Slides and Logs

I believe that learning the “old ways” of doing things has a place in prepping. Knowing how to do things without the aid of modern gadgets will give you more options for the serious SHTF scenarios, such as having to do without electricity anywhere nearby for months or years. Building or rebuilding anything large takes math, that's just a fact of life, and so the more math you understand the better. I'm not saying you have to memorize everything; just knowing how it works and where to find it is a big step towards using it.

50-odd years ago, computers were in their infancy; an average smartphone of today has more memory and computing power than the largest supercomputer of the 1960s. The engineers, machinists, astronomers, and planners of the time all used analog equipment rather than digital. One of the main analog computing devices of the era was the slide rule, a pocket calculator that didn't require batteries and could give quick, accurate results as long as you know how to use it properly. Sadly, the last maker of slide rules went out of business many years ago, but so many millions of them had been made in the hundreds of years prior that you can still find them if you look around.

Slide rules work by using logarithmic scales on two parts, one fixed and the other movable, to perform rapid multiplication and division. Let me explain logarithms first, and then I'll get back to slide rules.

Logarithms

Logarithms are a mathematical function. The easiest way to understand common logarithms (I'll use the shorthand “log”) is to ask, “what exponent of 10 will equal this number?” 

If you're not sure what an exponent is, it's the little number placed above and to the right of a number to express a large number in a shorter way (I'm not sure if all of the possible browsers out there can interpret superscript so I'll use an alternate method of denoting exponents: instead of 2² I'll use 2^2.) 4 is 2^2, 32 is 2^5, and 4096 is 2^12.

The nice thing about exponents is that multiplication of numbers is the same as the addition of their exponents as long as you are using the same base number. So to multiply 4096 by 32, you could just add their exponents (5+12=17) and look up the results on a table, which gives you 131,072. Division is the opposite of multiplication, so you can perform that function by subtracting exponents.

Using a log table takes some practice, but once you get the hang of it it's a lot easier than filling pages of paper with long multiplication or division of large numbers. I had to dig out one of my older reference books to find a good log table; most of them are carried out to 4 or 5 decimal places, but I've seen tables much larger.

Here's a sample of a log table. 

https://www.abelard.org/sums/four_figure_log_tables.php

Using a log table starts with simplifying your large number. To use the example above, 4096 is expressed as 4.096 * 10^3. Simplifying your large numbers to “scientific notation,” aka a number less than 10 times some exponential power of 10 is essential. Log tables only cover the numbers from 0 to 10 because once you go past 10, they repeat.

Since adding logs is the same as multiplying the numbers, you end up with:

log 4.096 + log 10^3

since we're working with the base of 10, the log of 10^3 is 3, and looking at a table tells me that the log of 4.096 is 0.6124. That makes the log 4096=3.6124

Doing the same to 32 gives me: log 32=1.5051

Adding 3.6124 and 1.5051 equals 5.1175, which is 10^5 (100,000) times whatever has a log of 0.1175. Looking that up on the same table tells me that 1.3107 has a log of 0.1175, so our answer is 1.3107 times 100,000 or 131,070. Not exactly the same as 131,072 but it's close enough for most work. Using log tables carried out to more digits will get you closer to the exact number, but this is far less than 1% error (0.000015 to be exact) and was good enough for engineers for a couple hundred years.

 

Slide Rules
If you're still with me it gets easier. People who worked with math a lot didn't want to have to go back and forth to a table every time they multiplied or divided a large number, so they engraved a logarithmic scale on two pieces of wood, and by sliding the two scales against each other they could mechanize the addition of the logs and read out an approximate answer. This is basically a slide rule. Using the scales engraved on the bars eliminates the need for tables, and as long as you kept your decimal points straight, the answers were within acceptable ranges. 

Courtesy of https://www.pepysdiary.com/encyclopedia/6104/

Here's a picture of the logarithmic scales and how they're used. In this example they're multiplying 2*3, so they lined up the “2” on the bottom scale with the beginning of the top scale and by “adding” the “3” from the top scale they see that the answer is “6” on the bottom scale. Once you have the bottom scale set, you can get answers to several equations just by looking top scale and following it back down to the bottom. This is why a lot of slide rules had a clear slider with a thin line, it lets you see the answer on the bottom scale a little quicker and also allows for easy follow up equations. Look and you'll see that 2 * 1.5 lines up with 3, 2 * 2.5 lines up with 5, and so on. 

