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Re: Magnetic propulsion theory revisted.

 

reactor1967

 

Dang, there would have to be a pushing agent. I kind of liked this. But, the pushing agent has to be taken out to get ufo propulsion.

I still think UFO's abide by Newtons Laws too. I believe their craft operate by pushing and pulling against spacetime. That would indicate that time becomes a variable. I have lots of ideas to try in the next year that will give me more data on how spacetime connects to electric field and gravity field phenomena.
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Re: Magnetic propulsion theory revisted.

 

reactor1967

 

Have you ever looked at the searl disk? I was curious if that really worked.

Searl says it works. But claims he doesn't have a working model at present. What the device does, seems to fall outside of normal understanding. And in my opinion Searl doesn't do a very good job of connecting known physical processes to help comprehend how his device works. It takes lots of money and effort to put one of his devices together. So I'm just taking a wait and see attitude.

Of course no one understands how a homopolar generator makes more energy than it consumes. But there are working devices in existence.

 

 

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Re: Magnetic propulsion theory revisted.

 

I kind of forgot about this thread and the following question:

 

In reply to:

 

--------------------------------------------------------------------------------

 

The integral seeks to find the area underneath a curve.

 

--------------------------------------------------------------------------------

 

1 question. How much area?

It depends on the limits you are seeking an answer for. Give me some time and over this weekend I will put a chart together that graphically shows how we can determine the position of a moving body by integrating its velocity...in much the same way I showed you graphically how we can determine the lift-curve slope of an airfoil graphically. This one chart should (hopefully) show you what we mean by "taking the area under a curve" when we talk about integration.

Standby...

 

RMT

 

 

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Re: Magnetic propulsion theory revisted.

 

The integral seeks to find the area underneath a curve.

Reactor,

The integral is just the sum of the differentials. If you look at a n oddly shaped ceramic lamp, for instnace, you can directly measure its volume. If its holllow just fill it with water, pour the water out and measure the volume of the water.

 

The power of the integral is that when you have an object or situation that varies over distance or time in a form that can't be described by plane geometry (as an example) you can't use simple algebra or plane geometry to determine the volume or (in 2D) area of the "thing". But if you use integral calculus and add up all of the differentials (the meaning of an integral) you can very precisaly state the area or volume even if the algebraic solution to the problem doesn't make sense. In algebra you have many problems that converge on "something" divided by zero. In those cases, using the postulates of algebra, you conclude that the problem is unsolvable when the denominator goes to zero. But if you use the calculus you can make a very precise determination of the values as the denominator goes to zero. In integral "division by zero" is the place where you want to be because it actually is solvable.

 

The power here is that things like time versus distance can be described in terms of a quadratic equation even if the variations in the problem are not smooth. Taking the problem down to the scale of infinitesimals solves the problem if you apply the proper math systems - maths like differential and integral calculus.

 

Integral calculus takes what we "see" about the real world and transforms it into a math that matches our well founded view of reality.

 

True, calculus is a tough nut to crack. But it does make mathematical predictions that not only fit our view of reality, it extends that view to the abstract - an abstract that is as real as our personal view of reality. It's real power is that is can make well verified predictions about situations that defy common sense and places the outcomes in terms that people can live with as reality. It's not that the outcomes are magic - rather its a matter of the outcomes defined by differential and integral calculus match the experimental outcomes of researching "reality" in whatever form we attempt to investigate.

 

Because this is a time travel site and time travel is a form of physics, I implore you to remember that math is not physics. Math is the language used to describe physics. The math is as precise as we can make it but the math isn't physics itself. If that were the case then we wouldn't have physicists investigating physical mechanics and dynamics - we'd have mathematicians doing all the work. The real world about us is to a certain degree inderterministic. Math alone can't handle indeterministic situations. Physicists are creative thinkers (assuming that the physicist under consideration is worth the time thawe spend contemplating his/her POV). Physicists interpret the meaning of the math, theory and experimental results involved in their search for the "truth". But that interpretation is never, at least legitimately, a matter of PAF theories, where PFA = Picked from the Air. They are verified by experimental results and supported by the math that describes them.

