The Todeschini/Di Bella Device Part I

Inertial Propulsion

In my blog post of 14 April 2014, I raised the idea of a perpetual motion machine having a number of inertial propulsion devices arrayed around its rim. Of course, these would have to work very efficiently, if the device was to achieve a net energy gain. But even if we set aside the question of efficiency for now, is any inertial propulsion device even possible?

In my next few posts, I'll look at some ideas that could generally be described as inertial propulsion, which I have personally found interesting and worthy of further investigation.

The first Di Bella device

In 1968 Professor Alfio Di Bella of the Institute of Naval Architecture, University of Genoa, published a paper titled "On Propulsive Effects of a Rotating Mass." This paper discussed in detail the extensive testing that was done on some real physical devices constructed by Di Bella and his team. 

(Reference: "On Propulsive Effects of a Rotating Mass", Prof. Alfio Di Bella, Proceedings of the 7th Symposium of Naval Hydrodynamics, Rome, 1968, pp1373 - 1396.)

This paper is one of the less well known, but most interesting and well-researched documents on inertial propulsion. I'll devote this post to Di Bella's original device, and two more to developments of it.

Not an inertial propulsion
 

Fig. 2 from Di Bella's US Patent 3,404,854

Initially, Di Bella's paper discusses this device, from his US Patent 3,404,854. Briefly, the motor 1 turns frame 4, carrying axle 9, counterweight 11 and bevel gear 10, which meshes with the fixed bevel gear 14. This causes the out-of-balance mass m to follow the locus drawn below, known to mathematicians as the "Window of Viviani".

Locus for the mass of Di Bella's original device: the Window of Viviani

Tests

Di Bella says "The device was tested extensively on the ground and on the surface of the water with satisfying results on the whole." Nevertheless, it's apparent (as Di Bella realises and points out) that this device relies entirely on interaction with its surroundings, generally by friction, in order to operate at all.

My own version

For reasons I'll give in my next post, I decided to make a modified version of Di Bella's device. First step: design and make the bevel gears!

Two bevel gears, to my design (but not made by me — bevel gears
require a specialised tooth generating machine, which I don't have)

Some Attempts to Exploit Centrifugal Force

Fig. 1  A mass m in a turning wheel

Offsetting

As the wheel of Fig. 1 turns with rotational speed ω, the mass m, at radius r, travelling at velocity v, experiences a centrifugal force of F  =  mv²/r  =  mω²r.  As a force, F is a vector quantity, whose line of action passes exactly through the wheel's center. If the line of action could be offset even slightly, as shown in Fig. 2,  F would exert torque on the wheel, accelerating its rotational speed.

Fig. 2  An offset centrifugal force vector

While it isn't possible to achieve a simple offset of centrifugal force like this, there are other possibilities. Let's now look at a few of them.


Splitting forces and torques

Fig. 3  Centrifugal force split into two equal forces and torques

Fig. 3 shows the mass centrally located on a bar, with vertical arms linking to other arms on the wheel's centerline, each with a torsion link (solid circle) to the wheel. 

The single, centrally-directed centrifugal force has now been split into four components: two torques and two forces which are no longer centrally-directed. Obviously the forces and torques balance out for this model, but could it be possible to find a case where there is some imbalance?


A lower arm reversed

Fig 4  Split forces and torques with a lower arm reversed

Fig 4 shows one of the lower arms reversed, so that it is attached to the wheel at a larger radius than the other arm. Here the effect of the left side force being exerted at a larger radius is balanced out by the higher force on the right side, and the torques being exerted in the same anticlockwise direction. There is no overall torque on the wheel.


Split torques turning in the same direction, with equal torsion links

Fig. 5  Split torques in the same direction. All torsion links are equal

Fig. 5 shows another linkage from the mass to the wheel.  If the model could be made stable with equal torsion links (solid circles) as shown, then both the left and right split forces would be equal to F/2, balancing out, yet the two torques would both turn the wheel anticlockwise. 

I made some silux models of this idea (below), all with 1m diameter wheels. The first one does have equal torsion links installed as shown in Fig. 5.

Fig. 6  Silux model of Fig. 5, with equal torsion links

Details:—
wheel mass: 100kg
all arm masses: 0.1kg
mass: 4kg

all torsion links: 50 N-m/rad
wheel speed 12.5 rad/s.

The model reaches the equilibrium position shown in Fig. 6, with no net torque on the wheel.



