An idealized energy fluctuation model of a bird's body undergoing horizontal flapping flight is developed, focusing on the biomechanical power discernible to a body-mounted accelerometer. Expressions for flight body power constructed from root mean square dynamic body accelerations and wingstroke frequency are derived from first principles and presented in dimensionally appropriate units. As wingstroke frequency increases, the model generally predicts a gradual transition in power from a linear to an asymptotically cubic relationship. However, the onset of this transition and the degree to which this occurs depends upon whether and how forward vibrations are exploited for temporary energy storage and retrieval. While this may vary considerably between species and individual birds, it is found that a quadrature phase arrangement is generally advantageous during level flight. Gravity-aligned vertical acceleration always enters into the calculation of body power, but, whenever forward acceleration becomes relevant, its contribution is subtractive. Several novel kinematic measures descriptive of flapping flight are postulated, offering fresh insights into the processes involved in airborne locomotion. The limitations of the model are briefly discussed, and departures from its predictions during ascending and descending flight evaluated. These findings highlight how body-mounted accelerometers can offer a valuable, insightful and non-invasive technique for investigating the flight of free-ranging birds and bats.