 

 

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Re: Magnetic propulsion theory revisted.

 

Just to make the point clear, if one has a theory of physics but can't simultaneously describe the theory in the proper math then the theory is very likely not true.

 

We don't now why physics can be described by math but we do know that it is the case that physics always lends itself to mathematical descriptions.

 

And I'm sorry but I have to add that when you see posts from the Fruitbats who claim that they have a theory but can't describe it in terms of mathematics then you are dealing with a Fruitbat (Yes , I know. I used Fruitbat twice in that sentence). They're just guessing about a situation that they don't understand even in the sense of the situation that they're arguing against let alone the situation that they are proposing as an alternative.

 

Anyew theory that attempts to refute a well founded theory, a theory that has been experimentally verified, has to both explain why the new theory is better as well as explain why the old well documented theory was wrong. In general it has to incorporate and explain the old theory as a limiting situation that is supplanted by a new, more extreme, situation.

 

 

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Re: Magnetic propulsion theory revisted.

 

Thanks Darby for the brief verbal discriptive math lesson. Fruitbat was good. I will have to add that one to nutcase and fruitcake and other terms I have heard around here. Darby don,t worry none about me I have math tutor dvd calculus 1 & 2 now so I will have a really good review of this material. It will take me at least 16 hours of my time to get through it though. I've had business calculus and engineering calculus but that was a long time ago.

 

 

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How Integral Calculus Models Reality

 

Hi Reactor,

 

As promised, here is an introduction to the principles behind the integral in calculus and how/why "the area under a curve" is the integral's analagous description to the deriative computing the slope of a line. Our Einstein friend recently was making noise about how mathematics (the language of physics) does not or cannot reflect reality. This introduction to why the integral is so important (and why it works) is a good example of why he is incorrect.

 

Let us look at two very simple examples of a car's velocity over a span of 10 seconds to help you understand why "the area under the velocity vs. time curve" will tell us the history of the car's position in space. From this we can extend the idea to approach a basic understanding of the mathematics behind the integral calculus.

 

spacer.png

 

Here we can see two lines. The red line represents a car traveling at a constant velocity of 20 miles per hour over the 10 seconds we see in the chart. In this case the car is not accelerating at all (i.e. its acceleration = zero miles/hour^2). The blue line represents the car linearly accelerating at a constant rate-of-change of velocity, from 20 miles per hour up to 70 miles per hour at the end of 10 seconds (i.e. an acceleration of 50 miles/hour in 10 seconds).

 

When we integrate velocity to compute the position of the car at any time, we are trying to discover the area under the velocity vs. time curves we see above. To understand how this works let's first compute the area under the curve for the red line (constant velocity, zero acceleration). This is simple to do because that area is a perfect rectangle. So we multiply one side by the other: 20 miles/hour x 10 seconds. Our units here are not consistent, so let's change them to make them consistent as well... 20 miles per hour is the same as 29.333 feet/second. So now if we multiply 29.333 feet/second x 10 seconds, we discover that in this 10 seconds of constant velocity the car has moved 293.33 feet in total. By finding the "area under the red line" we have determined by how much the car's position in space has changed in that 10 seconds.

 

Now let's do the same thing for the blue line. This is just a little bit harder, because the area under the blue line is essentially the area under the red line (AREA #1) added to the triangular-shaped area between the red and blue lines (AREA #2). We can use the fact from geometry that the formula for the area of a triangle is the (1/2) of the base times the height. So:

 

AREA#2 = (1/2) x (70 miles/hour - 20 miles/hour) x (10 seconds)

 

Again if we convert miles/hour into feet/second this turns out to be:

 

AREA#2 = (1/2) x (73.33 feet/second) x (10 seconds) = 366.67 feet

 

Adding this to AREA#1 that we already calculated, and we get:

 

AREA#1 + AREA#2 = 293.33 + 366.67 = 660 feet that the car represented by the blue line has traveled in the same time that the car represented by the red line has only traveled 293.33 feet.

