Design data for VDGRF experimenters (fwd)

[Steven Roys <sroys@xxxxxxxx>]

---------- Forwarded message ----------
Date: Wed, 21 Jan 2004 00:00:52 -0600
From: Dr. Resonance <resonance@xxxxxxxxxx>
To: High Voltage list <hvlist@xxxxxxxxxx>
Subject: Design data for VDGRF experimenters


I'm posting some design data for Van de Graaff designers and experimenters:


The spark discharges occur as "bright" with a lot of capacitance and "weak" with less capacitance due to small ground terminals, etc.

Bright spark output to insulating column ratio:

    Bs / Tl  = 2.3:1 ratio   (43%) where:

Bs = bright spark length in inches

Tl = tube length in inches



Weak spark output to insulating column ratio:

    Ws / Tl = 1.4:1 ratio  where:

Ws = weak spark length in inches



HV main terminal to ground ball ratio for bright & long sparks:

    Tm / Tg = 2.4:1   (40%) where:

Tm = main terminal dia in inches

Tg = ground terminal dia in inches



Belt length required for best output (up to 1  MEV):   note:  This assumes a good HV terminal dia as well.

    Tm / Bw =  3.7:1  (27%) where:

Tm = main terminal dia in inches

Bw = belt width in inches            (assumes belt speed of 60-100 ft/sec)



    Q = CFRS    where:

Q = belt speed in ft/sec

F = .0833  (conversion factor)

R = pulley speed in rev/min (RPM)

C = pulley circumference in inches

S = .0167  (conversion factor based on 1 min/60 sec)



also,  R = Q/(1.39x10e-2 x C)



and Q = DR(.00437)  where:

D = pulley dia. in inches

R = pulley rev/min (RPM)



Io =  (R x M/B x 1 min/60 sec x C x W) / k   where:

Io = max theorectical output in microAmperes

R = rev/min  (RPM)

M = belt pulley dia. in inches

B = motor pulley dia. in inches

W = belt width in inches

C= belt pulley circumference in inches

k = 50 in^2/sec  (to produce 1 uA of DC current)


In practice one can assume approx 80% of above theorectical value.


Total stored charge on the HV terminal:

Q = CV  where:

Q = stored charge in Coulombs

C = capacitance in Farads

V = potential difference in Volts


and,  peak current in Amperes is:

I = Q/t  where:

I = current in Amperes

t = time in seconds  (assume 1 x 10e-6 average time)


Charging time for the HV terminal is:

t = Q/Itg where:

t = time in seconds

Q = stored charge in Coulombs

Itg = maximum terminal to ground current

note, the inverse of the above will give you the number of sparks/sec from the HV terminal.


Most air-insulated VDGRF's require only 7 kV DC at 1 mA to achieve full charge on a belt width of 1 inch through 20 inches.

Be absolutely sure that the spray screen is equal to or less than 80% of the belt width.  This prevents charge from "leaking" at the corners of the screen directly to the metal pulley.  Short the HV terminal to ground and observe this in a very dark room --- you should see a completely uniform blue corona across the entire belt --- and not just corona spray at the edge of the screen to the pulley (poor performance).



Dr. Resonance

Resonance Research Corporation
E11870 Shadylane Rd.
Baraboo   WI   53913