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Fig. 12. Numerical model for force balance in freely flying fruit flies. (A) Forces produced by the flying insect and forces acting on the fly body during flight on a curved path. Total flight force F_t is equal to the vector sum of horizontal (F_h), vertical (F_v) and lateral forces (F_l). (B) Total force of each fly and the corresponding force components within the flight recordings that fell within the top 10% maximum of total force. Data are sorted after F_t for all 131 tested animals. (C) Minimum flight path radius at a given forward velocity and level flight, shown for four estimates of total flight force. (D) Alterations in vertical climbing velocity when horizontal flight velocity is kept constant at 0.6 m s^–1. Grey indicates path radii at which the fly loses flight altitude while turning. The numerical model predicts that at 0.6 m s^–1 forward speed fruit flies may only support their body weight when the flight path radius exceeds 50 mm (dotted line). F_g, gravitational force (body weight); CoR, centre of radius of a flight turn; r, radius of the flight path; u_l, lateral (side-slip) velocity; u_h, horizontal velocity; u_v,max, maximum vertical velocity.

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