The Lee-Tseung Lead Out Theory

[Top Gun]

Top Gun,

You ask for it.  If Slides 10-12 were correct, there would be some important consequences.

(1)   Does that mean humans no long depend on the Sun for their energy needs?  They can get gravitational energy from the earth, the moon, the stars and even each other?

(2)   Does it mean that a country such as China need not buy oil from the Middle East any more?

(3)   Is Gravitational Energy really non-polluting?

(4)   Will Gravitational Energy ever get exhausted?

(5)   How would that affect the power structure of this World?  Would USA lose its grip as the most powerful Nation in the World?

Dear Devil,

Your questions are good and relevant.  However, I am Top Gun only in Physics and Mathematics.  Mr. Tseung covers everything ? from morality to mutual credits. He will love to answer all your questions.

I shall only answer questions (3) and (4) from the Physics point of view.

(3)   Is Gravitational Energy really non-polluting?

When we talk about pollution, we normally think in terms of chemical pollutants.  In some cases, we talk about global warming.  From my understanding so far, no chemical changes need to take place to extract or lead out gravitational energy.  Thus Gravitational Energy is non-polluting in this aspect.

However, I believe much more gravitational energy will be transformed into heat.  Global warming is likely to increase.  However, there might be a ready scientific solution.  In the other extraction of energy from air invention, Mr. Tseung described the global cooling effect.  This should be researched further.

(4)   Will Gravitational Energy ever get exhausted?

I do not claim to have a unified theory that can explain all energies.  I know and accept that masses attract each other.  I can even reproduce the mathematics.  However, I cannot answer the deeper question of ? why is there such an attraction force. 

My answer to the question is ? I do not really know.  I only guess that such Gravitational Energy are abundant and easily exceed the known reserves of oil and coal.  They seem to be renewable as planets attract each other and may be in a constantly ?exchanging mode?.

[Top Gun]

I would like to comment now on the Second and subsequent Ideal Lee-Tseung Pull.  In the first Lee-Tseung Pull, the external force F is perfectly horizontal.  The analysis was very detailed and thorough.

After the first Lee-Tseung Pull, we can let the Bob swing back freely.  The Bob will go in direction to a maximum LHS position and then swing back to a maximum RHS position.  We can then apply the second Lee-Tseung Pull to the Bob.  This second Pull does not need to be perfectly horizontal.  The best or ideal pull is tangential to motion as shown.

Note that the mathematic treatment is now somewhat different.  Previously, in the first Lee-Tseung Pull, tan(a) = F/Mg.  In the second and subsequent ideal Lee-Tseung Pull, tan(a) = F1/T2.

As you might expect, much more mathematics will follow.  However, I would like the forum members to understand exactly when and how the second ideal Lee-Tseung pull will be applied.  Hopefully, the picture will be clear.  Please post if the picture is not clear to you.

[Top Gun]

Before I go into the mathematics, I would like to define what I mean by the ideal pull.

My definition of ideal pull is the minimum supplied energy to lead out the maximum gravitational energy.

Note that the ideal pull is no longer perfectly horizontal.  It has a vertical component contributing directly to the further lifting up of the Bob.  However, part of the force and energy supplied is still from the tension of the string.

[Top Gun]

For the mathematical analysis of the second ideal Lee-Tseung Pull, I shall refer to the spreadsheet file "The ideal Lee-Tseung Pull1.xls" posted as an attachment by Mr. Tseung awhile back.

Mr. Tseung used the line integral concept in his spreadsheet.  He first used the case of the angle a equal to 30 degrees and calculate the displacement of the Bob from 30 to 32 degrees.

(1)   He can work out the exact horizontal and vertical displacement at 30 degrees.  No approximation is required.
(2)   He can also work out the exact horizontal and vertical displacement at 32 degrees.  No approximation is required.
(3)   Thus he can work out the change in vertical displacement from 30 to 32 degrees exactly.  No approximation is required.
(4)   He can also work out the change in horizontal displacement from 30 to 32 degrees exactly.  No approximation is required.

Mr. Tseung then used the equilibrium condition at 31 degrees with the three forces. (Weight of bob, tension of string, Lee-Tseung pull).  The various forces can be determined exactly.  No approximation is required.

(1)   Weight has only the Vertical Component.  It does negative work as the vertical displacement is upwards.
(2)   The Lee-Tseung Pull has both vertical and horizontal components. Both components do positive work as the directions of force component and displacement are the same. (upwards and towards RHS).
(3)   The tension of the string has both vertical and horizontal components. The vertical component of force and displacement are both upwards.  Thus positive work is done.  However the horizontal component of force is towards LHS whereas the horizontal component of displacement is towards RHS.  Thus negative work is done by the horizontal component of the tension.

From the spreadsheet, the total energy supplied by the second Lee-Tseung Pull (from 30 to 32 degrees) = 0.018494 units.  This energy will Lead Out Gravitational Energy = 0.012929 units.  The ratio is approximately 0.018494/0.012929 = 1.4304189

In other words, approximately 1.43 units of supplied energy will Lead Out 1 unit of Gravitational Energy.  This is more efficient than the first Lee-Tseung pull when the external force is perfectly horizontal (requiring 2.014 units).

(to be continued)

[Top Gun]

In the spreadsheet, the various starting angles from 10, 20, 30, 40 ....90 degrees are also calculated.  With the imbedded formulae, one can easily change the increment angle of 2 degrees to other values (e.g. 0.2 degrees).

The Line Integral technique is to take a small interval (angle in this case) and use the average (force, work and energy in this case) to calculate the value at this interval.  The same is repeated at the next small interval.  The sum from these intervals can then represent the value of a very complex function.  (This is the technique used by the ancients to estimate the area of a circle.)

In this more accurate and advanced line integral technique, there is still the Lead Out gravitational energy.  This give me much stronger conviction that the Lee-Tseung Lead Out theory is correct.  I do not mind arguing these equations in front of the top physicists and mathematics at MIT, Cambridge, Tokyo, Paris, Moscow, or any other great universities. 

In supplying the actual spreadsheet, Mr. Tseung allowed other mathematicians to double check his formulae and calculations.  (I have problem uploading that spreadsheet again as the new upload size limit is only 50kb.  The .xls file is more than 60kb.  I winzip it.)