When Mork & Mindy was on the air, I wanted to grown up to be a comedian, like Robin Williams. In an interview, Mr. Williams once said he ignored the instructions for model airplanes and made his own creations. I tried that and was terrible at it. I also tried to emulate his sort of manic persona at school. That is frowned upon, apparently.

As he once said to an egg:

“Fly! Be free!” -Mork from Ork

In modeling and simulation, a problem that has often occurred for me is the problem of low ballistic coefficient particles through the atmosphere. The oddness here is that the least energetic of debris is the most difficult to model. The debris which is considered below the kinetic energy threshold for injury is the worst of all. There is a very good reason for this.

Bounce.

When we model an object propagating through the atmosphere, the particle’s path is modeled as undergoing the influence of the following acceleration components:

1) geocentric gravity
2) centripetal acceleration coaxial with Earth’s rotation
3) Coriolis acceleration due to Earth’s rotation
4) aerodynamic drag
5) aerodynamic lift
6) thrust

Any control can, of course, be modeled simply applying drag and lift to a body of known moment of inertia in three vehicle axes in a 6 degree-of-freedom (6DOF) simulation. Most, however, can be modeled more simply in a three degree-of-freedom (3DOF) simulation.

Let’s assume no commanded directional or thrust. We will also consider lift similar to how we consider drag. Then our model should be that the acceleration due to drag (per Prandtl’s interpretation of Bernoulli) is the atmospheric density divided by twice the ballistic coefficient. Here, ballistic coefficient is defined as the mass divided by the empirically derived drag coefficient multiplied by the presented area. The drag coefficient at high velocities will be a function of the velocity, of course, but may be averaged over a trajectory to find a mean Cd.

Anyway, this ballistic coefficient or beta can be used in aerodynamic analysis.

The topic is optimization of propagation of particles at terminal velocity. What we do here is to find terminal velocity as a function of the atmospheric density. We iterate using a fourth order Runge-Kutta algorithm based on the Prantdl model of aerodynamic drag, the Coriolis model of acceleration in a rotating frame of reference, and the Newtonian model of acceleration due to gravity along with Galilean relativity and the Newtonian laws of motion.

With these things in mind, we can find the terminal velocity of an item as the square root of the velocity whose downward component is is such that the deceleration due to drag in the up direction (that is to say, the descent rate) exactly counterbalances the acceleration due to gravity. This is simply done within the propagation routine.

Next, we find the point at which the item achieves terminal velocity. This is when we change the algorithm. Now, what I suggest, is to alter the model.

From the terminal velocity time on, we simply calculate the amount of time it will take a particle of a given ballistic coefficient to transverse an atmospheric layer. We consider that the particle now takes the wind velocity over the entire altitude layer and calculate the time it will take such a particle to make the distance. In this way, the only real difficulty is in accurately modeling the fall time of the particle. I will see how this works next week.

Pretty soon, the useless U.S. yellow journalism/infotainment-lobotomy casserole will inform us that the Supreme Court has “made a decision” that Hobby Lobby (which is a corporation, and corporations ARE people, my friend) is within its rights to refuse to allow those filthy whores to get their whore pills on Hobby Lobby’s dime, nosireee Bob. They will then act as if it had been anything but a fait accompli long before any of the interested parties brought it to this level. A few years back, interested parties provided the ridiculous Citizens United case as an absurdly over-the-top flouting of the Constitution that demanded immediate action. The Supreme Court had, at that point, been appointed largely by purchased politicians of the past few decades. The strategy of purchasing politicians paid massive dividends to the original investors. With the foregone conclusion of the Citizens United case, effectively legalizing bribery as an branch of political campaigning, the path has been forged for the long fight to completely unravel the ideals presented in the Constitution.

Establish the primacy of corporations over people.

Put “those people” back in their place.

Overrule Separation of Church and State.

The sentences above appear on the manifestos of a disquietingly high percentage of “conservative” power brokers.

By the way…

Why didn’t Hobby Lobby ever raise objections to health plans offering Viagra coverage?

Whores.