Abstract We assess the uncertainty with which a balloon-borne experiment, nominally called Tau Surveyor ( τ S), can measure the optical depth to reionization σ ( τ ) with given realistic constraints of instrument noise and foreground emissions. Using a τ S 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 midlatitude 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 sky between 40% and 54%. We carry out the analysis using both parametric and blind foreground separation techniques. We compare the σ ( τ ) values to those obtained with low-frequency and high-frequency versions of the experiment called τ S-lf and τ S-hf, which have only four and up to eight frequency bands with narrower and wider frequency coverage, respectively. We find that with τ S, the lowest constraint is σ ( τ ) = 0.0034, obtained for one of the foreground models with f sky = 54%. σ ( τ ) is larger, in some cases by more than a factor of 2, for smaller sky fractions, with τ S-lf, or as a function of foreground model. The τ S-hf configuration does not lead to significantly tighter constraints. The exclusion of the 30 and 44 GHz data, which give information about synchrotron emission, leads to significant τ misestimates. Decreasing noise by an ambitious factor of 10, while keeping f sky = 40%, gives σ ( τ ) = 0.0031. The combination of σ ( τ ) = 0.0034, baryon acoustic oscillation data from DESI, and future cosmic microwave background B-mode lensing data from the CMB-S3/CMB-S4 experiments could give σ (∑ m ν ) = 17 meV.