Split torques turning in the same direction, with unequal torsion links

Fig. 7  Silux model of Fig. 5, with unequal torsion links

This silux model was similar, except for the torsion link values:

torsion links left: 70 N-m/rad
torsion links right: 5 N-m/rad

wheel speed 12.5 rad/s.

This time, the model reaches the approximately symmetrical equilibrium position shown in Fig. 7, but once again there is no net torque on the wheel. The higher torque on the left side means there must also be a higher force on that side, and the two effects cancel out.



Split torques with torsion links only on lower arms

Fig. 8  Silux model of Fig. 5, with torsion links only on lower arms

This silux model was again similar, except that:

torsion links were installed between the arms: both 25 N-m/rad
only simple links were installed between upper arms and the bar.
torsion links lower arms to wheel: both 50 N-m/rad

wheel speed 12.5 rad/s. 

The model reaches the equilibrium position shown in Fig. 8. Note that there is no torque exerted on the lower arms, and hence on the wheel.


Other possibilities

Fig. 9  Both force and torque are exerted on the right of the wheel, tending to cancel out.
On the left, force is still exerted on the wheel, but torque is reacted by the carrier (blue)
which has rollers running in the fixed, circular earthed track (green).

There are obviously many other possibilities that could be investigated, such as having split forces and torques, both exerted on one side against the wheel, but with only the force on the other side exerted on the wheel, for example as shown in Fig. 9. Another option would be to have force and torque exerted only on one side, again with the force but not the torque acting on the wheel, as shown in Fig. 10.

Fig. 10  Here force acts only on the left of the wheel, with torque acting on the earthed track via the carrier.
The mass oscillates radially because of the torsion link, possibly together with a spring added between the mass and the wheel center, opposing the centrifugal force. This oscillation is intended to permit resetting of the carrier as required in the non-circular earthed track, when the mass is at its minimum radius, four times per revolution.

These possibilities, or something like them, could be worth further work; but overall I think it's unlikely that centrifugal force, by itself, can be exploited to give a net torque on a wheel.

Production of Centrifugal Force

I have a little more to say about theoretical aspects of centrifugal force, before looking at some practical cases next time.

A century-old textbook

A very good textbook, written during the First World War

I sometimes find it useful to check present-day concepts in science and technology against earlier ideas, to see what different insights those earlier writers had, even on apparently straightforward concepts like centrifugal force.

Nearly a century ago, Prof. Andrew Gray, F.R.S. of the University of Glasgow wrote what many think is still the best English-language textbook on gyroscopic theory:  A Treatise on Gyrostatics and Rotational Motion. It was republished by Dover Publications, Inc. in 1959.

A turning vector causes a time-rate production of itself

In discussing how turning the axis of a spinning gyroscope can cause a time-rate of production of angular momentum, i.e. a torque, Prof. Gray writes the following footnote (page 8):—
 

My interpretation of Prof. Gray's footnote on p8 of his book.
A turning vector (momentum) causes a time-rate of production of itself ( = force)

"For example, a particle of mass m is moving at any point P along a curve, that is along the tangent to the curve at P, and therefore the direction of motion is changing at P with angular speed v/r, where r is the radius of curvature at P. We may regard the tangent as an axis with which is associated the momentum mv, and which turns with angular speed v/r, as the point of contact advances along the curve. Thus along the direction towards the center of curvature at P, which direction is fixed for P, and towards which the tangent at P is turning, there is a rate of growth of momentum measured by mvω = mv.v/r = mv²/r, a very well-known result. The same process holds for any directed [i.e. vector] quantity (momentum, angular velocity, angular momentum, etc., associated with an axis)."

Reading this, I understood for the first time that the production of centrifugal force, considered as a time-rate of growth of momentum (d(mv)/dt = force) can be regarded as just a specific application of a much more general principle.

Centrifugal and Other Inertial Forces

Will there ever be a stable definition for centrifugal force?

Centrifugal force is the most obvious, and is usually the first mentioned of the so-called "inertial" forces. But from my earliest years as a student, I can remember that there has always been controversy over what centrifugal force is, and is not.