Yes, I have slide rules. Most of them have other functions and scales that are more complex than I care to cover here, but the trigonometric functions are handy if you have them. For a cordless, battery-free calculator, they will work long after your cell phone has died and will still give good enough results to put a man on the moon. Follow the link under the picture above for a good article on slide rules and their history.

Prudent Prepping: Red Dot pt. 2

The dust has settled and the First 72 Hours have passed. Follow along as I build a long term plan via Prudent Prepping. 

In last week's blog post I glossed over the base and mount for the red dot sight I installed. I was asked elsewhere to give more detail on the RS Regulate parts that were used. Here is the expanded explanation!

RS Regulate

I have to say it was really interesting to see how well the RS Regulate mount and base went together. Not only was it easy to build, but it mounted extremely easily. 

I can't take pictures as nice as the ones on the website, and so this link shows the details of how simple and strong everything is. 

This picture shows the adjusting bolt and locking bar mentioned in Figures 3-6. 

Bolt, Bar and Latch

If you are as unfamiliar with AK-style mounts like I am, the bracket on the side is where all additional optic mounts are attached.

 

AK Optic Rail 

AK Optic Mount

The base slides onto this bracket from Right to Left (towards the muzzle) and then the latch shown in Figure 7-8 is closed after making sure there is no play or wiggle room between bracket and optic mount.

Before anyone asks, the odd inverted "L" shape in front of the trigger guard is a CA Approved device that requires a tool to remove the magazine, allowing me to use the ones I already own. Yes CA is special in all the wrong ways.

One thing I almost didn't mention last week was the RS Regulate proprietary rail and why I needed to hunt so hard for the actual red dot base: the base and mount are a special shape that allows the owner to mount optics on the centerline of the gun, since most AK pattern firearms have a sheet metal bolt cover. Yes, there are replacement covers that are much sturdier with standard-width rails, and I chose not to do that.

Top View

Base, Mount and Red Dot

Here is a top view of the rail, mount and red dot. If you look closely at the cap screws you can see the amount of room for left and right adjustment that is available. This means that the red dot itself will need only minor adjustment to sight in, since the bulk of the movement will be done with the mount screws.

The red dot is placed in the middle of the base as a starting point for me, as I have no experience with red dots and don't know the amount of eye relief I might need. Unfortunately, I don't have a vise or a steady enough place to prop things so I can't get a nice view through the Swampfox Kingslayer Red Dot. I don't expect problems, though, as the Kingslayer is clear and the brightness adjustments are easy. 

Again, I can't say enough about how nice everything came together as I finished a project that I put off for much too long.

Recap And Takeaway

• Please look at last week's post for info on the Kingslayer Red Dot. I recommend that everyone look at Swampfox for great products at outstanding prices.
• The only bad news is the RS Regulate mount and base I used are now both out of stock. A friend joked that I must have sent too much business their way, but in fact I believe it's because their line of AK accessories so good that they sell out really quickly!
• Nothing was purchased this week, but there are items on my shopping list. 

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Just a reminder: if you plan on buying anything through Amazon, please consider using our referral link. When you do, a portion of the sale comes back here to help keep this site running!

If you have comments, suggestions or corrections, please post them so we all can learn. And remember, Some Is Always Better Than None!

NOTE: All items tested were purchased by me. No products have been loaned in exchange for a favorable review. Any items sent to me for T&E will be listed as such. Suck it Feds.

Pooping In The Cold

Yes, I said it. Yes, I'm serious. Doing your business in the cold is a valuable life skill, and today I'm sharing it with you.

While this video is about using outhouses in cold weather, the same principle applies in the woods; just find a log to sit on. 

Lokidude

Product Review: the Luxe Bidet Neo 120

Not actually Erin.

Picture by KJ Photography

& is used with permission.

Just hang on a moment, Erin! I hear you saying. Why is a prepping site talking about a bidet?

