Just thought I'd share pictures of the lap afghan so far .. and the 'after surgery' doll I made my sister. You can see the problem I have with all the 'tied off' ends along the edge.
So far the lapghan (?) is 27" x 18", but I'm making it larger .. probably at least 3 times longer.
Beginning crocheters tend to have this problem with the ends hanging out, because most people teach you how to crochet, but not how to finish it neatly! I remember I did the same thing, cut the yarn really short after changing colors for a stripe and it left my work with ends hanging out, and though I crocheted over some on the wrong side, they popped out after washing.
Here's how to fix it: Keep working the stripes like you are, but instead of leaving only 1/2 inch of yarn hanging, leave more like 4-8 inches, depending on how secure you want the ends woven in. I recommend 8 inches of yarn.
Next, take a tapestry needle, which is a big blunt needle with a large eye (mine is 2-3/4 inches long with an about 3/4 inch eye), and thread the yarn into it. I got one of those permanent needle threaders that does both thread and yarn so I don't have to keep buying threaders to work with yarn, because those wire ones don't last long with yarn for me.
After the yarn end is threaded onto the needle, determine which side of your afghan is the wrong side, as this is the side you'll be weaving the end in on.
Run the yarn through the last row of the color of the end across the back under the legs that stick down for at least 6 stitches. I usually go across 8 now.
Now, turn your work around, and you'll be going back the same direction you just came from. Only this time, use the blunt end of the needle to split the stitches and the end you've just threaded through those stitches, weaving up and down back across securing both sides of that running thread by going through it and the legs of the stitches you first pulled the end under. Stop before you reach the edge of your afghan on the weaving return, so you go into the afghan 8 stitches, but come back only 4-6. If you want it really secure, go out 8 and come back 5, so you are 3 from the edge, and your end won't poke out at the edge. Now, the hardest part. Make absolutely sure you pull the yarn snug, but not tight to secure your weaving, or it will warp some stitches. Then, being very careful not to cut your afghan, take scissors and snip that pesky yarn end as close to the afghan as possible.
Since I started darning in my ends like that, I've never had a loose end, and after washing articles, I've had trouble finding where I wove those ends in. Plus, since I don't knot my yarns to change colors, I've never had work unravel in teh wash anymore either.
To cover the ends you already have, You have 2 options. Take yarn of the same color and knot it tightly to the ends you have and weave it in, being careful to secure those knots under 1-2 stitches on the back, or put a decorative edging around the whole thing when you're done. I'd probably do both to make sure the work won't unravel. You might take some washable fabric glue to further ensure those knots don't come undone if you splice yarn for weaving in the ends you've got so far.
BTW, since I learned that finishing trick, I've never regretted leaving an extra long tail. It's the short ones I've had trouble securing so the work looks the neatest.
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