  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 $\Lambda$ is such a carpet, and certain natural irrationality
conditions hold, then every orthogonal projection of $\Lambda$ in a
non-principal direction has Hausdorff dimension $\min(\gamma,1)$, where
$\gamma$ is the Hausdorff dimension of $\Lambda$. This generalizes a recent
result of Peres and Shmerkin on sums of Cantor sets.
