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Count the number of teeth on your smallest gear on the cranks. If it is a 24 you might be able to put on a 22, and that will make a noticeable difference at a small cost. If it is 24 then I would pull the cranks and do a search for a 22 tooth that fits your cranks. They are usually pretty cheap and available on ebay or amazon.
 
Just one other thing. I was having knee issues and made my last set-up work with a 22 in the front and a 42 in the rear and it was over-geared. I found that on difficult hills it wanted to lift the front wheel up too easily which made me have to back pedaling off a lot. It was a good test that lower isn't always better. It also irritated my knee more because of all the extra pedaling.
 
chain wrap capacity = (large chainring - small chainring) + (large rear cog - small rear cog)

maximum chain wrap capacity for a RD-m591 is 45 teeth. it's there in plain black-and-white on the linked PDF. so with a 11-40t cassette, the largest chainring your could theoretically use is 16t, if you use a single ring. no one makes a single ring crankset that tiny. so you're outta luck.

(40-11) + x = 45
29 + x = 45
x = 45-29
x = 16

If you used a modern 2x10 type crankset with 36 and 24 teeth:

(40-11) + (36-14) = y
29 - 12 = y
17 = y

that's 28t short or 19 chain links short of minimum wrap capacity. you could run a chain with 19 extra links, but when you use the bottom end of your cassette, the chain is going to basically drag on the ground.

if you have, say, chainrings with 42, 32, and 24 teeth, the range 42-24 = 18.

(40-11) + (42-24) = y
29 - 18 = y
11 = y

45-11 = 34, so your a full 34 ring/ cog teeth short, or 17 chain links, short of making that jump. that's a big jump.

yeah, you're going to rip your derailleur off your frame.

since you still have not given us specifics, I can't answer that question any other way but theoretically. what size rings do you have in the front?

if you limit yourself to the middle and small rings, it might work. still, most middle rings + a 40t cassette is a ridiculously low gear. are you riding with 36" tires? are you, in fact, towing a horse trailer up a mountain? I am not judging, just asking.
Turtle, You jack up the figuring in your two examples. By chain wrap alone the m-591 would work but it would be unlikely to clear 45 teeth with the stock B screw.

Sent from my Moto E (4) Plus using Tapatalk
 
Turtle, You jack up the figuring in your two examples. By chain wrap alone the m-591 would work but it would be unlikely to clear 45 teeth with the stock B screw.
Yeah, I might have screwed that up. which part did I get wrong?

to clarify, I was talking about chain wrap capacity, not maximum cassette cog. if you read the rest of what I wrote and check the linked PDF by Shimano, it clearly shows that the CWC is 45 teeth. you have to do a little math to figure out what CWC a drivetrain will require of the rear derailleur. chain wrap capacity was a tough concept for me to wrap my head around, but it's important to understand when you start messing around with stock drivetrains.

The Trek FX 7.4 (if I am looking as the same year and model that the OP has) has 48, 36, and 26t rings, and the cassette is 11-32.

(48-26)+(32-11)= 22+21 = 43. since the CWC of that derailleur is 45 teeth, that drivetrain will work safely. you could also put a 34t cassette on that bike and it still could work, but if you go larger than that, you need to limit use of one of the chainrings or use a derailleur that can handle the bigger jumps.

if the owner of that bike were to remove or lock out the 48t ring on the front...

(36-26) + (40-11) = 10 + 29 = 39. that's smaller than 45, so it would work. 26/40 is still an absurdly low gear - so low that it would be impractical, but it would work.

fun story- I've seen several bikes from a certain brand that were built with a medium-cage derailleur when it had a triple chainring and enough of a range on the cassette that it clearly needed a long-cage. one of the big manufacturers specced the bike like this and customers kept coming in with mangled derailleurs. funny what happens when you don't listen to the drivetrain manufacturer.
 
