This is one of the harder solder joints to make. When I was in school this was my favorite solder joint. This joint is almost 100 years old and it's history goes back to the days of the telegraph. This was a common joint that linemen would use and when used with solid wire it does not require solder to keep it together if done right.
From Wikipedia -
"The Western Union or Lineman splice was developed during the introduction of the telegraph to mechanically and electrically connect wires that were subject to loading stress. The wrapping pattern is designed to cause the termination to tighten as the conductors pull against each other. This type of splice is more suited to solid, rather than stranded conductors, and is fairly difficult to complete.
The Western Union Splice is made by twisting two ends of a wire together counterclockwise 3/4 of a turn each, finger tight. Then, using needle-nose pliers, the ends are twisted at least five more turns, tightly. The cut off ends are pushed close to the center wire. "Short tie" and "long tie" variations exist, mainly for purposes of coating the connection with solder. The longer version may aid in solder flow. NASA tests on 22 and 16 AWG wire showed that the Western Union Splice is very strong and is stronger than the wire alone if done properly."
You will need:
Solder and soldering iron
The wires you want to join
and a 3rd hand set up like I have to hold the wires wile I work. Note this is only needed when working with stranded wire.
Shrink tube of the right size. Please do not use electrical tape as it just makes a mess and doesn't work worth a hoot when it gets hot or old. Besides it makes a nasty sticky mess. You can use the liquid "electrical tape" but that too looks terrible
And lastly a banana. I don't know why you need one but you do need a banana.
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Step 1: Prepping Your Wire
Because we are using stranded wire this joint becomes much harder to do. First we strip back about 1" on each wire we want to join. Then we twist the wire strands together to make a more solid wire. When wires are twisted in a tight bundle you can better manipulate it and it accepts solder much better.
SAFETY: Wear safety glasses when doing this. Hot solder can do extreme damage to your eyes should you get even a dot in your eye. I know I had it happen and I was blind for a whole summer; never again.
Before we solder there is a point that must be made. Solder when used with heat has a capillary action meaning that it will gravitate to the heat source. When the wire is properly heated and solder is introduced the solder should almost "soak" into the joint. When joining wires I always put the iron on the bottom and the solder on the top. This speeds the completion of the joint which makes sure I do not overheat the wires insulation, compromising the joint.
Step 2: Twisting the Wires
Now we will start the joint. FIRST make sure you put your shrink tube on one of the wires and slide it down the wire so the soldering iron does not start it shrinking. I can not count the number of times I have made a beautiful joint only to find that I forgot the shrink tube and now have to cut out the joint. Now at the half inch mark twist the right wire up and twist it around the wire on the opposite side of the joint. Then do the same for the other wire. With solid wire we would pull the wires to make them tight and then pinch down the last 1/8" of the wire with a pliers. We can not do this with stranded wire as the joint would fail before we soldered.
Step 3: Soldering the Joint
Are you wearing your safety glasses?
First make sure your iron is hot enough to do the job. With it turned on try putting solder on the iron first. If it accepts solder take it right over to the joint and heat the joint and then introduce the solder the instant the solder you put on the iron starts moving. The primer solder as I call it helps heat the joint faster. If it is not hot enough "Have you tried turning it off and on again?"
The solder should appear shiny when done. If it is dull or has a brown residue on it the joint did not achieve proper temperature and is called a cold joint. Cold joints are what makes most cheap electronics from China fail fast or not work at all. If your solder joint looks like I described it go back and heat it up again. Basically when it stops smoking you have the right temperature as it has burned off all the flux. Do not heat it so much that the insulation starts to melt.
When done your joint should look like the last picture here.
Step 4: Tidy Up and Insulate
Here we center the shrink tube over the joint. At this point if there is any sharp points from the solder joint you must correct them or they will render the shrink tube insulation useless. This correction can be done by gently smashing them down with a pliers. Once you have the shrink tube in the right placement apply heat to the tube and it will begin to shrink. Be a bit stingy with the heat as you can burn the tube and then it just looks nasty or doesn't work at all. We want a professional looking joint don't we? As the tube shrinks keep moving the heat until it appears that the tube has finished shrinking. In the photo here I used open flame. This is ok because there are no flammable vapors near me. Should you have to do this is a flammable vapor situation you will need to ventilate the vapors or remove them. Heat guns and hair dryers suck in air and super heat it so they too will ignite fums. Even the switch on them makes spark when starting them.
Do not use this joint in a situation in which it is continually subjected to water or liquid as it will fail. I would call this joint water resistant rather than water proof. This is a great joint for things like car radios should you have to make a harness because one is not available (see Audi Quattro). These joints also have almost no bulk when done right.
Should you have to use multiple joints in the same area stagger the joints so that the don't line up with each other and create bulk in the harness. Generally 1" offset from each joint is best especially if you want to put it in a harness sheath.
Oh I forgot.......Eat your banana.