And incidentally, it was posted above that the JVN gear calculator would give you 7 ft/s. That's probably a decent estimate, but it's worth discussing some of the theory behind that result.
First, you take your wheels, which are designed to be Ø3.00 in. (From examining that drawing by eye, based on the size of the CIM, which is Ø2.50 in, I'm guessing the wheels are actually slightly larger than that. Did you account for the thickness of the tread backing, and maybe some of the tread?) We'll stick with Ø3.00 in for simplicity.
Then find the circumference per revolution:
C =
π ×
d = Ø9.42 in/rev = Ø0.785 ft/rev. That's the distance the wheel travels in one revolution. Though I'd really rather work in SI, it would just confuse the Americans—so were going to calculate the speed of the robot in ft/s.
That means we need rev/s, or its familiar cousin, rev/min. This is determined by the speed of the motor, at its operating condition. Note that this is distinct from free speed. Most of the time, when we talk about robot speeds, we're either talking about the theoretical free speed (when calculating), or the actual speed (when measuring).
Since the free speed of the CIM motor is
ωfree = 5 310 rev/min = 88.5 rev/s, and we've got a 10:1 gear ratio (
Z = 0.1) a little multiplication gives:
ωfree × C × Z = v
88.5 rev/s × Ø0.785 ft/rev × 0.1 = 6.95 ft/s
v ≈ 7 ft/s
In JVN's calculator, there's usually an arbitrary factor of 81% corresponding to operating condition (graphed on a torque curve)—in other words, the motor is operating at 81% of free speed. It's arbitrary in the sense that there's no physical reason why it has to be 81%, but based on JVN's testing and experience, it was a reasonable value. (I've occasionally picked a slightly higher value for this—around 85% or even 90%. Again, it was just a guess, but I've designed several drivetrains with lots of motors, which tend to be less heavily loaded under ordinary driving, so the motors presumably run closer to their free speed.)
In the calculations presented by Isaak* above, I think he's either using a 100% (i.e. at the free speed) calculation, inputting the correct speed and rounding up to 7 ft/s—in other words, using JVN's calculator to do the math I showed above—or else he's using the
rough free speed JVN preloads it with (5 500 rev/min) and a weird speed loss constant of 97.25%. In any event, remember that the speed loss constant is just a way of saying "when the wheels are off the ground and spinning under power, their speed is 81% of what it would be in a frictionless gearbox." That's different from, but related to efficiency.
Anyway, in my estimation, your wheels are probably more like Ø3.25 in (due to the tread thickness), so that might skew things a bit. Using speed loss of 81% and efficiency of 90%, using 1.2 as the coefficient of friction, substituting in the correct values for CIM motors instead of the rough/old ones in some versions of the JVN calculator, and taking robot weight to be a rather plump 167.5 lb
f (hostbot + minibot + battery + bumpers), I'm actually estimating that you'd see something closer to 6.10 ft/s and 201.0 lb
f pushing force.
By the way, remember that all of this is predicated on your battery actually being able to deliver that performance—which it won't. As the load on the battery increases, its voltage drops, basically shrinking your speed curve (and hence your power). The more advanced versions of the JVN calculator will let you model motor performance over time at some voltage, from which you can determine the (constant-voltage) load on the battery. If the load on the battery is significant for a long enough period (e.g. when accelerating), it may be time to look at a few cases where the applied voltage is lower, in order to estimate mid- and late-match performance.
For now, though, don't worry too much about the battery voltage and power consumption, because your design isn't crazy enough for it to matter too much. (I've had a few designs where these absolutely did matter.) Estimate a desirable speed, then try to find gears to match.
* I just realized he's not "Hawaiian" or even "Hawaiʻian", but rather "Hawiian Cadder"...I'm not sure what to make of that.