When I was in my first year at university, back in the 1960s, the textbook we used for Applied Mathematics I was An Introduction to the Theory of Mechanics by K. E. Bullen M.A., ScD., F.R.S., who was Professor of Applied Mathematics at the University of Sydney, Australia.  Prof. Bullen always had an appropriate quotation to introduce each chapter of his book, often "tongue-in-cheek", and from unexpected sources. I can't resist giving a few now:—

For Chapter XI, Centers of Mass and Moments of Inertia

"One should be concerned not merely with the weight of one's body, but with how this weight is distributed."
— Australian Women's Weekly

At the end of Chapter XVII, on the page headed Advice to Examinees

"But though they wrote it all by rote
   They did not write it right."
— "Louisa Caroline", The Vulture and the Husbandman

Getting back to the topic of this post, here is the quotation introducing Chapter VII, Dynamics of a Particle Moving in a Circle:

"Instead of debating whether it (centrifugal force) is a force 'seeking the centre' or 'fleeing from the centre', we should expedite its 'flight' from the subject of (elementary) mechanics altogether."
— E. G. Phillips, Mathematical Gazette, Feb. 1946.

Wikipedia

If we turn to the modern "fount of all knowledge" the internet, and specifically Wikipedia, we find that its definition of centrifugal force has inched forward slightly over the last decade, from total denial to minimal recognition:—

In 2004, we were told that "Centrifugal force is actually not a force..." 

Five years later, it was no longer "not a force", but had become a "fictitious" force and was "one of several pseudo-forces..."

Earlier this year it had changed from "fictitious" to "apparent", and as this is posted it is "apparent" and "fictitious" a.k.a. "inertial," and also a reaction force corresponding to centripetal force. See http://en.wikipedia.org/wiki/Centrifugal_force.

Whether it's labelled "fictitious", "pseudo" or "apparent", some force expels water from the clothes when my washing machine goes into its spin cycle. Some force caused those high-revving flywheels/clutches to explode in the early days of drag-racing, causing serious injury and damage before scattershields became mandatory. Surely we are entitled to recognize and name it as a true force?

Once Wikipedia has finished assuring us about how "fictitious" it is, I don't really have a problem with its current explanation(s) of centrifugal force.

Other inertial forces

There is a lot more about the inertial forces, once again labelled "fictitious", at http://en.wikipedia.org/wiki/Fictitious_force. However, for general readers this is quite a lengthy and complex discussion. The best short account of the inertial forces that I've seen is on p82 of Prof. Andre Assis' book Relational Mechanics. Setting out the orthodox view, he says:—

"In an inertial frame S we can write Newton's second law of motion as  m(d²r/dt²) = F  where r is the position vector of the particle m relative to the center O of S.

Suppose now we have a non-inertial frame of reference S' which is located by a vector h with respect to S (r = r' + h, where r' is the position vector of m relative to the origin O' of S'), moving relative to it with translational velocity dh/dt and translational acceleration d²h/dt². Suppose, moreover, that the axes x', y', z' rotate relative to the axes x, y, z of S with an angular velocity ω. In this frame S' taking into account the complete "fictitious forces" Newton's second law of motion should be written as ... 

m(d²r'/dt²) = F'  -  mω × (ω × r')  -  2mω × (dr'/dt)  -  m(dω/dt) × r'  -  m(d²h/dt²)

The second term on the right is called the centrifugal force, the third term is called the Coriolis force, the fourth and fifth terms have no special names."

Recently the fourth term above has been named the "Euler force".

Why orthodox science doesn't like inertial forces

There is a deep-seated reason for the problems with defining centrifugal force, and by extension, all of the inertial forces, although orthodox science is unlikely to admit it. The following quote explains it well:—

"Possibly due to the fact that the inertia forces are so uniform and also that a search for their source implies the currently unfashionable non-local interaction principle, they have been treated differently from the other forces in modern textbooks and are often only described as "pseudo-forces". Part of the problem with the image of inertial forces is that nobody has yet proposed a Newtonian non-local force law which can give the inertial force the same "true-force" status as the laws of gravitation, electrostatics, and electrodynamics. Such a law is proposed in Chapter 12 of this book. Like its predecessors, the laws of Newton, Coulomb and Ampère, it makes no assumptions regarding the mechanism of non-local interaction, but simply aims to fit the observed acceleration measurements."

Reference: In the Grip of the Distant Universe — The Science of Inertia, Peter Graneau and Neal Graneau, p19.