Discussion starter · #28 ·
with 11-50 cassette
(36-26)+(50-16)=44 <45 so i can use 2 in the front and 7 in the back!
the only question is whether the extender would distance the derailleur enough from its current position.
the radius of 34, 46, 50 is 69, 93 , 101, so the difference between first two 24, second two 32 mm. that should be the length of extender. is that correct?

but it says that extender could only allow 4t more, 38, r=76 difference 8mm. visually it's longer than that.
also there are two types of them - one is called extender and another hanger dropout. the second one is for a particular frame? my frame has a simple hole for the derailleur.
 
Discussion starter · #29 ·
as far as I can understand the concept of dt capacity is for the derailleur to be able to handle slack when chain is on the smallest rings in front and back ( that combination is never practically used) what about chain length a derailleur can handle? is it on the biggest rings in both front and back? i need to know that in order to find out how much lengthening chain may need.
 
I don't know how else to say this- the ridiculously low gear you are trying to get is a waste of time. I don't know what kind of gear this guy is spinning, but it took him forever to spin like a maniac to get up a hill. I'll bet he's in amazing shape to be able to hold that cadence for more than 30 seconds, or he utterly destroyed his knees by the end of this.

I think you need to try a bike with a gear that low to see how pointless this experiment is, because you don't seem to believe the people who are telling you the truth. you're getting ahead of yourself here.

theoretically, that works, but you're going to spinning your legs so fast at that low a gear just to keep moving and not fall over that you're going to cause different kinds of injury to your knees. if you can't pedal up a hill with a 26/34 gear (you could do this by changing to a new 9 speed cassette with a 34t cog), you just can't do it. you need to ride more, get your body stronger, and persevere until you get it.

look up gear-inches and try some combinations that will get you the lowest practical gear. you could use a crankset with smaller rings on it, which would just mean replacing the cranks, maybe the bottom bracket to get the chainline correct, and moving the frond derailleur down.

but theoretically, are you planning to lock out half of your drivetrain so you can only use the lowest hamster wheel gears? what happens when you get to a flat section of road and you spin out at 9 mph? do you only ride uphill? why do all this weird kludging and just buy a drivetrain that actually has a lower gear?

weird suggestion- that bike has disc brakes and 700c wheels, correct? you could get some 26" wheels with narrow road tires and bring your gearing down quite a bit without changing much else.
 
26f/40r isn't really a ridiculous ratio. It's a 1.54 ratio. Much the same as many 2 x 10 set-ups which have a 24f/36r gearing which is also 1.5. It's also the same as keeping the 34 in the back and buying a 22 for the front small ring which would be a 1.55 ratio. I personally run a 42 in the back with a 28 in the front which is also 1.5. It works well for long steep rocky climbs. That's why I think if he can fit a 22 in the front it would be the cheapest solution, assuming he can fit a 22tooth 64bcd on his crank set-up. If he's worried about having capacity he can stop using the largest 3x chainring and eventually replace it with a bash guard.
 
as far as I can understand the concept of dt capacity is for the derailleur to be able to handle slack when chain is on the smallest rings in front and back ( that combination is never practically used) what about chain length a derailleur can handle? is it on the biggest rings in both front and back? i need to know that in order to find out how much lengthening chain may need.
After reading this thread. You do not listen ( read) or pay attention what others are saying ( writing) which Is some damn good info. Mack_turtle has explained it very clearly.

In the end, You do what you want. Or sack up and get the right stuff from the start and skip all the BS
 
...bike is a hybrid bike with deore, 3x9.
Dude, not sure how you've managed to drag these experts along with your obtuse postings, but let me try:

1) Switch your front chainrings from 26/36/48 to 22/32/44 or 22/32/bash-ring or 22/32/blank(if you don't use the biggest one). You'll have to move your front derailleur down a bit.

For example: https://www.ebay.com/itm/NEW-Shiman...2462623760?hash=item56b8809c10:g:QlEAAOSwAI9bunof:sc:USPSFirstClass!75207!US!-1

2) Get the Sunrace 11/40 9 speed cassette if you still need more ratio.

3) Depending on your bike you might also need a "road link" to make it shift decently.

https://www.wolftoothcomponents.com/products/roadlink

4) Replace the chain... don't try to lengthen the old one.
 
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