I was going through some old work and thought I would update some of my programs in a recent version of Microsoft Visual Studio. Old dogs and new tricks so to speak, but Visual C# is sufficiently similar to Visual C++ so it wasn't too bad. One of those was a program to fit curve parameters. The routine and the results are shown below the break. I will be making the executable file available on the Google Drive in the Downloads area in the very near future.
It has been about 15 months since I first did my original SIR modeling concerning the progression of Covid 19. That post is here. I thought I would re-visit the model and the data after all the things that have come to pass since that time. In my initial simple model I used a scaled population (1 being the total U.S. population.) I have subsequently made some numerical changes such that I could use the actual U.S. population and compare the confirmed cases and the estimates from the CDC.
As was mentioned in a previous post the CDC has esitmated that the total disease burden is off by a factor of 4.0 due to a variety of reasons they have published. That post is here. To my knowledge no one seems to take real issue with their estimates. In my model I used the multiplication factor published by the CDC and re-plotted it. It is shown below the break.
In my previous post on the subject I mentioned how I didn't have the eccentricity of the Earth's orbit quite right yet. I have pretty much corrected that. The old data set and the new are shown below the break.
Well, back to writing some posts. A fellow I know needed me to help him move some cattle. That meant quite a bit of time in the saddle, and then hauling winter feed to the new location. Oh great I get to ride drag, and no that doesn't mean riding in women's clothes. It's where you get to smell the cow flatulence all day and eat dust for hours on end at the back of the drive.
I have worked with a lot of people over the years in what I call planetary sciences. This also includes atmospheric research. Over the years I have built a number of instruments and conducted experimental studies in support of this type of work so I naturally developed an interest in the subject. One aspect of this field is obviously the climate of earth both in the past and the present. The present day arguments over modern climate change don't hold much interest for me but the past or paleoclimate studies do.
One major use for explosives is in the oil and gas industry to complete a well. For a simple well the process is straightforward. The well is drilled, cased and then perforated. This involves inserting a length of tubing with a series of shaped charges along it's length into the cased well and setting off the charges that perforate the casing and the oil and gas bearing strata.
A shaped charge in its simplest form is nothing more than a metal cone surrounded by explosives. The charge is end initiated and the explosive collapses the conical liner into a jet of material that penetrates at very high velocity. The jet penetrates in the same manner as I previously posted about hypervelocity penetration. A model of a simple 65 degree angled shaped charge is shown in the first video. As the detonation proceeds up the charge the cone collapses inward in a symmetrical manner with an upwards momentum. At the collision point the cone coalesces into a jet of material that has a high velocity and has a final form of a long slender rod.
I've been meaning to do this for some time. That is developing a Windows based system for fitting equation of state terms to experimental data, rather then relying on other people's fitting routines. One of the more common equations of state (P-v relationship) people like to use in the explosives world is the Jones-Wilkins-Lee (JWL) equation of state. There are others but I won't go into them for now. One form of the JWL equation of state for the products of detonation is given by:
The data to fit to has to be in an Excel file and can be imported directly into the application. The data file needs to be in the form displayed. The pressure units are in GPa.
Energetic materials in general and explosives in particular are incredibly important to an industrial/technological society. For propellants it's their ability to produce large volumes of gas in a short time frame during combustion. Rocket motors put our satellites in space that provide us with other forms of important technology. The airbags in your car are nothing more than an energetic material undergoing rapid combustion to fill the bag. I don't think you want to know what energetic material is probably in there.
The usefulness of explosives comes from the fast generation of gas, on the microsecond timeframe or less, that provides a large power density and amount of work available. This allows us to do extensive momentum transfers for a relatively low cost (blasting for mining and construction). The metals production industry, and subsequent manufacturing industries heavily depend on the low cost production of raw materials. The power densities in explosives allow for the high velocity acceleration of metals which produces the shaped charge effects needed in oil and gas well completion.
I've posted about some aspects of interior and exterior ballistics but I haven't mentioned the last part of the puzzle, terminal ballistics. Approximately 65 million years ago, it was a very bad day for planet earth. An asteroid impacted at hypervelocity speeds and the ensuing disaster killed off a vast percentage of life on earth (nearly 75% of all species). So this post is about terminal ballistics or impact phenomena.
But first, a video simulating that asteroid impact. The projectile is a nickel/iron mix and the planet is simulated with a layer of water over silica. Consider the scale of the impact. In the model the projectile is scaled such that it would have been about 8 miles long by about 5 miles in diameter. The resulting crater depth would have been nearly 10 miles or roughly twice the height of Mt. Everest.
Every so often I'll get in a conversation with someone about our droughts here in the mountains of California. The snow pack in the Sierra Nevada mountains is the major source of fresh water in the state so knowledge about it is vital. Fortunately there is data to be had that I can use to inform myself. I get the snow pack data for the two watersheds I am interested in from the California Data Exchange Center.
