Ancient History

[Chuck Tomlinson]

>I believe the point that is trying to be made is that if HP = Torque 
>only at 5252 (which is agreed).  

True.  If power is measured in hp and torque in lb-ft, then the 
torque and power curves must cross at 5252 rpm.  No exceptions.

>Then this is the only place where 
>they CAN both be a maximum.  Not that they are a maximum.  But that 
>this is the only point where they can both be a maximum at the same 
>time.

Not true.  At peak hp, the torque vs rpm curve has a slope equal 
to (-Torque/rpm). That's the only requirement.  So if the torque 
curve peaks at some rpm and assumes that negative slope immediately 
after the peak, then hp and torque will both peak at that rpm.  In 
theory, that can occur at any rpm.

In practice, it is unlikely to happen at all.  Having peak hp and 
torque at the same rpm means that the torque curve *must* have a 
discontinuity in its slope.  IMHO, this is so unlikely that it's 
difficult for me not to use the word "impossible".

Math crap follows...

P(ower) = T(orque) * n(rpm) * k(constant).  In USCS, k = 1/5252.

P = T * n * k.  At peak hp, power curve's slope dP/dn = 0.  

But dP/dn = k * d(T.n)/dn = k * (T + (dT/dn * n))

So dP/dn = 0 when dT/dn = -T/n

--
Chuck Tomlinson