We study the complexity of infinite-domain constraint satisfaction problems: our basic setting isthat a complexity classification for the CSPs of first-order expansions of a structure A can be transferred to aclassification of the CSPs of first-order expansions of another structure B. We exploit a product of structures (thealgebraic product) that corresponds to the product of the respective polymorphism clones and present a completecomplexity classification of the CSPs for first-order expansions of the n-fold algebraic power of (Q; <). This is provedby various algebraic and logical methods in combination with knowledge of the polymorphisms of the tractable firstorder expansions of (Q; <) and explicit descriptions of the expressible relations in terms of syntactically restrictedfirst-order formulas. By combining our classification result with general classification transfer techniques, we obtainsurprisingly strong new classification results for highly relevant formalisms such as Allen’s Interval Algebra, then-dimensional Block Algebra, and the Cardinal Direction Calculus, even if higher-arity relations are allowed. Ourresults confirm the infinite-domain tractability conjecture for classes of structures that have been difficult to analysewith older methods. For the special case of structures with binary signatures, the results can be substantiallystrengthened and tightly connected to Ord-Horn formulas; this solves several longstanding open problems from theAI literature.