it looks like there has been a force pulling it outwards. It is easier here to think of a straight line acceleration equivalent, lets say like the van used in the posts above, with a passenger inside the van on rollerskates. The van accelerates, and the guy inside gets slammed into the back of the van, and continues to get "pushed" into the back of the van as long as it accelerates. We know that the acceleration force is acting toward the front of the van, but if the force is high enough that the van doors can no longer transfer that force to the guy on skates, the van doors break open and the guy on skates becomes sore. Why? Becuase the accelerative forces were more than the than the van doors could handle. Back to the stump. We saw that the tractor's constant directional changes were due to a constant acceleration, and as force equals acceleration X mass, and the tractor has much mass, there must be a large amount of force being applied. As in the van doors, it is simply a matter of the at rest inertia of the stump being overcome by the amount of force to continue changing the direction of the tractor.

Now to you question: you say >>you could easily say the stump had centripital force holding the tractor, but when the tractor wasnt spinning around the stump what would this be called?<<

This is the bit where it gets really confusing (well it did for me when I learnt it). The stump is NOT exerting centripetal force. Remember from above, the cenripetal force acts toward the stump. Therefore the question is not really answerable, but I think I can see where you are comming from. Remember that the van doors busting open above? Well that was because the force required to accelerate the mass of the guy on skates became greater than the ability of the doors to stay closed. Just as in our tractor case, the force required to move the stump was overcome by the acceleration (changing direction) of the tractor's mass. So what are the van doors without the guy being accelerated and what is the stump without the chain? They simply adhere to Newton's law that a body will remain at rest unless acted upon by a force (see Step 1 of the logic chain). How mush force is required to move them is dependant upon mass, friction with the ground, etc. Thats what the stump is before the chain - a big mass with huge friction which would therefore require someone to exert heaps of force to move it!!

Too tired to make the above brief. Sorry vorticey.

Is it not correct to say that the centripetal force on the 'rotating object' is opposed by an equal and opposite centripetal force on the 'central object'?

Which of the two objects is rotating about the other is dependent upon the perspective of the observation.

Assume that the difference in mass between the two objects is very large. If the person is located on the item with the smaller mass, he will feel the centrifugal effect. Alternatively, if the person is located on the item with the larger mass, he will not feel the centrifugal effect.

<img src="confused.gif" border="0"> <img src="confused.gif" border="0"> <img src="confused.gif" border="0">

When the tractor is driving around the stump, the tension in the chain supplies the required centripetal force. The tension in the chain also pulls on the stump. The stump isn't moving in a circular path so it doesn't need or feel centripetal nor centrifugal forces.

When the tractor pulls on the stump in a straight line, there are equal and opposite forces on the tractor: tension in the chain, and the driving force developed by the tractor. The system is in equilibrium so there is no acceleration.

If centripetal and centrifugal added up to zero, then there would be no circular motion since an object in circular motion is not in equilibrium.

The stump doesn't create any force...it reacts. Consider doing a chin up on a chin up bar. The bar doesn't pull you up, your muscles do.
_________________

Dave, there is no centripetal force acting on the central object. A force pulls on it, but if the object is truly central then that force cannot be centripetal. When the moon orbits the earth, neither body is central, they both orbit a point in between. (it's easy to calculate ratio of masses equals ratio of distances from the point...and it's closer to the heavier object).

Hi heedm

I would beg to differ; <img src="eek.gif" border="0"> and submit the following argument.

&gt;"... there is no centripetal force acting on the central object."&lt;
There is no object that can truly be considered central.

&gt;"... if the object is truly central then that force cannot be centripetal."&lt;
The concept of centrality is only a point of reference.

I agree that the earth and the moon are rotating about a central point. They rotate about this point because there is an equality of opposed centripetal forces.

Using the merry-go-round as an example;
If this merry-go-round could be in absolute balance, then its very center is the point of reference. There is no mass (object) at this point, only opposed centripetal forces.
.
If the merry-go-round is out of balance, because there is only one rider, then this point has shifted slightly. It must now be said that the earth, which is attached to the physical center of the merry-go-round is experiencing an infinitesimal amount of centripetal force about the rider.
_____________-

Got little to do with helicopters but it's fun. <img src="smile.gif" border="0"> http://www.UniCopter.com/7up.gif

To Dave and vorticey:

I think I have put my finger on part of the confusion. I note that you have both spoken of Newtons law in terms of each force has an equal and opposite force. But the law actually states each action has an equal and opposite reaction relating to a body in equilibrium. Not semantics, but quite crucial to our discussion here.

