Brian Schott:
> I am trying to produce a printout of gear ratios
>for a 24-speed bicycle.
You must have to tackle some steep mountains... I'm more into road
racing, and this is my code and gear. The code works for both my
double and your triple cranks, of course.
NB. First, keep output simple by limiting decimal places.
NB. Two places after the decimal point seem sufficient here.
9!:11 ] 2
f =. 39 53
r =. 25 23 21 19 17 16 15 14 13
r2=. 27 24 21 19 17 15 14 13 12
r3=. 21 19 18 17 16 15 14 13 12
markers =. {&'.|'@=
markers r
|........
.|.......
..|......
...|.....
....|....
.....|...
......|..
.......|.
........|
marker_combos =. ;:^:_1@(,/)@(;"1/&markers)
f marker_combos r
|. |........
|. .|.......
|. ..|......
|. ...|.....
|. ....|....
|. .....|...
|. ......|..
|. .......|.
|. ........|
.| |........
.| .|.......
.| ..|......
.| ...|.....
.| ....|....
.| .....|...
.| ......|..
.| .......|.
.| ........|
ratios =. ,@(%/)
f ratios r
1.6 1.7 1.9 2.1 2.3 2.4 2.6 2.8 3 2.1 2.3 2.5 2.8 3.1 3.3 3.5 3.8 4.1
f (marker_combos /: ratios) r
|. |........
|. .|.......
|. ..|......
|. ...|.....
.| |........
|. ....|....
.| .|.......
|. .....|...
.| ..|......
|. ......|..
|. .......|.
.| ...|.....
|. ........|
.| ....|....
.| .....|...
.| ......|..
.| .......|.
.| ........|
f (marker_combos (([ ,. 6j2&":@,....@]) /: ]) ratios) r
|. |........ 1.56
|. .|....... 1.70
|. ..|...... 1.86
|. ...|..... 2.05
.| |........ 2.12 <-- not to be used
|. ....|.... 2.29
.| .|....... 2.30 <-- not to be used
|. .....|... 2.44
.| ..|...... 2.52
|. ......|.. 2.60
|. .......|. 2.79 <-- not to be used
.| ...|..... 2.79
|. ........| 3.00 <-- not to be used
.| ....|.... 3.12
.| .....|... 3.31
.| ......|.. 3.53
.| .......|. 3.79
.| ........| 4.08
A few remarks:
I found Catalogue to be a helpful starting point here, too:
{ f ; r
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|39 25|39 23|39 21|39 19|39 17|39 16|39 15|39 14|39 13|
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
|53 25|53 23|53 21|53 19|53 17|53 16|53 15|53 14|53 13|
+-----+-----+-----+-----+-----+-----+-----+-----+-----+
Oblique chain runs are to be avoided since the result in excessive
wear on the chain. Out of the theoretical 2x9 or 3x8 positions,
one would avoid "largest chain wheel + first or second largest
sprocket", "smallest chain wheel + first or second smallest sprocket",
"middle chain wheel + smallest or largest sprocket". (See markers
above.)
Fitting in a J expression to filter out such illicit gear combos
is probably another nice exercise.
Martin
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