Birds have evolved over millions of years to master the art of flight. Their ability to fly allows them to migrate long distances, forage over large areas, escape predators, and more. But staying aloft requires overcoming gravity and a variety of aerodynamic forces. Understanding the physics of bird flight begins with identifying the major forces at work.
Weight/Gravity
The pull of gravity on a bird’s mass exerts a downward force called weight. The weight force vector points straight down towards the earth. The magnitude of a bird’s weight depends on its mass. Heavier birds like swans have greater weight than lighter birds like hummingbirds. On the ground, weight supports the bird and must be counteracted to initiate flight. Once airborne, the lift force produced by the bird’s wings must equal its weight in order to maintain level flight. The weight force remains relatively constant during flight at a value equal to the bird’s mass multiplied by the gravitational acceleration constant (9.8 m/s2 on Earth).
Bird Weight Estimation
The weight of a bird can be estimated by measuring its mass. Mass is most easily found by weighing a bird on a scale. But it can also be estimated from the bird’s length and wingspan measurements. Researchers have developed regression equations relating mass, length, and wingspan for many bird species and groups. These allow estimating the weight of a bird too small, rare, or hard to catch for direct weighing. For example, the mass of many passerine species in grams can be estimated as:
Mass = 0.0305 * (Wing chord length in mm) ^ 1.911
Where wing chord is the distance from the wing’s leading edge to trailing edge. So for a songbird with a 60 mm wing chord, the estimated mass is:
Mass = 0.0305 * (60 mm) ^ 1.911 = 19.8 grams
Which corresponds to a weight force of 19.8 g * 9.8 m/s2 = 0.194 Newtons.
| Bird | Mass (g) | Weight Force (N) |
|---|---|---|
| Hummingbird | 3 | 0.029 |
| Sparrow | 24 | 0.235 |
| Bald Eagle | 4000 | 39.2 |
Thrust
Thrust is the forward-directed force that propels a bird through the air. It is generated by the flapping motion of the wings. On each downstroke, the wings push air backwards, according to Newton’s 3rd law producing an equal and opposite forward thrust force. Thrust must exceed drag in order for a bird to accelerate forward. The magnitude of thrust depends on the air density, wing shape, wing area, flapping speed and amplitude. Thrust varies throughout the flapping cycle, reaching its maximum mid-downstroke when wing velocity is highest.
Mechanisms of Thrust Production
There are several mechanisms by which flapping wings generate thrust:
- Drag Based Thrust – Pushing airflow backwards like an oar or propeller
- Clap and Fling – Trapping air between wings then flinging it backwards
- Wake Capture – Redirecting air accelerated over the wings to produce rearward thrust
- Circulation – Generating lift-based vortex forces that have a rearward component
Researchers are still working to fully understand the contributions of each mechanism across different bird species and flight modes. But it’s clear that both drag and lift-based effects play important roles in producing the required thrust to overcome drag.
Thrust Requirements
The thrust required depends on the flight condition:
- Steady Cruising – Thrust equals drag, maintaining constant velocity
- Accelerating – Thrust must exceed drag, speeding up the bird
- Maneuvering – Thrust redirected to turn or change altitude
- Hovering – Vertical thrust balances weight, zero forward velocity
- Takeoff/Initial Climb – Maximum thrust needed to overcome weight and rapidly gain speed
Estimating the actual thrust produced by flapping wings is challenging. But measurements of wake velocities and accounting for drag forces provide reasonable estimates. For example, the average thrust generated by a slowly flying pigeon has been measured around 2-3 Newtons.
Drag
Drag is a rearward aerodynamic force acting opposite to the direction of flight. It arises primarily from two sources:
- Parasite Drag – Resistance from moving the bird’s body through air
- Induced Drag – Vortex drag resulting from the generation of lift on the wings
Additional minor sources of drag include interference between body surfaces and friction from moving parts of the wings. Drag continually acts to slow birds down. So thrust is needed to overcome drag and maintain flight speed. The amount of drag depends on the bird’s speed, wing morphology and the projected frontal area of the body and wings. Larger, faster-flying birds like geese experience much higher drag forces than smaller, slower ones like swifts.
