I just did some more calculations under the following assumptions:
Actually there are very few possible combinations:
p; s; a; g
10; 44; 24; 17/11
14; 64; 36; 25/16
15; 66; 36; 17/11
20; 88; 48; 17/11
21; 96; 54; 25/16
a = #teeth annulus
s = #teeth sun gear
p = #teeth planet gears
g = gear ratio
Let me offer a new theory: from the first picture I posted before, a sun gear with 31 teeth seems reasonable. With that the annulus would turn out to have 62 teeth (planets with 14 teeth given), resulting in a gear ratio of 48/31, which is pretty close to 17/11. So after 11 revolutions of the cranks, the wheel would have performed 17.03 revolutions. That derivation of 0.03 is something that can easily be overseen.
BTW, I am still waiting for a response from Florian Schlumpf. He for sure should be able to answer that question.
sun gear 31 with ring gear 62 = ratio of exactly 1.5 and means planet gear of 15.5 teeth 
Sorry, my mistake. I wanted to say sun gear 34, ring gear 62.
Hey guys. really looks like 36 for the sun to me. There are 6 teeth between each planet gear and they all appear to be in the same position.
36 sun, 14 planet would mean 64 ring and a 25/16 (1:1.5625) gear ratio. unfortunately I do not have my hub here to do a spin test.
Forget about that theory. I just did a spin test with 2 different hubs (M0502 and M0360). In both cases 17/11 looks perfect (even after 22 crank rotations), 25/16 is close but not more, and 48/31 is close as it’s close to 17/11, but after 31 crank rotations a clear derivation of the wheel position of about 1/10th rotation could be observed.
I have to recognize my mistake 
Schlumpf hub ratio is 17/11 (1 + 36/66 = 1.5454) as said by Florian and others
it’s based on : ring gear 66 teeth (and not 64 as I estimated) / planet gear : 14 / sun gear : 36
for that, Florian is using a special teeth machining (offset of cogs) to allow cogs meshing because impossible with standard machining as 36 + 2x14 = 64 and not 66 !
and this is also compatible with 6 planets (condition is : ring gear teeth + sun gear teeth)/ number of satellites = integer number --> 36+66/6=17)
Can you please elaborate a little bit on special teeth machining and offset of cogs, or provide some link to respective information. I’d like to understand that concepts.
Sorry but not easy, in French I can but in English is very difficult for me as I’m not sure of the correct wording for “cog offset”, in French we say “deport de denture”.
This is usual way to match cogs on an automotive manual gearbox as distance between input and output axis is fixed but with couples of gears for the different ratios and it’s not possible for a same axis distance to have different ratios with normal machining. So there is a special machining to allow gear matching. This machining gives a little bit modified teeth shape, can be thicker (stronger cog) or thinner (more fragile) depending if positive or negative offset.
It’s also used to reinforce the smallest cogs which are more fragile and I think this is the reason of Florian choice for a planet of 14 teeth instead of 15 which should be the standard with sun gear 36 and ring gear 66. 14 teeth planets with offset are stronger than 15 teeth for the same (in fact almost) cog diameter.
Additionally, epicyclic train of 36/14/66 is compatible with 6 planets against 5 planets for an epicylic train of 36/14/64 and so planets receive less stress as they are 6 instead of 5 !
Great concept !
Thanks for explanation.
I know Florian worked hard to get the right cogs manufactured, as it was not easy to find a machine shop who was able to fulfill his special needs and provided excellent quality. He even rejected several batches of cogs, as they did not meet the specifications. In the end I think he started manufacturing the cogs himself.
That all fits together with that non-standard teeth shape you described.
Check this out -> from the posted pictures I assume the sun has 42 teeth - 6 (between planet intervals) x 6 teeth + 6 teeth fully engaged by each planet. I would normally assume the annulus has 70 (42+2x14) teeth but taking that theory with “offset teeth” it may be different.
Any comments on that?
I still believe that the sun has 36 teeth (as pointed out by saskatchewanian)
and that the planet gears have 14 teeth. They don’t have to have 15 teeth because of profile offset which allows the gears to have different numbers of teeth than suggested by their diameter. The ring gear has 66 teeth.
Only the numbers of the ring gear and the sun gear determine the gear ratio
(as already mentioned in this thread before).
It’s clear that only the sun and annulus are determinant in gear ratio, no question about that. Moreover, I counted more attentively the sun teeth and found you guys were right -> 36!
In theory, the implementation used in actual KH/Schlumpf (by varying the teeth numbers) can be scaled in the (input : output) range 1:1+[0…1)
Additionally, I would like to see more ideas on 3+ internal gear designs!
Florian finally responded to my request. He confirms an annulus with 66 teeth and a sun with 36 teeth. Resulting in a ratio of 17/11.
Last year, Roger Davies told me that at the origin, the Schlumpf hub had 5 planet gears.
Probably, Florian moved from 5 to 6 further to reliability concerns during the early development for both reduce the sun gear stress by the number and teeth cog offset without any change on the ratio (17/11)
I searched for this because I’m sure someone has asked before but I was wondering about the safety of using a Schlumpf hub in winter? I’m not worried about the cold or snow, but rather the salt and grime that covers the roads. I was wondering if anyone has ridden their Schlumpf all winter (I’m talking about real winter, not California winter) with or without any issues. Also, if anyone has asked Florian about this and gotten a response. I want to keep riding my Schlumpf all winter but its not worth ruining it to do so. Thanks guys!