I'm now sold on the method, but will not claim it is the "best" method, that will be up to your evaluation. However, it is a method you should consider, along with water stones, ceramic stones, oil stones, and diamond stones.
Step 1: Why Sandpaper?
One excellent method using water stones is already published in Instructables: https://www.instructables.com/id/Tool-Tip-How-to-Sharpen-a-Chisel/
So why consider another method, and why would you consider using a piece of crude sandpaper on your precious woodworking chisels and plane iron?
Here is the main reason: cost. Cost of good water stones is $100 and up each (you should have several of various grits). And sandpaper? Less than $2 per sheet. This is not a fair comparison, however. A water stone will last years; you will have to buy many pieces of sandpaper and replace as they wear out. But bottom line is that the sandpaper method is a lot cheaper.
Second reason: Simplicity. The sandpaper method is pretty easy.
Third reason: For most of us the sandpaper method, if done carefully, will produce the sharpest cutting edges we have ever experienced.
Step 2: Materials Needed
The condition of your tools and how good an edge you want will determine what sandpaper grits you need. The photo shows what I have in my shop. You will not need all these, three should suffice: 600, 1200, and 2000; or 800, 1500, and 2500.
Most often you will find these in auto supply stores and some hardware stores. The really fine grit paper can be bought at an auto paint and body shop. It will all be the black "wet or dry" paper. If you want to go a step further, buy a sheet or two of 2500 grit, but anything over 2000 grit will be harder to find.
For the final finish I use a honing compound, which I get from Lee Valley Hardware, where various fine grit sharpening paper is also available.
This Instructable assumes the blade bevel is in reasonably good shape and does not require grinding on a power grinder.
Step 3: You Will Need a Flat, Smooth Surface to Mount the Sandpaper
Better is to buy sandpaper with self-adhesive backing, but these can be hard to find.
A good, practical solution is to glue strips to a piece of 3/4" MDF, as in this photo. You can use spray adhesive or a thin coating of wood glue. Then, place another piece of MDF over the sandpaper and clamp the "sandwich" in a vise to flatten the sheet and ensure it is smoothly attached.
Make up a few of these honing blocks of various grits, toss them when they wear out. This one cost about 50 cents.
The block in the photo is 3 1/2" x 12".
Step 4: You Will Need a Honing Guide...
In the bottom row, left to right:
- Mark II honing guide from Veritas Tools. This is top of the line, I finally splurged.
- Shop made honing guide I made for a woodworking magazine.
- Shop made ultra-basic guide from a piece of scrap. Cut the angle to the bevel angle of your tool; most chisels are 30 degrees. A piece of double stick tape holds the blade.
- In the back, in use, is a basic, generic, guide. You will find many of these online for about $15, Google "chisel hone guide" .
Step 5: Start With the Back of the Blade
The initial grit depends upon the condition of the back of the blade. If it is scratched, rusty, or uneven, start with 400 grit, then 800, working up to 2000 grit or higher at the tip.
In this photo, "lapping plate" is the MDF block with sandpaper glued to the surface.
Step 6: Now Hone the Primary Bevel.
Most blades will have either a 25 or 30 degree angle.
Similar to lapping the back, the grits depend on the quality of the blade. Start with a lower grit if the blade is in bad shape. As a rule of thumb, you can double the grit number for each successive step. So if you start with 400 grit, progress to 800, then 1500, then 2500.
In this photo I'm using 2500 grit abrasive on a self adhesive Mylar backing.
Step 7: How to "see" the Honing
Here is a good way to "see" your progress. Mark the bevel area with a felt tip Sharpie marking pen, as in the first photo above.
Then, after a few strokes of honing, look at the bevel: the shiny area is where you are taking off material. If the shiny area is a thin band at the tip, as in the second photo, you are exactly where you want to be for the next step, honing the micro bevel.
Step 8: Now Hone the Micro Bevel
Some honing guides have an additional setting for this micro angle. Some craftsmen do this final stage by hand. I usually do it by placing a couple of square pieces of Formica, or some other thin sheet material, under the wheel of the honing guide. Raising the wheel only makes the angle steeper by a few degrees.
Step 9: Final Polishing
Scrape off the compound onto a scrap of MDF, it goes on like a heavy color crayon. Then polish the bevel, especially the tip. It will be obvious when you are holding the blade, as you increase the angle, it will begin to dig into the MDF. So, you need to polish by holding the blade at an angle just before it begins to dig into the MDF.
Good luck, hope it works for you.