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We report numerical simulations based on normal coupled mode theory of the fundamental-mode loss and backscattering induced in air-core fibers by random longitudinal perturbations of the core diameter. To quantitatively explain the measured loss of ~24 dB/km at 1550 nm of air-core fiber HC-1550-02 from crystal fibre, these simulations predict that the autocorrelation function of the perturbation is close to an exponential and characterized by a ratio D/sigma2 of ~2.36 times 1013 m-1, where D is the characteristic length and sigma the amplitude of the perturbation. This analysis yields a characteristic perturbation length for this fiber in the range of ~1 to ~30 cm. That this is much shorter than in a conventional fiber is consistent with the slower speeds at which air-core fibers are pulled, which reduces the length of the fiber perturbations. The same exponential perturbation and D/sigma2 ratio also predict that the backscattering coefficient for the fundamental mode of this fiber is 1.5 times 10-9 mm-1, which agrees well with a measured value. When applied to a 19-cell air-core fiber from the same manufacturer (HC19-1550-01) the same perturbation predicts a loss of 4 dB/km, which agrees with the measured range of 1.2 to ~10 dB/km. These independent agreements between modeled and measured loss and backscattering coefficients and the reasonable predicted range of perturbation lengths confirm that core dimension variations are the dominant mechanism behind the loss and backscattering of current air-core fibers.