4 Ways to Calculate the Area of a Hexagon - wikiHow

hexagon diameter formula

hexagon diameter formula - win

"He poisoned our water supply, burned our crops, and delivered a plague unto our houses!"

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Monoprice Delta Pro: What I had to find out the hard way

Hey all!
So, if you didn't notice, monoprice just sold off and discontinued their Delta Pro printer for a ridiculous deal ($450! It's worth it for the components alone!). I picked one up, and over the last week and a half have been desperately trying to figure out any information I can about it.
Now that they're sold out and not coming back, I doubt too many people will be interested, but here goes:
First off, this is a rebrand of the Atom 3 Lite (https://atom3dp.com/zh/atom3/). Yes, that's the chinese site, no they do not have an english version.
Second, the controller board and all electronics are the Lerdge X series (https://www.lerdge.com), which are actually half decent. It has trinamic drivers, and(nope) some hefty steppers, especially on the extruder.
Third, this thing is a dumpster fire as configured. It's based off an old lerdge firmware before they figured out their motion control issues, and it will cause some serious vibration and noise.
On top of that, it's missing basic features. Wifi is entirely broken, though it includes the ESP8266 board for it. You cannot input a linear advance value (K value) for the massive bowden tube, and it LOVES to spit out some pimples, let me tell YOU.
Firmware update to v4.2.0 nice
The first thing you're going to want to do is hop into the settings and take photos of all of the configuration values. You cannot dump these in this firmware revision, and they're incredibly important. Do this now. Right now. I'll post photos of mine, but yours may be different.
Second, you're going to want to download the newest firmware from Lerdge (version 4.2.0 nice as of the date of this post) and install it following their instructions.
As a nice aside, the monoprice firmware is unable to upgrade via USB. You need to use a microsd card. Don't see a microsd card slot? LOOK UNDERNEATH, DUH!
The microsd card slot is hidden underneath in a cutout under the wifi board and above a bunch of cables that can be pushed out of the way. Be careful when inserting the SD card, because the wifi card is only held in by the pin headers it's socketed onto the board with.
DO NOT ATTEMPT TO CONTROL MOTION AFTER FIRMWARE UPGRADE, YOU MUST MANUALLY ENTER ALL SETTINGS FIRST!
This will require those settings values from before. Set the structure to Delta, then tap Delta again, and enter all values you photographed earlier.
One value does need to change, and that's the "Number of Leveling Points" setting under "Structure > Delta > Auto Leveling Setting". 7 is the default value. 7 is broken. Anything under 10 is broken. Set it to 10, this will tap out a 10x10 grid, or 100 touch points. You can go up to 32 for 1024 touch points, but that's insane.
Once this is done, your printer will be MUCH quieter, and you'll have control over linear advance (even DURING the print!), and your print quality will improve MASSIVELY.
You can also change the boot screen, you'll find how to do that on lerdge's site.
I'll update this with more info, this is just a brain dump so the information exists SOMEWHERE on the internet.
Update: Reading more of the lerdge manual, the Lerdge X board included is incapable of running trinamic drives in UART mode, and isn't even USING trinamic drivers as advertised (I think that's what's advertised anyhow) which would enable sensorless bed leveling via motor stall detection and much quieter drive modes. I believe the sound and vibration reduction I've experienced is just due to their motion firmware rewrite.
I've decided to quadruple down on my idiocy with this machine, and spring for a Lerdge K board with TMC2209 drivers configured in UART mode for the thrill of polishing a turd. I'll keep you posted on the progress. This is a $90 upgrade using parts from Lerdge's aliexpress store (parts are the Lerdge K board w/TMC2209 drivers and 6x dupont SH1.0 connector breakout cables).
Wifi Update: The wifi board shipped with this machine seems to be a one-off made for the Monoprice machine, and the firmware is woefully out of date (imagine that!). The firmware is available in the PC control software archive on the Lerdge site. I'm pulling the board out today to attempt to flash it with the newest firmware made for a board with a USB-B port on it. If it doesn't work, I'm not too worried, as I've ordered a the newer board, which uses one of those mini ESP8266 boards for Wifi serial control AND usb functionality (I'll get it configured for octoprint for fun and document the process).
Here's the photos promised: https://imgur.com/a/tRczMLd
Calibration Update: I've been going through Lerdge's manual, and I've noticed a few things monoprice didn't do when it comes to calibration. They've relied on autoleveling to figure out any slack in endstop offsets and pushrod error (somewhat, more on this later). To get the bed actually "level", you'll need to adjust the endstop offsets. This increases print accuracy a not insignificant amount, as the controller does not need to apply as many leveling offsets to moves as it would if the endstops were not calculated in the correct positions.
The columns and axes are so:
X motor = Column A = Left side of display Y motor = Column B = Right side of display Z motor = Column C = Rear column
Choose a column and leave its endstop offset at 0. This one is going to be what you reference the other two on.
Set the bed to 60c (always do this when autoleveling), then run an auto level sequence, watching the position of the nozzle on the bed and the Z axis readout. You'll notice the value decrease or increase as it moves. The directions you're going to be most interested in are straight out from the columns, imaginary lines leading from the columns you wish to adjust to a point directly between the two opposite columns.
For example, endstop adjustment for column C (Z motor, rear column) adjusts the "tilt" of the bed forward and back. If you see the Z axis readout decreasing as it works its way back towards the rear column, increase the endstop offset for column C by double the difference between the maximum Z axis at the front, and the maximum Z axis at the rear.
In my case, it was -1.2mm and -0.5mm, so I adjusted the column C endstop offset to 1.4mm. This got me in the ballpark of level front to back. It was now "tilted" in the opposite direction, -1.2mm front and -1.4mm rear, so I adjusted it down to 1.250, and the deviation was 0.0mm front to back. Good enough.
Repeat this process for the other non-reference column, and you should see a Z axis variance of 0.1mm max across the entire bed.
Now adjust ALL column endstop offsets to zero out the bed. In my case, all readings were -1.0 to -1.1, so I adjusted my offsets by -1.050mm (decreasing their "height from the bed" since Z was going past 0), and my bed now measures 0.0mm to 0.1mm during auto calibration.
Auto calibrate one last time, then remove the sensor. Set the print head to 200c (you did remove the sensor, right?) and set the bed to 60c. Test the center point with a piece of printer paper, and set the Z offset (mine was 0.000, but it can be off by 0.050). Don't worry about the rest of the points being too low, this is due to pushrod error as far as I can tell.
Once the endstop offsets are properly set, you can move on to push rod calibration, which I'm working on now, I'll update once I get there.
Pushrod length calibration update:
Don't do this unless X/Y are very close in dimension
Pushrod length affects the scale of items printed. Shorter pushrod = larger print, longer pushrod = smaller print. The maximum print resolution on this printer is somewhere in the area of 0.008%, so if you're off by +/-0.008% or +/-2.2mm over 270mm, you're off in the weeds and cannot get any more accurate. It's unlikely to get any better than this without upgrading your stepper drivers (TMC2209s will double this resolution, +/-0.004%, or +/-1.1mm over 270mm with the side benefit of shutting your steppers up).
To update the pushrod calibration, print out something of a known X/Y dimension. In my case, I'm printing a 150x150x10mm box. Measure the completed print on the X/Y dimensions with calipers, and average the deviation from ideal dimensions.
Mine was 149.29x148.89, so -0.00473% in the X dimension, and -0.00073% in the Y dimension. This averages to -0.00273% Now multiply this by the previous push rod length and subtract that from your currently entered push rod length. In my case the initial push rod length was 283.200mm, so 283.2*-0.00273 = -0.773, 283.200 + -0.773 = 282.427mm push rod length.
Not much of a difference, but significant nonetheless. After changing this value, my calibration print came out to 150.13x149.74mm X/Y. Not amazing, but better.
I may DID print a large hexagon to get the individual axis's pushrod offset in the future for even finer grained tuning, see below. This is worth it.
You'll need to run the automatic equivalent radius, followed by an autolevel again after this. Don't forget to set your bed temperature to 60c before running these.
Automatic Equivalent Radius:
You'll see an automatic equivalent radius option in the delta machine settings in the new firmware. This uses the film bed level sensor to calculate the equivalent radius of the machine, which does not require slider offset and effect head offset at all, as it takes them into consideration. Once you have your pushrod length accurate, set the bed to 60c, nozzle to 0c, put the sensor on the print head, and run the automatic equivalent radius measurement. This is more accurate than punching in the slider and effect head offsets.
Per-axis pushrod length offset:
Guess what? Yeah, I printed a hexagon.
This is essentially the same process as the pushrod length calibration procedure but more better, as it sets the overall pushrod length AND the error for each pushrod.
Print a hexagon of known diameter flat to flat, aligned so a flat faces each axis. Measure each opposite pair of flats. Each pair aligns with one of the columns (A = left , B = right, C = rear). Take the deviation from the STL measurements as a percentage and multiply that by the pushrod length, and add it to the pushrod length.
Formula for each axis: (((Expected dimension - Measured Dimension) / (Expected Dimension)) * (previous pushrod length)) + (previous pushrod length) = Pushrod length for axis
The smallest pushrod length for a given axis is the overall "Pushrod length"
The error for the other pushrods is calculated with this formula:
(Axis pushrod length) - (Shortest pushrod length)
Input these as pushrod errors for these axes, then run an "Automatic Equivalent Radius" followed by an automatic bed leveling with the bed at 60c for both. You should now be very well calibrated.
Linear Coefficient:
You'll probably notice after calibration that your prints are coming out as thin lines next to eachother rather than bonded together. This is because your printer moves are very precise and not running over eachother anymore. You'll need to adjust the linear coefficient now, also known as the K value. This makes up for bowden tube flex. Since you can adjust this during printing with the new firmware, I suggest you do that. Increase in increments of 0.1 until you get nice knitting between lines without overflow. The value I arrived at for mine was 1.1.
Very soon I will add a link to an archive of gcode files, the printer firmware, and my calibration values from the new firmware to get you to a functional state without needing to manually enter all values to get motion working with sane values.
TMC2209 Drivers:
I replaced the LV8729 drivers with TMC2209s, and the machine has shut up significantly. This requires the following modifications:
  1. Under each driver there is a set of 3 jumpers, these directly set the MS1, MS2, and MS3 (if equipped) pins. Remove jumpers 1 and 3, so MS1 and MS3 (doesn't exist on TMC2209) are set to low, and MS2 is set to high. This sets 1/64th step mode. You can hang these jumpers off of one of the pins so you don't lose them.
  2. Divide all step values by 2 (x/y/z = 320, extruder = 380), as the LV8729 drivers are set to 1/128 step from the factory. The TMC2209s max out at 1/64th step. This reduces accuracy somewhat, but honestly the machine is not precise enough to be able to benefit from 1/128th step divisions and is SUPER loud with the original drivers.
  3. Reverse the direction of all steppers in firmware, as the TMC2209 motor outputs are reversed
Note when testing that the extruder stepper IS DISABLED unless the print head is warm. I had my oscilloscope out and everything, ready to pronounce the board dead until I decided to check this, and I'm glad I did.
Lerdge K Board Upgrade:
I want to print multiple materials on my printer. To do so, I need more than the 4 stepper channels included. This necessitated an upgrade to the control board. For ease of transition and the ability to migrate settings, I upgraded the included Lerdge X board to the Lerdge K board.
This new board cost me $50 shipped from aliexpress. Make sure you're ordering the V2.0.0+ board, the older ones make UART configuration more difficult than it needs to be.
Everything above applies to this new board, except for some small variations:
  1. When using TMC2209 drivers, you have the option to use UART control I highly suggest this mode, as it allows for a resolution of 1/256th step, up from 1/128th on the default drivers, and 1/64th on the TMC2209 drivers.
To use this mode, follow the Lerdge documentation EXACTLY, you will need to blob solder bridge two pads on the drivers to enable this mode, then set the jumpers to connect the txrx pin. If you do not solder bridge the pads, the steppers will sing you the song of their people. It goes SCREEEEEEEEEEEEEEEEEEEEEEEE
You will also need to grab a multimeter and sample each driver's reference voltage (the voltage on the potentiometer screw) and enter it into the trinamic control settings directly. Do not assume it's correct even though it works without setting this value. You could be running a LOT more current than you expect through the driver and motor without this value set properly, damaging your drivers or control board or steppers.
Make sure to set your step values correctly (1280 on xyz 1540 on the extruder).
  1. There are additional settings available to control more extruders.
The move to UART stepper driver control significantly increases the resolution of the steppers, which increases dimensional accuracy. When I upgraded, I was UNABLE to measure an error in my print dimensions.
I'll repeat: after upgrading to a lerdge K board with UART TMC2209s, I was COMPLETELY UNABLE TO MEASURE ERROR IN MY PRINT DIMENSIONS. 150mm printed was 150.00mm on all of my calipers in X, Y, and Z dimensions.
I also noticed a reduction in noise (even over the X board with TMC2209s), stringing, and much smoother prints overall.
To install the board, you'll need to drill new mount holes, and install tall standoffs. Look at the imgur album I linked before, I've added photos of the process and notes where needed.
Vibration Dampers
Put some vibration dampers on the steppers today (nema 17). They’re smoother and quieter for sure, but honestly not worth the effort. It didn’t significantly affect sound or print quality vs the work put in. If you’re tearing down to replace the control board with the K, it’s worth the effort. If not, definitely don’t.
Future Plans
I’ve got some 0.9 degree steppers on order now to try and smooth out the vibrations a bit, I will update once that’s done. 2560 microsteps per mm is excessive, sure, and at 200khz motor drive speed, that limits the max speed to 100mm/sec without UART, but with UART mode, there is no such limitation.
I also have a dual material single head extruder supported by lerdge on the way, I’ll update with the install process and stl files for the mount and spool holders.
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The "End Times", the Bible, and Divine Numbers

