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The Hausdorff dimension of the projections of self-affine carpets

We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if $Λ$ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of $Λ$ in a non-principal direction has Hausdorff dimension $\min(γ,1)$, where $γ$ is the Hausdorff dimension of $Λ$. This generalizes a recent result of Peres and Shmerkin on sums of Cantor sets.