Do you remember the Great Toilet Paper Shortage of Spring 2020? That's why. I don't know how well the rest of you fared, but even though we didn't ever run out of TP, we did get down to the single-ply emergency stocks and that was unpleasant. So when I heard that there was another run on TP due to an expected surge of COVID-19 this flu season, I decided to go ahead and get a bidet, the Luxe Neo 120, to help make our supplies of TP last longer. 

Disclaimer: In order to write a useful post about this subject, I need to talk about things which a lot of people find distasteful and/or embarrassing. Everybody poops and everybody needs to wipe, so let's just be adults about this. 

https://amzn.to/3mMPjQC

I admit that I wasn't sure how I would feel about a stream of cold water right on my anus, but my friends who own bidets (and it turns out I have a surprisingly large number of them) told me that it wasn't a big deal and that I'd get used to that pretty quickly. I'm going to jump ahead in this review and say a few things about this now:

1. It really isn't a big deal. I can feel that it isn't warm water, but it isn't the shock to my system that I feared it would be. 
2. If you have anal irritation, such as from hemorrhoids, cold water can be a relief and help reduce swelling. 
3. If it's still important to you, it's possible to get warm water bidets. 

Price and Features

I paid $35 for mine, which I felt was entirely reasonable. The Neo 120 is one step up from the bare bones model; it features a self-cleaning nozzle feature which the Neo 110 ($28) lacks. Models 180 ($40) and up feature dual nozzles for feminine cleansing; I skipped that because neither my mother or I need that particular function. The Model 320 is the only one which is heated, but costs $50 and requires a hose which runs from the toilet to the under-sink hot water taps. Given that our toilet is several feet away from the sink and the taps are behind cabinets, I decided this was more trouble than it would be worth. 

Installation

I can only speak for the Luxe Bidet which I bought, although I figure other Luxe models install in more or less the same way. Installation took me about an hour, and some of that was due to the fact that my toilet seat isn't exactly standard and didn't want to cooperate with the mounting hardware, but I got it work nonetheless. I consider myself to be competent with tools but not especially skilled, yet I had no problems with the installation (other than the toilet seat); someone who is more proficient would install it sooner and have the same amount of trouble I experienced, which is none. 

The only tools I needed were those to remove my toilet seat, which in my case was a socket wrench. All other tools were included, and the instructions were clear. 

Pro Tip: Make sure that the hose from the cold water feed to the bidet is fastened tightly, and slowly turn the tap back on. If it's not tight enough you'll have a leak, and it's better to have a dribble than a spray. 

Performance

First of all, this doesn't eliminate the need for toilet paper; you still have to wipe yourself dry. That said, I have found my TP use greatly reduced to somewhere between 1/2 and 1/4 of my normal use. For preppers, that ought to be enough to convince you to buy it. 

It also makes me feel cleaner. We've all had bowel movements where it seemed like we'd never get clean, and this solves that problem every time. 

Finally, if you ever have a really bad case of intestinal upset, this will pay for itself in no time. The cold water is soothing on an inflamed anus, and if you're having to use the toilet again and again (such as if you are preparing for a colonoscopy and you need to take a laxative before the procedure), this will prevent that feeling of rawness and chafing that you get after continual wiping. 

Also

Be sure to get the package of Toilet Seat Bumpers. Trust me, the bidet raises your toilet seat up enough that it won't sit flush (hah!) on the commode bowl, and you really don't want to break the seat by bending it where it doesn't want to bend. I bought these and I'm happy I did. 

https://amzn.to/3gmPFuY

Two warnings, though:

1. The plastic over the adhesive is a massive pain to peel of. Be prepared for that; I had to use a knife to get it started and then tweezers to grab it. 
2. Don't drop the adhesive. Especially not into the toilet water. They stick great if you apply them to the seat straight off the plastic, but if there's other stuff on the adhesive then it may not stick and you might end up having to order a second set. 

http://amzn.to/1X5kJ1P

Finally, some of you may be asking I have a Squatty Potty. Does the Luxe Bidet work well with it?

The answer is Yes, very much so. In fact, if you position yourself just right with the Squatty Potty, you can basically give yourself an enema with the bidet. 

That may sound gross, but let me tell you this: if you've ever been constipated, that can really help soften and loosen your stool and just might speed up the process. I know that it helped me a great deal. 

