  We perform a Fisher matrix calculation of the predicted uncertainties on
estimates of the cosmic string tension Gmu from upcoming observational data
(namely, cosmic microwave background power spectra from the Planck satellite
and an idealized future polarization experiment). We employ simulations that
are more general than others commonly used in the literature, leaving the mean
velocity of strings, correlation length of the string network, and "wiggliness"
(which parametrizes smaller-scale structure along the strings) as free
parameters that can be observationally measured. In a new code, StringFast, we
implement a method for efficient computation of the C_l spectra induced by a
network of strings, which is fast enough to be used in Markov Chain Monte Carlo
analyses of future data. Performing a calculation with the string parameters
left free results in projected constraints on Gmu that are larger than those
obtained by fixing their values a priori, typically by a factor of ~2-7. We
also find that if Gmu is equal to the current observational maximum, Planck
will be able to make a confident detection of strings. However, if Gmu is two
orders of magnitude smaller, even a perfect, lensing-free measurement of
polarization power spectra will not be able to detect a nonzero string tension
at better than 2 sigma confidence.
