SI torque & power

JimmyJazz

1 mW
Joined
Sep 1, 2016
Messages
11
Good day. I followed a link to the Sur-Ron page and noticed this image:

SUR-RON-180-B-SERIES-GRAPH.jpg


I noticed that the torque & power lines crossed at roughly 1500 rpm. I thought, "Hmm, that's interesting. I'm used to the imperial formula of (lb.ft. * rpm)/5252 = hp, but I now realise I don't know the corresponding SI formula that would be more useful in the electric world. Let's see if I can recreate it." And of course, I'm having trouble doing so.

First I just subbed in the torque & power units with their conversion constants:

1 lb.ft. = 1.356Nm

1 hp = 0.7457kW

(1.356Nm * rpm)/5252 = 0.7457kW

Then I just started dividing out constants to pare the 5252 down to the new crossover RPM, where metric torque & power should coincide:

(1.356Nm * rpm)/3916 = kW

(Nm * rpm)/2888 = kW

My 2888 crossover point would seem to be about double what the Sur-Ron graph shows. When I try a sanity check using their chart, I get this:

(24.5Nm * 1500rpm)/2888 = 12.73kW, versus the roughly 3500 watts that they show.

What am I missing? Everything on their graph seems to be zero-indexed, so it's not like I'm being fooled by misleading advertising or anything. Did I make a stupid math error or something? I tried reverse engineering the imperial formula to see where the 5252 comes from, knowing that 1 hp = 550 lb.ft./s, but I was having trouble when I went to discombobulate "rpm" -- uhh, 2*pi radians per 60s, or what? I was lost. lol I feel like I'm getting stupid as I age. Can anybody help me here?

Thanks,
Jim "JimmyJazz" Jones
Calgary, Alberta, Canada
 
You're just missing one small thing: rotational speed should be in radians per second (rad/s) for SI units, rather than rpm. There are 2*pi radians in a circle. so rpm / 60 x 2pi.

I.e.

JimmyJazz said:
(24.5Nm * 1500rpm)/2888 = 12.73kW, versus the roughly 3500 watts that they show.

1500rpm = 157.1 rad/s

24.5Nm x 157.1 rad/s = 3848W



Or if you want to stay with RPM you can use a conversion constant, just like the 5252 for HP:

Power (kW) = Torque (N.m) x Speed (RPM) / 9.5488


Online calculators always useful to check your working:

http://www.wentec.com/unipower/calculators/power_torque.asp
https://planetcalc.com/1908/
 
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