Time

We are currently in an important transition period of human history as we finish out the old ways of doing, and being, and usher in a new Era of peace, love, and enlightenment. The Bible contains messages/warnings of these times, in both The Book of Daniel and Revelation.
In this article, we will discuss how we have entered a final set of allotted days, the synchronistic and Divine creation of the Bible, and how it is all based upon Pi.
Daniel and Revelation both discuss certain periods of time which are supposed to take place at the end of the world's age. Daniel mentions periods such as:
Revelation reiterates the relevance of the 1260 days, and refers to it in multiple ways such as by saying "a time, and times, and half a time" (1 + 2 + .5). A "time" is a set of 360 days, and so 360 * 3.5 = 1260. This period is also called the "42 months" because a prophetic month is 30 days, and 42 * 30 = 1260.
Continuing forward, the timeline is confirmed and expanded by the Mayan King K’inich Janaab’ Pakal, ruler of the Maya city-state of Palenque. This king dubbed himself the messenger of the time cycles and left us an important prophecy. The prophecy simply tells us that there will first be a period of 1144 years. Those 1144 years are made up of 22 cycles of 52 years. The first 13 cycles are called Heavens, and the last 9 cycles are called Hells. Then there are another 13 Heavens and 9 Hells, 22 cycles of 360 days totaling 7920 days. Then there are 40 days, then 1260 days, and finally 60 days.
The chosen numbers for the timeline are synchronistic. 360 is 3 * 4 * 5 * 6 and 7920 is 8 * 9 * 10 * 11.
The numbers of the timeline, and the timeline itself, were designed specially so it would coincide with Pi. 360 is one of the "self locating" numbers of Pi, occurring at the end of 360 digits. Another example of this is that if you sum every decimal digit of Pi before the first occurrence of "7920", you get 14159, the first five digits of Pi! It's also interesting to note that 5280, the number of feet in a mile, multiplied by 1.5, is 7920. There are 7920 inches in a furlong, and the diameter of the Earth is approximately 7920 miles.
14159 is the first five decimal digits of Pi, and also the first prime number of it. Multiplying 14159 by 2 gives 28318, a number which has its first appearance in Pi at the end of 12600 digits. The 1260 days of the Bible * 10 equals this number. Then, summing those 12600 digits of Pi equals 56636 which is 14159 * 4!
When searching for a doubled prime number in Pi, 28318 (1667th prime * 2) is the first doubled prime to satisfy the fact that the digits leading up to and including its first occurrence in Pi, sum to a multiple of the prime. This is proven here.

Primer

To study some of the subjects later in this article, we will have to know the basics about some things:
The Bible is made up of 66 books. The Old Testament contains 39 books/929 chapters written in Hebrew. The New Testament contains 27 books/260 chapters written in Greek. There are 31102 verses and 1189 chapters in total.
To investigate certain subjects, we will be using the lexicon in Strong's Bible Concordance. This lexicon takes all of the original Hebrew/Greek root words of the Bible and puts them in alphabetical order. This list was originally published in 1890 by James Strong.
For example, if you take all of the Greek root words of the New Testament and put them in alphabetical order, "Jesus" becomes word #2424. The order was designed in this way because 2424 first appears in Pi at the end of 1111 digits, a very spiritually significant number.

Gematria

Gematria is an alphanumeric code of assigning a numerical value to a name, word or phrase based on its letters. Gematria is technically a Hebrew practice, and Isopsephy is its Greek counterpart. We can use the word "gematria" interchangeably to describe the assignment of numbers to letters, whether they be Hebrew, Greek, or English. The method for calculating the gematria, however, will change between languages.
To tie some of these concepts together, let's examine the Greek word for Jesus:
Ἰησοῦς (Iēsous) Ι Iota 10 η Eta 8 σ Sigma 200 ο Omicron 70 υ Upsilon 400 σ Sigma 200 Add the values of each Greek letter for the total of 888
Triple digit repeating numbers stand out, and cause you to ponder whether they are there by coincidence, or if they have deeper meaning. As Jesus was the focus of the New Testament, Israel was the focus of the Old Testament. The Hebrew word for Israel has a gematria value of 541 which is noteworthy, as it is the 100th prime numbe10th star number, and also occurs in Pi directly next to 2424, the number of Jesus, like so: 2424 541
Examples of different Gematria Ciphers
Date/NumbeGematria Analyzer Multi-tool — download link available here

Making Sense of Numbers

When one analyzes numbers, it is important to keep in mind that any number can mean anything, and that one should use precaution to interpret the best fitting meaning for that number. The number 104 can have multiple meanings:

Numbers of the Bible

The Bible was masterfully crafted so that it would contain numbers relevant to Pi. 262 is a fundamental number of reality as the first 262 decimal digits of Pi, Phi, and e all sum to the same number, 1192. The 262nd prime number is 1667 and the 1667th prime number is 14159, the first 5 decimal digits of Pi. It goes on that the number "1667" first occurs in Pi with a 3 immediately following it as 16673. 262 + 1667 = 1929, and the 1929th prime number is 16673.
262 + 667 = 929, the number of chapters in the Old Testament. The New Testament contains 260 chapters, the same number of days in the Mayan Tzolkʼin cycle.
When you add 929 to 260 you get 1189, a master number of the timeline. This will be explained further:

17

The number 17 seems to somehow represent God, or the Divine. This is why the first Grand Lodge in Freemasonry was founded in 1717. Francis Bacon had a serious impact/involvement in Freemasonry and Rosicrucianism, and the number values for his name using Pythagorean Cipher (now called Full Reduction Gematria) is "Francis" (34) "Bacon" (17) for a total of 51. To add upon this synchronicity, his wife's name "Alice Barnham" also sums to 51, and she was born on 5/14/1592 (Pi is 3.141592). This is also why we have the base named "Area 51", as 51 is 17 * 3, and 17 represents a godlike being. A common theory suggests that this base has had contact with or knowledge of aliens, so the number 51 reflects this, as aliens are considered to be godlike in their advanced consciousness and technological capabilities.
To continue with 17, we also see that the 17th letter of the alphabet is "Q", with "Q" being the name of the godlike and mischievous being in Star Trek. It's also the name of the military intelligence operation which has gained much notoriety, which started on 10/28/2017.
As the Bible contains 1189 chapters, it is important to note that 189 first appears in Pi at the end of 1717 digits. We also see a synchronicity take place as we raise our awareness to the fact that 189 Jesuit institutions of higher learning exist throughout the world.
From this we see the emergence of a "Pi Code". A hidden way to express a concept based on a number's association with Pi. As for the year of Alice Barnham's birth, 1592 is considered a special number because 7777 first appears in Pi at the end of 1592 digits. We could additionally point out the 51 seen in Alice Barnham's birthday, or how the 5 taken from the month multiplied by the year 1592 = 7960, or 7920 + 40 like from Pakal's timeline.
It is known well that 3.14 is equal to Pi, and such a confounding relationship presents when one observes that if you take the first 314 digits of Pi, they sum to 1392, then 1392 digits of Pi sum to 6251, a number which intersects the numbers appearing at the end of 1717 digits of Pi like so 625189. We also see that 6251 digits of Pi sum to 28318, a number which is well known to be the first five digits of 2Pi.
The whole of the timeline seems to boil down to a 17 in one way or another. The year the 1260 days ends is 2023, which is 7 * 17 * 17.

Divine Construction of the Bible

We have discussed 929, 260, and 1189, as well as 17, 51, and 189, so we will now introduce 294 and 895.
294 occurs directly next to the number 895 in Pi, and these are the first two numbers to occur directly next to each other while summing to 1189. This is why the mode (as in mean/median/mode) for gematria totals in the Bible is 895.
Another important Pi code is 691, which first appears in Pi at the end of 895 digits. The 691st prime is 5189, and 5189 first appears in Pi at the end of 1717 digits. 51 is 17 * 3 and 8 + 9 = 17. We also see that 17 * 17 is 289, and 289 occurs at the end of 1586 digits, as 691 + 895 = 1586. 1586 digits of Pi sum to 7200, the number of days in the Mayan calendar unit called the "kʼatun".
249 first appears in Pi at the end of 294 digits, and 249 represented in duodecimal is 189. We also see that 51 digits of Pi sum to 249 and 249 digits of Pi sum to 1129, the 189th prime number.
On top of this, we see that the verse with the largest gematria total in the Bible is Luke 6:42, which is the 25189th total verse of the Bible. It was designed in this way because 25189 first appears in Pi at the end of 1717 digits.
According to Biblewheel's database of the original Hebrew and Greek text, there are 445797 words in the Bible. If you divide this by the 31102 verses of the Bible, you get 14.333 which is profound because 14333 first appears in Pi at the end of 1700 digits, as 1700 is a very important Pi/Timeline code.
The Bible is made up of sections of 297 or 3 * 3 * 33 chapters. Therefore 1189 is also represented as 297 + 297 + 1 + 297 + 297. The middle chapter of the Bible is Psalm 117, which is also the shortest chapter of the Bible, containing 33 English words.
Chapter #297 is 1 Kings 6:1, which discusses the building of Solomon's Temple. Interestingly, this is even the 8898th verse in the Bible, as 1931 (294th prime) + 6967 (895th prime) = 8898.

261 - 262 - 263

By observing the way that primes sequence next to each other, we see three numbers stand out distinctly in decimal:
Number: 260 Prime #260 is 1657 The sum of these two numbers is 1917 Prime #1917 is 16561 Number: 261 Prime #261 is 1663 The sum of these two numbers is 1924 Prime #1924 is 16633 (matches 1663) Number: 262 Prime #262 is 1667 The sum of these two numbers is 1929 Prime #1929 is 16673 (matches 1667) Number: 263 Prime #263 is 1669 The sum of these two numbers is 1932 Prime #1932 is 16699 (matches 1669) Number: 264 Prime #264 is 1693 The sum of these two numbers is 1957 Prime #1957 is 16979
Using this formula, a special balancing point takes place in the decimal numbering system in which the numbers 261, 262, and 263 seem to "self-resolve" or revolve back on themselves. The middle number, 262, of these perfect three numbers, is extraordinarily special because its 1667th prime number is 14159, the first five decimal digits of Pi! Another interesting fact to point out is that 260 multiplied by 1.5 is 390, a number which occurs at the end of 1189 digits of Pi.
This fact may clue us in as to why the New Testament has 260 chapters, which is also the number of days in the Tzolkʼin cycle. There are 260 standard numbers before this anomaly occurs. The numbers then run out of range, and this balancing point does not take place again in the sequence of infinite primes.
The sum of divisors for 260 is 588 which is 294 * 2, and the sum of divisors for 261 is 390. Also, 261 digits of Pi sum to 1188. What's most interesting is the fact that the number 262 as well as 263 both hone in on the number 7920 in Pi, the number used for Pakal's timeline.
Prime #262 is 1667, and prime #1667 is 14159. When you sum every digit of Pi before the number 7920, you arrive at 14159. Including the number 7920 in your digit sum test gives you 14177. We see that 14159 is prime #1667 and 14177 is prime #1669, just as these numbers fall right next to each other in the sequence of primes.
It's interesting how 16633 + 16699 = 33332, or how 16633 + 16673 + 16699 = 50005, a nice palindromic number. We also see that 1663 + 1667 + 1669 = 4999, the number which appears by a famous area of Pi called the Feynman point. This area contains the digits 134999999

Timeline Fundamentals

Here is the base timeline which the Bible references with encoded numbers:
In addition to this base timeline, there are some supplementary dates:
222 is an extremely relevant number of the timeline, which can be seen by the fact that 5/31/2017, 7/20/2019, and 2/9/2023, are all day 222 of the Tzolkʼin cycle (meaning these dates are all a multiple of 260 days apart). It's also interesting to point out that the 222nd prime number is 1399, and 1399 days after 11/12/1997 is 9/11/2001. 9/10/2001 was actually the last day of Coptic year 1717. We spoke of 294 above, which first occurs in Pi like this: 2294 895. 2294 - 895 = 1399.
From 12/21/2012 to 4/25/2023 is 3777 days, which can also be represented as 1399 + 1189 + 1189.
As 4/25/2023 is also considered to be the completion of a final 1189 day period, the midle day (595th day) of that final 1189 day period is 9/7/2021, day 222 of the Tzolkʼin, and also the first day of Hebrew Civil Year 5782.
Let's work in the numbers 691, 895, and 5189 again now that we have a basic understanding of the timeline. 5189 - 895 = 4294, and of course we see that the number 294 has been revealed from this simple calculation, but there is two ways in which 4294 relates to the timeline:
We see that this type of alignment causes an almost undeniable "synchronicity" to take place. This is because 9/11/2001 takes place 1 day forward from the last day of Coptic Year 1717, and because 4/11/2020 also takes place 1 day forward in a similar way:
Back to the number 1399: We also see that 1399 backwards is 9931, and 9931 first appears in Pi at the end of 22222 digits. 9931 is the 1225th prime like 12/25 for Christmas. The importance of the number 222 is seen in pop culture, such as in 222 Records by Adam Levine, who founded his company on 2/9/2012, a date which seems to closely resemble 2/9/2023.
9/11/2001 is an example of a date which is not explicitly mentioned in the Bible, or by King Pakal, but is a date which is closely aligned with other timeline dates nonetheless. For example, 9 * 9 * 9 * 9 or 6561 days after 9/11/2001 is 8/29/2019, the start of the 1260 days. Terminator 2: Judgment Day, names the date 8/29/1997 as “Judgment Day”, a day in which nuclear destruction occurs in the movie. This date is 22 years before the actual 1260 day period.
9/23/2017 is a date which is commonly believed to be the fulfillment of the prophecy mentioned in Revelation 12. This is interesting as 222 first appears in Pi at the end of 1737 digits, and because 12/21/2012 + 1737 days = 9/23/2017.
One last attribute of the number 222 which I will mention is that the first 222 digits of Pi sum to 1005, and 7/24/2020 + 1005 days = 4/25/2023.
Another important date of the timeline is 5/14/1948, the founding of Israel. Three examples of how this date relates to the timeline:

Pi / Timeline Codes (abridged)

666 is the "number of the beast", the number which is mentioned in Revelation 13:18. This is a number which points us to multiple timeline dates. 666 first appears in Pi at the end of 2442 digits. 2442 is 1221 * 2:
12/21/2012 + 2442 days = 8/29/2019, the start of 1260 days
We also see that 666 digits of Pi sum to 2961:
12/21/2012 + 2961 days = 1/29/2021, the completion of a 1189 day period which started on 10/28/2017 (Q start date).