 

So with these simple examples, we have actually proven that by being able to compute the area under a curve of velocity vs. time, we can determine the body's position as it moves through space. Let's stop here and make sure you have understood this before we move on to a more complex example. Let me know if you have any questions before we move on, OK?

 

These are very simple lines for velocity that give us very simple shapes under them to make it easy to calculate the area under these curves. In the next post we will see how things get more complex when signals we wish to integrate (velocity or even acceleration) are not straight lines, but curvy variations.

 

RMT

 

 

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Re: How Integral Calculus Models Reality

 

Here we can see two lines. The red line represents a car traveling at a constant velocity of 20 miles per hour over the 10 seconds we see in the chart. In this case the car is not accelerating at all (i.e. its acceleration = zero miles/hour^2). The blue line represents the car linearly accelerating at a constant rate-of-change of velocity, from 20 miles per hour up to 70 miles per hour at the end of 10 seconds (i.e. an acceleration of 50 miles/hour in 10 seconds).

 

When we integrate velocity to compute the position of the car at any time, we are trying to discover the area under the velocity vs. time curves we see above. To understand how this works let's first compute the area under the curve for the red line (constant velocity, zero acceleration). This is simple to do because that area is a perfect rectangle. So we multiply one side by the other: 20 miles/hour x 10 seconds. Our units here are not consistent, so let's change them to make them consistent as well... 20 miles per hour is the same as 29.333 feet/second. So now if we multiply 29.333 feet/second x 10 seconds, we discover that in this 10 seconds of constant velocity the car has moved 293.33 feet in total. By finding the "area under the red line" we have determined by how much the car's position in space has changed in that 10 seconds.

 

Now let's do the same thing for the blue line. This is just a little bit harder, because the area under the blue line is essentially the area under the red line (AREA #1) added to the triangular-shaped area between the red and blue lines (AREA #2). We can use the fact from geometry that the formula for the area of a triangle is the (1/2) of the base times the height. So:

 

AREA#2 = (1/2) x (70 miles/hour - 20 miles/hour) x (10 seconds)

 

Again if we convert miles/hour into feet/second this turns out to be:

 

AREA#2 = (1/2) x (73.33 feet/second) x (10 seconds) = 366.67 feet

 

Adding this to AREA#1 that we already calculated, and we get:

 

AREA#1 + AREA#2 = 293.33 + 366.67 = 660 feet that the car represented by the blue line has traveled in the same time that the car represented by the red line has only traveled 293.33 feet.

 

So with these simple examples, we have actually proven that by being able to compute the area under a curve of velocity vs. time, we can determine the body's position as it moves through space. Let's stop here and make sure you have understood this before we move on to a more complex example. Let me know if you have any questions before we move on, OK?

 

These are very simple lines for velocity that give us very simple shapes under them to make it easy to calculate the area under these curves. In the next post we will see how things get more complex when signals we wish to integrate (velocity or even acceleration) are not straight lines, but curvy variations.

Got it. We convert speed to feet per second then we take the shape and use the proper math to find its area using the units of feet per second and time. First was a perfect rectangle so its the lenght times the width the second was a triangle so it is 1/2 the base times the hight. Then we take both areas and add them together to find the 660 feet that the car represented by the blue line as traveled in the same amount of time as compared to the car represented by the red line has traveled which was 293.33 feet. I hope this is correct.
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Re: Magnetic propulsion theory revisted.

 

Thanks Darby for the brief verbal discriptive math lesson. Fruitbat was good.

Welcome. And I do hope that you didn't think that I was refering to you. I wasn't. I was making reference to the "drive-by" poster who drops some off-the-wall theory onto the board that they insist is absolutely true and as valid as any other theory.

