km is the same:
100kv - 10 turns - 1 cross section - 0.1ohm
60/(2 * pi * 100kv)=0.09549296585513720146133 newton meters torque per motor amp
(4v battery - 0v bemf) / 0.1ohm = 40a motor & battery current at 0rpm
4v * 40a = 160w electrical
40a * 0.09549296585513720146133nm/a = 3.819718634205488058453nm
3.819718634205488058453nm / sqrt(160w electrical) = 0.3019752726269222102173km
200kv - 5 turns - 2 cross section - 0.025ohm
60/(2 * pi * 200kv)=0.04774648292756860073067 newton meters torque per motor amp
(4v battery - 0v bemf) / 0.025 ohm = 160a motor & battery current at 0rpm
4v * 160a = 640w electrical
160a * 0.04774648292756860073067nm/a = 7.639437268410976116907nm
7.639437268410976116907nm / sqrt(640w electrical) = 0.3019752726269222102173km
^km (torque per square root of watt) is the same
1:1 gearing - 10mph ground speed
100kv - 10 turns - 1 cross section - 0.1ohm
1000rpm = 104.719755 radians per second
(11v battery - 10v bemf) / 0.1ohm = 10a motor/battery current
torque per amp: 60/(2 * pi * KV) = 0.095492nm/a
10a * 0.095492nm/a = 0.95492newton meters torque
11v battery * 10a current = 110w electrical
0.95492newton meters torque * 104.719755 radians per second = 99.99w mechanical
copper loss: 10a * 10a * 0.1ohm = 10w
wheel torque at 10mph @ 110w electrical = 0.95492nm * 1 gear reduction = 0.95 newton meters
summary: 10mph ground speed, 0.95nm wheel torque, 99.99w mechanical, 110w electrical, 10w copper loss
2.150:1 gearing - 10mph ground speed
200kv - 5 turns - 2 cross section - 0.025ohm
2150rpm = 225.14747 radians per second
(11v battery - 10.75v bemf) / 0.025ohm = 10a motor/battery current
torque per amp: 60/(2 * pi * KV) = 0.047746nm/a
10a * 0.047746nm/a = 0.47746 newton meters torque
11v battery * 10a current = 110w electrical
0.47746 newton meters torque * 225.14747 radians per second = 107.49w mechanical
copper loss: 10a * 10a * 0.025ohm = 2.5w
wheel torque at 10mph @ 110w electrical = 0.47746nm * 2.15 gear reduction = 1.02 newton meters
summary: 10mph ground speed, 1.02nm wheel torque, 107.5w mechanical, 110w electrical, 2.5w copper loss
^same ground speed, same voltage battery, same battery current and motor current, different gearing & the higher kv appears more efficient… it would seem if the 100kv is at constant speed @ 10mph from the load, with the same ground speed & load the 200kv is still accelerating because there is more torque at the wheel…