Biblical Code Confirmation

One way we can verify the timeline is by looking deeper into the Bible verses themselves. For example:
Daniel 12:12 (KJV) Blessed is he that waiteth, and cometh to the thousand three hundred and five and thirty days.
In this verse, the word for "waiteth" is Hebrew word #2442. As a reminder, 12/21/2012 + 2442 days = 8/29/2019, the start of the 1260 / 1290 / 1335 days. We now see that 2442 and 1335 are complimentary numbers, and that 2442 + 1335 = 3777.
The relationship between 2442 and 1335 is seen in other sections of the Bible as well. See these two verses:
Matthew 24:42 (KJV) Watch therefore: for ye know not what hour your Lord doth come.
Mark 13:35 (KJV) Watch ye therefore: for ye know not when the master of the house cometh, at even, or at midnight, or at the cockcrowing, or in the morning:
The verses mirror each other almost exactly and reiterate to us the fact that 2442 and 1335 are complimentary numbers of the timeline. We also see that Matthew 24:42 is the 24000th total verse of the Bible. With this verse placed at an even 1000 verses, it lends credibility to the idea that this was a "planned synchronicity" rather than just a coincidence. Daniel's verse was the 22094th total verse, showing the number 2294, which first occurs next to 895 in Pi.
I try to refrain from giving too much information at once, but most of the Bible is strongly based off of Pi. Even the important names are usually created from Pi. The word "Moses" is H4872 because the number "487" first appears in Pi with a 2 after it like so: 4872. We see that from the start of Daniel's 70 weeks to the 1260 days is 487: 4/29/2018 -> 8/29/2019 = 487 days ... Then a connection occurs as 4872 digits of Pi sum to 22094.
For additional confirmation, we see that the number 829 (representative of 8/29/2019) first appears in Pi like so 829 2540. Greek word #2540 means "time", and is first used in this verse:
Matthew 8:29 (1611 Authorized Version) — And behold, they cryed out, ſaying, What haue we to doe with thee, Ieſus thou ſonne of God? Art thou come hither to torment vs befor yͤ time? Verse #23375 (Ch. #937) — 18 words, 80 letters — Total = 7147
The importance of this verse is confirmed by the fact that it is the first verse in the New Testament of the 1611 KJV to use the special word abbreviation "yͤ" which stands for "the". We also see the number 3375 in the total verse number, which is 15 cubed, and the sum of every digit of Pi before the "Feynman Point" (999999).
We then see that Greek word #2540 is the same word used for "time" in this verse of Revelation which mentions the 1260 days:
Revelation 12:14 (KJV) — And to the woman were given two wings of a great eagle, that she might fly into the wilderness, into her place, where she is nourished for a time, and times, and half a time, from the face of the serpent. Verse #30906 (Ch. #1179) — 32 words, 153 letters — Total = 17897
This verse contains a very important code which relates to the 1260 days. The 1260 days are mentioned 7 times in the Bible, twice in Daniel, and five times in Revelation. Revelation 12:14 is the only verse in Revelation that uses the term "time, and times, and half a time" to refer to the 1260 days. This causes the verse to stand out. The term "great eagle" is used only three times in the Bible, with this verse being the last occurrence, and Ezekiel 17:3 being the first occurrence. This rare phrase links Ezekiel 17:3 and Revelation 12:14 together. Ezekiel 17:3 also stands out significantly because it is the only verse in the original 1611 King James Bible to use the apostrophe (') punctuation character.
Ezekiel 17:3 is verse #20829, another code for 8/29/2019. If you move up 1000 verses, you arrive at verse #21829, which is Daniel 3:21, the only verse in the Bible to use Hebrew word #6361, as 6361 is the 829th prime number. If you then move up another 130 verses, you arrive at verse #21959 which is the first of two verses in Daniel which mentions the 1260 days. Move up 130 more verses and you arrive at verse #22089, the second of two verses of Daniel mentioning the 1260 days.
In total you have moved up 1260 verses from Ezekiel 17:3 to arrive at the last mention of the 1260 days in Daniel. 173 is also an interesting number as it is the 40th prime, and the 40 day period ends on 8/29/2019.

Pi / Timeline Codes (continued)

We have stated the significance of 1667. It first appears in Pi at the end of 10499 digits:
We then see that:
10/28/2017 is the start of a 1189 day period, and this particular period can be broken up into 895 + 294 days:
1000 days after 10/28/2017 is 7/24/2020. We have already noted that 189 days + 7/24/2020 = 1/29/2021. 189 digits of Pi sum to 843.
Many numbers have dual/multiple meanings. For example, the Bible mentions the number 12000 numerous times (Revelation says that 12000 are sealed from each tribe) because 7140 first appears in Pi at the end of 12000 digits. This relates to the timeline as such:
As 5/31/2017 is known for being the start of 2300 sacrifices, another relevant Pi Code is seen by the fact that Hebrew word #1818 means "blood". 1818 first appears in Pi at the end of 1575 digits, and those 1575 digits of Pi sum to 7140. Blood is shed when a sacrifice occurs.
It's interesting that 5/31/2017 is 780 or 260 * 3 days from 7/20/2019. Adding 780 days to 11/12/1997 brings you to 1/1/2000, the start of the new millennium. Other interesting alignments exist in the timeline as 9/30/2019 (First day of Hebrew Civil Year 5780) + 1189 days = 1/1/2023.
7/26/2020 is a date encoded into the Bible as the "Harvest", and is often seen as the start date for the age of Aquarius. There are 2184 days in one degree (1/360th) of each 2152 year Zodiac age. 2184 is an interesting number because 2184 digits of Pi sum to 10000. We then see that:
11/12/1997 + 1740 + 2184 + 2184 + 2184 days = 7/26/2020
This was a highly planned synchronicity for 2184 to be the number of days in a degree because 2184 first appears in Pi at the end of 1740 digits. There are 2184 * 360 or 786240 days in a Zodiac age and 786240 * 12 or 9434880 days in the complete 25831 year Zodiac Time cycle. From this we see another planned synchronicity as 2184 + 1740 = 3924, and 3924 digits of Pi sum to 17916. 10/24/1948 -> 11/12/1997 = 17916 days and 10/24/1948 -> 7/26/2020 = 26208 days, as 26208 * 360 = 9434880.
We then see that 3924 first appears in Pi at the end of 7473 digits, and adding 7473 days to the start of the 7920 days gives you the date 4/29/2018, which is the start of the 70 weeks of Daniel.
An important aspect of the time code is that certain numbers can be generated by summing digits consecutively like so: 104 digits of Pi sum to 492 ... 492 digits of Pi sum to 2184 ... 2184 digits of Pi sum to 10000
We see the Mayan Long count for 5/31/2017 is 13.0.4.9.2, and how the start of the 1150 days, and the start of the 70 weeks are spaced 333 days apart.
12/21/2012 is a very important timeline date, and it is interesting to note that the second occurrence of 1221 appears in Pi like so 5519 1221. This is also the second occurrence of 5519 in Pi. The number 5519 is the 729th prime number, or the 9 * 9 * 9th prime number. 12/21/2012 is the 5519th day of the 7920 days!
While we're at it, we should show why Daniel split up his 70 weeks into 7 weeks + 62 weeks + 1 week. The first 69 weeks equal 483 days, a very special number of Pi, because 483 is the three digit number which takes the longest to have its first occurrence in Pi. This means that every other 3 digit number has at least one occurrence in Pi before the first occurrence of 483. 483 first occurs in Pi at the end of 8555 digits.
6716 is the four digit number which takes the longest to see its first occurrence in Pi.
Daniel mentions the significance of the middle day (4th day) of the final week of the 70 weeks, and says that a sacrifice ceases on this day. That day which is singled out is 8/28/2019, the first day of the Tzolkʼin cycle.
On top of this, we see that from the start of the 70 weeks to the start of the 1260 days is 487 days. 487 is a special number because it first appears in Pi like this 216829 989487 2 2658
The Pi code was designed to be very synchronistic with the given timeline. An example of this is how we see 216 and 829 besides each other in Pi above. This could be interpreted to mean:
6 * 6 * 6 or 216 days after 8/29/2019 = 4/1/2020 (start of 10 day period in Revelation)
The Pi code is special because you could also interpret this to mean 6829 days after 4/1/2020, which is 12/12/2038 (13.1.6.6.7)
The total length of time from 11/12/1997 to 4/25/2023 is 9295 days. 9295 first appears in Pi at the end of 7715 digits like so: 2402 9295. This is relevant because 2402 days after 12/21/2012 is 7/20/2019, completion of the 7920 days.
This is also what seems to make 691 such a deep number. 691 first appears in Pi at the end of 895 digits 1776 691. Its second occurrence is like this 7715 691
7/26/2020 is also considered as the middle day of a 1189 day period, which would make the completion of this period 3/13/2022, 8887 days after 11/12/1997. 3/13/2022 - 895 days = 9/30/2019, Hebrew date: 7/1/5780. 7/26/2020 is also the 117th day of a period which begins on 4/1/2020, just as Psalm 117 is the middle and 595th chapter of the Bible.
The 1000th prime number is 7919, one less than 7920, the number we studied above. 7919 * 2 = 15838, and 15838 digits of Pi sum to 71214.
7/26/2020 has the long count 13.0.7.12.14
12/21/2012 -> 5/7/2016 = 1233 days. This is a special date because we see that the number 1233 occurs for the first time in Pi like so: 2774 7 1233 88 1740 with 1233 at the end of 22470 digits... This is significant because 12/21/2012 + 2774 days = 7/26/2020
Then, we see that the long count for 5/7/2016 is 13.0.3.7.13, which is special because 3713 first appears in Pi at the end of 1929 digits!
Finally, 5/7/2016 -> 7/26/2020 = 1541 days, and 1541 first appears in Pi at the end of 5280 digits, directly next to the first occurrence of the number 3418. This is a special alignment, as we see that the actual digits 5280 first appear in Pi at the end of 3418 digits.
Prime #1541 is 12941 (294 seen) and 1541 digits of Pi sum to 6967 (the 895th prime number)
There is seemingly no limit to the vast synchronicity of this timeline. As 4/25/2023 is the completion of the 1335 days, we see that 1003 first appears in Pi at the end of 12294 digits, like so: 1003 1541
Remember that 4/15/2014 is the first blood moon of a tetrad, and is also the middle day or 595th day of a 1189 day period. We see that 595 first appears in Pi at the end of 415 digits.
To relate 6/29/2016 to Pi again, we see how 552 first appears in Pi at the end of 1665 digits
12/26/2014 is an ultimate timeline date.
This is why the famous word "giraffe" is loved by occultists, as the numbers of it show as:
g i r a f f e 7 9 18 1 6 6 5
7/17/2019 is both the 7918th day of one period of time and the 1665th day of another.

Other Timeline Dates

Another one of the very significant dates of the timeline is 7/17/2019. This date is symbolic of the crucifixion of Jesus, as he arose 3 days later, and 7/20/2019 then marks the completion of the 7920 day period.
Matthew 20:19 (KJV) — And shall deliver him to the Gentiles to mock, and to scourge, and to crucify him: and the third day he shall rise again. Verse #23812 (Ch. #949) — 17 words, 98 letters — Total = 10425
We have mentioned above that 7/20/2019 takes place 25999 days after the founding of Israel, which is interesting as the 25999th verse of the Bible is:
Luke 24:7 (KJV) — Saying, The Son of man must be delivered into the hands of sinful men, and be crucified, and the third day rise again. Verse #25999 (Ch. #997) — 19 words, 107 letters — Total = 13766
We have mentioned above the significance of the number 262. A similar number to this is 232. The 232nd prime number is 1459, and 232 + 459 = 691. 232 first appears in Pi like so 627 232 7917 8608. This is interesting because:
7/17/2019 is a very synchronistic and relevant date for multiple reasons. First, the diameter of Earth is sometimes stated as 7917 miles, or is rounded up to 7920 miles, depending on the source. Also, the 717 in 7/17/2019 is a representation for 1717. We have already stated that 189 first appears in Pi at the end of 1717 digits. This date is special because if you add 189 days to it, you arrive to 1/22/2020, the start of a 1189 day period. The middle day/595th day of this section is 9/7/2021 which is the 222nd day of the Tzolkʼin cycle, and the first day of Hebrew Civil Year 5782.
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The "End Times", the Bible, and Divine Numbers

Time

We are currently in an important transition period of human history as we finish out the old ways of doing, and being, and usher in a new Era of peace, love, and enlightenment. The Bible contains messages/warnings of these times, in both The Book of Daniel and Revelation.
In this article, we will discuss how we have entered a final set of allotted days, the synchronistic and Divine creation of the Bible, and how it is all based upon Pi.
Daniel and Revelation both discuss certain periods of time which are supposed to take place at the end of the world's age. Daniel mentions periods such as:
The numbers of the prophecies work together in such astounding ways, that it seems the true intent of these messages were to give humanity insight into a timeline structure correlated with numbers based off Pi, rather than to express that an event must happen on any day.
The 7 + 62 week segment of the 70 weeks is 483 days, the 3 digit number which takes the longest to have its first occurrence in Pi.
Revelation reiterates the relevance of the 1260 days, and refers to it in multiple ways such as by saying "a time, and times, and half a time" (1 + 2 + .5). A "time" is a set of 360 days, and so 360 * 3.5 = 1260. This period is also called the "42 months" because a prophetic month is 30 days, and 42 * 30 = 1260.
Continuing forward, the timeline is confirmed and expanded by the Mayan King K’inich Janaab’ Pakal, ruler of the Maya city-state of Palenque. This king dubbed himself the messenger of the time cycles and left us an important prophecy. The prophecy simply tells us that there will first be a period of 1144 years. Those 1144 years are made up of 22 cycles of 52 years. The first 13 cycles are called Heavens, and the last 9 cycles are called Hells. Then there are another 13 Heavens and 9 Hells, 22 cycles of 360 days totaling 7920 days. Then there are 40 days, then 1260 days, and finally 60 days.
Brazilian medium Chico Xavier spoke of the date 7/20/2019, which coincides with the completion of the 7920 days for our timeline. The timeline is also confirmed in multiple coded Bible verses.
The chosen numbers for the timeline are synchronistic. 360 is 3 * 4 * 5 * 6 and 7920 is 8 * 9 * 10 * 11.
360 is one of the "self locating" numbers of Pi, occurring at the end of 360 digits. Another example of the timeline's relation to Pi is that if you sum every decimal digit of Pi before the first occurrence of "7920", you get 14159, the first five digits of Pi! It's also interesting to note that 5280, the number of feet in a mile, multiplied by 1.5, is 7920. There are 7920 inches in a furlong, and the diameter of the Earth is approximately 7920 miles.
14159 is the first five decimal digits of Pi, and also the first prime number of it. Multiplying 14159 by 2 equals 28318, a number which has its first appearance in Pi at the end of 12600 digits. The 1260 days of the Bible * 10 equals this number. Then, summing those 12600 digits of Pi equals 56636 which is 14159 * 4.
When searching for a doubled prime number in Pi, 28318 (1667th prime * 2) is the first doubled prime to satisfy the fact that the digits leading up to and including its first occurrence in Pi, sum to a multiple of the prime. This is proven here.

