Whats the difference with these two fishing fly lines?
A weight forward line and a double taper line
you've gotten some good answers. Let me see if I can add my two cents.
Fly lines are designed with various tapers to help them perform best for the species and circumstances you are fishing for.
A double taper is shaped essentially exactly the same on both ends- the very tip is smaller and narrower, and it tapers to a thicker portion towards the middle.
A weight forward has a short tip section, a "Front taper" where it gradually gets thicker, then a head section, then a "Back taper" where it gets narrower, and the the running line- the rest of the line.
The purpose of the head is to give weight to the line, and load the rod- like a sling shot- so it will shoot the line out, and the energy transferred wil "Turn over" your leader- Make it lay out straight at the end of the cast.
Fly lines are mostly 90 feet in length-
A double taper may have a 8-9 foot end taper on each end, and a 65 foot body. Because there isn't a pronounced head you are casting, it can make more delicate presentations, but can also make you work harder, as the line won't load the rod as easily- You'll have to do the work. Thise lines work well, but if you are not as experienced, I would go for a weight forward.
A good weight forward line not only makes the rod and line do the work, you can FEEL the rod load, and can know when to reverse your casting stroke by feel, rather than by watching. good example would be a 6 foot front taper, 23 foot head, 7 foot back taper, and a 55 foot running line.
There are a lot of good fly lines out there, but its easy to get overwhelmed by the technical stuff.
Cortland makes lines with what is called a rocket taper- this is a weight forward design and is VERY good. I recommend them highly.
Rio makes a WF line called a Gold- this line is nice for several reasons, one of them somewhat unique- the head is a moss green- a neutral color that is less likely to spook fish- but the running line is a gold color, easier to see on the water. Most line makers give you a choice- a drab line that is a little stealthier, or a bright line that is easier to see on the water, but might spook the fish- so the Gold line is a great compromise.
Look for a line with a welded front loop- easier rigging, less tip sinkage.
Scientific Anglers makes great lines, as does the Wulff Triangle Taper.
There are also a lont of specialized designs that are meant specifically for bass- to turn over bug bushy flies, saltwater- also for larger flies, and so one. Its endless.
Talk to your fly shop, see if they will let you test cast some lines- you won't beleive what a difference the RIGHT line will make in your casting.
If you can buy only one line, and your budget allows it, then buy the RIo gold.
If you are on a budget, buy a Cortland Rocket taper.
Good luck and have fun!
PS- buy a floating line- there are Cortland sink tip pieces you can buy and loop onto your floater to convert it to a sink tip. (may not cast very gracefully, but it will work)
And you can buy Rio's new tungsten impregnated leaders which will quickly get your fly deep.
One final note- I do not have any vested interest in either Rio or Cortland- I simply have had a lot of success with their products. Just thought I should throw that in there.
Currently Available on eBay
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 Snowbee XS Double Taper Floating DT3 Fly Line  £43.00
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 Cortland 444 Classic Double Taper Floating Fly Line Available in 5 6 7 8 9 £34.90
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 cortland fly lines £12.00
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 DAIWA LOCHMOR TROUT FLY LINES DT WF 4 5 6 7 8 FL N SINK £14.99
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 Scientific Anglers Specialty Taper Fly Line Trout WF 5 F Dark Willow BRAND NEW £11.70
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 Shakespeare double taper salmon fly line £12.99
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 Scierra HMT Taper Fly Density Compensated Sinking Lines £18.00
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 Scierra HMT Taper Fly Lines Floating WF7 WF8 or WF9 £18.00
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 Scierra HMT Taper Fly Lines Intermediate WF6 WF7 WF9 £18.00
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 FLY FISHING LINE DT3 DOUBLE TAPER LINE NEW UK 100FEET £9.99
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 BN Cortland 444 Precision Taper Clear Camo Intermediate Fly Line WF6 Tuit CD £22.99
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 BN LOOP opti adapted belly and interchangable front taper for fly line system £19.95
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 Wulff Triangle Taper Salmon Fly Line TTSP10F £49.99
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 Fly Fishing Line DOUBLE TAPER 5 DT5 Free UK Postage UK £12.99
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 WSB DOUBLE TAPER INTERMEDIATE TROUT FLY LINE DT6 £16.99
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 LOCHMOR TROUT DOUBLE TAPER NEUTRAL DT4N FLY LINE £14.99
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 LOCHMOR TROUT DOUBLE TAPER NEUTRAL DT6N FLY LINE £14.99
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 LOCHMOR TROUT DOUBLE TAPER NEUTRAL DT7N FLY LINE £14.99
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 AIRFLO SIXTH SENSE RIGEL DISTANCE TAPER FLY LINE WF6F £20.00
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 Scientific Anglers Sharkskin WF8F GPX taper fly line £30.00
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 Scientific Anglers Sharkskin WF6F GPX taper fly line £49.99
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 fly fishing line £17.00
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 2 X FLY LINES WHITE IS FLOATING FW7 CR GREEN WT 6 INTERMEDIATE FORWARD TAPERED £20.00
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 Cortland 444 Classic Fly Line Floating Double Taper Peach £39.99
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 AIRFLO RIDGE CLEAR FLOATING FLY LINE DELTA TAPER WF5 6 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR FLOATING FLY LINE DELTA TAPER WF6 7 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR FLOATING FLY LINE DELTA TAPER WF7 8 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR FLOATING FLY LINE DELTA TAPER WF8 9 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR SLOW GLASS FLY LINE DELTA TAPER WF6 7 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR SLOW GLASS FLY LINE DELTA TAPER WF7 8 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR SLOW GLASS FLY LINE DELTA TAPER WF8 9 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR FAST GLASS FLY LINE DELTA TAPER WF5 6 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR FAST GLASS FLY LINE DELTA TAPER WF6 7 35YD 2012 STOCK £35.99
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 AIRFLO RIDGE CLEAR FAST GLASS FLY LINE DELTA TAPER WF7 8 35YD 2012 STOCK £35.99
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 DT3 Cortland 444 Floating Peach 30yds Double Taper Fly Line Free Zinger £34.99
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 DT4 Cortland 444 Floating Peach 30yds Double Taper Fly Line Free Zinger £34.99
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And a selection of products from Amazon
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Cortland 444SL Floating Rocket Taper Weight Forward Fly Line
Sale Price: £34.99  |
Description444SL Floating Rocket Taper Weight Forward Fly LineThis is one of the best distance fly lines ever produced and is a firm favourite with UK stillwater fly fishermen.It has a longer belly than the standard 444 and the line is made on a slightly stiffer core and a harder coating... |
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Airflo Velocity Floating Fly Line Weight Forward AFTM# 4-9 Double Taper AFTM#4-8 - DT 7 F
Sale Price: £14.95 |
DescriptionAirflo Velocity Floating Fly Line Weight Forward AFTM# 4-9 Double Taper AFTM#4-8,****RRP: £19.99****,My Price**£9.95**,Airflo Velocity Fly Lines -The Airflo Velocity series has been engineered to give superb performance and extreme value... |
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Airflo Velocity Floating Fly Line Weight Forward AFTM# 4-9 Double Taper AFTM#4-8 - DT 8 F
Sale Price: £14.95 |
DescriptionAirflo Velocity Floating Fly Line Weight Forward AFTM# 4-9 Double Taper AFTM#4-8,****RRP: £19.99****,My Price**£9.95**,Airflo Velocity Fly Lines -The Airflo Velocity series has been engineered to give superb performance and extreme value... |