They usually say that Einstein, Bohr, Heisenberg, SR, GR and QM are wrong, that their personal theory is correct, that mainstream science has suppressed their theory for years...and then say that the "only" problem is that they can't put their theory into mathematical terms. Alternatively they futher insist that not only is modern science all wrong - modern math is also all wrong.

 

Oh, boy...

 

 

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Re: How Integral Calculus Models Reality

 

reactor,

 

Got it. We convert speed to feet per second then we take the shape and use the proper math to find its area using the units of feet per second and time. First was a perfect rectangle so its the lenght times the width the second was a triangle so it is 1/2 the base times the hight. Then we take both areas and add them together to find the 660 feet that the car represented by the blue line as traveled in the same amount of time as compared to the car represented by the red line has traveled which was 293.33 feet. I hope this is correct.

Yes. And just a side note: Making sure our units are the same (i.e. changing the velocity to feet/second so it matches with the seconds of elapsed time) is really not important to the concept of the integral. It is one of those things you just always do in engineering (make sure your units are consistent so they will cancel properly). What we wish to focus on is the concept of the integral calculus as being concerned with the area under a curve. And I think you got that.

So now let us look at what happens when the curves we are interested in become much more irregular. We will see with an irregular velocity curve it becomes harder to compute the precise value of the integral...

 

spacer.png

 

Now we see a red line that represents a continuously-varying velocity of a car over the same 10 seconds. So no longer can we use simple shapes like rectangles and triangles to figure out the area under the curve. But we can approximate the area under the curve using a summation technique. Let us "cut up time" into equally-sized strips of (approximately) 0.333 seconds each (and let's call this width "dt"). And we extend each of these uniform-width strips until they touch the wiggly red velocity curve. If we continued to fit these strips under the curve all the way out to 10 seconds, we could then approximate the area under the curve by computing the area of each, individual strip, and then summing up all these stripwise areas from time=0 to time=10. If we wanted a better approximation of the area under the curve, we could simply do the same thing but make the size of the "dt" strip even smaller... say, .1 seconds wide. To get an even better approximation we make "dt" even smaller, say .01 seconds wide. As we make "dt" strips more narrow, obviously there will be more and more strips to add up, but the errors we can see at the top of the strips where they do not precisely fit the red curve become smaller.

 

This is where the concept of the integral of Newton's calculus comes from. The precise definition of the integral of a function (any function, even curvy ones) is by taking the limit as "dt" approaches zero. The concept of asymtotic limits is an entire area of mathematics we could go into, but we really do not need to in order to understand why the integral is important. For the purpose of dynamic simulations and "6 Degree of Freedom" simulations, we only need to understand that some dynamic variables are the integrals of other variables. Computers can perform numerical integration of these signals to sufficient accuracy by applying the "small strips of dt" model.

 

So in these two charts we have used to understand the integral, we have come to understand that "The position of a moving body is the numerical integral of the body's velocity." In the form of an equation we would write it as:

 

Position = Integral(Velocity*dt)

 

This is the opposite of the definition of the derivative, where we would say:

 

Velocity = diff(Position)/dt

 

So the derivative and the integral are inverse functions. Now let's make some other true statements about derivatives and integrals with respect to another measure of motion, a body's acceleration. We can write complementary equations like the above, but with respect to a body's velocity and acceleration:

 

Acceleration = diff(Velocity)/dt (read as: "Acceleration is the time-derivative of Velocity")

 

and alternately:

 

Velocity = Integral(Acceleration*dt) (read as: "Velocity is the time-integral of acceleration")

 

There is a device that can directly measure a body's accleration. And it is no coincidence that we call such a device an "accelerometer". When we use an accelerometer in an airplane and measure the vertical acceleration of the airplane as it moves, we call this a "g-meter" because it will tell us how many "g's" of acceleration a pilot will feel when he maneuvers the airplane.