Primer

To study some of the subjects later in this article, we will have to know the basics about some things:
The Bible is made up of 66 books. The Old Testament contains 39 books/929 chapters written in Hebrew. The New Testament contains 27 books/260 chapters written in Greek. There are 31102 verses and 1189 chapters in total.
To investigate certain subjects, we will be using the lexicon in Strong's Bible Concordance. This lexicon takes all of the original Hebrew/Greek root words of the Bible and puts them in alphabetical order. This list was originally published in 1890 by James Strong.
For example, if you take all of the Greek root words of the New Testament and put them in alphabetical order, "Jesus" becomes word #2424. The order was designed in this way because 2424 first appears in Pi at the end of 1111 digits, a very spiritually significant number.

Gematria

Gematria is an alphanumeric code of assigning a numerical value to a name, word or phrase based on its letters. Gematria is technically a Hebrew practice, and Isopsephy is its Greek counterpart. We can use the word "gematria" interchangeably to describe the assignment of numbers to letters, whether they be Hebrew, Greek, or English. The method for calculating the gematria, however, will change between languages.
To tie some of these concepts together, let's examine the Greek word for Jesus:
Ἰησοῦς (Iēsous) Ι Iota 10 η Eta 8 σ Sigma 200 ο Omicron 70 υ Upsilon 400 σ Sigma 200 Add the values of each Greek letter for the total of 888
Triple digit repeating numbers stand out, and cause you to ponder whether they are there by coincidence, or if they have deeper meaning. As Jesus was the focus of the New Testament, Israel was the focus of the Old Testament. The Hebrew word for Israel has a gematria value of 541 which is noteworthy, as it is the 100th prime numbe10th star number, and also occurs in Pi directly next to 2424, the number of Jesus, like so: 2424 541
Examples of different Gematria Ciphers
Date/NumbeGematria Analyzer Multi-tool — download link available here

Making Sense of Numbers

When one analyzes numbers, it is important to keep in mind that any number can mean anything, and that one should use precaution to interpret the best fitting meaning for that number. The number 104 can have multiple meanings:

Numbers of the Bible

The Bible was masterfully crafted so that it would contain numbers relevant to Pi. 262 is a fundamental number of reality as the first 262 decimal digits of Pi, Phi, and e all sum to the same number, 1192. The 262nd prime number is 1667 and the 1667th prime number is 14159, the first 5 decimal digits of Pi. It goes on that the number "1667" first occurs in Pi with a 3 immediately following it as 16673. 262 + 1667 = 1929, and the 1929th prime number is 16673.
262 + 667 = 929, the number of chapters in the Old Testament. The New Testament contains 260 chapters, the same number of days in the Mayan Tzolkʼin cycle.
When you add 929 to 260 you get 1189, a master number of the timeline. This will be explained further.

232

Another important number to keep track of is 232 and its components.
The 232nd prime number is 1459, and 232 + 459 = 691. The 1459th prime number is 12203.

17

The number 17 seems to somehow represent God, or the Divine. This is why the first Grand Lodge in Freemasonry was founded in 1717. Francis Bacon had a serious impact/involvement in Freemasonry and Rosicrucianism, and the number values for his name using Pythagorean Cipher (now called Full Reduction Gematria) is "Francis" (34) "Bacon" (17) for a total of 51. To add upon this synchronicity, his wife's name "Alice Barnham" also sums to 51, and she was born on 5/14/1592 (Pi is 3.141592). This is also why we have the base named "Area 51", as 51 is 17 * 3, and 17 represents a godlike being. A common theory suggests that this base has had contact with or knowledge of aliens, so the number 51 reflects this, as aliens are considered to be godlike in their advanced consciousness and technological capabilities.
To continue with 17, we also see that the 17th letter of the alphabet is "Q", with "Q" being the name of the godlike and mischievous being in Star Trek. It's also the name of the military intelligence operation which has gained much notoriety, which started on 10/28/2017.
As the Bible contains 1189 chapters, it is important to note that 189 first appears in Pi at the end of 1717 digits. We also see a synchronicity take place as we raise our awareness to the fact that 189 Jesuit institutions of higher learning exist throughout the world.
From this we see the emergence of a "Pi Code". A hidden way to express a concept based on a number's association with Pi. As for the year of Alice Barnham's birth, 1592 is considered a special number because 7777 first appears in Pi at the end of 1592 digits. We could additionally point out the 51 seen in Alice Barnham's birthday, or how the 5 taken from the month multiplied by the year 1592 = 7960, or 7920 + 40 like from Pakal's timeline.
It is known well that 3.14 is equal to Pi, and such a confounding relationship presents when one observes that if you take the first 314 digits of Pi, they sum to 1392, then 1392 digits of Pi sum to 6251, a number which intersects the numbers appearing at the end of 1717 digits of Pi like so 625189. We also see that 6251 digits of Pi sum to 28318, a number which is well known to be the first five digits of 2Pi.
The whole of the timeline seems to boil down to a 17 in one way or another. The year the 1260 days ends is 2023, which is 7 * 17 * 17.

Divine Construction of the Bible

We have discussed 929, 260, and 1189, as well as 17, 51, and 189, so we will now introduce 294 and 895.
294 occurs directly next to the number 895 in Pi, and these are the first two numbers to occur directly next to each other while summing to 1189. This is why the mode (as in mean/median/mode) for gematria totals in the Bible is 895.
Another important Pi code is 691, which first appears in Pi at the end of 895 digits. The 691st prime is 5189, and 5189 first appears in Pi at the end of 1717 digits. 51 is 17 * 3 and 8 + 9 = 17. We also see that 17 * 17 is 289, and 289 occurs at the end of 1586 digits, as 691 + 895 = 1586. 1586 digits of Pi sum to 7200, the number of days in the Mayan calendar unit called the "kʼatun".
249 first appears in Pi at the end of 294 digits, and 249 represented in duodecimal is 189. We also see that 51 digits of Pi sum to 249 and 249 digits of Pi sum to 1129, the 189th prime number.
On top of this, we see that the verse with the largest gematria total in the Bible is Luke 6:42, which is the 25189th total verse of the Bible. It was designed in this way because 25189 first appears in Pi at the end of 1717 digits.
According to Biblewheel's database of the original Hebrew and Greek text, there are 445797 words in the Bible. If you divide this by the 31102 verses of the Bible, you get 14.333 which is profound because 14333 first appears in Pi at the end of 1700 digits, as 1700 is a very important Pi/Timeline code.
The Bible is made up of sections of 297 or 3 * 3 * 33 chapters. Therefore 1189 is also represented as 297 + 297 + 1 + 297 + 297. The middle chapter of the Bible is Psalm 117, which is also the shortest chapter of the Bible, containing 33 English words.
Chapter #297 is 1 Kings 6:1, which discusses the building of Solomon's Temple. Interestingly, this is even the 8898th verse in the Bible, as 1931 (294th prime) + 6967 (895th prime) = 8898.

Alignments of the Timeline

Now that we have learned some fundamental numbers, we can appreciate how they create alignments in our timeline. We'll first look at three essential dates:
Adding 1592 days to 12/21/2012 creates an incredible alignment:
Another simple example of a timeline date shows a correlation between 1667 and 929:

261 - 262 - 263

By observing the way that primes sequence next to each other, we see three numbers stand out distinctly in decimal:
Number: 260 Prime #260 is 1657 The sum of these two numbers is 1917 Prime #1917 is 16561 Number: 261 Prime #261 is 1663 The sum of these two numbers is 1924 Prime #1924 is 16633 (matches 1663) Number: 262 Prime #262 is 1667 The sum of these two numbers is 1929 Prime #1929 is 16673 (matches 1667) Number: 263 Prime #263 is 1669 The sum of these two numbers is 1932 Prime #1932 is 16699 (matches 1669) Number: 264 Prime #264 is 1693 The sum of these two numbers is 1957 Prime #1957 is 16979
Using this formula, a special balancing point takes place in the decimal numbering system in which the numbers 261, 262, and 263 seem to "self-resolve" or revolve back on themselves. The middle number, 262, of these perfect three numbers, is extraordinarily special because its 1667th prime number is 14159, the first five decimal digits of Pi! Another interesting fact to point out is that 260 multiplied by 1.5 is 390, a number which occurs at the end of 1189 digits of Pi.
This fact may clue us in as to why the New Testament has 260 chapters, the same number of days in the Tzolkʼin cycle. There are 260 numbers before this anomaly occurs. The numbers then run out of range, and this balancing point does not take place again in the sequence of infinite primes.
The sum of divisors for 260 is 588 which is 294 * 2, and the sum of divisors for 261 is 390. Also, 261 digits of Pi sum to 1188.
What's most interesting is the fact that the number 262 as well as 263 both hone in on the number 7920 in Pi, the number used for Pakal's timeline. Prime #262 is 1667, and prime #1667 is 14159. When you sum every digit of Pi before the number 7920, you arrive at 14159. Including the number 7920 in your digit sum test gives you 14177. We see that 14159 is prime #1667 and 14177 is prime #1669, just as these numbers fall right next to each other in the sequence of primes.
It's interesting how 16633 + 16699 = 33332, or how 16633 + 16673 + 16699 = 50005, a nice palindromic number. We also see that 1663 + 1667 + 1669 = 4999, the number which appears by a famous area of Pi called the Feynman point. This area contains the digits 134999999.

Timeline Fundamentals

Here is the base timeline which the Bible references with encoded numbers:
In addition to this base timeline, there are some supplementary dates:
222 is an extremely relevant number of the timeline, which can be seen by the fact that 5/31/2017, 7/20/2019, and 2/9/2023, are all day 222 of the Tzolkʼin cycle (meaning these dates are all a multiple of 260 days apart). It's also interesting to point out that the 222nd prime number is 1399, and 1399 days after 11/12/1997 is 9/11/2001. 9/10/2001 was actually the last day of Coptic year 1717. We spoke of 294 above, which first occurs in Pi like this: 2294 895. 2294 - 895 = 1399.
From 12/21/2012 to 4/25/2023 is 3777 days, which can also be represented as 1399 + 1189 + 1189.
As 4/25/2023 is also considered to be the completion of a final 1189 day period, the middle day (595th day) of that final 1189 day period is 9/7/2021, day 222 of the Tzolkʼin, and also the first day of Hebrew Civil Year 5782. (represented as 7/1/5782)
5189 - 895 = 4294, and we see that the number 294 has been revealed from this simple calculation, but there is two ways in which 4294 relates to the timeline:
Back to the number 1399: We also see that 1399 backwards is 9931, and 9931 first appears in Pi at the end of 22222 digits. 9931 is also the last four-digit number to appear in this list of primes sequenced by how much they have increased from their most previous prime number. 9931 is the 1225th prime like 12/25 for Christmas. The importance of the number 222 is seen in pop culture, such as in 222 Records by Adam Levine, who founded his company on 2/9/2012, a date which seems to closely resemble 2/9/2023.
9/11/2001 is an example of a date which is not explicitly mentioned in the Bible, or by King Pakal, but is a date which is closely aligned with other timeline dates nonetheless. For example, 9 * 9 * 9 * 9 or 6561 days after 9/11/2001 is 8/29/2019, the start of the 1260 days. Terminator 2: Judgment Day, names the date 8/29/1997 as “Judgment Day”, a day in which nuclear destruction occurs in the movie. This date is 22 years before the actual 1260 day period.
It is a common Jewish belief that both the first and second temples were destroyed on the same day. According to Josephus war Chronology, "the stream of blood was more copious than the flames." He observes that this was on the very day and month that the First Temple had been burnt by the Babylonians". The date for this is set as August 29 (Lous / Av 10).
Let's now review the date 7/17/2019. This date is used as symbolism for Jesus' crucifixion in the Bible because it is said that he arose in 3 days, just as 7917 is 3 less than 7920. The number 189 appears in Pi at the end of 1717 digits, and 189 days after 7/17/2019 is the start of a final 1189 day period.
We have noted above 232's connection to 691. 232 first appears in Pi like so 627 232 7917 8608. This is significant as:
We have mentioned that the founding of Israel is core to the timeline:
25999 is a very powerful prime number, and is the 2860th prime. We see an odd "synchronicity" here as:

Pi / Timeline Codes

666 is the "number of the beast", the number which is mentioned in Revelation 13:18. This is a number which points us to multiple timeline dates. 666 first appears in Pi at the end of 2442 digits. 2442 is 1221 * 2:
12/21/2012 + 2442 days = 8/29/2019, the start of 1260 days
We also see that 666 digits of Pi sum to 2961:
12/21/2012 + 2961 days = 1/29/2021, the completion of a 1189 day period which started on 10/28/2017.

