6. Levitation versus equilibrium - the primary cause of rotation

As has been mentioned above, the greatest braking impact of gravity occurs during the passing of the loads through the sector A₈ - O - A₁₁ (Fig. 2). Here the centers of gravity of the loads are separated from the axis of rotation at the maximum distance (R_max), i.e. the corresponding lengths of the lever arms of rotation are increasing to the maximum size, and direction of the resultant impact of gravity is opposite to the desired direction of rotation. Therefore, just in this sector is most expedient to introduce the external force that can offset the negative influence of gravity.

If we equip the movable loads of cylindrical shape, which were shown in Fig. 4, with the permanent magnets of annular shape with radial magnetization, and place under them, in the sector A₈ - O - A₁₁, the stationary permanent magnets rectangular in shape, then we can use the phenomenon of levitation of permanent magnets. The practical utilization of the phenomenon of levitation is possible under the condition that both the opposing magnets are mechanically constraint by disposition along a single axis and oriented so as to repel each other. Such state of levitation is defined as “Mechanically constrained pseudo-levitation”^[6],[7]. In our case, the movement of the cylindrical loads in space are mechanically constrained by the inclined paths, which are embedded in the disks, that is, by means of profile of the ways on which the wheels of the loads can roll down under the influence of gravity.

Fig. 5

Let us consider Fig. 5, where is shown schematically the mutual arrangement of the movable cylindrical loads, fitted up with annular magnets, and the stationary magnets rectangular in shape, which are under the movable loads. This figure shows a cross section of the magnets by a plane perpendicular to the axis of rotation of the disks and passing in the space between two disks. The orientation of the magnetization is conditionally shown in red and blue. The geometrical shape of the stationary magnets can match Fig. 5, or each of them can have the shape of a rectangle with the pole’s tip from the material having the sufficiently high magnetic permeability.

On passing this sector, the movable loads will be climbing up and “will hover” over the stationary permanent magnets as a result of the repulsive interaction of magnetic fields. At the same time the force of gravitational attraction of the loads, directed downwards is balanced by the force of magnetic repulsion, directed upwards. As a result, when passing through this sector, the loads will not create torque.

Thus, owing to levitation, the loads, designated as the A₈, A₉, A₁₀, A₁₁, no longer render a negative impact on the creation of the net torque in the required direction, and in calculating the total torque the loads A₈, A₉, A₁₀ can be excluded from consideration. As for the load A₁₁, then it should be considered as approached to the rotation axis by a distance corresponding to R_min, i.e. locating in the state of a₁₁.

Now, taking into account these changes, and turning once again to the results of calculation in a general form of the net torque, which have been given in table 1 of the “Appendix 1” (calculations which have been made for the state of the disk, corresponding to Fig. 2), we can make an estimate of the net torque on the motor shaft of the disks, corresponding to Fig. 5. To obtain such an estimate in numerical form, let us set quantitative values of certain geometrical dimensions of disks, cylindrical loads and average value specific weight of the each load.

Using the calculation method which has been set forth in “Appendix 1”, we will perform such an evaluation, as an example.

1. By means of removing from the net torque, which is created by all sixteen loads, the values of the torques which are created by the loads A₈, A₉ , and A₁₀, and by reducing the torque that is created by the load A₁₁ by 2.64 times, in view of its shift into the position a₁₁, i.e. corresponding reduction in the length of its lever arm, we obtain the value of the resultant torque represented in the general form:

   ∑M_g = (+6.988 −4.646)F_gR_min = +2.342F_gR_min

2. As the initial data for the calculation we will take the following:
   • R_min = 34cm (at this, R_max = 2R_min = 68cm, and the outer diameter of each disk is approximately equal to 150cm);
   • L₁ = 142cm - the length of the working part of the cylindrical load, located in the space between the disks (at this, the distance between internal surfaces of the disks approximately equal to 160cm);
   • R₁ = 4.5cm - the radius of the outer surface of the cylindrical load;
   • Υ_g = 6kg/dm³ - average specific weight of all the materials from which made the cylindrical load.
   The relations between the other linear and angular dimensions we will take the same as those were taken in the calculation in general form.
3. We will calculate the force of gravity of each cylindrical load F_g:
   • the volume of the working part of the cylindrical load (excluding the wheels on its ends) is:

     V₁ = πR₁²L₁ = 3.14·0.45²·14.2 dm³ = 9dm³;

   • the weight of the load is:

     W_g = Υ_gV₁ = 6kg/dm³·9dm³ = 54kg,

     i.e. with such initial data, the force of gravity of the load is F_g = 54kgf.
4. We will calculate the magnitude of the net torque:

   ∑M_g = +2.342F_gR_min = + 2.342·54kgf·0.34m ≈ 43kgf·m,

   what corresponds to the value of 422 Newton-meters (Nm).

The calculation was made at precondition that the stationary magnets, shown in Figure 5, must provide a complete counteraction gravity to brake the rotation when the movable loads are moving into this sector. And only! That is, the impact of the levitation on the centers of gravity of the movable loads must only provide the compensation influence of the gravitation, but the forces of interaction of the magnets must not be too large, i.e. they must not create an additional moment of rotation. Thus, the net torque received from this calculation is determined only by the impact of gravitation into others sectors of rotation, into the sectors where the centers of gravity of the movable loads form unequal lever arms of rotation about the axis of rotation of the motor. At the same time, due to the impact of levitation, the states of stable equilibrium in the system are eliminated, and as a result, the net torque is created only by the use of the kinetic energy of the gravitation. The rotatory impact (net torque) arising at such conditions we will call henceforth as the "Initial rotatory force".

Is it a lot of ∑M_g ≈ 43kgf·m = 422Nm, or a little? - In my opinion*, since for the evaluation were taken relatively large dimensions of the motor rotor, it is quite little.

Then the question arises: - "What are the technical means are able to increase the net torque on the motor shaft of the proposed device?

But before we answer this question, we will consider the possible design of cylindrical loads, equipped with annular shaped magnets.

Note:

^*The phrase "In my opinion" should understand as the point of view of an amateur, a dilettante in the field of physics and mechanics, but not a professional. Professional knowledge I had in radio engineering. After graduating from the Moscow Institute of Communications up to the age of retirement I had been working on profession at one of the Moscow Research Institutes. I have got interested in physics, mechanics, and in particular in magnets, only from the age of seventy years old.

This page was last modified on 18 September 2014