Page 1 of 1

### Estimating accelerations?

Posted: Jun 30 2015 7:28pm
I'm trying to estimate acceleration times, and as long as my math is right hopefully it'll be helpful for others too. Someone mind helping me double check the physics?

Question: how long does it take you to reach top speed if you weigh 200 lbs and are running a 6s LiPo setup with a Turnigy SK3 6374 motor (170 kV, 70 A "max current" quoted on HobbyKing, which I take to mean the stall current) and 83mm wheels, geared at 1.84:1 for a theoretical top speed of roughly 20 mph. First lets verify the gearing ratio gets us to the right top speed:

s_max = V_max * kV * gearing ratio * wheel circumference
s_max = 6 cells * (3.7 V/cell) * (170 motor rpm/V) * (1 wheel rpm / 1.84 motor rpm) * (Pi * 83 mm/revolution) * (0.001 m/mm) * (1 mi / 1609 m) * (60 min / hour)
s_max = 20 mph

Moving on, some unit conversions on the motor's kV constant tells us its torque constant:

kT = 1 / kV
kT = (1 volt / 170 rpm) * (W / A*V) * (N*m / s) * (1 rotation / 2 Pi rad) * (60 sec / 1 min)
kT = 0.0562 N m / A

Calculating the torque at the wheel is a matter of combining this torque constant, the motor's max current draw, and the gearing:

T_max = kT * A_max * gearing ratio
T_max = 0.0562 N*m / A * (70 A) * (1.84 wheel torque / 1 motor torque)
T_max = 7.24 N*m

Calculating the rate of acceleration is simple Newtonian physics:

a = F / mass = T_max / (wheel radius * mass)
a = (7.24 N*m) * (1 / 41.5 mm) * (1 / 200 lb) * (1000 mm / m) * (2.2 lb / kg)
a = 1.92 m/s^2

20 mph is 8.94 m/s, so at 1.92 m/s^2 it should take you (8.94 / 1.94) = 4.65 s.

All of this is of course assuming that we live in a frictionless, spherical vacuum yada yada...

Anything look glaringly wrong to you? Seems pretty quick, given that a reasonably fast family-car hits 0-60 mph in ~6 seconds. 5 seconds to get to cruising speed seems very resasonable, especially for such an underpowered design compared to what people here are building.

I'm guessing that my assumption that kT is constant with respect to motor speed could be wrong.

### Re: Estimating accelerations?

Posted: Jun 30 2015 8:12pm
kT's a constant, but your applied torque will fall as speed rises.

If your torque was always equal to T_max you wouldn't have a top speed. ### Re: Estimating accelerations?

Posted: Jun 30 2015 10:07pm
Hah good point. What do you mean by applied torque, and quantitatively, how is it related to speed?

### Re: Estimating accelerations?

Posted: Jun 30 2015 10:19pm

### Re: Estimating accelerations?

Posted: Jun 30 2015 11:47pm
I did some real world testing that you might be interested in, I also made a video and posted it on youtube back when I was doing lots of motors & drive train testing, check it out.