Biblical Code Confirmation

One way we can verify the timeline is by looking deeper into the Bible verses themselves. For example:
Daniel 12:12 (KJV) Blessed is he that waiteth, and cometh to the thousand three hundred and five and thirty days.
In this verse, the word for "waiteth" is Hebrew word #2442. As a reminder, 12/21/2012 + 2442 days = 8/29/2019, the start of the 1260 / 1290 / 1335 days. We now see that 2442 and 1335 are complimentary numbers, and that 2442 + 1335 = 3777.
Daniel 12:12 also uses word #5060 which is a companion number to 4009, as they appear directly next to each other in Pi:
The relationship between 2442 and 1335 is seen in other sections of the Bible as well. See these two verses:
Matthew 24:42 (KJV) Watch therefore: for ye know not what hour your Lord doth come.
Mark 13:35 (KJV) Watch ye therefore: for ye know not when the master of the house cometh, at even, or at midnight, or at the cockcrowing, or in the morning:
The verses mirror each other almost exactly and reiterate to us the fact that 2442 and 1335 are complimentary numbers of the timeline. We also see that Matthew 24:42 is the 24000th total verse of the Bible. With this verse placed at an even 1000 verses, it lends credibility to the idea that the Bible has a planned structure to show the importance of this verse. Daniel's verse was the 22094th total verse, showing the number 2294.
The Bible is strongly based off of Pi, with many of the names being derived from its numbers. The word "Moses" is H4872 because the number "487" first appears in Pi with a 2 after it like so: 4872. From the start of Daniel's 70 weeks to the 1260 days is 487 days:
This area of Pi containing 487 has many different important codes: 7848 216 829 989 4872 2658
There are multiple interpretations for this:
Then in addition:
To continue our confirmation of the 1260 days in the Bible, we see that 829 (representative of 8/29/2019) first appears in Pi like so 829 2540. Greek word #2540 means "time", and is first used in this verse:
Matthew 8:29 (1611 Authorized Version) — And behold, they cryed out, ſaying, What haue we to doe with thee, Ieſus thou ſonne of God? Art thou come hither to torment vs befor yͤ time? Verse #23375 (Ch. #937) — 18 words, 80 letters — Total = 7147
The importance of this verse is confirmed by the fact that it is the first verse in the New Testament of the 1611 KJV to use the special word abbreviation "yͤ" which stands for "the". We also see the number 3375 in the total verse number, which is 15 cubed, and the sum of every digit of Pi before the "Feynman Point", 999999.
We then see that Greek word #2540 is the same word used for "time" in this verse of Revelation which mentions the 1260 days:
Revelation 12:14 (KJV) — And to the woman were given two wings of a great eagle, that she might fly into the wilderness, into her place, where she is nourished for a time, and times, and half a time, from the face of the serpent. Verse #30906 (Ch. #1179) — 32 words, 153 letters — Total = 17897
A coded tweet referring to this verse was made by Trump's team, containing an RFR gematria value of 666:
Donald J. Trump - June 13, 2019 After 3 1/2 years, our wonderful Sarah Huckabee Sanders will be leaving the White House at the end of the month and going home to the Great State of Arkansas....
The verse mentioned above contains a very major code which pertains to the 1260 days. The 1260 days are mentioned 7 times in the Bible, twice in Daniel, and five times in Revelation. The term "great eagle" is used only three times in the Bible, with this verse being the last occurrence, and Ezekiel 17:3 being the first occurrence. Ezekiel 17:3 links to Revelation 12:14. Ezekiel 17:3 is marked as extremely important because it is the only verse in the original 1611 King James Bible to use the apostrophe (') punctuation character.
Note: The 1611 KJV is highly coded, and contains 2860 question marks "?" throughout the Old Testament, Apocrypha, and New Testament.
Ezekiel 17:3 is verse #20829, another code for 8/29/2019. If you move up 1000 verses, you arrive at verse #21829, which is Daniel 3:21, the only verse in the Bible to use Hebrew word #6361, as 6361 is the 829th prime number. If you then move up another 130 verses, you arrive at verse #21959 which is the first of two verses in Daniel which mentions the 1260 days. Another 130 verses up and you arrive at verse #22089, the second of two verses in Daniel mentioning the 1260 days.
In total you have moved up 1260 verses from Ezekiel 17:3 to arrive at the last mention of the 1260 days in Daniel. 173 is also the 40th prime, and the 40 day period ends on 8/29/2019.

Insight into the 1260 Days

We have already mentioned the significance of 262 and how it relates to 14159. We have also stated this fact:
Multiplying 14159 by 2 equals 28318, a number which has its first appearance in Pi at the end of 12600 digits. The 1260 days of the Bible * 10 equals this number. Then, summing those 12600 digits of Pi equals 56636 which is 14159 * 4.
The number 262 is the foundation for some of the most interesting aspects of the Pi code.
Here are the attributes of 262:
These numbers relate to the date 12/26/2014. They create these incredible alignments:
And now to include some additional understanding about the number 1667:
10499 relates to other numbers through the way digits sum in Pi. These two numbers are its relators:
Now for an interesting correlation:
From the completion of the 1260 days on 2/9/2023 to 2/28/2042 is 6959 days. This is interesting as 14159 occurs for the second time in Pi at the end of 6959 digits.
Here is some connecting information about 7/26/2020 to tie this together:
We have come upon an interesting date here because of the fact that:
1541 is a complete number of the timeline for multiple reasons:
On top of this, Prime #12941 is 139241. Both 294 and 3924 inside these numbers are relevant as to the timeline.
12/21/2012 -> 5/27/2048 = 12941 days
To restate the importance of "relator numbers" in Pi, another example of this is seen here:

The Importance of 17 and 1667 in the Timeline

17 * 17 is 289, and the 289th prime is 1879. It first appears in Pi with a 6 in front like this 6 1879
This is interesting as 61879 is the 6222nd prime!
One of the important dates which relate to Harvest is this:
Note that this number can accurately represent 5/31/2017 (start of the "2300 sacrifices").
The date 4/10/2020 has an excellent connection to this date:
Notice that 3555 * 2 = 7110, a number we mentioned earlier in this article.
The reason these numbers have importance is because they are directly connected to 14159, or Pi.
We can see that the days leading to 7/26/2020 can be split up in many ways:

Ordered Primes

As we have said, looking into the order of primes based on how much they have increased from their most previous prime number reveals some interesting things (list here).
Here is an example:
1|2, (100%) 2|5, (66.6666666667%) 3|11, (57.1428571429%) 4|3, (50.0%) 5|7, (40.0%) 6|17, (30.7692307692%) 7|29, (26.0869565217%) 8|23, (21.0526315789%) 9|37, (19.3548387097%) 10|13, (18.1818181818%) 11|53, (12.7659574468%) 12|127, (12.389380531%) 13|19, (11.7647058824%) 14|59, (11.320754717%) 15|41, (10.8108108108%) 16|67, (9.83606557377%) 17|47, (9.3023255814%) 18|97, (8.98876404494%) 19|79, (8.21917808219%) 20|89, (7.22891566265%) 21|149, (7.19424460432%) 22|31, (6.89655172414%)
2 is the first prime on this list because nothing comes before it. 3 is the fourth item on the list because it increases 50% from 2, its most previous prime number.
When you compare this list side-by-side with the usual order of primes, you will see that summing these two numbers and searching for the first 4-digit palindromes reveals 2442 and 2772.
Genesis 1:1 totals 2701 as we have said, which is 37 * 73. Israel is also word #3478, 47 * 74. Then, 3478 - 2701 = 777. The 777th number on the list is 24317, which is the 2701st prime number.
777 is a relevant number of Pi for many reasons, such as:
Doing research into the first / last n-digit number to appear in our ordered prime list reveals:
First n-digit nums: 2, 11, 127, 1361, 10007, 107441 Last n-digit nums: 7, 73, 883, 9931, 99991, 999961
I find it highly interesting to see 9931 on this list as it was mentioned above. It is the reverse of 1399, and occurs at the end of 22222 digits of Pi. It also intersects 1600 (40 * 40) like this: 9931600. It should be noted that the 1600th prime is 13499 which appears by the "Feynman Point" of Pi.
It is also interesting to note that 9931 is #5630 on this list, as it reminds me of an interesting Pi correlation:
The list we have created of ordered primes seems to have an immediate connection to Pi. When the primes are concatenated with the order number of the list, we see certain numbers become visible.
1319, 1459, 1541, and 1667 stand out well. I also 617 and 729, and that diagonally it could be 717 and 629, numbers which appear directly next to each other in Pi: 717 629
Some of these numbers sum to numbers which have significant connections to Pi:
Moving down, 1459 and 1541 read diagonally show us 1441 and 1559 which is an alarming synchronicity as both of these numbers have a relation to the date 7/26/2020.
The verse Matthew 11:12 seems to confirm both the 7920 days and the date 7/26/2020.
25189 - 1717 = 23472, and Matthew 11:12 is the 23472nd total verse of the Bible. It has a gematria total of 12700 because 12700 digits of Pi precede 1112 (as in 11/12/1997). It is as so: 1441 1112
The number 989 represents the end of an age because this number appears at the end of 1000 digits of Pi. 1000 represents completion in this sense. There are five Greek words which have a value of 989. Included are my picks for what the numbers represent:
415 989 (4/15/2014) 726 989 (7/26/2020) 1112 989 (11/12/1997) 2111 989 3449 989 (3449th day of a period starting 7/26/2020)
This is the first verse to use word G726. 726 + 2020 = 2746 and 2746 digits of Pi sum to 12700.
1897 and 1979 diagonally also show us 1879 (the 289th prime number) and 1997.

Pi / Timeline Codes (continued)

10/28/2017 is the start of a 1189 day period, and this particular period can be broken up into 895 + 294 days:
1000 days after 10/28/2017 is 7/24/2020. We have already noted that 189 days + 7/24/2020 = 1/29/2021. 189 digits of Pi sum to 843.
submitted by 3375000000 to LightWarriorAscension [link] [comments]

