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We assess the uncertainty with which a balloon-borne experiment, nominally called Tau Surveyor ($τS$), can measure the optical depth to reionization $σ(τ)$ with given realistic constraints of instrument noise and foreground emissions. Using a $τS$ fiducial design with six frequency bands between 150 and 380 GHz with white and uniform map noise of 7 $μ$K arcmin, achievable with a single mid-latitude flight, and including Planck's 30 and 44 GHz data we assess the error $σ(τ)$ obtained with three foreground models and as a function of sky fraction $f_{\rm sky}$ between 40% and 54%. We carry out the analysis using both parametric and blind foreground separation techniques. We compare $σ(τ)$ values to those obtained with low frequency and high frequency versions of the experiment called $τS$-lf and $τS$-hf that have only four and up to eight frequency bands with narrower and wider frequency coverage, respectively. We find that with $τS$ the lowest constraint is $σ(τ)=0.0034$, obtained for one of the foreground models with $f_{\rm sky}$=54%. $σ(τ)$ is larger, in some cases by more than a factor of 2, for smaller sky fractions, with $τS$-lf, or as a function of foreground model. The $τS$-hf configuration does not lead to significantly tighter constraints. Exclusion of the 30 and 44 GHz data, which give information about synchrotron emission, leads to significant $τ$ mis-estimates. Decreasing noise by an ambitious factor of 10 while keeping $f_{\rm sky}$=40% gives $σ(τ) =0.0031$. The combination of $σ(τ) =0.0034$, BAO data from DESI, and future CMB B-mode lensing data from CMB-S3/S4 experiments could give $σ(\sum m_ν) = 17$ meV.