Re: Calculus problems

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Mark Fergerson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <mfergerson1-at-cox-dot-net>

Tesla list wrote:
> 
> Original poster: "Jim Lux by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<jimlux-at-earthlink-dot-net>
> 
> A straight forward one:
> 
> What is the length of the primary winding for a given number of turns and
> spacing? Easiest is for a flat or cylindrical coil, a bit trickier is for a
> conical shape.  Hint: use r=k*theta and integrate in terms of theta.
> 
> A classic differential equation one:
> 
> What is the voltage on the primary capacitor as it charges through a
> resistor/inductor just before the spark gap fires.
> 
> An even more classic differential equation
> 
> What is the voltage and/or current in the primary (without considering fixed
> voltage drop across spark gap, or effect of coupled secondary)

  For some reason I didn't see the
origianl post, but I agree the quoted
text below _does_ seem to be asking for
real-world problems, not textbook
recommendations.

  I never did "get" calculus, but I can
think of a few semi-practical apps that
look amenable to it.

  Frinst, s'pose you wanted to wind a
secondary on the bottom half of a 2'
diameter spherical hollow fiberglass
coil form, with a coil radius at the
bottom pole of say, 2" with 22 ga. wire.
Topload is a toroid sitting on top of
the coil rim, 4" minor dia. Bottom of
coil grounded to a 5' Cu pipe, which
stands centered on a 3' dia. Cu ground
plane.

  Find: number of turns, inductance and
capacitance of the coil w/wo toroid,
resonance frequency w/wo toroid, voltage
and current profiles w/wo toroid (all
for close-, constant-spacing 1 wire
dia.-, and Archimedes- wound), max V
without arcing to ground plane in dry
air at STP.

  S'pose you want to wind a spiral
secondary: 2' dia., 22 ga., 2" center
hole, 4" minor diameter (major dia to
slip-fit coil rim) toroid. Center
grounded as above.

  Find values as above.

  (Extra credit)

  Think about primaries for these coils.
Which would you use; flat spiral, cone,
solenoid, or some other shape, and why?
Where would you put them, and why? Where
would you put the gap, and why?

  (I've read enough textbooks to get the
style, just not the substance) ;>)

  Mark L. Fergerson

> > ...What Im asking is for
> > applications in Engineering OR tesla coils that use Calculus Problems.I
> can understand math when it has a direct use such as a problem I need to
> figure for a telsa coil or something.