Mike Keitz wrote:

> If the "NDT equipment" is effectively a resistor, then the solution
> for RMS power delivered

  I know I am being picky, but can we please refrain from this fetish of
referring to the *meaningless* term "RMS power"?  Use of this term
indicates an essential lack of grasp of the situation in question!
Let's just look at it calmly:

  An RMS Voltage or Current is ONE WHICH results in a certain MEAN
power.  In a steady-state situation, we can assume we are referring to
the heating effect integrated over a large number of cycles and consider
the integral over one half or full cycle.  If the load is essentially
resistive, it is straightforward to perform this integral as Mike noted:

> ... just to integrate sin^2(x) over ranges up to a complete half
> cycle:
>       > x=pi
POWER = | sin^2(x) dx
>       < x=f

>       ^ (ASCII integral sign)

> where f is the firing angle from 0 (earliest firing, maximum power) to
> pi (latest firing, minimum power).  As a check, the result for f=0
> should be sqrt(2)/2 (maybe half that since it is a half cycle)

  No, it is sine SQUARED, so no square root.  The integral for a half
cycle should be pi/2, and I seem to recall the formula as pi(cos(x)+1)/2

  Graphically, the sin^2(x) is visualised as a full inverse cosinewave
of amplitude 1/2 bounded by zero and 1 and extending from zero to half a
cycle which is pi radians.  The full area bounded is therefore pi, and
the curve is entirely symmetrical so the area underneath it is pi/2.  In
practice, you normalise this to your full power level.

  Note that I keep referring to power, since that is what lights the
lamps, not RMS voltage.  Even then, the effective lamp brightness is not
a linear function.  Please however FORGET RMS and forget voltage (other
than the RMS value of the sinewave going in, used for full-scaling)!

  To calculate the phase table, simply match (cos(pi*x)+1)/2 which is
scaled from 0 to 1 (proportional power); against values of x from 0 to
1 (phase angle scaled to a half cycle).  I would reckon QBASIC the
easiest tool to use for this, NOT C.  Perhaps QBASIC fits the
description of "a general-purpose math package" anyway?

  Cheers,
        Paul B.