Torque BS Filter - explained

[Stephen Dubovsky]

...
>:By definition:
>:Horsepower = (rpm * Torque) / 5252
>:
>:Thus, at 5252 RPM, HP = 5252*Torque/5252 = Torque
>
>
>Please don't stop now., the bulbs are going off....  What are the units
>used to get the 5252 number?
>
...

  Ok, Ill try to get all of this right;)

  By definition Force = mass * acceleration (F=m*a) (Ill work in the metric
system first and give the conversions later - soory, Im a 'new' math kind
of person) so Newtons (N) = kg * a which will have units of kg*(m/sec^2)=N.

  Torque is force times a distance (NOT a distance traveled, but how far
away the force is applied.  i.e. 1 lb-ft is 1 lb of force applied on a
lever/bar 1 ft away).  So T (in Newton meters (Nm)) = N * m which will
carry the units of kg*m^2/sec^2 (which is exactly 1 Nm - isn't the SI
system great;).

  Rpm is a is an angular rate of change (has units of 1/sec - actual
constant is 1/(60*sec)).

  Work (Joules) is Force times a distance traveled (apply 1 N of force to
move something 1 m = 1 joule or work).  
  
  Now Power is the rate at which you do work.  Watt = joule/sec = N*m/sec =
kg*m^2/sec^3

  So if you have a motor rotating at 'x' rpm w/ 'y' Nm of torque.  You have
'y' N of force (at 1m) traveling 2*pi*1m (the circumference of a 1m radius
circle) every 1/(60*sec).
x*rpm * y*Nm/m * 2*pi*m = 
[x * 1/(60*sec)] * [y * kg*m/sec^2] * [2*pi*m] =
x*y * (2*pi/60) * kg*m^2/sec^3 = 
x*y * (2*pi/60) * watt

i.e. 1000rpm and 500Nm -> 1000*500*(2*pi/60) = 52360 watts of power

So for you non SI guys:
1 lb*ft = 1.356 Nm
1000 * watt (1 kW) = 1.341 hp
1 hp = 745.7 watts

And:
So, 'x' rpm and 'y' lb-ft yield:
x * y*1.356 * 2*pi/60 * (1/745.7) = 
x * y * 1.9042*10^-4 = hp 

The above example becomes 1000rpm and 500 Nm = 369 lb*ft
1000*369*1.904*10^-4 = 70.2 hp (which is the same as 52360Watts/745.7)

The reciprocal of the constant yields the magical 5252 rpm number.

Nuf' physics for everybody?  I hope I got everything right.  Please flame
me if I left something out, or got it wrong;)
SMD

---
Stephen Dubovsky
dubovsky at vt.edu
95 Yamaha FZR600 - to go fast
83 Porsche 911SC - to go a little faster
84 Jeep Cherokee - to haul things that go fast