 

Now, if we attach a digital processor to the output of the accelerometer, we can program the processor to numerically integrate the acceleration signal as time ticks by... this numerical integration will yield a measure of the airplane's vertical velocity:

 

Aircraft Vertical Velocity = Integral(Vertical Acceleration*dt)

 

And then if we program the processor to take this computed vertical velocity and numerically integrate it once more, it will yield the time-varying position of the body:

 

Aircraft Vertical Position = Integral(Vertical Velocity*dt)

 

What I have just described is the basic design of what is called an Inertial Navigation System (INS) used on all aircraft. Each INS has 3 distinct accelerometers mounted at right angles to each other. One points in the vertical direction of the airplane, one points in the lateral direction of the airplane (along its wingspan), and the third points along the nose of the airplane. If we integrate the outputs of all 3 of these accelerometers, as described above, we can constantly compute NINE different dynamic quantities that describe the airplane's linear motion:

 

Accelerations along the x (fwd/back) , y (left/right), and z (up/down) axes

 

Velocities along the x, y, and z axes

 

Positions along the x, y, and z axes

 

These linear dynamic quantities in three directions (x, y, z) describe THREE of the SIX Degrees Of Freedom (DOFs) of an airplane. The other 3 DOFs are the three rotations the airplane can exhibit by rotating ABOUT the x, y, and z axes. We call these rotations PITCH (rotating about the y axis), ROLL (rotating about the x axis), and YAW (rotating about the z axis).

 

I will leave it here and see if you have any questions again. If you are good with the above, I can describe the device that an INS uses to measure and calculate the 3 rotational degrees of freedom (DOFs).

 

RMT

 

 

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Re: Magnetic propulsion theory revisted.

 

Thinks Darby. Yes I took it a little personal but I am ok. Some people tend to forget that science has a plan that is why it is science. Verify, testing, and proving is all part of the plan. I am guilty of drive by posting. Before I came to TTI I did it once in a while. I would drop my theory and later come back and look at the responses which usually were not very nice. Usually I did not follow up on the responses. I think one time on usenet you responded to someone else about one of my post by saying "I have been responding to that *?#@ for years now." Something to that effect. I have noticed you are kinder with your language here than on usenet if I got you correctly with the person I am thinking of. I have not done a drive by posting for a while now.

 

 

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Re: Magnetic propulsion theory revisted.

 

I think one time on usenet you responded to someone else about one of my post by saying "I have been responding to that *?#@ for years now." Something to that effect.

Hmmm...that wouldn't be me. I don't use profanity and I think that I've only posted half a dozen times (or less) on UseNet. Not to mention that I'd never heard of you until you started posting here a few months ago.
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Re: How Integral Calculus Models Reality

 

Ok, Im good.

Excellent. OK, then before I "wrap this up in a bow" for Christmas, let me just complete the description of how an Inertial Navigation System works to compute the 6-DOF navigation state vector of a moving body. I have already described how we get the rectilinear measures of motion (linear acceleration, velocity, and positions in 3-D) by employing 3 accelerometer sensors (one for each axial dimension), and we simply integrate those accels to get velocities, and then integrate the velocities to get positions. So this part of the INS descibes the full motion of a point-mass through space. What it does NOT tell us is the rotational dynamics or the attitude of the body with respect to some (inertial) reference. That is where the Ring Laser Gyro (RLG) comes into play.

An INS has 3 linear accelerometers, but it also has 3 RLG's. Like the accelerometers, the 3 RLG's are arranged to align with the 3 orthogonal planes of motion. This allows one RLG to measure the body's rotational velocity about the axis that it is perpendicular to. For example: Let us say that the "X-accelerometer" measures the acceleration along the axis of the airplane that passes through the nose and the tail. That is the same axis that the airplane will roll about when it flys a lateral maneuver. So if we mount the "X-Ring Laser Gyro" such that it is perpendicular to the "X axis", then this RLG will measure the ROLL RATE of the airplane around it's X axis. We mount the "Y" and "Z" RLG's in similar fashion. This means that the "Y-RLG" will measure the body's rotation rate about the axis that passes through the wings. This is measuring the PITCH RATE. Finally, the "Z-RLG" is going to measure the rotational rate of the body around the vertical axis of the airplane. This RLG is measuring YAW RATE.