I update my files every year at the end of the snow season. This is usually April 1st. It's always surprising to me when people talk about the Sierra snowpack from news reports they hear or see, but don't actually look at the numbers. In fact some of the things I hear from people is so far from what the data implies it's troubling. Let me be clear from the outset, this is not about the overall water situation in California. It is about the two watersheds that directly impact my life. They are the Kern River Watershed and the Owens River Watershed.
Charles Dodgson who wrote the wonderful book Alice's Adventures in Wonderland under the pen name Lewis Carroll was a mathematician by training and practice. His book was admirably illustrated by Sir John Tenniel. Dodgson made some good strides in mathematical logic, linear algebra, and matrix operations. Of course, who doesn't remember who Alice spotted one fine day and decided to follow.
I've gone back and cleaned up my basic SIR Model as described in a previous post. I have added some features and put some more thought into it. I hope to describe it here and what might be some of the ramifications. Given the current state of political affairs here in the United States and being the election season it has helped me wade through some of the effluvia that is always present in politics. Especially concerning this matter.
From the first post in this series I wrote about determining the performance of an explosive using the Cylinder Expansion test, or Cylex as it's commonly known. As I mentioned the radial velocity of an expanding cylinder (copper for the cylex test) is measured. This is done a number of different ways. The earliest method used a streak camera.
This is the first part of a series on the properties and application of explosive materials. I suppose the first thing to do is define some terms. An explosive is any system, gas, liquid, or solid, that will propagate a supersonic wave front at a characteristic velocity that is supported by chemical reaction. A graphical relationship helps to show this.
Much of my work over the years involved testing and developing explosive systems. What I hope to do with this series of posts is to describe in a succinct form some of the background, both theoretical and experimental, that went into my work. This series of posts is an overview of explosive materials and their uses. It's similar to some texts available but I will be including links and various downloadable items that some readers might find useful.
There are three basic types of explosive materials: primaries like azides and fulminates; secondaries such as HMX, RDX, and TNT; commercial, which include variants of ammonium nitrate/fuel oil used in the mining industry.
I've been exploring the model space and it's a dark, cold place. You can get lost out there. I developed a basic SIR model for disease transmission and recovery and set out to turn the knobs on the values. Recall the original model looked like the graph below. What you can see is that the blue line is very nearly at zero and the green line is approaching 1000 or the total population that I used.
The blue line being very nearly zero means there are very few members of the population left that are susceptible to the disease. The red line indicates the infectious which are the people currently suffering from infection and potential death. "Flattening the curve" is spreading out the red line in time which can be accomplished by reducing the transmission rate (social distancing.)
In my "What This Blog is About" page I mention about doing something yourself and then explaining it to someone else so you can really start to understand something. I have been asked a number of times my take on the Covid 19 business, and I have tried to stay honest and say I don't know enough about it to offer up much in the way of an opinion. I have been trying to rectify that ignorance and have made the first steps. This is my description of what I know to this point and what I have done.
I decided to put together a simplified burn model to incorporate into the Android App I put together for re-loading and exterior ballistics calculations. It gives me a little better feeling for the overall veracity of the application. The powder mass function was developed with a 4th order Runge-Kutta scheme which can be found in the Open Calculators downloads section of the blog. The velocity was derived from a lumped parameter energy balance model. I used a thermochemical solver for developing some of the powder constants. I'll probably put together a thermochemical solver for here which will also be useful for detonation and explosive properties calculations which I plan to write about in the future.
During my undergraduate days I ran a shock physics lab primarily studying the welding window for explosively welding dis-similar materials. You can find a very brief article on the subject here. The gentleman I worked for at the time was considered one of the world's experts on the subject. I published a few journal articles and learned quite a bit. A few years later I was working at my career job and I got a phone call out of the blue. The caller told me that he got my name and organization from a quite obscure thing known as a world wide web search, Netscape was still fairly new and the only real browser, and he understood I knew something about explosive welding.
As I've been developing my Android application for a shooter's assistant I've also been putting the pieces I need to make it function in spreadsheet format. The recent one I have completed was looking at the exterior ballistics problem using Pejsa's Methodology which you can read about at the link. An internet search will bring up a number of uses of it. I have provided my version of it in my downloads area. The spreadsheet can be found here.
Over the years a lot of experimental work I did was centered around high strain rate phenomena in solids. Which, there are probably more people attending your hometown high school football game than are interested in that field.
I have always had an interest in steel, its chemistry, its properties, and also its role in human history. Thus, my interest in knifemaking which embodies the art and craft of steel as well as the science.
In testing explosives a steel witness plate is often used to give a quick qualitative look at what the explosive output may have been. Often times it's more of a convenient way to rest the test item on a more stable surface. Over the years I must have used thousands of steel plates of various sizes and deformed them, punched holes in them and generally scattered them everywhere. I think I may have spent half a year out of my life just collecting them up afterwards. Needless to say I still have a few of them lying around.
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