Hub Motor Basic Calculations

[Lurkin]

I've realised to date, I've really gotten by relying on vendors information to calculate or understand the specifications of the ebike products I am buying. But as I find new vendors, the information changes and I need to convert it to be able to actually use it. Using various calculators has become a bandaid for not learning the actual underlying calculations.

I realise that Kv, Turn Count, Voltage, Current (therefore power), wheel diameter all all functions of overall wheel (and ergo my) speed.

For instance:
Motor RPM: 206
Voltage: 36v
Motor max power: 800w
Wheel size: 26"

26" wheel = 660.4/100,000 x Pi = 0.002074708 kms
206 RPM = 206 x 60 = 12,360 RPHR
km/h = 0.002074708 / 12,360 = 25.64338827 km/h

Does this mean I can derive kv as follows:

kv = rpm/V
kv = 206/36
kv = 5.7222 rpm/V

therefore at 48v
48 x 5.7222 = 274.7rpm
274.7 RPM x 60 = 16,480 RPHR
km/h = 0.002074708 / 16,480 = 34.19km/h

Is it possible to derive the turn count?
Is it possible to calculate the torque?

 

[cycborg]

Motor RPM: 206
Voltage: 36v
Motor max power: 800w
Wheel size: 26"

26" wheel = 660.4/100,000 x Pi = 0.002074708 kms
206 RPM = 206 x 60 = 12,360 RPHR
km/h = 0.002074708 / 12,360 = 25.64338827 km/h

Does this mean I can derive kv as follows:

kv = rpm/V
kv = 206/36
kv = 5.7222 rpm/V

therefore at 48v
48 x 5.7222 = 274.7rpm
274.7 RPM x 60 = 16,480 RPHR
km/h = 0.002074708 / 16,480 = 34.19km/h

This is all correct, except I think the assumptions change in the last couple lines. Everything up to that point is unloaded, but when you start figuring out how fast you can go, you switch to loaded conditions. Your speed on the flat will probably drop by ~30% from the unloaded condition. So somewhere in the 20-25 km/h range.

Is it possible to derive the turn count?

Nope. But turn count itself isn't that important. It affects Kv, but you already have that.

Note that motors are sometimes offered in "36 V" and "48 V" versions. These are typically just different windings of the same motor. If the two different unloaded RPMs are specified, you can divide by 36 and 48 to get the two different Kv's.

Is it possible to calculate the torque?

If you divide 30/pi by Kv, you get Kt, the torque constant in Nm/A, where the current is motor current, not battery current. If your controller limits phase current, then the maximum low-speed torque is just Kt*Iph. If your controller only limits battery current, then it's... more complicated.

 

[Lurkin]

Perfect. Any idea on the best way to calculate (rather than estimate) loaded speed?

 

[Punx0r]

Assuming top speed on flat ground of around 70% of no-load speed as cycborg suggested should be about right

 

[John in CR]

Assuming top speed on flat ground of around 70% of no-load speed as cycborg suggested should be about right

If so you're WAY underpowered to be running that speed. All of my DD hubbies have pushed me on flat ground well beyond 80% of no load speed.

The important motor characteristics are Kv, Phase-to-phase resistance (Rm), and no-load current.
-Kv gives you the torque constant (Kt). ie Divide 9.549 by Kv and the result is Kt, Nm of torque per amp.
-Phase-to-phase resistance gives you and idea of how much current a motor can handle, since heat is our limitation, and heat in the copper comes from resistance of the windings at Current squared X Rm = Watts of heat.
-No-load current is a measure of the heat created in the iron and magnets at that rpm, since that loss is rpm dependent

Low resistance for a motor that operates in the rpm range you need at your voltage, and low no-load current at that rpm, result in better efficiency, which is single best measure of motor quality.

 

[cycborg]

I think the goal is to get the best sense of performance given the information available. Sometimes, all you get is "36 V 350 W" which is essentially meaningless. In this case, we at least have an unloaded RPM (we assume it's unloaded!) which, along with the nominal voltage, gives us Kv and thence Kt. Since the seller isn't bragging about any efficiency-related data, we can assume we're dealing with the typical 75-80% peak efficiency, So we lowball the loaded speed at 70%. So yes we have a cheap motor with minimal data but we can nonetheless get a ballpark idea of real-world performance.

I am all for pushing vendors in the direction of high copper fill, thin lams, and complete perfomance data. But if a low-efficiency, lightweight gear hub does the job required, the cost and weight penalty for fill, lams, and data may not be worth it.