Forces and movement
To move, an animal must push on something, the ground, the water or the air, and that thing pushes back (Newton’s third law). At the same time it has to support its weight and overcomedrag, the resistance of the fluid it moves through. When the forces balance, the animal moves at a steady speed; when they do not, it speeds up, slows down, climbs or sinks (Newton’s first and second laws).
Flying
A bird’s wing is curved and tilted slightly upwards (the angle of attack). As it moves forward it deflects air downwards, and the air pushes the wing up: lift. Lift grows with the square of the speed and with the wing area, so slow birds need big wings. Flapping produces thrust to overcome drag. Tilt the wing too far and the airflow can no longer follow the upper surface; lift collapses in astall. Birds use stalls to land, and soaring birds such as albatrosses have long, narrow wings that make a lot of lift for very little drag.
Swimming
Water is about 800 times denser than air. This makes it easy to stay afloat but costly to push through, so fast swimmers such as tuna, dolphins and penguins have smooth, streamlined bodies tapering at both ends. Most fish swim by sweeping the tail from side to side, pushing water backwards; a fish typically moves forward about 0.6–0.8 of its body length with each tail beat. Bony fish have a gas-filled swim bladder that makes them neutrally buoyant; sharks lack one and must keep swimming, using oily livers and wing-like fins for lift.
Walking and running
When you walk, each leg acts like an upside-down pendulum: the body vaults over a stiff leg, swapping kinetic and potential energy. This only works up to a certain speed. Animals of all sizes, from mice to elephants, switch to running at about the same Froude number, around 0.5. Running uses springy tendons, which store and return energy like a pogo stick, and four-legged animals change to a trot and then a gallop at higher speeds.
Size matters
Small animals have huge strength for their size, can fall from great heights unharmed and can walk up walls, but drag and stickiness matter more to them. Large animals must support weight that grows faster than their bone and muscle strength, so elephants have pillar-like legs and cannot jump. Insects can hover easily; birds above about 15 kg cannot take off by flapping alone.
The formulas
Lift = ½ ρ v² S C_L · Drag = ½ ρ v² C_d A · Froude number Fr = v² ÷ (g × leg length)
ρ is the density of air or water, v the speed, S the wing area, A the frontal area, and C_L and C_d coefficients that depend on shape and angle. The simulator uses these with typical values for birds, fish and legged animals.
Key terms
- Lift / thrust / drag
- Upward force from the wings / forward force from flapping, swimming or pushing / resistance from the air or water.
- Streamlined
- Smoothly shaped to reduce drag.
- Gait
- A pattern of leg movement: walking, trotting, galloping.
Common misconceptions
- “Birds flap to push themselves up.” Flapping mainly provides thrust; wings moving through air make most of the lift.
- “Fish swim by pushing against the riverbed.” They push on the water itself.
- “Running is just fast walking.” It is a different mechanism, with a bouncing, springy body instead of a vaulting pendulum.
Key takeaways
- All locomotion relies on pushing back on the surroundings (Newton’s third law).
- Flight needs lift equal to weight and thrust equal to drag.
- Swimming is dominated by drag, so streamlining is vital.
- Animals switch from walking to running at a Froude number of about 0.5, whatever their size.
Model note: simplified formulas with typical coefficients. Real flight involves flapping wing motion, and real gaits vary between species.