OBLIGATORY FILLER MATERIAL – Breaking Bad, Part 9

Continuing
I wrap the six road flares, now spray-painted brick-red and stickered with the appropriate manufacturer's labels, with black electrician’s tape into a hexagonal cross-section, closest-fit bundle. I have a black plastic project box that contains a battery for ‘long-lasting power’ or so the manufacturer claims. An Arduino board that I programmed the other night that runs the wee little speaker and set of blinking LEDs I had mounted on the box. From the box sprout a pair of tightly coiled lengths of demolition wire. Not detonating cord, but just insulated copper wire. These attach to the blasting cap and blasting cap super-booster from which I’ve taken the time to extract all the explosives.
I have to admit, it certainly looks authentic; but there’s a small problem. The aesthetics don’t hit me properly. So, I decided to hot glue a cheap-ass Casio digital watch, removed from its band to the large blank spot on the black box. I run a few more coils of tightly wrapped demolition wire, to give it that more earnest and decidedly homebrewed look.
Perfect. A faux time bomb that could fool anyone.
Smiling, I set it into a drawer of the desk in the portable office. Once all the glue, paint, and mastic dries, I’ll shift it to its permanent home.
That done, I wander outside to see how things are progressing. I walk over to the whiteboard to see what sort of ideas they’ve cooked up in my absence.
“Hey, Rock”, Yogarasa asks, “What do you think of this?” as he points to the red-lined ship’s schematic.
“On, no”, I reply, “I’m JAFO here. Just Another Fucking Observer. Let me know when you guys come to a consensus.”
“Right, Rock”, he smiles, “Will do.”
I fire up a heater and wander around the job site. I may be in JAFO-mode, but I do make a few comments on personal safety. I note how some jobs they’re attempting could be done with a bit more care, introspection, and attention to Safety, Health, and Environment.
“Damn”, I think, “But that’s a big fucking boat.”
I’m standing down on the sand, under the prow of the ship. It’s well and truly beached and the farthest point frontwards of the boat, the bow, is easily 50 or 60 feet above my head.
“Gonna take come real cunning and cuteness to chop up this little dinghy”, I think to myself.
“ROCK!” I hear my name.
I’m being paged.
I ease over to the whiteboard. They have a list of items necessary for the job they’re proposing. They have a set of procedures as well. Now they have to sell me on the project.
“OK, I’m here. What’s the deal?” I ask.
Vik takes the initiative and tells me they want to cut the forward 150 feet, or 45 meters, of the ship off in one fell swoop. There are three station keeping bow thrusters in the hull at 50 meters back, so those will not only be safe, but more exposed for reclamation. Lots of copper, zinc, and other saleable metals there.
The front 150 feet of the ship, if cut off flush, will relieve everyone of dealing with all those sharp angles commonly found at the pointy end of the front of the boat. It will be easier for both the explosives mavens and the torchbearers to work on a 900 surface, rather than having to futz with all those pointy front end bits.
Initially, I agree. I ask for the more detailed set of schematics for the ship. I want to see what needs to be cut through in order to remove the bow of the boat. On the surface, it seems like a good idea. There’s only a helipad on the front deck of the ship, and below it appears to be a large ballroom or something similar. Whatever it is, it isn’t a fuel storage bunker or anything like that. Basically, they want to cut the bow off where the forward sheer meets the forward perpendicular.
“OK”, I say, “Sounds like it might work. What next?”
“Tour of the craft”, Sanjay says, “We need to get a licensed master blaster on board to take a look at what we’re up to.”
“And when will this be transpiring?”, I asked.
“As soon as you finish your cigar?” Vik asks.
In the forward-most bow of the ship, it is indeed an empty storage area. No telling what was here previously, but whatever it was, it’s gone now. Come to find out, it was crew quarters. They’re modular and were removed before the ship was beached. They are now in service on some other sea-going vessel; second-class.
There are several watertight chambers that can, or could have been, electronically and/or pneumatically closed if they ran aground or walloped a whale out on the high seas. I check and see there are no hydraulic lines. Those pose special problems, especially if check valves are over-ridden and lines are not de-energized.
I’ve seen what 5,000 psig hydraulic fluid can do coming out of an outlet no bigger than a pencil point. Besides mashing them in the jaws of an oil rig’s power tongs, it’s a good way to lose body parts quickly.
Electrical cables jump, spark, and short out. Pneumatic line spit accumulated water and pffft! themselves out fairly quickly. Hydraulics will cut you in half rather than say Good Morning.
Of course, all of these will be triply checked, but there’s always one rogue line stuck behind a bulkhead or tucked behind some flashing that you never count on. That’s why you have three different people check three different times.
Up on the foredeck, I’m looking at the specs supplied with the schematics. We’re going to be dealing with some 40 mm thick deck plate. That’s treated, hardened, tempered, annealed, and nasty 1.5 inch thick marine-grade high-carbon steel.
That shit’s a tough customer. Most carbon steel is not well-suited for marine environments, however, there are several marine-grade carbon steels available. AH36, DH36, and EH36 are all examples of commonly used marine-grade carbon steels approved by the American Bureau of Shipping. These grades will have slightly more alloying elements such as manganese and chromium compared to their ASTM grade counterparts, which helps achieve higher strength and more corrosion resistance. There are also marine grades of alloy steel as well. Grades MD, ME, MF, MG, and others can provide the strength that normal alloy steel is known for, and have also been approved by the American Bureau of Shipping for use in shipbuilding applications.
Here. We’ll be dealing with EH36, 40mm thickness, nominal. Also referred to as Mil-S-22698 Gr Dh-36. It contains carbon, manganese, silicon, sulfur, and chromium, for toughness.
We’re going to need some test coupons before we tackle this job.
A coupon is a small sample of the material under test that has been prepared in such a way that its failure mechanism will be representative of the larger production pieces.
Just FYI.
“Sanjay,” I ask, “How are you with a K-12 unit?”
Since the boat is going to be scrapped anyways, we’re standing next to the keel with a gas-powered 3.5 horsepower unit that drives a carborundum wheel up front at amazingly absurd rotational velocities. Sure, EH-36 marine steel eats carborundum-diamond sintered disks like candy, but the K-12 will allow us to cut some samples of the hull material for blasting tests.
This is a job for the younger crowd.
Let them experience the pure joy of holding on to a bucking, snorting, spark-flinging hunk of cranky high-velocity machinery. Let them experience the delight of the screaming whine of high-speed carborundum upon high-carbon steel, even while wearing hearing protectors. Let them revel in getting absolutely covered with metal filings and carborundum schmoo from the cutting marine steel and rapidly spinning, eroding, decreasing-diameter saw blades.
Fuck it. I’ll be in my office. I need a cold drink as it’s all hot and dusty and real out there.
I’ve got my feet up on the desk and actually catching a quick cat nap when I hear “THUNK!”
Five of my guys covered head to foot in black cutting residue, toss several 36” x 6” lengths of what was, until recently, the lower hull of a very expensive, indeed, cruise ship on the desk.
“THESE DO?” I am asked in a rather pointed manner.
I am endeavoring to stymie snickering at the situation.
“Told you it wasn’t all skittles and beer, Gents.”, I note.
Picking up a coupon, I give it the once over. “They could be a bit wider, but I guess these’ll have to do.”
I’m sitting at a desk with a large cold drink and five of my guys are standing in front of me with less-than-amicable looks on their faces, sweating and definitely needing a shower.
“Yes?” I ask.
“Well?” they reply.
“Hmmm?”, I hmmed.
“What?” they query.
“¿Que?” I query.
“WHAT DO WE DO NEXT?” they ask in unison.
“Oh, I thought we were having a contest to see how long we could keep conversing in monosyllables,” I replied.

