thepronghorn said:
There's nothing to concede. The math isn't very hard. It's just ohms law and basic motor theory.
Say we have a motor that spins 10k rpm no load at 100V which means its Kv is 100 rpm/V and its Kt is 0.0954 Nm/A. Suppose its internal resistance is 0.01 ohm.
Now say we're in 3rd gear, our motor is spinning at 1000 rpm, so our BEMF is 10V.
To make 9.5 Nm of torque from our motor, we need 9.5Nm / 0.0954Nm/A = 10A which requires 10V + 10A*0.01ohm = 10.1V into the windings.
Now say we have the same motor in 1st gear which has a ratio 3x lower than 3rd gear. Now our motor is spinning at 3000 rpm to get the same rear wheel rpm, so our BEMF is 30V.
Since our ratio is 3x lower, now we only need 3.16 Nm of torque, which is 3.16Nm / 0.0954Nm/A = 3.33A which requires 30V + 3.33A*0.01ohm = 30.0333V into the windings.
Our two different scenarios result in the same torque and rpm to the rear wheel, but one requires 10.1V into the motor windings while the other requires 30.0333V into the windings. Guess which one needs a higher duty cycle in the controller? Guess which one results in more power being drawn from the battery?
That's right, it's the one needing ~3x higher voltage into the windings and the one in low gear.
Maby the math isn't very hard, and sure there's more to it than this nice simplified example, but you got it wrong.
Turns out the example here of producing 1kw requires 100A to the phases in 3rd gear and results in 100w of winding loss, and 33.3A in 1st gear results in only 11w of loss.
9 times less total motor winding losses (and lower controller losses) from a 3 times lower gear ratio.
And Luke i believe, is making the same point here:
liveforphysics said:
Some folks still don't get that it's less burden on your battery.
If you had a lower ratio gear you could shift into, this would get the motor BEMF higher and draw more power off the pack.
If you have an EV with gears, and you want to pull the most current from your pack, then start in 1st gear. If you want to pull the least current start in 4th gear (or whatever you have ).
If we are talking about the same starting acceleration here (and its a pointless comparison if we are not) then you Luke are also are flat out wrong.
Nice to have spotted this one pop up somewhere new again though.
On the original topic of racing and efficiency though motomoto, the bikes ive built with a ca120 or colossus type motors do benefit from a 2 speed gearbox (that adds 385 grams and 13w of loss vs single speed) but the Joby powered bike doesnt really need it, however the sprockets can be changed from 8:1 through to 12.4:1 and we dial the gearing in to the track.
There are noticeable benefits from getting the gearing dialed in for the conditions, even if we can get the acceleration we need with taller gearing on an open speedway track in 450cc class by using more phase amps, these losses build so not surprisingly if we are talking gear ratio for a machine in the real world there is compromise required and theres no way any simple philosophical or blanket statement about taller gearing for best efficiency in all occasions can be correct.
Put simply there is a price to pay for additional motor torque, the winding losses for ALL these motors at ANY torque level rise by the additional amps, squared.
You also have likely observed this in action Dave, with your sweet Tangentdrive climbing a steep hill in a low gear using 1000w vs a taller gear using 3000w, most hub motor setups on 26" wheels that are clearly making use of all the "greatness" of direct drive and tall gearing are claiming (consuming) 5000w may not even get up the hill.
If we enter an otherwise identical machine to the Joby bike but with a cro motor it gets lapped twice in a 6 lap race haveing used around 1.5 times more power off the battery and now with a stinky motor, a while back with an x5 motor and a decent ride the sideplates were still to hot to touch after 2 hours rest. -I dont mind leaving hub motored bikes outside because of the smell, its really the wasted battery power that bothers me. :wink: