Need Help with Stepper Motor Data (Completely Off Topic)

Hi All,
I apologise the is has nothing to do with the Duet but i know a lot of you guys from here are very smart and know a lot on the topic of stepper motors.
I am conducting a study on NEMA 17 and NEMA 23 stepper motors and trying to find the highest torque i can get from each motor when attaching them to a gearbox. I have already selected a specific NEMA 17 and NEMA 23 and i am using pull out torque data from the manufacturer of the selected motors.
The blue and orange lines above show the pull out torque of the NEMA 17 and NEMA 23 respectively. In essence, the pull out torque is the maximum torque the motor can output whilst rotating at certain speed (RPM).
This data is fine and the results are as expected, at low RPMs, the NEMA 23 has a much higher torque than the NEMA 17, whereas at higher RPMS the NEMA 17 can output higher torque than the NEMA 23.For the project i will be using a gearbox on the motors, therefore i wanted to find the gear ratio that yields the highest output torque of the gearbox, given a desired output RPM of the gearbox. For this example i have said the desired output speed of the gearbox is 60RPM. For the range of different RPMs of each motor, i calculated the gear ratio required for the stepper motor rotating at X RPM to create an output speed of the gearbox of 60 RPM. This calculated gear ratio can then be multiplied by the pull out torque of the motor at X RPM in order to find the output torque of the gearbox.
Here's the part i need help with:
Looking at maximum output torque of each motor with a gearbox (The green and red lines), it can be seen that the NEMA17 outputs the most torque at 600 RPM, which means a 10:1 gear ratio is used (600RPM of motor / 60RPM of gearbox output), whilst the NEMA23 outputs the most torque at 200RPM with a gear ratio of 3.3:1 (200RPM of motor / 60RPM of gearbox output).
This seems odd to me as the results show that with a gearbox, a NEMA 17 is actually stronger than a NEMA 23. This seems odd, simply due to the shear size and mass of the NEMA 23 i would expect it to be stronger. However looking at how quickly the torque of the NEMA 23 drops off at higher RPMs, it seems this could be true.
Can a NEMA 17 with a 10:1 Gearbox REALLY output more torque than a NEMA 23 with a 3:1 Gearbox if the output speed of the gearbox is fixed at 60RPM???

The critical factors you are missing are the inductance of the stepper motors, the supply voltage, and whether or not a constant current driver is used. The blue line is for a motor using constant current drive. The orange line is characteristic of a motor that is being driven using a constant voltage drive. It would be flat at low speeds if a constant current driver was used  like the blue line, but higher.
Don't forget that gearboxes have output shaft torque limits too.

@dc42 Thanks for your help!!
That does make sense to me but i am still a bit of an amateur in regards to this topic.
The NEMA17 Inductance is 3.0mH ± 20%(1KHz) and the NEMA 23 inductance is 5.4mH ± 20%(1KHz).
Correct me if i am wrong, so this means the PullOut data from the manufacturer, for the NEMA17 constant current varying voltage was used and for the NEMA 23, constant voltage varying current was used?
Thanks again for you support!
Does that mean that the NEMA23 will actually output more torque than the NEMA17?

In general, you could have a long Nema17 motor which is stronger than a short Nema23 motor yes. Nema designation only concern the faceplate and mounting holes, not the rest of the motor specifications.

@bearer these are the motors i am using:
The torque curve for each can be found on the website. This is the torque curved used in my calculations. For these two motors, are my calculations correct in saying the NEMA 17 with a 10:1 gearbox will produce more torque than the NEMA 23 with a 3.33:1 gearbox if the gearbox output is to be 60RPM as seen on the graph???

@mattling9 From a purely mechanical perspective, there isn't much in it if you just take the maximum quoted torque and using ozin as a common unit. The Nema 17 size with with 10:1 gearing would produce (84 x 10) 840 ozin. The Nema23 size using 3.33:1 gearing would produce (269 x 3.33) 895.77 ozin. That's assuming zero transmission losses (which there would be in practice).
But as you have noticed, each motor would be on a different part of the torque curve with the Nema 17 size with 10:1 gearing running considerable slower than the Nema 23 size with 3.33:1 gearing. So yes, it's perfectly feasible that a Nema 17 with 10:1 gearing could produce more torque than a Nema 23 with 3:1 gearing, even without taking the electrical characteristics such as inductance account (unless you have horrendously high transmission losses).

@mattling9 said in Need Help with Stepper Motor Data (Completely Off Topic):
Can a NEMA 17 with a 10:1 Gearbox REALLY output more torque than a NEMA 23 with a 3:1 Gearbox if the output speed of the gearbox is fixed at 60RPM???
High speed motors have much greater power density than low speed motors, so your results aren't particularly surprising. When building model airplanes we often have to decide between a heavy directdrive motor and a lighter geared motor.
For model airplanes the heavy direct drive motor typically wins after considering the weight, cost, efficiency, and complexity of a gearbox. But in your situation both motors would require a gearbox so its not surprising that the Nema17 wins. Just make sure the 10:1 gearbox survive the planned load.

The curve for the 17HS192004S looks sensible to me. Selecting that motor in the EMF calculator at https://reprapfirmware.org/ and selecting half stepping, the calculator predicts that the torque will start to drop off at 2.9kHz (low slip angle) or 4kHz (high slip angle). The figure for high slip angle can be compared to the pullout torque curve, and it agrees reasonably well.
The curve for the 23HS302804S looks completely wrong to me, as if it has been measured at a constant voltage of 3.2V, not at a constant current of 2.8A with a driver supply of 24V. It doesn't show a flat area at all. The calculator predicts that loss of torque will start at 1.2kHz (low slip angle) or 1.6kHz (high slip angle). Whereas the curve suggests that torque falls right from the start of the curve at 0.5kHz.
I also looked up the 23HS222804S which is a shorter Nema 23 motor that I use to test Duets at maximum current. The calculator suggests that torque should start to drop off at 2.2kHz or 3.1kHz. This fits reasonable well with the curve published at https://www.omcstepperonline.com/download/23HS222804S_Torque_Curve.pdf.