Also voltage sag
i went ahead and solved this:
60a battery limit / 95% duty = 63.1578a motor current at peak mechanical power
63.1578a^2 * 0.05ohm = 199.445385042w copper loss per motor at peak mechanical power
60a battery limit * 48.1v battery = 2886w electrical power at peak mechanical power
2886w peak electrical - 199.445385042w copper loss = 2686.554614958w peak mechanical power per motor
2686.554614958w peak mechanical power per motor * 4 motors = 10746.218459832w peak mechanical
60 / (190kv * 2 * pi) = 0.05025945571323010603228Nm per motor amp
63.1578a * 0.05025945571323010603228Nm per motor amp = 3.174276652045044390766 Nm torque at peak mechanical power
2686.554614958w peak mechanical / 3.174276652045044390766 Nm = 846.3517548878964569933rad/sec @ peak mechanical
(60 / (2 * pi)) * 846.3517548878964569933rad/sec = 8082.063923094534641801 motor rpm @ peak mechanical power
^peak mechanical power is 10746.218459832w @ 8082.063923094534641801 motor rpm
A = meters per second = XX.XXX B = drag coefficient = 0.75 C = frontal area = 0.6m^2 D = fluid density of air = 1.225kg/m^3 E = wind drag force in watts F = sine of 5% slope = sin(atan(5/100)) = 0.04993761694389223373491 G = acceleration of gravity = 9.80655m/s^2 H = vehicle mass in kg = 90.7184kg = 200lb / 2.20462lb/kg I = mechanical watts required for constant speed up slope with no wind drag J = mechanical watts required for constant speed up slope including wind drag K = H * G * F L = (1/2) * D * C * B
E = ((1/2) * D * C * (A^2) * B) * A
I = H * G * A * F
J = E + I
J = (((1/2) * D * C *(A^2) * B) * A) + (H * G * A * F)
J = (1/2) * D * C * B * A^3 + H * G * F * A
J = (L * A^3) + (K * A)
^this can be rearranged to:
A=(sqrt(3) * sqrt(27 * J^2 * L^4 + 4 * K^3 * L^3) + 9 * J * L^2)^(1 / 3) / (2^(1 / 3) * 3^(2 / 3) * L) - ((2 / 3)^(1 / 3) * K) / (sqrt(3) * sqrt(27 * J^2 * L^4 + 4 * K^3 * L^3) + 9 * J * L^2)^(1 / 3)
we know:
J = 10746.218459832w peak mechanical L = 0.275625 = (1/2) * D * C * B K = 44.42622815547907982077 = H * G * F
therefore:
A=(sqrt(3) * sqrt(27 * 10746.218459832^2 * 0.275625^4 + 4 * 44.42622815547907982077^3 * 0.275625^3) + 9 * 10746.218459832 * 0.275625^2)^(1 / 3) / (2^(1 / 3) * 3^(2 / 3) * 0.275625) - ((2 / 3)^(1 / 3) * 44.42622815547907982077) / (sqrt(3) * sqrt(27 * 10746.218459832^2 * 0.275625^4 + 4 * 44.42622815547907982077^3 * 0.275625^3) + 9 * 10746.218459832 * 0.275625^2)^(1 / 3)
A=32.32551993764664323864 meters per second
^therefore the peak velocity up slope is 32.32551993764664323864 meters per second
72.31024856931928212624mph = 32.32551993764664323864 meters per second * 2.23694 mph per m/s
^72.31mph is the maximum possible top speed up 5% slope w/ 200lbs, 0.75 drag coefficient, 0.6m^2 frontal area, 4x 190kv 0.05ohm motors & 120a motor current limit & 60a battery current limit per motor w/ 48.1v battery
therefore we need:
8082.063923094534641801 motor rpm @ peak mechanical power @ 72.31024856931928212624mph w/ 83mm tires
83mm * pi = 260.7521902479528387924mm per rotation
1mph = 0.44704 meters per second
72.31024856931928212624mph * 0.44704 meters per second per mph = 32.32551993764664323864 meters per second
32.32551993764664323864 meters per second * 1000mm per meter = 32325.51993764664323864mm per second
32325.51993764664323864mm per second / 260.7521902479528387924mm per rotation = 123.9702719540260136714 tire rotations per second
123.9702719540260136714 tire rotations per second * 60 seconds per minute = 7438.216317241560820284 wheel rpm required for 72.31024856931928212624mph @ 83mm tire diameter
8082.063923094534641801 motor rpm / 7438.216317241560820284 wheel rpm = 1.086559408652925905457 gear ratio
^1.08:1 gear ratio is needed to obtain maximum possible 72.31mph top speed up 5% slope w/ 200lbs, 0.6m^2 frontal area, 0.75 drag coefficient, 4x 190kv 0.05ohm motors, 83mm tires, 120a motor current limit, 60a battery current limit per motor & 48.1v (13S) battery
answer:
72.31mph & 1.08:1 gear ratio
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In ideal world 
^graphed out it looks about like this 25T wheel & 23T motor = 1.088:1 ratio for ~72mph up 5% slope w/ 4x 190kv 0.05ohm, 83mm tires, 120a motor current and 60a battery current limit per motor, 13S (48.1v) w/ 200lbs, 0.6m^2 frontal area and 0.75drag coefficient.
I don’t really know what I just witnessed as I lost you at the point where the legend ended but great work. It seems like based on those calculations the NGV board has pretty similar specs with 170ish kv quad hub motors running at either 6s or 12s
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^the hardest step was this…
i’ll admit i cheated…
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Haha, I use something like that in maths class when I can’t solve the answer and there isn’t an answer for me to check with. It’s called maths papa and it goes through all the steps, it’s rather helpful for rearranging things like that too
Fixed some minor issues, I know people with Microsoft Edge has some issues I will try to address them later on 
In mean time use real browser 
3 Likes
Really cool tool @Kug3lis! One suggestion I have is to add the formulas for how things are calculated either on the side, or as tooltips.
Specifically, I’m still confused as to how the estimated range is calculated. Reading this thread has made me no wiser on how much usuable WH a battery pack might have, and none of my guesses have matched the answer I get from the calculator
Ur battery Wh / (avg consumption next to motor * motor configuration)
Yup! Checks out! If that’s true, then pretty crazy that having dual motors reduces range in half! Too bad I don’t have a bluetooth module to test this myself. Thanks!
Do you count this way your car tank mileage too?
Normally people use their average miles/galon Wh/mi or etc number to determine their range as that average number is based on their driving style and hardware
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@rusins …we can say that dual motors extends the range at constant speed for a given mechanical load (compared to single) because the total copper losses are cut in 1/2 (each motor needs half the motor current, which equates to ((1/2)^2 * 2) = 1/2 the losses…
Yeah, that’s what I would have expected. I guess riding style from dual motors is what does the opposite?
@rusins what speed and quantity of mechanical watts are required for the range you want to calculate? and what is your kv, gear ratio, wheel size & # motors?
Why you need to know? I was just playing around with the calculator, I don’t know the mechanical load off the top of my head.
Can the left side build config module be sticky when you scroll down in desktop mode? I want to be able to see stuff on the motor module for example, and modify the config to see what changes without having to scroll up again.
That or could you compress the right side modules so that we don’t have to scroll.
2 Likes
I like this idea, would make it easier to see how things affect the outputs