When pushing on an object that stays at rest (i.e. in equilibrium), it can be said that the object has an equal an opposite reaction to that force therefore it doesn't move. Using the chin up bar from Heedm, you are applying a force upwards, and the bar remains stationary (in equilibrium) but you wouldn't say it is applying a force downwards would you? As you lift your self off the ground (assuming you are not as fat as me) your speed has changed (upward). Accordingly you have applied an acceleration upward. But still, the bar has not applied any force or acceleration has it? The bar is still at equilibrium, therefore you are still getting an equal and opposite reaction from the bar. But not a force. See the distinction?

<img src="smile.gif" border="0">

OK helmut fire, here goes


&gt;"But the law actually states each action has an equal and opposite reaction relating to a body in equilibrium. Not semantics, but quite crucial to our discussion here."&lt;

A couple of separate sources say;

" Newton's second law of motion can be formally stated as follows:
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object."

"By Newton's Second Law, such acceleration implies that there must be a force acting on the object, directed at the center of the circle."

Even if the word 'action' is substituted for the word 'force', there must be a reaction to the action.
___________________

&gt;"Using the chin up bar from Heedm, you are applying a force upwards, and the bar remains stationary (in equilibrium) ."&lt;

&gt;"As you lift your self off the ground your speed has changed (upward). Accordingly you have applied an acceleration upward."&lt;

As the athlete accelerates upward, the earth accelerates downward (damn little of course).
____________________

&gt;"But still, the bar has not applied any force or acceleration has it? The bar is still at equilibrium."&lt;

Neither the bar (and the world which is attached to it) nor the torso of the athlete have applied any force, but the arm muscles located between the two have.
__________

Your serve <img src="smile.gif" border="0">

It seems so strange that members of this forum are attempting to finesse each other by publishing their interpretation of Newton three laws. Each has his own interpretation and tries to convince the other guy that his version is right. It is analogous to my arguments with the Brits and Ausies about gyroscopic precession. My reason for making this post is to state that last night I heard a report that scientists have found a way to accelerate light beyond light speed. If this is true many new scientific breakthroughs are on the horizon and Isaac Newton’s laws will go along the wayside along with other scientific concepts. All of this most likely in an alternate universe.

Lu

Some people enjoy having non-confrontational arguments.

As you know, there's a pleasure in contributing knowledge to others. There's also the greater pleasure of broadening one's knowledge, thanks to the contributions of others.

Its fun provoking and being provoked into reassessing one's beliefs. In fact, doesn't helmut fire have an unanswered question pointed in your direction. <img src="wink.gif" border="0">

[ 21 December 2001: Message edited by: Dave Jackson ]</p>

Dave said, "There is no object that can truly be considered central." and "The concept of centrality is only a point of reference.".

Those statements contradict each other. Since 'centrality' is only a point of reference, then by choosing your point of reference appropriately, an object can truly be considered central.


Just because two bodies are gravitationally attracted, it doesn't mean they are orbiting each other. To call something a centripetal force, the body on which the force acts must be moving in a curved path.

___________

Of course, now we're getting really picky. At this level of detail we should be considering relativistic mass of the rotor tips and how that affects tracking. <img src="wink.gif" border="0">

"The greater our knowledge increases the more our ignorance unfolds." --John F. Kennedy

heedm

To continue a hypothetical argument, in the hope that there may be a practical conclusion. <img src="smile.gif" border="0">

&gt;" Dave said, "There is no object that can truly be considered central." and "The concept of centrality is only a point of reference.".

Those statements contradict each other. Since 'centrality' is only a point of reference, then by choosing your point of reference appropriately, an object can truly be considered central. "&lt;

Going into deep space ( or getting into deep sh-t), assume that two planets of equal mass are rotating about each other; or to be more exact, rotating about a central point. If the mass of one planet is increased visa-vie the other, the central point will shift toward the planet of heavier mass. They still should be considered as rotating about each other.

No matter how great the difference in mass becomes;
1/ they will still be rotating about a central point (rotating about each other).
2/ this central point will never be concentric with the large planets center of mass.


&gt;" To call something a centripetal force, the body on which the force acts must be moving in a curved path. "&lt;

From a remote perspective, both the above planets are moving in curved paths. For the perspective of one of the planets, only the other planet is moving and that is with a curved path.


Could not the above be said about the helicopter, in respect to two (or more) blades? <img src="confused.gif" border="0">
__________

Lu: If you've read this far and are answering questions.

Leonardo da Vinci designed a vehicle that was intended to 'screw' its way up into the atmosphere. Do Newton laws disprove Leonardo's thinking, or do they compliment it with a higher level of technical understanding? <img src="frown.gif" border="0">

[ 21 December 2001: Message edited by: Dave Jackson ]</p>