indexing.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# indexing calculator for an alfine internal gear hub
# The SRAM 3x10 00.7018.068.004 10 speed shifter has a drum diammeter of 21.8mm, or a circumference of 68.4867mm
# The SRAM 11 and 12 gears speed shifter seem to have a 25.6mm drum diammeter, or a circumference of 80.42477mm
# Accounting for the 1.1mm of cable width by adding half the cable width to the radius or 1.1mm to the diameter.
#
# OD 22.9mm / C = 71.942 / 0.5C = 35.97 for the 10 Exact Actuation
# OD 26.7mm / C = 83.88 / 0.5C = 41.94 for the 11 and 12 X-Actuation
#
# since X-Actualtion should be 3.48mm of cable pull per gear on average even 12 movements are 41.76 
# and should fit, although only 11 are needed for 12 gears.
# http://blog.artscyclery.com/science-behind-the-magic/science-behind-the-magic-drivetrain-compatibility/

import json
import math

def to_json(node):
    return json.dumps(node, sort_keys=True, ensure_ascii=False, indent=4)

indexing = {
    'cable diameter': 1.1,
    'spool diameter': 25.6,
    'hub': {
        'sg s501': {
            'indexing': [
                {
                    'gear': 1,
                    'offset': 0
                },
                {
                    'gear': 2,
                    'offset': 5.49
                },
                {
                    'gear': 3,
                    'offset': 5.05
                },
                {
                    'gear': 4,
                    'offset': 5.18
                },
                {
                    'gear': 5,
                    'offset': 6.22
                },
                {
                    'gear': 6,
                    'offset': 5.05
                },
                {
                    'gear': 7,
                    'offset': 5.05
                },
                {
                    'gear': 8,
                    'offset': 5.05
                },
            ]
        },
        'sg s501 sheldon brown': {
            'indexing': [
                {
                    'gear': 1,
                    'offset': 0
                },
                {
                    'gear': 2,
                    'offset': 4.9
                },
                {
                    'gear': 3,
                    'offset': 5.3
                },
                {
                    'gear': 4,
                    'offset': 5.0
                },
                {
                    'gear': 5,
                    'offset': 5.9
                },
                {
                    'gear': 6,
                    'offset': 4.7
                },
                {
                    'gear': 7,
                    'offset': 5.0
                },
                {
                    'gear': 8,
                    'offset': 5.8
                },
            ]
        }
    }
}

indexing['spool circumference'] = math.pi * indexing['spool diameter']
indexing['corrected spool circumference'] = math.pi * (indexing['spool diameter'] + indexing['cable diameter'])

for name,hub in indexing['hub'].items():
    hub['total pull'] = 0
    hub['total angle'] = 0
    for gear in hub['indexing']:
        gear['offset angle'] = 360.0 * (gear['offset'] / indexing['corrected spool circumference'])

        hub['total pull'] += gear['offset']
        gear['absolute'] = hub['total pull']

        hub['total angle'] += gear['offset angle']
        gear['absolute angle'] = hub['total angle']


print(to_json(indexing))

output.json

{
    "cable diameter": 1.1,
    "corrected spool circumference": 83.88052385084748,
    "hub": {
        "sg s501": {
            "indexing": [
                {
                    "absolute": 0,
                    "absolute angle": 0.0,
                    "gear": 1,
                    "offset": 0,
                    "offset angle": 0.0
                },
                {
                    "absolute": 5.49,
                    "absolute angle": 23.56208460875071,
                    "gear": 2,
                    "offset": 5.49,
                    "offset angle": 23.56208460875071
                },
                {
                    "absolute": 10.54,
                    "absolute angle": 45.23576899384926,
                    "gear": 3,
                    "offset": 5.05,
                    "offset angle": 21.673684385098557
                },
                {
                    "absolute": 15.719999999999999,
                    "absolute angle": 67.46738980866323,
                    "gear": 4,
                    "offset": 5.18,
                    "offset angle": 22.23162081481396
                },
                {
                    "absolute": 21.939999999999998,
                    "absolute angle": 94.16250206120046,
                    "gear": 5,
                    "offset": 6.22,
                    "offset angle": 26.69511225253723
                },
                {
                    "absolute": 26.99,
                    "absolute angle": 115.83618644629901,
                    "gear": 6,
                    "offset": 5.05,
                    "offset angle": 21.673684385098557
                },
                {
                    "absolute": 32.04,
                    "absolute angle": 137.50987083139756,
                    "gear": 7,
                    "offset": 5.05,
                    "offset angle": 21.673684385098557
                },
                {
                    "absolute": 37.089999999999996,
                    "absolute angle": 159.18355521649613,
                    "gear": 8,
                    "offset": 5.05,
                    "offset angle": 21.673684385098557
                }
            ],
            "total angle": 159.18355521649613,
            "total pull": 37.089999999999996
        },
        "sg s501 sheldon brown": {
            "indexing": [
                {
                    "absolute": 0,
                    "absolute angle": 0.0,
                    "gear": 1,
                    "offset": 0,
                    "offset angle": 0.0
                },
                {
                    "absolute": 4.9,
                    "absolute angle": 21.029911581580777,
                    "gear": 2,
                    "offset": 4.9,
                    "offset angle": 21.029911581580777
                },
                {
                    "absolute": 10.2,
                    "absolute angle": 43.77655063920896,
                    "gear": 3,
                    "offset": 5.3,
                    "offset angle": 22.746639057628183
                },
                {
                    "absolute": 15.2,
                    "absolute angle": 65.2356440898016,
                    "gear": 4,
                    "offset": 5.0,
                    "offset angle": 21.45909345059263
                },
                {
                    "absolute": 21.1,
                    "absolute angle": 90.5573743615009,
                    "gear": 5,
                    "offset": 5.9,
                    "offset angle": 25.321730271699302
                },
                {
                    "absolute": 25.8,
                    "absolute angle": 110.72892220505798,
                    "gear": 6,
                    "offset": 4.7,
                    "offset angle": 20.17154784355707
                },
                {
                    "absolute": 30.8,
                    "absolute angle": 132.18801565565062,
                    "gear": 7,
                    "offset": 5.0,
                    "offset angle": 21.45909345059263
                },
                {
                    "absolute": 36.6,
                    "absolute angle": 157.08056405833807,
                    "gear": 8,
                    "offset": 5.8,
                    "offset angle": 24.89254840268745
                }
            ],
            "total angle": 157.08056405833807,
            "total pull": 36.6
        }
    },
    "spool circumference": 80.4247719318987,
    "spool diameter": 25.6
}