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# Calculating a Theoretical Top Speed

TheAllConsuming
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Join Date: Oct 2018
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Received 0 Likes on 0 Posts 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 RustyUs Join Date: Oct 2012
Location: PA
Posts: 4,763
Received 27 Likes on 25 Posts Uuuuh...you forgot internal (tranny's) gear ratio? I believe the Slash, Bandit, Rustler, and Stampede have 2.72:1 internal gear ratio. RustyUs Join Date: Oct 2012
Location: PA
Posts: 4,763
Received 27 Likes on 25 Posts First time I ever seen percentage of cells, battery amperage, and percentage of kVa numbers being taken into account for speed calcs. I scratch my head on that one . TheAllConsuming
Junior Member

Join Date: Oct 2018
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Received 0 Likes on 0 Posts First time I ever seen percentage of cells, battery amperage, and percentage of kVa numbers being taken into account for speed calcs. I scratch my head on that one .
It was the only way that I could figure out for different cell counts. Though, i did forget about trans gear ratio.

The reason I used amperage was because i was trying to base it off of current flow. I've tried searching for a better way to calculate top speed, but came up short everywhere. RustyUs Join Date: Oct 2012
Location: PA
Posts: 4,763
Received 27 Likes on 25 Posts I believe the diff gear on the Rustler/Bandit etc. is 49T and the topshaft is 18T = 2.72 internal gear ratio
FDR (Final Drive Ratio) = Spur/Pinion x Internal Gear Ratio

The was as one time, up until recently, a great site for estimating/calculating speed/charging calculations...scriptasylum. The site is no more, and I haven't found another site like it. The speed estimator on scripasylum...you could even plug in numbers to allow for tire ballooning effects . Sorry to see that site disappear. phmaximus Join Date: Jun 2008
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Received 1 Like on 1 Post yep.... \$10 on a old smartphone and \$3 for a speed app....

but in saying that... most people give away there old smart phone... have a look online someone might be giving away a old samsung 4 or something

think of it like this, u could measure how much water is in the cup by checking the reflection, but wouldn't it be easier to measure the water??

What im trying to get at... there is much simpler ways to do it that are well proven methods. why over complicate something unesseraly and how accurate is it going to be? You may not post new threads
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