A rotary bag machine and method for making bags from a film are disclosed. They include a rotary drum, an accumulation nip, a blanket that positions the film against the drum, and a blanket tensioner located away from the accumulation nip. The drum includes at least one seal bar mounted thereon, and the accumulation nip provides the film to the drum. Various aspects include the accumulation nip being in a fixed position independent of changes of the drum diameter, and/or the path from the accumulation nip to the drum being fixed in length, independent of changes of the drum diameter. An accumulation sensor and a controller that controls the accumulation nip speed and the drum speed in response to the sensor are provided in one embodiment. The speed control is in response to the speed of the film, the rate of change of a function of the input, response history, and/or a setpoint, in various alternatives. A drawtape module and a powered unwind are disposed in a single module with the rotary drum, in another embodiment. A registration mark sensor is located upstream of the accumulation nip, along a path having a fixed length to the drum, in another embodiment. The sensor may be a print sensor.