In takeoff planning, which speeds define rotation, climb, and engine-out performance?

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In takeoff planning, three speeds define how you handle rotation, climb, and engine-out performance. Rotation is set by rotation speed, VR, which is the speed at which you initiate the nose-up rotation to lift off. After liftoff, you aim for a safe climb with one engine inoperative, which is the takeoff safety speed, V2, ensuring you can continue the takeoff and maintain a positive climb if an engine fails. Engine-out performance centers on the decision speed, V1—the point up to which you can reject the takeoff and still stop safely on the runway; after V1 you commit to takeoff and must be able to reach V2 for a safe climb with one engine out. These three speeds—VR for rotation, V2 for climb with an engine out, and V1 for engine-out decision—together define the takeoff performance envelope (with the usual ordering V1 < VR < V2). Other speeds like Vne/Vmo or Vs1 pertain to limits or stall, not this takeoff planning trio.