Estimating Drag
Total drag can be estimated by summing parasite and induced drag components:
Drag = Parasite Drag + Induced Drag
Parasite drag increases with velocity and frontal area. It is approximated using the drag equation:
Parasite Drag = 1/2 * Air Density * Velocity^2 * Projected Frontal Area * Drag Coefficient
The drag coefficient encapsulates the streamlining effects of the body shape. Induced drag arises from generating lift and the resulting tip vortices. It can be estimated as:
Induced Drag = Lift^2 / (Air Density * Wing Area * Aspect Ratio * Efficiency Factor)
Where aspect ratio is the wing span divided by average chord length. The efficiency factor accounts for non-ideal wing geometry. Using estimates for these parameters, the parasite and induced drag on a bird can be calculated for different flight scenarios.
Lift
Lift is the upward aerodynamic force that counteracts the bird’s weight and enables it to become airborne. It is generated by the wings as they accelerate airflow over their top surface. According to Bernoulli’s principle, the resulting decrease in pressure produces an upward force. Lift is perpendicular to the oncoming airflow. Its magnitude depends on wing area, airspeed, angle of attack and the lift coefficient of the wing shape. The lift must equal weight for a bird to maintain altitude in steady flight.
Generating Lift
As the wings flap, they take on different angles of attack that modulate lift production:
- Downstroke – Leading edge angles down, generating positive lift
- Upstroke – Leading edge angles up, producing negative lift
- At end of upstroke – Wings rotate rapidly to flip angle of attack
Small birds like hummingbirds can flap their wings in a horizontal stroke plane to produce lift on both downstroke and upstroke. Larger birds must flap with an inclined stroke angle, only generating lift during the downstroke. Wing twisting and bending also help optimize angles of attack across the wing to maximize lift.
Wing Design for Lift
Bird wings have evolved many structural adaptations to improve lift generation:
- Streamlined cross-section to reduce pressure drag
- Smooth upper surface to facilitate airflow
- Curved upper surface to increase camber
- Slotted wing tips to reduce induced drag from vortices
Wing shapes vary widely depending on flight style. Broad, rounded wings generate greater lift for soaring species like eagles and vultures. Long, pointed wings are more efficient for migrating over long distances.
Side Forces
In addition to the four primary forces, side forces act on birds during turning and wind gusts:
- Centripetal Force – Acts towards the center of a turn to change flight direction
- Crosswind Force – Pushes the bird sideways in windy conditions
Banking helps incline the lift force to balance the centripetal force when turning. And angling into the wind counters crosswind forces. These are important for navigating and maintaining stability in gusty conditions.
Net Aerodynamic Force
At any instant during flight, the total aerodynamic force on a bird is the vector sum of all the individual forces:
Net Force = Lift + Weight + Thrust + Drag + Side Forces
The magnitude and direction of the net force dictates the bird’s flight dynamics including its accelerations, turning rates, and stability. Birds continuously adjust their wing motions to manipulate the component forces for control. They also exploit interactions between the forces to their advantage. For example, flapping faster increases both thrust and lift simultaneously.
Force Measurement Techniques
Researchers have developed various methods to study the aerodynamic forces acting on birds in flight:
Wind Tunnels
Scale models of wings and frozen bird specimens can be mounted in wind tunnels to directly measure lift, drag and side forces using load cells.
Particle Image Velocimetry
High speed cameras and lasers are used to visualize airflow patterns around flapping wings and calculate forces based on measured velocities.
Computational Fluid Dynamics
Computer simulations solve the Navier-Stokes equations governing airflow to predict aerodynamic forces for different wing geometries and kinematics.
Onboard Sensors
Custom sensor packages can be mounted on birds to record flap motions and airflow measurements to estimate forces during free flight.
Role of Wings
Bird wings play a crucial role in flight by generating the required aerodynamic forces. Their shape, size, motion and orientation determine the magnitudes of lift, thrust, drag and side forces. Different types of wings have evolved for specialized flight abilities:
- Long, pointed – Efficient long distance flight
- Short, broad – Powerful takeoff and landing
- Slotted wing tips – Reduce induced drag from wingtip vortices
- Stretchy wing skin – Passively deforms to optimal shape during flapping
Wing muscles must also provide sufficient power to sustain flapping motions. Optimizing the design of wings and their control is critical to producing the necessary balance of forces for different modes of flight.
Conclusions
In summary, the four primary forces acting on a bird in flight are:
- Weight – Downward pull of gravity
- Lift – Upward force produced by wings
- Thrust – Forward force generated by flapping wings
- Drag – Rearward resistance from air
Additionally, side forces arise during turns and wind gusts. The complex interplay and variations of these forces allow birds to takeoff, land, soar, glide, maneuver and fly in a myriad of styles. Aerodynamic force generation dependent on wings lies at the heart of their remarkable flight abilities.