“OK”, I smirk, “We need to test these against various explosives and see the results. Which ones do you think would be applicable to the whole job, not just the task at hand?”
“What do you mean?” Vik asks.
“Well”, I reply, “Seeing what DOUBLEHELIX liquid binary does to these coupons would be a hoot. But since it’s not terribly applicable to the job of cutting the nose off that scow outside…think about it. Liquid binary. Curved ship’s hull. How to affix to the hull? Contain energy how?”
“Ah, yes”, They reply, “I see.”
“Good”, I say, “So?”
“Obviously C-4, that’s a given”, Vik says.
“Yes, good”, I note, “And…?”
“Primacord?” came one query.
“Are you asking me or telling me?” I reply.
“Telling?” came the response.
“Yes. Primacord. Of course. The heavy stuff.” I add. “What else?”
“PETN? RDX? Dynamite? SEMTEX? Sprengkörper DM12?” came some more answers.
“Yes to all”, I replied, “But remember the job. Any idea how much it might take of these explosives? You have your Blaster’s Handbooks. You have your measurements. Have you done your calculations?”
“Not yet.” They reply.
“So, why are you here, stinking up my office?” I growl. They know I’m messing with them.
The all vacate. At least I know I’ll have half an hour or so to plug the numbers into my blaster’s computer.
But first, a refreshed drink and a new cigar.
Priorities, mate. Priorities.
OK, it’s time to bone up a bit on shaped cutting charges. Dynamite and other solids would work well, but there’s be all that futzing around with affixing them to the hull. Could use blasting putty, i.e. ‘Elephant Shit’, to affix them to the hull and contain the blasts for a few microseconds, but that would be a real pain in the cojoñes. I want ‘quick and dirty’ here, as I need to haul ass in the next couple of days. So, moldable explosives it is and I do believe a ‘cut along the dotted line’ approach would work a treat here.
But first, we have some coupons to play with. Truth be told, I’m interested to see what some of the more exotic formulae explosives will do to 40mm thickness EH36 marine sheet steel.
I tell my guys to go get hosed off, pneumatically or hydraulically, and we’ll call it a day. Can’t foul Mr. Maha’s Magic Bus with you guys looking like nasty bag ladies in downtown New Delhi. Besides, I need to write some reports, as does Sanjay.
Later, as I finish up an entirely fictional expose on Goodgulf Greyteeth, noting how his team always wears brown shirts and how he’s always going on about his CEO-furnished dictatorial power, forcible suppression of opposition, strong regimentation of society and of the economy. I mention the picture of Mussolini he has on his desk next to the covered up, though not very well, copies of the manifesto and other works of the far-extreme right. I mention the Luger Pistole Modell 1900 he keeps in his middle desk drawer. I fail to mention it’s actually a cigarette lighter.
I also write up and time stamp a real report. I’ll need these for later.
Sanjay is really getting into the spirit of things, He’s noticing how I absently greet everyone with a “Hello, Comrade” early in the morning. He makes note of my subtle change in demeanor, the more and more I talk about Best Korea and how “they might not be all that bad”. He notes with alarm how I mentioned what I thought the crew would do on the final exam as “from each according to his ability”. Sanjay also notes the current growing obsession I have with referencing my time spent in Russia; even before the wall fell.
I caution Sanjay not to lay it on too thickly nor too quickly. I’ve got stories of the Rodina and anecdotes that paint me red as a Peter Pirsch fire engine . The funniest part will be a certain couple of agents going slowly collectively crazy over my supposed behavior because *they *did my background checks all those years ago and professed that I was as All American as Jack Armstrong.
Between Gulfy and me, a certain couple of sneaky agents are going to be sweating their collective asses off. Either I’ll call their bluff and spill the beans before I leave, or I might just pull some sort of palace coup and declare Alang a new country. Hell, we’ve got enough soldiers and plenty of armaments. I always wanted to be a sultan…
With that done, I’ve reviewed Sanjay’s real report, which I am time-stamping and archiving on my encrypted drive which documents all my duplicity. Hell, I really don’t care at this point; I’m off to Academia and a DSc. They kick me off the proscribed roles and they lose all that wonderful intel. They take as the well-intentioned poke in the snoot and we’ll have a better understanding that you don’t really want to fuck with a future double Doctor of Petroleum Geology and Detonics. Have people surreptitiously reporting on me? Yeah, let’s just see how that’s going to work out for you…
After all that, I retire to the drawing-room and partake of an eminently drinkable potato juice and citrus over rice. I have a couple of fresh cigars thanks to Operator 214 and the evening Times. For what more could I possibly ask?
“Holy fuck!”, I snort, “UREE is up 3 and 1/3rd!”
The next morning after a quick ignoring of phone calls from Virginia “Sorry. The party you wish to contact has gone bush. Please leave your name and number…” and a quick breakfast of Greenland coffee and clotted crumpets, we’re back in the field, gathered right by the soon to be noseless bulk of the Scandinavian cruise ship.
“Right gents”, I say, “We have here a selection of steel coupons taken from the ass of the boat behind us. Recall that a coupon is a small sample of the material under test that has been prepared in such a way that its failure mechanism will be representative of the larger production pieces…which means we are assuming that these hunks of steel represent what will happen to the rest of the boat when we upscale.”
There are noises of agreement.
“In your field notebooks, which I will grade before I leave, “ I note, “I want some ideas why this is and is not a good idea. Always list what you think are good reasons for a course of action. Also, perhaps, more importantly, list reasons why it might not be such a good idea. The scientific method, gentlemen. Multiple working hypotheses. Like I ‘ve always said: “Don’t believe everything that you read and don’t’ read everything you believe”. Make space there for your Doubting Thomas to bloom.”
Further noises of agreement.
“OK, scribble your notes and let’s get after its wild ass.”, I say, “First will be 60% Extra Fast dynamite. Make notes, make predictions. Who do you think it’ll do to this heavy, marine steel?”
I set a coupon on the sand and place a single stick of 60% on top of the coupon. There are immediate objections.
“You’ve not contained the blast in any way!” Vik objects, “It’ll just blow and do nothing more than push the coupon into the sand and scorch it a bit. 90% of the energy will be lost.”
“Quite right!”, I say, “Well noted. So what do we do about this lamentable situation?”
“Elephant shit!” was the universal cry.
“OK”, I reply, “Make it so.”
They do and hand me the trailing leads.
“OK, Safety Dance”, I say.
“Really, Rock?” I hear the objections. “There’s no one here but us.”
“That we know of”, I reply, “Look at it this way. We do it and it costs us nothing more than a couple of minutes. We don’t and suddenly the coupon goes ballistic and tears a hole through someone’s head that we didn’t know was taking a leak behind that dune over yonder…”
“NORTH CLEAR?”
“That’s better”, I smile.
Fire in the hole cited thrice, and we’re set to go. I’ll handle Captain America here, this is for learning, not just fucking around.
“KA-BOOM!”. Lots of noise and smoke. And a flat steel coupon turned into a hotdog bun.
“Look at that. Plastic or ductile failure mode.’ I note, “Is this what we’re looking for?”
“No, we need brittle fracture”, one of my acolytes remarks.
“Exactly.” I reply, “So. Now what?”
“Double the amount of explosive?” was one suggestion.
“That’s a lot of Elephant Shit.”, I remark, “Or we could see if other sorts of explosives give us different results.”
“Or we could see if other sorts of explosives give us different results.” Another wag answers.
I want to save the C-4 for a bit later. We try PETN, RDX, SEMTEX, and Sprengkörper DM12.
PETN has an in-built high brisance; that is, it tends to shatter objects. It reduced the coupon to shards, many of which were projectilized. Not a good choice for mass employment on something like this ship.
RDX has a lower degree of brisance than PETN, but failed to shatter the coupon, nor did it initiate any fractures. It warped the shit out of the coupon, twisting it into an Escheresque shape, like a Klein Bottle. SEMTEX resulted in very similar outcomes, as it is a combination of PETN and RDX.
Sprengkörper DM12 had some promising results, as it did initiate cracks in the coupons we were testing. It also had a bit of high brisance, and the edges of the coupon spalled off into nasty little high-velocity projectiles.
Which left us my favorite, C-4.
We had several coupons left, so I sent one of my crew over to the torch patrol which had shown up right after we began, and had then torch a series of holes, channels, and rifts into a couple of different test pieces.
We tried a blop of C-4 just mooshed down onto a coupon. It resulted in a very nice floral pattern. A hole in the center and the edges curled up skyward.
Then we tried rolling some C-4 ‘snakes’ and laid them in a cross-work pattern. That worked well, loads of fractures in the coupon. We had some obvious reinforcement of the detonic pattern as noted in the interference patterns on the scorched steel.
We were getting closer, but I wanted to take them step by step.
Now we took the coupon with a hole brazed through it. I made a dumbbell of C-4, split it along the long axis, so it had C-4 on both sides. It split that coupon like no one’s business.
Then we tried a coupon with a channel cut into it. The same sort of idea, C-4 on either side, set, charged and primed to detonate simultaneously. Worked a treat. Split that coupon like a prize Blue Point oyster.
We were getting close. We tried several other C-4 configurations until we ran out of test coupons. I laid them all out on the sand and asked my guys which one that we should use.
C-4 was the obvious choice. There was some discussion where we could just burn some holes in the hull, wire them up and shoot it off that way, or would channels be more efficient?
After some little lecturing on failure modes and fracture propagation in marine high-carbon steel, it was decided that a series of 3 foot-long channels would be torched or cut into the hull of the boat and puttied both sides with shaped-charges of C-4. I agreed.
“Now”, I asked, “How much will we need for the job?”
Grumbles and groans. I left them to their mathematical devices as I caught a personnel basket and went up to the foredeck. There was a wooden floor covering marine steel. This would complicate matters a bit until remembered we had a concrete saw. This would make mincemeat out of any flooring; tile, marble, wood, or linoleum. Problem solved.
Now we just needed to get the thing up there.
Well, wouldn’t you know it? It just fits into a personnel basket. It looks like I have my afternoon spoken for.
I receive a call on my cell-phone telephone. I shut down the concrete saw, turned off the water, and got away from the miasma of shredded hardwood, zipping xylem and phlowing phloem to see it’s the personal secretary of Goodgulf Grayteeth, one Achilles Starace.
“Yes”, I ask, shaking the cellulosic cuff off my hardhat, gloves, and boots, “I may help you how?”
“Um, yes, Doctor. We have a package here from Sinter’s Printers. It is addressed to you, but no one was available at Outbuilding #2 to sign for the delivery.”
“Outstanding”, I remark, “Hold it. I will have a duly-authorized deputy of mine come over to relieve you of the package. He will invariably be wearing a pair of orange coveralls, and well, overall, an offhand orange motif. You may feel comfortable releasing the package to his custody. “
“Yes, Doctor.”, he replies and rings off.
I walk over to the side of the ship and see a bunch of orange-clad ants scurrying around. I key the mic on my radio and call down to them.
“Hey you! You! Yes, you! There behind the outdoor heads. Stand still, Laddie!” I say.
“Whaddya want, Rock?”, comes the reply.
“Who wants to earn a break by running an errand for me?” I ask.
Somewhat stilted silence.
“Cigars or booze?” came one answer.
“Nice. C’mon. I’ll pay you.” I replied.
Nothing.
“You can take my bike,” I add.
Instant radio chaos.
“OK, Vis.”, I reply, “Keys are under the seat on the bike. Go to Goodgulf Greyteeth’s office, and see his secretary, one Mr. Starace. Take the package from him and put it on my desk in the Barn. Take a cigar out of petty cash. Then return. Got it?”
I could barely hear him over the roaring putt-putt-putt of the Enfield’s motor.
“Well”, I muse, “There’s another issue handled.”
I return to sawing apart the monstrously expensive, now kindling, hardwood floor.
Not much call to reclaim it. It’s all salt-water eaten and nasty. Too bad, nice patterns.
On one side of the boat, I’ve got the torch patrol in the personnel baskets. Sparks flying everywhere. On the other side, I’ve got the K-12 crowd, sawing away with sparks flying everywhere. Good thing I told them to start at the bottom and work their way up. Be a bad thing if we weakened the superstructure too much and the whole bow came crashing down on someone’s head.
I decided to just cut a square hole in the foredeck, one large enough to admit a scissor-jack. If we’re going to putty both sides of the bow with C-4, personnel baskets will work a treat on the exterior. Interior? Hell, we’re not Spiderman. Scissor-jack delivered via crane.
Well, there’s the whistle. It’s 1700 and I need to drop by the armory for a few bits and pieces before dinner. I get the crane operator to hoist me out of the hold and back down to terra firma. My bike is right where I left it, although the gas tank is suspiciously lower than it was when I parked it.
No matter. Gas is really cheap when you’re not the one paying for it. Much like most everything else here in-country for my stay.
I go to the bunker and do the required access dance to obtain entry. I fill my backpack with several dozen brick-red road flares, demolition wire, the copper variety, and the packing box from a case of Du Pont 60% Extra Fast Dynamite, broken down along the dovetailed connectors that make the crate. They also go into my backpack.
I spy several half-full boxes of blasting caps and boosters, so I consolidate them into a couple of full boxes and the empties go into my backpack as well. Nice little wooden boxes, finely crafted. They will make someone a most excellent gift.
I take my time locking up and fill out the inventory. I make notes for the warehouse foreman to order an excessive number of cases of C-4, spool after spool of Primacord, some more det cord, demo wire, and initiators. This cruise ship will be a huge job, may as well lay in a healthy supply of stock. Besides, I have an inkling that someone besides the warehouse foreman is taking notice of my ordering and usage activities. I fully intend on giving them something to read and worry about.
Yes, I sprinkled a little radioactive tracer, metaphorically speaking, around the job and home site. I have been watching the old scintillation counter, again, I speak allegorically, closely. Looks like I’ve found a sheep in the meadow, a cow in the corn, a dog in the manger a Balrog in the woodpile. Yeah, things here are all not as they first appear. So it would be remiss of me not to give them all something to talk about.
I take my time locking up and leave a voice-note for the warehouse manager to create the order and send it out posthaste. We’ll use much of the C-4, and other ancillary equipment, stock on the bow shot. Once I leave, it’ll be up to my crew to take over-ordering and keep stocks up to snuff. Besides, there are one or two items I’d hoped can be delivered before I depart in a couple-three days’ time.
I motor back to the Raj, taking the scenic route if that’s the term for any vista along this grubby stretch of beach. I am relieved of my motorcycle at the garage entrance, and I shoo the porter away as I am fully capable of carrying my backpack to my room. In my room, I stash my backpack and notice that my mini-bar needs replenishment. I take all the unusual bit and bobs out of my backpack and store them in one of my empty, and lockable, aluminum luggage cases.
I close my backpack and stick a post-it™ note, scribbled with an arcane language I just made up, on the dusty canvas. It’ll stick if undisturbed if you follow my meaning.
I call the Majordomo and explain my angst.
“My mini-bar is almost empty and I have much work this evening…”
He immediately apologizes and says he’ll take care of the matter personally.
I figured he would. I explain that I’ll be in the library or bar while he rectifies this most egregious situation.
I set up a few more field craft booby traps and lock the door behind me.
Sanjay saunters in with the package from the printers. He was changing in the Barn and saw the package on my chair. He thought it’d be best for me to hang onto the tonight rather than to tempt fate.
I thank him for his forethought and think “Tempt fate? Whatever do you mean?”
I have another couple-five post-work cocktails and figure that I’ve given the Major enough time to take care of my mini-bar situation. I say “Spokoynoy nochi” to Sanjay and head back to my room.
Well, the good news is that my mini-bar is stocked to the gills.
The not so good news is that someone here has a very bad and sloppy case of nose poker-inner-itis.
Every one of my little traps had been sprung., and it’s not that just casual wandering around this room or even cleaning and stocking a mini-bar would have set these off.
Someone was deliberately looking for something. Evidently it wasn’t my print of Das Kapital or my ‘autographed’ copy of Quotations from Chairman Mao that I leave on my desk, taking care to change the pages daily. Nor was it my field notebooks from Best Korea which are written in a very arcane and indecipherable code known only to me. But I do know I never ‘break the backs’ of my notebooks. Pages tend to work their way free over time if one does that. I am scrupulously careful with my notebooks. But wouldn’t you know it, several have their spines broken, just like what would happen if someone was trying to photocopy 2 pages at a time, quickly, surreptitiously, clandestinely, on a slow xerocopy machine.
“Good luck with that”, is all I can think. Then, a bit of deviltry pops into being.
I smile, pull out a new field book, use an old, old, old, and simple encryption code; one so easily broken that it can hardly be considered a code.
I spent many hours in the Jacuzzi creating a work of incredible Red fiction, making certain to spill a little of my drink, drop in a cigar ash or two, and get it splashingly wet in places to simulate the appearance of age.
Oh, someone’s going to have the finding of a lifetime tomorrow as I conveniently forget to lock the center drawer of my desk…
Before retiring, I call Es and make the near-fatal mistake of asking what she and her mother bought that day shopping. 45 minutes later, I am able to shoehorn in a word edgewise and tell Es that if Rack or Ruin or both call to chat about me, she’s to let on to nothing. Well, nothing more than the well-coached program I tell her about called “DM Part 1”. It’s just a little chain yankage via an injection of deliberate misinformation to a couple of agents who should have gotten this out of their systems long ago.
They should really know better than to try and sandbag a Doctor of Geology and his wife; especially when the wife’s mother was a resident of Berlin back in the 1940s. Yes, she’s in on the ruse as well.
The next morning at breakfast, I’m handed several notes that I have some missed phone calls. Not surprising, I was either on the phone, in the Jacuzzi, or had disconnected the phone, and turned off my satellite and GSM cell-phone telephones.
As expected, Rack and Ruin are clamoring to talk with me. Unfortunate that I’m so busy these days. I’ll get around to calling them in a couple of days or so.
Sanjay arrives and as were chatting about today’s bill of fare, blasting-wise, Mr. Kanada our redoubtable Majordomo, drops by. We say a casual hello, and I return to my conversation with Sanjay about the merits of Kim Jong-Il and how nice I found Best Korea. I also mentioned that Soviet Russia really go a bad rap in the press. It wasn’t all that bad…
Once Mr. Kanada was out of earshot, I let Sanjay in on the jape. He knows I’ve burned him enough to have him classified as ‘well done’. He is now a trusted auxiliary in this program of considered propaganda. He finds it now, that we’ve stripped away all façade of reality from it, hilarious. I mention that I’ve been poking the snoots at the agency this way for decades. He’s surprised that they haven’t responded with massive retaliation.
I explain that I know where a lot of bodies are buried and how many closets have skeletons.
Metaphorically, of course.
Anyways, it’s going to be a busy day. Lots of priming, setting, and charging of a couple of tons of high explosives. No, we don’t sensu stricto need all that firepowerful pyrotechnics, but since it will be my last blast before I depart, I am planning something of a show. We are rumored to have some company and national dignitaries in attendance tomorrow for the inaugural of the new blasting class, so I want to make this a show to remember.
At the barn, all my guys are dressed in their PPEs. I take this time to dispense the Certifications of Completion of my ISEE-sanctioned and accredited course and practical exams. These are the golden ticket for this batch of two dozen out of the much and mire of the legions of torchbearers. They are now certified to handle explosives, well, most of them are, and all will be after a bit more tutelage and will use that knowledge and experience to make much shorter work of the hulk of various watercraft that wash up along these shores.
25 certificates later, I had planned a blast of a party, but instead, we’re in Mr. Maha’s Magic Bus headed to the beach. We’re preparing for a different type of blast, and the party will follow immediately after.
I have Sanjay take 18 of the guys and split them into two teams, an outside and an inside team, who will load and prepare the channels which we’ve cut into the hull of this old boat. Sure, we needed some torch and saw work, but only a slight proportion of what would be needed if one were to just make these cuts with a torch crew.
The outside and inside guys will collaborate in placing the C-4 in the channels and holes we’re prepared. Between channels, we’ll alternate with a row of C-4 on the outside, a filled channel from both sides, and a row on the inside, down and around the entire prow of the boat, alternating as we go. That way, we’ll maximize the amount of bang we’ll receive per unit volume of pyrotechnic employed.
That will keep Sanjay hopping for a good portion of the day. I have my six guys come over to the whiteboard whilst I have an early morning smoke and explain what we’ll be up to this fine, humid morning.
I have a list of items that I need from the armory. I scrounge a one-ton pickup truck and tell Luke to take the one-ton and ride to the dispensary system and obtain the items on the list. I tell them that they are on point to both open, extract the necessary items, record, and close the armory as per procedures. I won’t be here forever, so I have to trust them to do as I had taught.
I have the other four commanded a crane and personnel basket along with an oxy-acetylene welding set. It seems most of these guys can handle welding as well as cutting with torches, so I instruct them to weld four 2’ long pieces of ¾” rebar to the outside of the ship. I want a rectangle 5 meters high by 3 meters in width. I let them figure out there where and how I’ve got to get inside as there’s a shit-ton of wiring and circuits that have to be created and galved.
The day progressed more or less as planned. The hull, where perforated, was C-4’ed inside and out. A quick inspection via the scissor lift on the ship’s interior provided a very nicely done job. I had Sanjay take a couple of guys and do the same due diligence on the C-4 outside the hull.
I began wiring in the appropriate scrub-circuits. These are basically the gross outlines of the circuits you’ll use to fire the pyros. I ran a huge loop of det cord around the inside of the ship’s bow, as I wanted it protected from the humid salt air overnight. I had Sanjay spray the exposed C-4 outside the bow of the ship with a special black tar-based preservative as he and his crew inspected the placement of the stuff.
I had a sheet of marine plywood scrounged and set up as a whiteboard in the dark belly of that boat. I drew my schematic wiring diagrams and after a while, I even ran out of different colors of pens to demote different sub-circuits of the plan. For insurance and back up purposes, I had my team go along and weld 4” diameter pipe footings in strategic places. These were normally used to build shades or awnings by bolting the pipe footings to thick wooden planks on the boat and using simple cold-rolled low carbon steel pipe as mainstays and uprights.
I also had my guys whip up a load, that is, as many as they could before the end of the day, lengths of threaded 4” pipe. Normally called ‘nipples’, these were 2-3 foot length of pipe, as noted, threaded at both ends. On end screwed into the pipe footings I had welding in strategic places and the other end accepted a 4” pipe cap. These might sound like pipe bombs in the making since I plan to fill them with various potions of my own creation, but they are more like downward-firing pipe cannons. The caps have much more mechanical strength and bearing capacity than the 3.5” hole of the pipe footing. When fired, the caps would remain intact and direct the rapidly detonating or deflagrating pyrotechnic downwards. Sort of a vertical shaped charge. These would come into play later on in the show.
We set, primed, charges, and wired all day. Finally 1700 hours rolled around and I told everyone that I had a few bits and pieces left to do and that I could handle it alone. True, I could have used some extra hands, but the time I’d waste explaining what I was doing would consume any time saved by their help.
I did bribe a crane operator to hang around and drive the personnel basket as I’d be the one inside it giving him the signs of which directions I needed to go. We had a couple of hours before dark and that’s when I’d have to quit. So as soon as everyone departed to the barn, I was in the basket and on the radio. I had 7 spools of det cord and a big job in front of me. That the crane operator was well paid and paid good attention to my directions meant we finished well before darkness fell.
To Be Continued…
submitted by Rocknocker to Rocknocker [link] [comments]

