I am actually glad that I found the spec sheets for the 9000 series motor. They contain a wealth of information which makes the entire story much more transparent to me. I used the following additional data - the weight of the locomotive as just over 6 kg, the current at max voltage of 22 Volt when free running and when slipping, to be 2 Amp and 2.7 Amp respectively (we assume that we have ideal adhesion with friction coefficient equal one, that is we permit slipping when the load is greater than the weight of the locomotive - i.e. we are not using rack and pinion system which makes possible to pull loads greater than the locomotive weight). The resulting picture is as follows (these figures may be about 10-15% off because I only have specifications for the 24 V motor while K-27 apparently uses a 19 V motor). 1) For the stock K-27 locomotive at maximum voltage exercising maximum tractive force of 6kg (ideal adhesion) motor torque: 14.5 oz-in current draw: 2.8 Amp motor revs.: 3991 rpm heat dissip.: 22.9 Watt scale speed: 32.7 mph (52.6 km/h) At this condition the motor is used optimally, it delivers 43 Watts of its maximum 47 Watt maximum power. It cannot deliver any more on this locomotive without increasing the weight of the locomotive but it is very very close to the maximum and this is why it is optimally used. You can see what happens in these figures. I marked with colour rectangle the range of operation at max speed for all permissible loads. The motor works in its optimal regime on the upward slope of the power curve while not reaching the maximum.
(http://farm4.static.flickr.com/3267/3099251143_eb1a88aa64_o.jpg)
- Now the same on a hypothetical locomotive with 1:29 gear ratio: motor torque: 7.5 oz-in current draw: 1.5 Amp motor revs.: 5025 rpm heat dissip.: 6.7 Watt scale speed: 20.6 mph (33.1 km/h) The motor can use at most only about 28 Watts of its available 47 Watts of power, you can see what happens in these plots. The regime of operation is sub-optimal in the sense that the motor will never even come close to using its full capacity. In other words, a cheaper considerably smaller motor could be used for this design (using 1:29 gear ratio).
(http://farm4.static.flickr.com/3075/3100116514_81b9d1ab3f_o.jpg)
Concluding, the design as available is optimal in the sense of utilising the motor capacity for the locomotive which it is supposed to move and pull the train which it is capable of pulling. In my opinion a design close to ideal. People who want to run it fast will be able to pull a maximum length train with the maximum speed of about 32.7 mph (52.6 km/h) Please note that the motor produces 22.9 Watts of heat at this maximum speed and pulling capacity condition which should be OK even without any cooling. Of course, if one wants to pull lighter trains and operate at lower speeds there is nothing to stop him/her from doing so with this design. In other words this design can be both enjoyed by people who want to run fast and heavy or light and those who want to run slow and heavy or light. On the other hand, the 1:29 design is sub-optimal in the sense that it involves a motor which only operates at a fraction of its capacity under maximum load at maximum voltage. In other words, for this design a weaker and therefore cheaper motor should be used, or a (much) heavier locomotive of course. This design is not capable of running fast - heavy or light. I am not interested in discussing who phoned whom, said what and when or whatever other fuzzy stories led to the current state of affairs - let’s leave this to model railroading historians;-)))… All I can see from the above, is that if there were suggestions to use 1:29 with 9000 series motor on a 6kg K-27 they were sub-optimal and mistaken, if a mistake happened which reverted this suggestion and coincidentally made use of a 1:14.5 gear ratio, that is fortune in misfortune, as we ended up with a near ideal design by pure chance;-)) this does not happen that often, so let’s celebrate and congratulate Bachmann!!! Best wishes from Tokyo, Zubi
