The Lee-Tseung Lead Out Theory

[ltseung888]

Part 2 of 6 in the reply to Tinu on slides 5-8 of Taiwan2a.htm

If Mg=60xg, F=10xg, then
Angle a = 9.48 degrees
Hori Energy/Vert Energy = 2.014?

When we apply the Pulse Force F, the tension (T) in the string must increase from 60xg to a larger value.  To be exact, we can calculate this larger value from the Pythagoras Theorem and get the answer as (sqrt of (10*10 + 60*60))xg = 60.828xg.

This increased tension of the string (which is a force) can be decomposed into the vertical and the horizontal components.  The horizontal component counters the horizontal Pulse Force F.  The vertical component is responsible for lifting the pendulum mass/weight.

The horizontal Pulse Force does work as there is horizontal displacement.  The vertical component of the Tension of the string does work as there is vertical displacement.  We can work out the ratio of these two energies.  That ratio horizontal energy/vertical energy is 2.014.  (In fact if you work out the various cases of small angles, the ratio is approximately 2.)  Thus Slide 8 is not an assumption.  It is the result of such mathematics.

End of Part 2

[ltseung888]

Part 3 of 6 in the reply to Tinu on slides 5-8 of Taiwan2a.htm

?Tinu wrote: ?Angle ?a? for a pendulum mass of 80kg and a horizontal force of 10kg*g is 7.125 degrees. This rationale is having a physical meaning in equilibrium only! (Static setup/no movement). However, the pendulum that is starting from the vertical will not stop at this angle. So, the force equality does not hold and you should know it. Then why applying this simple equality??

Let us focus on the Law of Parallelogram of Forces.  We know that after we applied the Horizontal Pulse Force and then let go, the pendulum will swing back. Let us isolate the two parts and analyze them separately.  Remember that the Law of Parallelogram of forces is a result of Newton?s Law of Motion.  If it fails, Newton?s Laws of Motion also fails. (At least in this case of Pendulum with a Pulse Force.)

If we apply the Horizontal Pulse Force from the vertical first time, the above configuration and calculation will hold.  Energy is added to the pendulum system.  However, the energy does NOT come from the horizontal pulse energy alone.

With pendulum mass of 60 Kilograms and Horizontal Pulse Force of 10g and a displacement of Lsin(a) where L is length of the Pendulum, a is the displacement angle, 2.014 units of horizontal Pulse Energy Leads Out 1 unit of vertical gravitational energy.  That vertical gravitational energy enters the Pendulum System via the tension in the string.

Note that the value of 2.014 is specific to the above example only.

End of Part 3

[ltseung888]

Part 4 of 6 in the reply to Tinu on slides 5-8 of Taiwan2a.htm

In our communication with the PCT patent examiner, we also showed the case of having a Pulse Force at an angle.  (Figure 4.2 in the document TPU-Theory1-5.doc in http://www.overunity.com/index.php/topic,2621.msg40277.html#msg40277)
The angle was deliberately set so that the tension of the string (T) and the Pulse Force (F) are equal with the Pendulum Mass at the mid-position.  At this initial position, the two forces are equal and a slight application of the Pulse Force will have displacement by both S and F.  Both will do work.

It is obvious that not all the energy comes from the Pulse Force.  We then extended the argument to Pulse Forces in all different directions.

End of Part 4

[ltseung888]

Part 5 of 6 in the reply to Tinu on slides 5-8 of Taiwan2a.htm

On the second and subsequent application of the Horizontal Pulse Force.

The Pulse Force F will now be applied to a moving pendulum system. Tinu is right in saying that if we completed our application of the Pulse, the pendulum system will keep going.  This is because it has acquired energy from the first application.

Tinu may be asking for an accurate mathematical representation of the general case of applying the Pulse Force in a moving Pendulum system.  The general horizontal energy may be thought of as the integral(T1(x)sin(a)dx where T1(x) is the varying horizontal force component of the Tension of the String; a is the angle of displacement and dx is the horizontal displacement.

T1(x) is a function of the pulse supplied externally.  That can vary greatly depending on whether mechanical, magnetic or electric means are used.  Without that knowledge, the equation cannot be vigorously solved.  (This is the reason why Tsing Hua University is involved to do a much more accurate mathematical and computer modeling.)

In our presentation, we use the simple first application of the First Pulse Force to demonstrate that some work (work implies energy used) is done by the tension of the String.  This is the Lead Out Energy.

End of Part 5

[ltseung888]

Part 6 of 6 in the reply to Tinu on slides 5-8 of Taiwan2a.htm

Tinu wrote: ?According to the above, knowing the angle ?a? (7.125 degrees), mass M (80kg at your wish) and force F (10 kgf) one easily can compute the ratio Hori Energy/ Vert Energy, as you asked me to do ??. I will not do it, because both equations are incorrect and so is the ratio between them. ??.. Please solve it correctly, using the right equations and then we shall talk again. Deal??

As mentioned and expanded in Part 5,

T1(x) is a function of the pulse supplied externally as well as the classical potential and kinetic energy exchange..  That can vary greatly depending on whether mechanical, magnetic or electric means are used.  Without that knowledge, the equation cannot be solved.  The classical treatment ignores the pulse totally.  Thus almost all University Students learned the Pendulum Theory with NO periodic pulse. (This is the reason why Tsing Hua University is involved to do a much more accurate mathematical and computer modeling.)

I know now Tinu can easily substitute the values and get the ratio of Hori Energy/Vert Energy.  It will be less than 2.014.  I shall leave the exact value for someone else interested to post.

You can wait for Tsing Hua University or other Top Academic Institutions to supply the comprehensive mathematical and computer modeling.

It took me a lot a write-ups and I know I still cannot provide an easy explanation for all.  It was very easy at Tsing Hua University because we could interact directly.  Internet is no substitute for tuition at a top University.

End of Part 6 (The End of Explanations)