# Anti-rotation washers (non-turn) washers in non-parallel dropouts?

I have a Shimano Alfine 11 Interally-geared hub and am fitting it to an "M5 559 shockproof" recumbent. The wheel is built and true and runs nicely.

However I have a problem with the anti-rotation washers and my dropouts. The upper and lower edge are not parallel - they diverge at about 24 degrees. The dropout is not damaged or bent open.

Normally this isn't a problem, but an IGH needs an antirotation washer that looks like this. The "5L" and "5R" version is what I have.

The problem comes in that the tang on the washer is way smaller than the angle of dropout.

I think the washer's tang should be pressed against the lower part of the dropout, because the hub will want to "roll" forward under tension from the chain. That is, NOT as pictured.

Your thoughts? I know I will have to get a set of 7 or 8 to make the cable entry angle work better, but am I risking the health of the frame's dropouts by putting an IGH in at all?

• Is the left dropout the same? – Nathan Knutson Nov 18 '18 at 7:24
• I can't even name this shape of dropout for a search engine - "non-parallel" returns cold-setting frame links, and "splayed" tends to be dropouts that have been opened up or dug out by electric motors. What would you call these dropouts ? – Criggie Nov 18 '18 at 8:21
• I'd call them tapered, but that doesn't seem to help much either. – Chris H Nov 18 '18 at 9:28
• I'm kinda at a loss on this one, I just haven't seen many or any dropouts like this. I intuitively suspect that the rotation washers are only doing their thing in one direction and so it's fine, but then I try and think through whether there's a bearing precession part in there to worry about and I get lost. – Nathan Knutson Nov 18 '18 at 23:01
• What are the washers made of? If steel, the best solution would be to braze or (spot) weld an extra wedge on there. Not so easy if Al, though a combination of glue and an interlocking shape might get you somewhere - fiddly work with a small file. If Al, perhaps fabricate a whole new one (in Al or brass) – Chris H Nov 19 '18 at 8:23

The torque that the axle sees relative to the frame can happen in both directions as gears change.

For example in the classic Sturmey Archer 3 speed, it's the second gear that is neutral and does not place a torque on the axle. In third gear the axle will try to twist forwards, and in first gear it will try to twist backwards.

For this reason you really do need an anti-torque washer and you can't leave the gap in the second picture above or below.

I would try to use a normal anti-torque washer against the inside face of the dropout. This washer will have the square hole to grip the axle. Then I would try to make a second washer-wedge-combo out of a softer metal (e.g. Al) to go on the outside. The wedge part of this piece would fill that gap between the red lines in the second picture, but it's strictly functioning as a wedge and can have a round center hole.

I think you need to ask your frame manufacturer if the dropout can handle the torque with only anti-rotation washers or if you need a torque arm. Below I derive the formula for the torque (verified, matches the values from Rohloff manual). The values for the Shimano Alfine 11 are (with 42 and 16 teeth sprockets):

1. 0.34191741212614074
2. 0.17844905950632817
3. 0.11379097093382806
4. 0.052934157717756794
5. 0.0019143335726249959
6. -0.04501553707902912
7. -0.08609759693351027
8. -0.12038303693570448
9. -0.15242665752563775
10. -0.17917675544794187
11. -0.2040121204078473

Expressed as a fraction of pedal torque.

To fit an anti-rotation washer you could, as mentioned by others and myself, put a wedge in the open space. Make sure you put the wedge on the side that gets less torque. To fix the wedge it could be glued to the frame or to the dropout or to a separate washer. A good glue connection should be ok because if done right there is little force on the connection and most on the wedge internally.

How to get the amount of torque that is applied to the dropout:

Power is torque times angular velocity. Power at the pedals is thus

P=τpedalωpedal

Power is conserved (minus some drivetrain losses which are ignored). So

P=τpedalωpedalhub-inωhub-ingroundωhub-inIGHratio(gear)

and thus the input torque to the hub is

τhub-inpedalωpedalhub-in

and to the ground

τgroundhub-in·/IGHratio(gear)

The quotient of the angular velocities can be calculated from the ratio of teeth counts of the sprockets. It's the inverse of the relation of the teeth counts (the more teeth in relation to the other, the slower the sprocket turns in relation to the other). There is a table for IGHratio(gear).

Now we use that

τhub-ingrounddropout=0

by construction and get the result

τdropout

groundhub-in

hub-in(IGHratio(gear)-1)

pedalpedalhub-in)(IGHratio(gear)-1)

pedal((#teeth hub)/(#teeth pedal)(1/IGHratio(gear)-1)

Skript:

#!/usr/bin/python3

# Rohloff Speedhub
#r = [0, 0.279, 0.316, 0.360, 0.409, 0.464, 0.528, 0.600, 0.682, 0.774, 0.881, 1.000, 1.135, 1.292, 1.467]

# Shimano Alfine 11
r = [0, 0.527, 0.681, 0.770, 0.878, 0.995, 1.134, 1.292, 1.462, 1.667, 1.888, 2.153]

def d(g):
return((16/42)*(1/r[g]-1))

for i in range(1,len(r)):
print(str(i) + ".\t" + str(d(i)))


And for the curious: The reason the torques are much smaller than with the Rohloff is because the gear ratios are more centered: They are between divided by 2 and multiplied by 2 for the Shimano one and between divided by 4 and times 3/2 for the Rohloff. A smaller part of the reason is that the gear range of the Rohloff one is larger overall.

• Please help with the formatting, I can't get the math (latex) to display. – Nobody Nov 21 '18 at 17:27
• I'm not sure tex is enabled on this site. It isn't on every site – Chris H Nov 21 '18 at 17:59
• I've had a go at it. Feel free to roll back or edit. I used a semi-automated approach as all the mappings like \tau->&tau; could be automated and regexes could handle things like _\{([^}]*)\}-><sub>\$1</sub>. You can't get decent fractions in html though; even Wikipedia couldn't last I checked. – Chris H Nov 21 '18 at 20:31
• @gschenk I think it's more likely there is some "easy" mistake in my attempt which I can't find. My values are much lower but the ratio isn't constant and I think it's too large for such dynamic effects which I think shouldn't be a large part of the total but I might be wrong again. – Nobody Nov 22 '18 at 11:01
• @gschenk Just found the mistake, now the values match. It was the simple stupid mistake I expected. – Nobody Nov 22 '18 at 11:07