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Beginner Robot Path Planning Math

Hello, new to building robots and I could use some help with my project. I am trying to build a two wheeled robot that will initially follow a perimeter of a hexagonal shaped "course". I want to solve everything mathematically and then simulate the robot using VREP.
How would I come up with an expression for each wheel as a function of velocity and duration of the command for each rotation and displacement that will provide the path along the perimeter?
My robot must maintain a 6" margin from the wall it is following and my robot has a diameter of 18" with 9" wheels. I'm thinking of using dead reckoning to start or maybe Manhatten pathing.
For each wheel, I know I can use a few formulas to solve but I'm having trouble putting that together with the pathing formulas. Below are what I was thinking of using:
V=WR, where V is velocity, W is the angular velocity with respect to the center of rotation, and R is the distance from the center of rotation to the midpoint of the bot.
Velocity of Left/Right Wheel = W (R-(d/2)) where d is the diameter of the bot.
R = d/2 (VL + VR)/(VR-VL) where VR and VL are the velocities of the right and left wheel respectively.
W=(VR-VL)/d
I appreciate any help or direction! Thank you for taking the time to read this post!
submitted by pineapple_swag to robotics [link] [comments]

Stealth - Part 1 - Measuring Stealth Technology's Performance

http://aviationweek.com/defense/measuring-stealth-technologys-performance

Measuring Stealth Technology's Performance

How low-observable technology enhances aircraft survivability
Jun 28, 2016 Dan Katz | Aviation Week & Space Technology
Stealth Science 101
A Closer Look At Stealth
This is the first article in a series. For the non-U.S. nations buying the Joint Strike Fighter, Lockheed Martin’s F-35 will be their first experience operating stealth aircraft. Since development of the aircraft began 15 years ago, radar technology has advanced and debate over the value of stealth has escalated. But several nations have now selected the F-35 in open competitions, citing in part the combat capability enabled by low observability. As the F-35 debuts at air shows outside the U.S., Aviation Week reexamines the fundamentals of stealth and whether it provides an advantage over the latest adversary radars.
http://aviationweek.com/site-files/aviationweek.com/files/uploads/2016/08/01/State_of_Stealth_LOgo.jpg
Stealth Basics
Stealth is the science of reducing an object’s detectability to radar. The goal is to minimize the electromagnetic energy reflected back to a radar so it cannot distinguish the return from the signals created by environmental clutter and noise of its internal electronics.
The metric of detectability is called radar cross-section (RCS), which normalizes the reflectivity of targets by comparing them to metal spheres. Human beings have an RCS of about 1 m2— they return as much radar energy as a sphere with a geometric cross-section of 1 m2. Since RCSs vary by orders of magnitude, it also is common to use the logarithmic unit “decibel square meters” (dBsm), in which 100 m2 converts to 20 dBsm and 0.1 m2 to -10 dBsm.
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Large “fourth-generation” fighters such as the F-15, Su-27 and Tornado have radar cross-sections (RCS) of 10-15 m2. The F-16 and “Gen-4.5” fighters—Typhoon, Rafale, Su-35 and Super Hornet—are believed to be in the 1-3-m2 range. The F-35 and F-22 RCSs are said to equal a golf ball and marble, respectively. Based on Sukhoi’s claims that its Su-35 can detect 3-m2 targets at 400 km in a narrow-angle, maximum-power search, Aviation Week estimated how far away it can detect these fighters. Note the detection range in a standard search is half as much. Credit: Colin Throm/AW&ST
RCS varies with the angle and frequency of the radar signal. The sector of greatest interest is ±45 deg. in azimuth and ±15 deg. in elevation, and the frequency band of greatest concern is X-band (8-12 GHz), where most fire-control radars operate. “All-aspect stealth”—minimizing detectability from any angle—and “broadband stealth”—reducing observability over a broader frequency range—can be achieved with greater cost or engineering tradeoffs.
Stealth technology reduces RCS by shaping an aircraft to “scatter” radar waves away from the emitter and using radar-absorbent material (RAM) to reduce reflections by turning the energy into heat. Traditionally, shaping accounts for 90% of stealth’s RCS reduction and materials 10%.
Shaping starts with a focus on “specular” scattering, in which waves bounce off a structure like billiard balls. Flat surfaces reflect most energy at an angle equal to the incident wave and are therefore preferred and oriented to minimize returns to the radar.
Engine intakes, cockpits, 90-deg. corners and other “multiple-bounce structures” reflect the most incoming energy back to their sources. Right angles are avoided entirely. Cockpit canopies are “metallized” with a few nanometers of gold or indium tin oxide to make them reflect radar energy. Engine fan faces can be shielded from radar illumination by external screens (F-117 and RQ-170), internal blockers (F/A-18E/F) or serpentine-shaped inlets (B-2, F-22 and F-35), all of which incorporate RAM.
Weapons and other stores are carried internally. Missiles, bombs and fuel tanks increase RCS with their pylons, round bodies, cruciform tailfins and sensor apertures. They also create multiple-bounce geometries with the airframes, which can increase RCS.
http://aviationweek.com/site-files/aviationweek.com/files/uploads/2016/06/23/F-STEALTH_gallery_5_USAF.jpg
This front view of the F-117 shows the screens covering the engine intakes. The screen blocks most radar waves and traps the rest inside. Note also the hexagonal auxiliary intakes with edges aligned with the main intakes and side of the fuselage and the sawtooth pattern surrounding the canopy. Credit: U.S. Air Force
Edges diffract radar energy in a narrow, fan-like pattern but still at an angle equal to the incoming wave, and wing and tail tips diffract waves in all directions. Both are kept narrow to minimize RCS, and edges are angled away from the direction of the threat.
Fuselage facets, control surfaces, leading and trailing edges, and gaps are oriented to concentrate reflections into a minimum number of angles. This “planform alignment” reduces detectability at every other angle. The surface is then covered with RAM, with special treatments for edges and tips.
When waves strike surfaces at grazing angles, they induce currents that travel until they hit a discontinuity, where they radiate waves and bounce back to radiate again. The longer they travel, the weaker they become, particularly if the surface contains RAM, but any discontinuity—an edge, gap or step in the surface, or a material change—reflects them. Gaps around access panels must be covered with conductive tapes or caulks to bridge any electromagnetic discontinuities. Access panels and doors that open in flight, such as those for landing gear and weapon bays, have edges angled to reflect traveling waves away from the threat sector, often creating a “sawtooth” appearance.
Estimating RCS
There are formulas to calculate the RCS of simple shapes and computer programs to estimate those of more complex structures, but due to the difficulty in accounting for nonspecular mechanisms, interaction among structures and RAM, it is better to rely on RCSs determined by testing. Those numbers, sometimes cloaked in terminology of objects, have been discussed publicly.
http://aviationweek.com/site-files/aviationweek.com/files/uploads/2016/06/13/F-Stealth_diagram2.jpg
Almaz-Antey says the S-400’s 92N6E “Gravestone” fire-control radar can detect a 4-m2 radar-cross-section target at 250 km. Based on this figure, Aviation Week estimated its detection range against modern fighter aircraft. Credit: Colin Throm/AW&ST
Conventional aircraft of similar geometries and size tend to have similar RCSs. The Boeing F-15 has a frontal RCS of around 10 m2. The Sukhoi Su-27 RCS is also in the 10-15-m2 range and the Panavia Tornado is likely in this neighborhood as well. The figure is larger if external stores are carried. The initial Boeing F/A-18’s RCS is believed to be in the 10-m2 realm, but F/A-18C/Ds began incorporating RAM in 1989. The smaller Lockheed Martin F-16’s RCS is believed to be around 1-3 m2; the later C model is slightly stealthier than the F-16A, and signatures have also been reduced under Have Glass programs, which include application of RAM.
Later “Generation 4.5” fighters all employ RCS reduction to some extent. The Eurofighter Typhoon program sought to reduce RCS by a factor of four compared to Tornado. The Sukhoi Su-35 claims reduction of 5-6 times over the Su-27. This likely puts the Su-35, along with Dassault Rafale, in the 1-3-m2 range. The F/A-18E/F, which Boeing says employs the most extensive RCS-reduction measures of any nonstealth fighter, is reported at 0.66-1.26 m2.
While low observability is a spectrum and not a binary quality, “stealthy aircraft” usually implies an RCS of less than 1 m2. Russia’s new T-50 PAK FA is believed to be in the 0.1-1-m2 range. Cruise missiles come in at 0.1-0.2 m2. The F-117 was said to have an RCS equal to a small bird (0.01-001 m2). The F-35 RCS is compared to a “golf ball” and the F-22’s to “a marble”; these objects have RCS of 0.0013 m2 and 0.0002 m2, respectively.
Detectability vs. Radar
How does stealth affect survivability? Since radar waves expand spherically going to and returning from targets, the range at which an aircraft can be detected is proportional to the fourthroot of its RCS. Every tenfold reduction decreases detection range by 44%.
The most advanced Russian fire-control radars yet deployed are the Irbis-E on the Su-35 and the ground-based 92N6E Gravestone, part of the formidable S-400 surface-to-air missile (SAM) system. The manufacturers of the Su-35 and S-400 claim good performance against “stealthy” targets, but their own numbers do not substantiate this.
Sukhoi states the Su-35 can detect a 3-m2 target at 400 km (250 mi.). That is a good range against an F-16 or Typhoon, but it means this newest Flanker cannot detect an F-35 until it is within 36 mi., and inside 22 mi. for an F-22. And the U.S. fighters can launch their medium-range AIM-120 AMRAAMs from more than 60 mi. away. Also, that detection range is for a maximum-power, narrow-angle search. In conventional search mode, the detection range is half as much.
Almaz-Antey’s S-400 is feared for many reasons, including its longest-range (380-km) missile, but it cannot fire until its Gravestone radar has a target. According to the manufacturer, Gravestone detects a 4-m2 target at 250 km (155 mi.). Again, good against “reduced RCS” fighters, but the F-35 would not be seen until 21 mi. away and the F-22 13 mi. away. The U.S.’s internally carried Small Diameter Bombs can be dropped from more than 40 mi. away.
Much of the debate over the continued value of stealth has been generated by developments in lower-frequency radars (to be addressed in the next installment of this series), able to detect aircraft optimized for X-band stealth at longer range. But these are search radars that lack the resolution to provide targeting data. The S-400’s 91N6E “Big Bird” search radar can detect 1-m2 targets at 338 km (210 mi.), almost twice the range of the Gravestone, but its batteries cannot launch until the fire-control Gravestone has a target.
These figures are only estimates, but they are based on established formulas and public data from manufacturers and specialist engineers. The numbers convey the continuing advantage of stealth fighters, which can remain undetected until well within weapons range, even against top-end fire-control radars. These numbers suggest stealth remains a strong contributor to survivability against state-of-the-art weapon systems.
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hexagon diameter formula video

Formula for calculating radius of a inscribed circle of a regular hexagon if given side ( r ) : radius of a circle inscribed in a regular hexagon : = Digit 2 1 2 4 6 10 F Hexagon Calculator. Calculations at a regular hexagon, a polygon with 6 vertices. The hexagon is the highest regular polygon which allows a regular tesselation (tiling). Enter one value and choose the number of decimal places. Then click Calculate. Edge length (a): Long diagonal (d): Short diagonal (d 2): Perimeter (p): Area (A): Incircle radius (r i): Round to . decimal places. Formulas: d ... To calculate the area of a hexagon, use the formula a = 3 × square root of 3 × s^2 divided by 2, where a is the area and s is the length of a side of the hexagon. Just plug in the length of one of the sides and then solve the formula to find the area. If you don't have one of the side lengths but you do have the apothem, you can use the formula a = 1/2 × perimeter × apothem, where a is the ... Hexagon area formula: how to find the area of a hexagon. We will now have a look at how to find the area of a hexagon using different tricks. The easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. For those who want to know how to do this by hand, we will explain how to find the area of a regular hexagon with and without the hexagon area formula. With the diameter of the hexagon or square bar, the size of the round bar can be calculated using the following formula: Round Bar Diameter = Hexagon Diameter * 1.154701 Round Bar Diameter = Square Diameter * 1.414214. Fabrication Bar Diameter: Round Bar Diameter Needed = Fabrication Bar Diameter: Round Bar Diameter Needed = Fabricate Flat Bar With the width and height of flat bar, the minimum ... Area and Perimeter of a Hexagon. A regular hexagon is a polygon with six edges of equal length. The adjacent edges form an angle of 120°. The radius of a circumscribed circle is the same as the length of the edges. Formulas The Perimeter of Hexagon Formula Hexagon is the polygon that has six equal sides and the six edges. Hexa is a Greek word whose meaning is six. Naturally, when all six sides are equal then perimeter will be multiplied by 6 of one side of the hexagon. Abd each internal angle is measured as 120-degree. 2] Permiter of a Hexagon. Perimeter will be the sum of all 6 side lengths. The formula for the perimeter of a hexagon is given as: \(P = 6 \times a\) 3] Diagonal of a Hexagon. There is no standard formula to find out the diagonals of irregular hexagons. In regular hexagons, there are nine diagonals in six equilateral triangles. So, it is easy ... Calculating the Diameter of a Hexagon. First, measure all the other sides of the hexagon to make sure the hexagon is regular. In a regular hexagon, all six sides will be equal. If the hexagon is irregular, it will not have a diameter. Next, there are two simple ways to calculate the diameter of a hexagon. Measure the side length and multiply it by 2. Multiply the radius by 2. (The distance ... The formula for finding the area of a hexagon is Area = (3√3 s 2)/ 2 where s is the length of a side of the regular hexagon. Similarly one may ask, how do you find the side of a hexagon given the diameter? Divide your value by 2 if your given value is the length of the center line that creates the middle two triangles within the hexagon.

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