Efficiency of Lower vs. Higher Gear ratios

Our robot currently has a dual 5" flywheels, with 4 motors geared 21:1.

At roughly 2/3 power 65%-70%, we can make full field high goals, and efficiency is pretty good - we don’t use that much battery power.
However, I would like to minimize the waiting in between shots. Would a lower ratio, like 15:1 be better? I figure it would give us more startup torque, and better acceleration, at the cost of some upper end speed we would never use. However, would this lower ratio mean that the motors have to run faster, using more energy?

What are your opinions on leaning towards lower vs. higher gear ratios?

At both too high and too low of gearing, you are going to have some undesired results. The trick is finding the sweet spot. What I would consider if you want to find the perfect gear ratio is to test it. make a list of all of the reasonable ratios that are possible with different types of internal and external gears. Test the top 3 and see which one shoots faster. Best gearing is going to be slightly different based off of mass of your wheel, compression and friction in your system.

If you look at the standard DC motor diagram, like down the page here:
Motor running faster for the same work should be more efficient.
But is is always possible to do it wrong.

It would be more efficient on torque and might improve firing to reduce to 1:18 or 1:16. I don’t know if 1:15 is high enough. Efficient on electric power is another thing. I’m running at about 55% power, which is really high on the efficiency curve, but running at a higher voltage might increase battery usage.

I remembered that I am using a form of TBH which means the 65-70 I posted earlier isn’t really a motor power, but rather a percentage of 127, meaning I am running the motors at roughly 2/3 power. If I were to switch to 18:1 ratio, how would I do it?
18:1 would be be around 1800 rpm, the best I could figure is Speed Gearing with 35/3 ratio, but this would be a pretty significant reworking for a small gain.

What is the optimal ball compression 3.5"? 3.75"?
It was around 3.46", but that compression level bordered on the high side. It required spring loaded pressure wheel to ensure the ball got properly gripped by the flywheels. By putting two flywheels on each side and spacing them out vertically, I feel we could get a more optimal compression level.
I drew it out in Inventor, and got slightly less than 3/4" as the vertical spacing between each flywheel.

The compression on my flywheel is closer to ~3.8". if you are not meeting the ball at it’s greatest diameter of course it can be lower, but you want just enough that it takes a little force to feed the ball through, but not enough that it needs to be forced. This reduces the amount of energy the ball takes from the flywheel because the flywheel doesn’t have to use to force through, but instead only to throw the ball. I took mine down from a single wheel with 3.75" to two wheels on one axle and 3.8"-3.9" and the flywheel only needs 2280RPM to fire full court compared to 2600.

Would having a low gear ratio (say, 21:1 with torque motors) have a better recovery rate than a higher one (for example, 35:1 with torque, or visa versa? I know @technik3k has a post in the Physics of the Flywheel thread about recovery rate, and how the power margin (how much power is used vs how much is available) affects it. A greater power margin (how much power is not used) results in a lower recovery time. However, this would not account for the behavior of electric motors, which must put out more torque at higher gear ratios, but spin slower.