 

So if the RLG is measuring the rotational velocities we know as PITCH, ROLL, and YAW RATES, then we can use the power of the integral to again help us compute what the actual Pitch, Roll, and Yaw (Magnetic Heading) angles are of the airplane over time. Similar to how we stated these integrals for the accelerometers, we would state them for the ring laser gyro as:

 

Pitch Angle = Integral(Pitch Rate*dt)

 

Roll Angle = Integral(Roll Rate*dt)

 

Yaw Angle (AKA Heading) = Integral(Yaw Rate*dt)

 

If we needed to know the pitch, roll, and yaw accelerations about their respective axes, we could also take the time derivatives of the rates, as follows:

 

Pitch Acceleration = d(Pitch Rate)/dt

 

Roll Acceleration = d(Roll Rate)/dt

 

Yaw Acceleration = d(Yaw Rate)/dt

 

We are now set to describe how all of this knowledge about integrals and derivatives can help us build a very realistic, dynamic simulation of any body in motion... And it should become clear why, when we started this discussion, I was encourging you to draw a free body diagram so that we can identify all the forces acting on the bodies involved (i.e. magnets and springs).

 

RMT

 

 

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Re: How Integral Calculus Models Reality

 

We are now set to describe how all of this knowledge about integrals and derivatives can help us build a very realistic, dynamic simulation of any body in motion... And it should become clear why, when we started this discussion, I was encourging you to draw a free body diagram so that we can identify all the forces acting on the bodies involved (i.e. magnets and springs).

Reactor,

The real magic in differentials and integrals is the little "d". In classical chemistry and most classical physics you see a delta triangle to indicate a change in some factor in the equation. The difference is that the "d" indicates an infinitesimal change taken to be virtually zero. If you plot the rise and run of an infinitesimal change you can make curved lines appear to be straight and precisely solve what was before Newton unsolvable problems in geometry, chemistry, thermodynamics, general physics, etc. As an example, Kepler proposed his second law of planetary motion (a radius joining the sun and a planet sweeps out equal areas in equal times). He was correct but he didn't have the proper calculus at hand in his time to prove mathematically that the law was true in fine detail. Planets carve out elipses as they orbit the sun. That means that the elongated rectangles that would be drawn as the planet moved from point A to point B have straight edges at the "top" while the actual top is curved and the sides are not parallel. Take a differential and the curve and lack of parallelity disappears and the solution to the area, upon integration, becomes precise. Unfortunately, he died 12 years before Newton was born.

 

To differentiate is to take the infinitesimals. To integrate is to add up the infinitesimals. That long curly line in front of an integral equation is just a long letter "S" - sum. It's the equivalent of the capital sigma in algebra with the difference that differentials "converge" from the left and right to a precise rather than an estimated result. When you add them up you have a very precise solution to the problem even though the overall shape of the cirve(s) is inconsistent and even very complex.

 

An example of a complex situation might involve Ray's roll rate. It's somewhat simple if the pilot pulls the stick a few degrees to the left and stops. But when the pilot slowly pulls the stick left and then accelerates the rate of the pull the rate of roll increases as a function defined by the pull rate of the stick times some constant that's built into the feedback system of the aeleron and stick systems (sensitivity). If you graph the roll rate it wouldn't be anything close to a triangle or a constant curve. It's the 2nd derivitive change in the roll rate (an acceleration) You can only solve that sort of problem of the overall change in the roll angle over time with integral calculus...well, at least safely. I suppose that you could have a pilot blindly test the "theory" of the stability of the aircraft's roll rate. If s/he survives you get feedback. If not, you...? :(

 

 

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Re: How Integral Calculus Models Reality

 

free body diagram

And now my light bulb came on. I think I finally understand you now. I draw a simple diagram and then model the forces acting upon uponit. Now that I understand the derivative and the integral that would be easier. Ok, this week I will look at free body diagrams some more. See what I can google and work a few examples. I want to think you for taking the time to show me this. Also, Darby I want to think you too for helping RMT explain this too me.
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Re: How Integral Calculus Models Reality

 

After reading this post ray- and understanding the dynamics of the forces involved.

