Suggestion: The following could be considered:
References:
1. Giacoletto L. J. "Electronics Designers' Handbook," 2nd Edition, McGraw-Hill Book Co., 1977
2. Warrington A. R. van "Protective Relays Their Theory and Practice," Volume I, Chapman & Hall, Ltd., 1971
Relay voltage range estimation:
1. Constraint: AWG B&S Wire Gage 39 has an operating current of Idc=0.01264 Amp listed in Table 3.14, Reference 1. This implies DC voltage (assuming that the relay has a solid iron core suitable for DC magnetization/operation):
Edc=Rdc x Idc=3,384 x 0.01264=42.77VDC
2. Constraint: The DC coil imput parameters Idc and Edc must develop relay operating force greater than 5oz relay spring force.
Elementary formula for the force F, magnetic induction (flux desity), length of wire L, and current I in the coil:
F=B x I x L which has to be properly applied to the relay coil magnetic geometry.
Reference 2 indicates "pull force F" Equation (2.10) on page 2.4 as
F=(2 * (pi) * (N * Idc)**2 * A)/(x**2)
where
F=force
Pi=3.14
N=coil turns
Idc=coil current
A=pole face gap area
x=air gap at the pole center
**2=exponent 2
Take-off appropriate relay parameters and substitute them into the above formula to make sure that the Idc is adequate to develop F > 5 oz