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Re: Wheeler

Jim Monte wrote:
> 
> Hi Ed,
> 
> I would be interested in the formulas you have along with their claimed
> accuracies.  Would you post them to tesla-at-pupman-dot-com or send them to me
> via private Email?  Thanks.
> 
> Jim Monte
> 
> >Date: Sat, 09 Jan 1999 09:11:21 -0700
> >To: tesla-at-pupman-dot-com
> >Subject: Re: Wheeler (Number of turns for a secondary?)
> >Original Poster: Ed Phillips <evp-at-pacbell-dot-net>
> >
> <snip>
> >
> >       Wheeler's approximation works within very acceptable accuracy for
any
> >coil geometry you will encounter in TC work.  I have much more accurate
> >expressions here, in case anyone wants one.  The limit on your accuracy
> >may well be the accuracy with which you really know the coil dimensions.
> >
> >Ed
> >
> >

Jim:  

	Hope the attachment comes through.  Sending it to pupman as well, for
those others who may be interested.  By the way, still think precision
in inductance calculation is intellectual simulating, but a waste of
time in practical Tesla coil design and/or analysis.

Ed
' THE FOLLOWING MATERIAL INCLUDES A QUICK BASIC PROGRAM TO COMPUTE
' AND COMPARE VARIOUS INDUCTANCE FORMULAE, AS WELL AS COPIES OF
' SOME FORMULAE FROM RADIOTRON DESIGNER'S HANDBOOK.  THE LATTER
' HAVE NOT BEEN CHECKED FOR ACCURACY OF TRANSCRIPTION.

' ALL EXPRESSIONS GIVE THE INDUCTANCE IN MICROHENRIES, AND DIMENSIONS ARE
' IN ENGLISH UNITS.  THE DIAMETER IN ALL CASES IS THE MEAN/AVERAGE DIAMETER OF
' THE COIL WHICH IS EQUAL TO THE FORM DIAMETER PLUS THE WIRE DIAMETER.

' QUICK BASIC PROGRAM:
'
' THIS IS INDUCTANCE, A PROGRAM TO CALCULATE CURRENT SHEET INDUCTANCE
' BASED ON EXPRESSION FOR NAGAOKA'S CONSTANT IN
' LETTER FROM RICHARD LUNDIN, PROC. IEEE, V75 #9, 9/85, PP1428-1429
' STATED TO BE GOOD TO 3 PPM
' LET:
'    D = MEAN DIAMETER (INCHES)
'    L = LENGTH (INCHES)
'    X = D/L
'    X2 = X^2 = (D/L)^2
'    N = NUMBER OF TURNS
' THEN:
'  FOR LONG COILS (L/D> 1)
'    A = (1+.383901*X2+.017108*X2^2)/(1+.258952*X2)
'    A = (1+.383901*(D/L)^2+.017108*(D/L)^4)/(1+.258952*(D/L)^2)
'    K = A - 0.42441318*X
'    K = (1+.383901*(D/L)^2+.017108*(D/L)^4)/(1+.258952*(D/L)^2)
'    K = K - 0.42441318*D/L '*EQUATION EDITED TO AVOID LINE WRAP
'   INDUCTANCE = .0250688*D*X*N^2*K MICROHENRIES
'  FOR SHORT COILS (L/D < 1)
'    A = (1+.383901*(1/X2)+.017108*(1/X2)^2)/(1+.258952*(1/X2))
'    B = (.093842*(1/X2)+.002029*(1/X2)^2-.000801*(1/X2)^3)
'    K=(.6366198#/X)*((LOG(4*X)-.5)*A+B)
'    OR
'    A = (1+.383901*(L/D)^2+.017108*(L/D)^4)/(1+.258952*(L/D)^2)
'    B = (.093842*(L/D)^2+.002029*(L/D)^4-.000801*(L/D)^6)
'    K=(.6366198#*(L/D)*((LOG(4*(D/L))-.5)*A+B))
'    AND AGAIN
'   INDUCTANCE = .0250688*D*X*N^2*K MICROHENRIES

QUICKBASIC PROGRAM:

PI=3.141592654#
BE:
CLS
DEF FNA(X)=(1+.383901*X+.017108*X^2)/(1+.258952*X)
DEF FNB(X)=(.093842*X+.002029*X^2-.000801*X^3)
DEF FNF(X)=1000/(2*PI*SQR(X))

GETPAR:
INPUT "DIAMETER, LENGTH, (INCHES) AND NUMBER OF TURNS"; D,L,N
X=D/L
X2=X^2
IF X<1 THEN LT1
K=(.6366198#/X)*((LOG(4*X)-.5)*FNA(1/X2)+FNB(1/X2)) 'L<D
A = (1+.383901*(L/D)^2+.017108*(L/D)^4)/(1+.258952*(L/D)^2) 
'TEST SHORT COIL FORMULA
B = (.093842*(L/D)^2+.002029*(L/D)^4-.000801*(L/D)^6)
K=(.6366198#*(L/D)*((LOG(4*(D/L))-.5)*A+B))
LS = .0250688*D*X*N^2*K 'TEST SHORT COIL FORMULA