My Recommendation: A+
If you're a human being who poops, buy this. It's more comfortable than dry wiping, it's probably better for the long-term function of your septic system to flush less toilet paper, and the paper you do use will last longer. It's easy to install, it's great if you have health problems (including reduced flexibility that makes wiping difficult), and if you register it comes with a 2 year warranty. 

If it ever breaks, I'll be sure to let you know. 

Basic Trigonometry

David's article from a week ago, where he covered distance calculation using simple geometry, reminded me of a level of math that is no longer taught. My high school math class was the last year to be taught how to use a slide rule and the first to see the introduction of electronic calculators; I learned a different kind of math than what is taught now, and it relies on basic mathematical functions instead of digital processing. Some of those basics could come in handy when your batteries are dead and you need to crunch some numbers.

Warning: Math ahead, so take appropriate precautions.

David covered how to determine the distance to an object by using angles from two points a known distance apart and the tangent of one of those angles. Tangents are one of the three basic ratios used in trigonometry and are derived from a “right triangle”. A right triangle is a three-sided shape where one of the corners is a “right angle”, or 90 degrees.

Pythagoras, a Greek philosopher and mathematician that lived about 2500 years ago, figured out that right triangles were important and had unchanging properties. No matter their size, certain ratios and relationships between the sides and angles were always the same. The Pythagorean Theorem states that the sum of the squares of the two adjacent sides of a right triangle will equal the square of the side opposite the right angle. We often see this expressed as a^2 + b^2= c^2.

A quick way to make a right angle is to use this theory and use sides that are 3, 4, and 5 units (whatever units you want to use; feet, inches, meters, dollar bills, cans of beans, etc.) to make a triangle. 3^2=9, 4^2=16, 5^2=25 and if you put those numbers into the Theorem you do get a true statement that 9+16=25.

You now have a basic right triangle to build from, and the rest of plane geometry follows from that building block. This works well in the field when trying to lay out fence corners and other things that need to be square.

Let's stick with right triangles for a bit. Here's a picture of a generic right triangle with sides a, b, and c and angles A, B, and C, courtesy of Wikipedia. The 90 degree angle is commonly annotated with a small square at the angle, especially for hand-drawn triangles.

https://en.wikipedia.org/wiki/Right_triangle

For our purposes, angle C is the right angle (90 degrees) and the side opposite it (c) is called the hypotenuse. Since all of the angles of a triangle have to add up to 180 degrees, A+B will always equal 90 degrees in a right triangle.

David's friend explained that the tangent of an angle is the ratio of the length of the side opposite that angle divided by the length of the side adjacent to it. That means that the tangent (tan) of angle A would be a/b. Expressed as tan A= a/b and using what used to be freshman math, you can convert that to a= tan A*b.

There are other useful constants that can be derived from a right triangle:

• Sine (sin) of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. Sin A= a/c
• Cosine (cos) of an angle is equal to the length of the side adjacent divided by the length of the hypotenuse. Cos A= b/c
• Tangent can also be expressed or found by dividing the sin by the cos (tan=sin/cos) of that angle.

(Editor's Note: You can remember these using the mnemonic SOH CAH TOA. 

• Sine = Opposite * Hypotenuse
• Cosine = Adjacent * Hypotenuse
• Tangent = Opposite * Adjacent

The Hypotenuse doesn't change, but the Opposite and Adjacent sides are always relative to the angle from which you are measuring. -- Erin)

Once you know one angle and either one of the trigonometric ratios or the length of one side, you can apply these formulas to determine all of the other parts of the triangle. 

Sin, cos, and tan tables used to be included in the backs of most math text books and every reference book had them. Digital calculators have made those tables obsolete, but they still exist and I'd recommend having a set somewhere in your library. If you're really lucky, you might be able to find an old slide rule that has the trigonometric functions on the static sides, handy for quick approximations.

I know that some eyes are glazed over by now, but these are basics of geometry which is the building block of engineering, architecture, and a lot of mathematics. Those are things you're going to need to understand if you want to do more than “eyeball” any construction or repair project. Think sloped roofs, fencing in odd-shaped areas, determining where a tree is going to fall, or how much cable you'll need to stabilize that radio antenna. Back when I worked around military imagery interpreters, they used this kind of math to determine the dimensions of buildings by measuring their shadows and the angle of the sun. Cartography (map making) uses this type of math extensively.