 

I look back to my father racing funny cars.

 

Obviously he only wants to accelerate as fast as possible, in a linear motion, along a plane.

 

The device you describe is an excellent way to achieve, engineering results, in a device like a funny car, except:

 

Two questions:

 

I noticed that although, this device can be used to measure results, It appears to me that the engineering of the "airplane/vehicle" seems a little further outside of, of just the measuring of the results, and there is some applied trial and error, in the mechanical aspect, of building the vehicle, can you see this as true?

 

Also, Is there a small unit, that can be utilized, in the situation I describe(on the cheap?).

 

 

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Re: How Integral Calculus Models Reality

 

And now my light bulb came on. I think I finally understand you now. I draw a simple diagram and then model the forces acting upon uponit. Now that I understand the derivative and the integral that would be easier.

Exactly. Well done. By being able to mathematically describe (model) all the forces acting on the magnets, we can predict the performance of the system. In the case of your device, we can begin by only building a "1-DOF" analysis model. The main degree of freedom of motion that reactor's device will respond in is the VERTICAL DOF (up/down). So that is the 1 DOF we wish to write the force equations to describe. Let's call this up/down axis the "Z" axis. We can write the Newtonian equation of motion for this axis as:

Sum(Fz) = m*az (Summation of all Forces in the Z direction equals mass times the acceleration in the Z direction).

 

Sum(Fz) represents the sum of ALL forces acting in the Z direction. Meaning not only the force due to gravity of the magnet/object, but also the oscillating force created by the magnetic field of the magnets. If we can model all of these forces acting on the object, and we measure its mass we can solve the equation as:

 

az = Sum(Fz)/m (Equation computing the resulting acceleration on a body when subjected to Fz forces.)

 

From this equation we can build a time-integrator simulation of your device by simply integrating the az acceleration model over time, to predict its velocity (+ and -) along the Z axis. Then we integrate the velocity along the Z axis to predict the displacement (+ and -) along the Z axis from its rest position.

 

This basic process is exactly how all flight simulators do their job. We can accurately model how the aerodynamic forces act on the airplane (thrust, lift, drag, weight) over periods of time. Except we build these models for ALL SIX Degrees Of Freedom (Vertical, Lateral, Longitudinal, Pitch, Roll, and Yaw) of these aerospace vehicles. Our simulations are much larger, much more detailed, and as a result much more complex. But the very heart of all vehicle simulations are based on this modeling technique which uses powerful equations from physics. We literally use the math to model how a system will peform, before we ever really build it.

 

This is the basis for what we call model-based systems engineering. It is the most accurate and organized way to develop any complex control system, such as aircraft and spacecraft. And as you can see, it is all backed-up by mathematics that describe how reality really works. :)

 

RMT

 

 

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Re: How Integral Calculus Models Reality

 

I saw this same design used in an electromagnetic wave function, Utilized on the "Superman" ride at "Six Flags magic mountain", if anyone here has rode it.

 

It used AC inverters, with a voltage step function, to achieve the desired acceleration. The "coaster" had no less than 12 "motors", they did this for efficiency. The track had to be no less that 300 foot of electromagnets.

 

You can hear an feel the "voltage stepping" on the motors.

 

In fact, they used this electromagnetic design only in the launch sequence, the cart in effect "coasts up" the last portion of the ride until internia wears out, Friction keeps it planted to the tracks.

 

They can then the the same devices to decelerate, the "coaster" in a "braking" pattern on the return cycle.

 

There are a couple people here that have road, the "coaster" I speak of.

 

By "Motor" I mean any two oscillating magnetic fields.

 

The "Coaster" would have too much mass, for "launch" and could not "propel itself" without Charged Electromagnets on the cart and the track doing the Inverter function, Please notice though, It did not take much, to get 30k pounds up to "launch speed".

