One of the most confusing concepts for young aerodynamicists is the relative velocity between objects. Aerodynamic forces are generated by an object moving through a fluid (liquid or gas). A fixed object in a still fluid does not generate aerodynamic forces. (Hot air balloons "lift" because of buoyancy forces, not aerodynamic forces.) To generate lift, an object must move through the air, or air must move past the object. [Some aircraft (like the Harrier) use engine thrust to "lift" the vehicle. But this, again, is not aerodynamic lift.] Aerodynamic lift depends on the square of the velocity between the object and the air. Now things get confusing because not only can the object be moved through the air, but the air itself can move. To properly define the velocity, it is necessary to pick a fixed reference point and measure velocities relative to the fixed point. In this slide, the reference point is fixed to the ground, but it could just as easily be fixed to the aircraft. It is important to understand the relationships of wind speed to ground speed to airspeed.

Wind Speed

For a reference point picked on the ground, the air moves relative to the reference point at the wind speed. Notice that the wind speed is a vector quantity and has both a magnitude and a direction. (A 20 mph wind from the west is different from a 20 mph wind from the east.) The wind has components in all three primary directions (north-south, east-west, and up-down). In this figure, we are considering only velocities along the aircraft's flight path. And a positive velocity is defined to be in the direction of the aircraft's motion. We are neglecting cross winds, which occur perpendicular to the flight path but parallel to the ground, and updrafts and downdrafts, which occur perpendicular to the ground.

Ground Speed

The velocity of the object measured relative to the ground is called the ground speed. Again, this is a vector quantity.

Airspeed

The important quantity in the generation of lift is the relative velocity between the object and the air, which is called the airspeed. Airspeed cannot be directly measured from a ground position, but must be computed from the ground speed and the wind speed. Airspeed is the vector difference between the ground speed and the wind speed. On a perfectly still day, the airspeed is equal to the ground speed. But if the wind is blowing in the same direction that the aircraft is moving, the airspeed will be less than the ground speed.

Examples

Suppose we had an airplane that could take off on a windless day at 100 mph (liftoff airspeed is 100 mph). Now suppose we had a day in which the wind was blowing 20 mph towards the west. If the airplane takes off going east, it experiences a 20 mph headwind (wind in your face). Since we have defined a positive velocity to be in the direction of the aircraft's motion, a headwind is a negative velocity. While the plane is sitting still on the runway, it has a ground speed of 0 and an airspeed of 20 mph [airspeed = ground speed (0) - wind speed (-20) ]. At liftoff, the airspeed is 100 mph, the wind speed is -20 mph and the ground speed will be 80 mph [airspeed (100) = ground speed (80) - wind speed (-20) ].

If the plane took off to the west, it would have a 20 mph tailwind (wind at your back). Since the wind and aircraft direction are the same, we assign a "+" to the wind speed. At liftoff, the airspeed is still 100 mph, the wind speed is 20 mph and the ground speed will now be 120 mph [airspeed (100) = ground speed (120) - wind speed (20) ]. So the aircraft will have to travel faster (and farther) along the ground to achieve liftoff conditions with the wind at it's back.

Significance of Understanding Relative Velocity

The importance of the relative velocity explains why airplanes take off and land on different runways on different days. Airplanes always try to take off and land into the wind. This requires a lower ground speed (as we saw in the above example), which means the plane can take off or land in the shortest distance traveled along the ground. Since runways have a fixed length, you want to get airborne as fast as possible on takeoff and stopped as soon as possible on landing. In the old days, a large "wind sock" was hung near the runway for pilots to see which way the wind was blowing to adjust their takeoff and landing directions. Now mechanical or electronic devices provide the information that is radioed to the cockpit.

The relationship between airspeed, wind speed, and ground speed explains why wind tunnel testing is possible and how kites fly.

• In the wind tunnel, the ground speed is zero. (The object is fixed to the walls of the tunnel.) The airspeed is then the negative of the wind speed that is generated in the tunnel. Whether the object moves through the air, or the air moves over the object, the forces are the same.
• A kite usually has no ground speed (the kite is held on the end of a string). But the kite still has an airspeed that is equal to the wind speed. (You can fly a kite only with the wind at your back.)

Guided Tours
• Into the Wind:

Beginner's Guide to Aerodynamics
Beginner's Guide to Propulsion
Beginner's Guide to Model Rockets
Beginner's Guide to Kites
Beginner's Guide to Aeronautics