Drag and buoyancy are two primary external forces acting on diving marine mammals. The strength of these forces modulates the energetic cost of movement and may influence swimming style (gait). Here we use a high-resolution digital tag to record depth, 3-D orientation, and sounds heard and produced by 23 deep-diving sperm whales in the Ligurian Sea and Gulf of Mexico. Periods of active thrusting versus gliding were identified through analysis of oscillations measured by a 3-axis accelerometer. Accelerations during 382 ascent glides of five whales (which made two or more steep ascents and for which we obtained a measurement of length) were strongly affected by depth and speed at Reynold's numbers of 1.4-2.8x10(7). The accelerations fit a model of drag, air buoyancy and tissue buoyancy forces with an r(2) of 99.1-99.8% for each whale. The model provided estimates (mean +/- S.D.) of the drag coefficient (0.00306+/-0.00015), air carried from the surface (26.4+/-3.9 l kg(-3) mass), and tissue density (1030+/-0.8 kg m(-3)) of these five animals. The model predicts strong positive buoyancy forces in the top 100 m of the water column, decreasing to near neutral buoyancy at 250-850 m. Mean descent speeds (1.45+/-0.19 m s(-1)) were slower than ascent speeds (1.63+/-0.22 m s(-1)), even though sperm whales stroked steadily (glides 5.3+/-6.3%) throughout descents and employed predominantly stroke-and-glide swimming (glides 37.7+/-16.4%) during ascents. Whales glided more during portions of dives when buoyancy aided their movement, and whales that glided more during ascent glided less during descent (and vice versa), supporting the hypothesis that buoyancy influences behavioural swimming decisions. One whale rested at approximately 10 m depth for more than 10 min without fluking, regulating its buoyancy by releasing air bubbles.