Calculating a Theoretical Top Speed
I do not have telemetry or a way to find the exact speed that my modified Traxxas Bandit tops out at. Nor have I been able to maintain traction through full throttle/acceleration. Using some formulas that I learned about while in a high performance drivelines class, I was able to modify and create formulas that get me in the ball park,as they say. These formulas are by no means and exact, accurate numbers. There are too many variables to get an exact number on how fast your r/c can go. There are most likely better ways to figure it out, but this way seems to get fairly close for me. This is based off of a 3s battery, so 11.1 will be a static number for one of the formulas. The formula I used for rpm gives a more realistic mph over kv × battery voltage. Using kv x battery voltage to get rpm for the mph formula, I would get 172+ mph on my old gearing. This is why I used my modified formula for finding the rpm.
If you know of an easier way to calculate a top speed for electric R/Cs, please let me know. If you have any questions on how to I arrived at any number, or how to came to a workable conclusion on any of the formulas, feel free to ask. I will answer when I can.
Numbers you will need for this formula:
Pinion tooth count (pT)
Spur gear tooth count (sT)
Gear ratio (GR)
Tire Diameter (TD)
Approximate RPM (~rpm)
KV rating ( kV)
Amperage of battery (mah/ah)
Voltage of Battery (bV)
Percentage of cell count (%s)
Percentage of kVa (%kVa) (2s only)
Formulas:
GR = sT ÷ pT (driven gear ÷ drive gear)
%s = (3s bV - 2s bV) ÷ 3s bV (for 2s battery)
%kVa = 1 - %s
%s = (4s bV - 3s bV) ÷ 4s bV + 1 (for 4s battery)
~rpm = kV × ah × %kVa (2s)
~rpm = kV × ah (3s)
~rpm = kV × ah × %s (4s+)
MPH (aka top speed) = (~rpm × TD) ÷ (GR × 336)
If you have multiple gear ratios, such as a f/r differential, the second () for the mph formula will look like this: (GR × GR × 336). This will use your overall gear ratio.
The 336 is a static number based on pi and a breakdown of distance over time converted in just distance (as far as I've been able to figure). I can give a better explanation of this if you would like.
Example using my bandit will the old GR vs new GR:
Old pT = 83t
Old sT = 24t
New pT = 33t
New sT = 76t
kV = 3800
TD = 4.25 ( This is only the rear tire, since only the rear tire sees power)
ah = 5
bV = 11.1
~rpm = 3800 × 5 = 19000
Old GR = 83 ÷ 24 = 3.458333 = 3.46
MPH = (19000 × 4.25) ÷ (3.46 × 336) = 69.4587806221 = 69.46
New GR = 76 ÷ 33 = 2.303030303 = 2.30
MPH = (19000 × 4.25) ÷ (2.30 × 336) = 104.4901656315 = 104.49
Just with gearing I see about 35.03 mph difference.
If i was to use a 2s the math would look like this (using numbers from new GR):
%s = (11.1 - 7.4) ÷ 11.1 = .3333333 = .33 or 33%
%kVa = 1 - .33 = .67
~rpm = 3800 × 5 × .67 = 12730
MPH = (12730 × 4.25) ÷ (2.3 × 336) = 70.0084109731 = 70.01