As I understand it, the "non-local interaction principle" mentioned above really implies IAAAD, (= instantaneous action at a distance). It apparently asks too much of modern orthodox scientists to accept IAAAD, but it would still be more honest for them to give the inertial forces their "true-force" status, and to admit that there is currently doubt and/or controversy over their origin. The option chosen instead, of pretending that they (sort of) don't exist, seems a bit puerile.

Series-parallel Springs

Exchanging potential and spring-stored energy

Suppose we allow a weight that is suspended from a tension spring to fall slowly ("isothermally") against a load. The spring is initially unstretched, and the falling weight delivers energy into the system until the spring force equals the magnitude of the weight. Then everything is in equilibrium, with no further movement.

Is it then possible, without adding any more energy, to extract all of the energy stored in the spring, and to raise the weight? The answer is yes. Of course the weight won't be raised back to its original height, because of the energy it already delivered, but we can still convert all of the spring stored energy back into potential energy of the weight. We can do this by initially constructing the spring as a pair of equal springs connected in series, and then reconnecting them in parallel.

Two equal springs connected in series, from a weight to the center of a wheel

The above silux model shows a series-connected pair of springs attached to a 4kg weight (red) which has fallen slowly as the wheel turned through 90 degrees, from an initial horizontal position with unstretched springs at 0.2m radius, to the vertical position shown, at 0.3180m radius. Each spring of k = 667N/m was stretched from 0.1m to 0.1590m.

If the low-mass spring joiner (purple) is now attached to the wheel, and the still stretched top spring is reconnected between the joiner and the weight (i.e. in parallel with the bottom spring), the springs will contract back to their unstretched length, pulling the weight up to a smaller radial distance of 0.2590m, where it can be caught and attached to the wheel.

The operating cycle is then finished by returning the weight back through 0.2590m to the horizontal position. Obviously, this will require energy of mgh = 4 × 9.80665 × 0.2590 = 10.16 joules. So, how much energy was delivered as the weight fell?

Graph of wheel torque vs wheel angle

Torque vs angle analysis

From the silux model, with the wheel turning at a very slow 0.01 radians/sec (to avoid any problems with centrifugal forces etc), we get the torque vs angle curve in the graph above. Integrating this curve, we get 10.15 joules of energy delivered, i.e. within 0.1% of the 10.16 joules required to return the weight.

A critic might say "O.K, you've just spent a lot of time and effort proving that there's no excess energy. That was obvious anyway from the conservation of energy principle." But to me, that was the point of this exercise, to carry out a detailed analysis for a particular case, and thereby get a fairly deep understanding of it.

From gravitational to inertial mass

More could be said about series-parallel springs, but I've decided not to say it just yet.

I have now finished my posts on devices that only exploit gravitational mass. Next time:— on to the second possibility mentioned in my post of 14 April 2014, i.e. "inertial" mass.

What if Only Momentum is Conserved?

Both energy and momentum always conserved

Two weights, about to fall from their highest position

This is just a "what if" post. Every physical process known (at least to me) always conserves both energy and momentum. But let's consider the two weights shown, on arms of negligible weight pivoted to the fixed axle, falling down together through 180 degrees to their lowest position. Each weight will reach a speed given by:—

      v² = u² + 2gh

where v = final velocity
            u = initial velocity = 0
            g = gravitational acceleration = 9.80665 m/s²
            h = total height of fall

If we set h = 1 meter, then we get

      v² = 0² + 2 × 9.80665 × 1

giving v = 4.4287 m/s for each weight when it has fallen down.

If each weight has a mass of 4kg, then, for the system as a whole:—

Total kinetic energy (½mv²) = 2 × ½ × 4 × 4.4287² = 78.45 J.
Total momentum (mv) = 2 × 4 × 4.4287 = 35.4296 kg-m/s.

An immediate transfer of momentum 

Let's also suppose that when it has fallen to its lowest position, one of the weights can immediately give up all of its momentum to the other weight. The first weight will obviously stop instantly, and from conservation of momentum, the still-moving weight must now have a velocity equal to the total momentum divided by its mass, i.e. 35.4296 ÷ 4 = 8.8574 m/s. So now the moving weight's kinetic energy is ½ × 4 × 8.8574² = 156.9 J, i.e. it now has twice the total energy that was gained when both the weights fell. That would certainly be an energy increase worth having!

Could it be done?

Could any process be found that would permit a weight to transfer all its momentum to another weight in such a way as to gain energy like this? I must admit I can't think of any, although I can understand why some people like to look into this idea.