Detailed experimental transmission properties of high numerical aperture air-clad undoped fibres are presented. Measurements of the angular transmissivity indicate a 15% lower numerical aperture (NA = 0.75) compared to theoretical predictions for the bridge thickness and wavelength ratio of δ/λ = 0.226. The discrepancy is attributed to skew rays that are deliberately launched and which are subject to larger loss rates through diffractive tunnelling in frustrated total internal reflection than meridional rays. Measurements of the angular propagation losses show that light launched at angles less than the critical angle for total internal reflection experiences low initial losses as well as low propagation losses. Light launched at steeper angles experiences a significant initial loss attributed to loss of skew rays within 1.5 m of propagation as well as larger general propagation losses.