Next week I'll see if I can really bore you and try to explain logarithms and how they were used before the invention of computers.

Prudent Prepping: Seeing Red (Dot)

 The dust has settled and the First 72 Hours have passed. Follow along as I build a long term plan via Prudent Prepping. 

Due to technical difficulties, further posts on map reading and distance measurements will be delayed; the compass I ordered was damaged in shipping and needs to be returned and a different model ordered. 

However, what did come in were the parts necessary to make aiming a firearm easier! Look at this:

All The Things!

The Base
Because I received recommendations from friends, I purchased a mount from RS Regulate. This company makes mounts for the AK family of rifles, including cousins not from the Soviet Bloc, and I have a rifle like that. I ordered the AK-303M, thinking I was good to go. 

AK-303M w/mount 

What I didn't realize (from failing to read the complete catalog) is that I needed a separate mount for the red dot I have. The red dot sight has a picatinny mount included, you see, and from looking at the catalog that seemed to be all I needed. 

How wrong I was! The AK-303M rail is a proprietary 1/4 width rail, which doesn't really show in the pictures. That's why the actual RS Regulate mount has such an odd extension. 

The Mount
The really nice thing about RS Regulate products is that the various bases will accept many different mounts, all the way from red dot mounts (like mine) to scope rings. My red dot uses one of the more common types: RMR/Trijicon/Holosun. 

 

AKMR

Unfortunately, the mount was listed as Out of Stock with no restocking date. After looking at the Authorized Dealer list there was one place with a single, solitary mount in stock.

In Canada.

Who wouldn't sell it to me.

But would sell it to someone with the proper paperwork.

I was able to find a friend who did the legwork and the paperwork,  and then attempted to forward the mount to me at cost. Unfortunately, that didn't fly; shipping and handling was added to the invoice.

By this point you're probably wondering what kind of sight is worth this much effort. 

Red Dot
I'd asked in a very friendly gun group for an ideas on a red dot that wouldn't break the limited budget I'm always working on. A member of the group, Michael Branson with Swampfox Tactical Optics, offered me the same discount as is offered to LEO, active duty and retired military, and I bought the Kingslayer compact red dot. There are three choices in center dots: 3 MOA red dot, red dot w/circle, or green dot w/circle. I picked the simple red dot, since I intend to use this under 100 yards. 

Kingslayer

From the Swampfox Kingslayer web page:

• Optic with sheath                                                   
  
• Picatinny Rail Mount
• Screwdriver
• Lens Cloth
• Battery
• Three screw sets
• Torx #6-32x0.315L T10
• TORX #6-32x0.393L T10
• TORX M3.5x10L T10

Mounting was extremely easy with all the different screws supplied by Swampfox. Not only do they include screws, they sent four of each, for those of us that tend to magically make screws disappear. 

Another cool feature is the battery drawer can be opened without removing the optic from the mounting plate. 

I also need to mention the box and how everything is packed. All parts are in separate slots and cut in some of the densest foam I've seen. There is no way for any parts to be damaged in shipping. 

I am more than impressed with the Kingslayer and everything included in the box. All in all I'm extremely happy with how everything works and went together. I need an open range to actually sight everything in and I will be golden!

Recap And Takeaway

• Nothing was purchased from Amazon, but RS Regulate sells many different mounts for AK pattern guns.
• I did buy the Kingslayer Red Dot from Swampfox direct with a 30% discount. Normally, $219.99.

* * *

Just a reminder: if you plan on buying anything through Amazon, please consider using our referral link. When you do, a portion of the sale comes back here to help keep this site running!

If you have comments, suggestions or corrections, please post them so we all can learn. And remember, Some Is Always Better Than None!

NOTE: All items tested were purchased by me. No products have been loaned in exchange for a favorable review. Any items sent to me for T&E will be listed as such. Suck it Feds.

Fish Traps

 

I love to fish, but in a survival situation, it's far from the easiest way to get food. This week, I look at a far more efficient way to get fish.

Lokidude