The four forces that affect WSC flight are thrust, drag, lift, and weight. [Figure 2-12] In level, steady WSC flight:
- The sum of all upward forces equals the sum of all downward forces.
- The sum of all forward forces equals the sum of all backward forces.
- The sum of all moments equals zero.
Note that the lift and weight forces are much greater than the thrust and drag forces. A typical example for many WSC aircraft is that the lift/weight forces are five times the thrust/drag forces.
Thrust—the forward force produced by a powerplant/propeller as it forces a mass of air to the rear (usually acts parallel to the longitudinal axis, relative wind, and flightpath).
Drag—the aerodynamic force acting on the wing and carriage in the same plane and in the same direction as the relative wind.
Lift—the aerodynamic force caused by air flowing over the wing that is perpendicular to the relative wind.
Weight—the force of gravity acting upon a body straight down and perpendicular to the Earth.
During level flight, these forces are all horizontal and vertical. During descents or climbing, these forces must be broken down into components for analysis.
Dynamic Pressure (q)
Both lift and drag are a direct result of the dynamic pressure of the air. Dynamic pressure (q) is created from the velocity of the air and the air density. An increase in velocity has a dramatic effect on dynamic pressure (q) because it increases with the square of the velocity. Doubling the velocity means “q” increases by four times. Increasing the velocity by a factor of three means that the dynamic pressure (q) increases by a factor of nine. This is a very important concept in understanding the aerodynamics of WSC.
Formula for dynamic pressure: q = V2 x ρ/2
V = velocity
ρ = density factor
Lift opposes the downward force of weight and is produced by the dynamic effects of the surrounding airstream acting on the wing. Lift acts perpendicular to the flightpath through the wing’s center of lift. There is a mathematical relationship for lift which varies with dynamic pressure (q), AOA, and the size of the wing. In the lift equation, these factors correspond to the terms q, coefficient of lift (CL), and wing surface area. The relationship is expressed in Figure 2-13.
Figure 2-13 shows that for lift to increase, one or more of the factors on the other side of the equation must increase. Generally, the lift needed is about the same for most flight situations. A slower speed requires a higher AOA to produce the same amount of lift. A faster speed requires a lower AOA to produce the same amount of lift.
Because lift is a function of dynamic pressure (q), it is proportional to the square of the airspeed; therefore, small changes in airspeed create larger changes in lift. Likewise, if other factors remain the same while the CL increases, lift also increases. The CL goes up as the AOA is increased. As air density increases, lift increases. However, a pilot is usually more concerned with how lift is diminished by reductions in air density on a hot day, or if operating at higher altitudes.
All wings produce lift in two ways:
- Airfoil shape creates a higher velocity over the top of the wing and a lower velocity over the bottom of the wing with Bernoulli’s venturi effect.
- Downward deflection of airflow because of the curvature of the wing with the principle of Newton’s Third Law of Motion: for every action, there is an equal and opposite reaction.
Both principles determine the lifting force. Review the Pilot’s Handbook of Aeronautical Knowledge to understand Newton’s laws of motion and Bernoulli’s venturi effect.
Figure 2-14 (top) shows the amount of lift produced along the wing for an airplane wing with an elliptical planform. Notice how the amount of lift generated is smallest at the tips and increases slightly towards the root of the wing. This is known as the “elliptical lift distribution.”
The WSC wing lift distribution is different because the wing twist at the root is at a higher AOA than the tips. Most of the lift is produced at the center of the wing with less lift produced at the tips. The WSC lift distribution is compared to the lift distribution for an optimum design elliptical wing in Figure 2-14.
Drag is the resistance to forward motion through the air and is parallel to the relative wind. Aerodynamic drag comes in two forms:
- Induced drag—a result of the wing producing lift.
- Parasite drag—resistance to the airflow from the carriage, its occupants, wires, the wing, interference drag from objects in the airstream, and skin friction drag of the wing.
Induced drag is the result of lift, and its amount varies as discussed above for lift. Induced drag creates organized circular vortices off the wingtips that generally track down and out from each wingtip. Refer to the Pilot’s Handbook of Aeronautical Knowledge for additional discussion on wingtip vortices formation.
These wingtip vortex formations are typical for all aircraft that use wings including WSC, PPC, helicopters, sailplanes, and all fixed-wing airplanes. The bigger and heavier the aircraft, the greater and more powerful the wingtip vortices are. This organized swirling turbulence is an important factor to understand and avoid for flight safety. Refer to the Aeronautical Information Manual (AIM) or the Pilot’s Handbook of Aeronautical Knowledge (FAA-H-8083-25) for additional discussion.
Parasite drag is caused by the friction of air moving over all the components of the aircraft. Just as with lift, parasite drag increases as the surface area of the aircraft increases, and dramatically increases as airspeed increases (the square of the velocity). Therefore, doubling the airspeed quadruples parasite drag. [Figure 2-15]
The WSC aircraft can be designed for the purpose of being a slow flying aircraft with a large wing where drag is not a major concern, or can be designed to be a fast flying aircraft with a small wing where drag is more of a concern.
The aircraft has plenty of items (area) for the wind to strike including wing, wires, struts, pilot, carriage, engine, wheels, tubes, fuel tanks, etc. Parasitic drag can be reduced by streamlining the items. Round tubes can be streamlined reducing the drag to one-third, and cowlings can be used to streamline the pilot and the carriage completely, but not without the additional expense and additional weight of the streamlining. Streamlining does make a noticeable difference in the speed and gas mileage of the WSC, especially for the faster aircraft. [Figure 2-16]
With the large speed range of WSC aircraft, weight, complexity, amount and expense of streamlining, and resultant drag reduction are determined by the specific mission for the aircraft and the manufacturers’ make and model. [Figure 2-17]
Total drag is the combination of parasite and induced drag.
Total drag = parasitic drag + induced drag
To help explain the force of drag, the mathematical equation D = CD x q x S is used. The formula for drag is the same as the formula for lift, except the CD is used instead of the CL. In this equation, drag (D) is the product of the coefficient of drag (CD), dynamic pressure (q) determined by the velocity squared times the air density factor, and surface area (S) of the carriage and wing. The overall drag coefficient is the ratio of drag pressure to dynamic pressure.
Induced and parasitic drag have opposite effects as AOA decreases and speed increases. Note the total drag in Figure 2-18. It is high at the slowest airspeeds at high angles of attack near the stall, decreases to the lowest at the most efficient airspeed, and then progressively increases as the speed increases. The WSC wing can fly with a large range of airspeeds.
Generally, the most efficient speed is at the lowest total drag providing the best rate of climb, glide ratio, and cruise economy. However, slower speeds provide higher angles of climb, and faster speeds provide quicker transportation. [Figure 2-18]