GOTO CALCL
LT1: 
' TEST LONG COIL FORMULA
K=FNA(X2)-.42441318#*X    'LENGTH>DIAMETER
KT = (1+.383901*(D/L)^2+.017108*(D/L)^4)/(1+.258952*(D/L)^2) 
KT = - .42441318#*D/L ' *EDITED TO ELIMINATE LINE WRAP
LT = .0250688*D*X*N^2*KT 'MICROHENRIES 

CALCL:
IND=.0250688*D*X*N^2*K    ' INDUCTANCE IN MICROHENRIES
WHI=D^2*N^2/(18*D+40*L)   ' WHEELER'S APPROXIMATION
CD=2.54*D*(.1126*L/D+.08+.269*SQR(D/L))  ' MEDHURST'S FORMULA
X=IND*CD
FSR=FNF(X)
PRINT "DIAMETER =";D" INCHES, LENGTH =";L" INCHES, INDUCTANCE = "IND"
MICROHENRIES
PRINT "LT =";LT  'TEST LONG COIL FORMULA
PRINT "LS =";LS 'TEST SHORT COIL FORMULA
PRINT "WHEELER'S INDUCTANCE =";WHI" MICROHENRIES"
PRINT "DISTRIBUTED CAPACITANCE =";CD"MMFD"
PRINT "SELF-RESONANT FREQUENCY =";FSR;"MHz"
PRINT "WHEELER/"TRUE" =" WHI/IND
INPUT "EXTERNAL CAPACITANCE =";CX
C=CD+CX
X=IND*C
FSRX=FNF(X)
PRINT "FINAL SELF-RESONANT FREQUENCY =";FSRX"MHz"
GOTO GETPAR
END
'*********************************************************


' ALL OF THE FORMULAE HERE, BOTH ABOVE AND BELOW, GIVE THE "CURRENT SHEET"
' INDUCTANCE, WHICH DIFFERS FROM THE TRUE INDUCTANCE..  LET THE INDUCTANCE BE
' "L".
' TO GET THE "TRUE" LOW-FREQUENCY INDUCTANCE  IT IS NECESSARY TO 
' APPLY CORRECTIONS FOR WIRE DIAMETER AND SPACING.  THE FOLLOWING
' IS TAKEN FROM RADIOTRON DESIGNER'S HANDBOOK, 3RD EDITION, PAGES
' 141 AND 144.  THE TRUE INDUCTANCE Lo IS DETERMINED AS FOLLOWS:
' Lo = L - 0.0319 * aN * (A+B)
' WHERE
' a = D/2 = RADIUS OF COIL OUT TO CENTER OF THE WIRE (in)
' N = TOTAL NUMBER OF TURNS
' A & B ARE GIVEN APPROXIMATELY FROM THESE "SLIDE RULE" VALUES:
' A = 2.3* LOG10 (1.73 S) (ACCURATE WITHIN 1% FOR ALL VALUES OF S)
' B = 0.336 * (1- (2.5/N) + (3.8/N^2))
' ACCURATE WITHIN 1% WHEN N IS NOT LESS THAN FIVE TURNS.  THE
' VALUE OF B (NOT THE INDUCTANCE DERIVED FROM IT) IS ABOUT 5%
' HIGH AT N=4 AND 20% HIGH AT N=3.
'
' SOME OTHER INDUCTANCE FORMULAS FROM THE SAME CHAPTER:
'
' "STANDARD WHEELER'S FORMULA:
' INDUCTANCE = D*N^2/(18+40*L/D)
' STATED TO BE ACCURATE WITHIN 1% FOR ALL VALUES OF D/L LESS THAN
' 3.  (L/D FROM 0.333 TO INFINITY.)
'
' ANOTHER MORE ACCURATE FORMULA:
' INDUCTANCE = 0.252 * D^2 * N^2 / ((10*L)*(1 + 0.46 * (D/L))
' ACCURATE WITHIN 0.1% FOR ALL VALUES OF D/L BETWEEN O.2 AND 1.5.
' (LENGTH/DIAMETER FROM 0.667 TO 5.
'
'
' FOR SHORT SOLENOIDS
' L = a^2 * N^2 / (9 - (a^2/5*L) + 10 * L)
' ACCURATE TO 2% FOR ALL VALUES D/L FROM 0 TO 20. (LENGTH/DIAMETER FROM
0.05 TO
' INFINITY.
'
' **** I HAVE PARAPHRASED SOME OF THESE FORMULAE IN MOVING
' THEM HERE, AND HOPE I HAVEN'T MADE A MISTAKE.  WILL CHECK IN
' THE FUTURE WHEN I HAVE SOME MORE TIME.