 

 

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Re: How Integral Calculus Models Reality

 

I saw how this thread started, and I also saw the costs involved of creating "this design" of a road propelled vehicle.

 

We do not need, a fully electromagnetic function on the entire road.

 

Simply, magnets , enough to overcome hills and to allow for a braking function(which can be recovered as energy) on the other side, in effect dynamic braking.

 

If and only if, every single "vehicle weighs the same".(for efficiency)

 

Not likely.

 

Or we can store the energy, for the next application of torque. the capacitor/battery banks would be huge and expensive.

 

So not to detract, from your Idea, but in effect make any cost that you have at least an exponential of Rays original cost to the road.

 

This is at least the technology that ,I know we have on a large enough scale.

 

It we be the most efficient also, because it could account for load.

 

But used as a launch vehicle, the limitations aren't the mass an speed that we can get it moving, we can do that, in actuality there are human and design limitation, that are simply beyond our experience.

 

The "g's" pulled on the body, and the acceleration, simply out scope out ability to design at the moment.The material requirements, might have well more mass than we are willing to pay to launch such a vehicle, In effect, It simply may not be able, to carry any weight, to overcome the friction involved on the "vehicle".

 

So ,I get back to "trial and error", at least in the design results that Ray has offered.

 

The mechanics of this design are horrendous, in either circumstance.

 

 

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Re: How Integral Calculus Models Reality

 

Exactly. Well done. By being able to mathematically describe (model) all the forces acting on the magnets, we can predict the performance of the system. In the case of your device, we can begin by only building a "1-DOF" analysis model. The main degree of freedom of motion that reactor's device will respond in is the VERTICAL DOF (up/down). So that is the 1 DOF we wish to write the force equations to describe. Let's call this up/down axis the "Z" axis. We can write the Newtonian equation of motion for this axis as:

 

Sum(Fz) = m*az (Summation of all Forces in the Z direction equals mass times the acceleration in the Z direction).

 

Sum(Fz) represents the sum of ALL forces acting in the Z direction. Meaning not only the force due to gravity of the magnet/object, but also the oscillating force created by the magnetic field of the magnets. If we can model all of these forces acting on the object, and we measure its mass we can solve the equation as:

 

az = Sum(Fz)/m (Equation computing the resulting acceleration on a body when subjected to Fz forces.)

 

From this equation we can build a time-integrator simulation of your device by simply integrating the az acceleration model over time, to predict its velocity (+ and -) along the Z axis. Then we integrate the velocity along the Z axis to predict the displacement (+ and -) along the Z axis from its rest position.

 

This basic process is exactly how all flight simulators do their job. We can accurately model how the aerodynamic forces act on the airplane (thrust, lift, drag, weight) over periods of time. Except we build these models for ALL SIX Degrees Of Freedom (Vertical, Lateral, Longitudinal, Pitch, Roll, and Yaw) of these aerospace vehicles. Our simulations are much larger, much more detailed, and as a result much more complex. But the very heart of all vehicle simulations are based on this modeling technique which uses powerful equations from physics. We literally use the math to model how a system will peform, before we ever really build it.

 

This is the basis for what we call model-based systems engineering. It is the most accurate and organized way to develop any complex control system, such as aircraft and spacecraft. And as you can see, it is all backed-up by mathematics that describe how reality really works

So pretty much it would be like taking the individual forces for the device that I proposed and graphing them in charts like we did then solving for the integral then taking all of the results and putting them in this equation for the summation of forces. Of course using the correct units and working the math correctly. And working with 1-dof for the z axis. Now I had a device on bottom and a device on top so I would have to subtract one z-axis from the other to see which force won out. I would do graphing, solving, and the summation equation twice. One for the top and one for the bottom. Then I would subtract the top from the bottom to see the final force. On gravity on one side gravity adds to acceleration but on the other side gravity takes away from acceleration. Anyone who likes figuring things out would love this.
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