• Simple Aerodynamics Part 1
• Simple Aerodynamics Part 2
• Simple Aerodynamics Part 3
• Simple Aerodynamics Part 4
• Simple Aerodynamics Part 5
• Simple Aerodynamics Part 6

SmokeDog's Note: In previous lessons we’ve presented 3 of the classic “4 forces of flight”, drag, lift and thrust. We will now move on to weight.

Weight is the last of the classic “four forces of flight” to be discussed. In the last lesson we discussed the meaning of vectors. If the vectors of the four forces balance we will have non-accelerated flight, that is, no changes in airspeed and no changes in climb (or descent) rate.

In the last lesson we discussed the balance of thrust vs. drag. In this lesson we will discuss the balance of lift vs. perceived weight. “Perceived” weight includes the concept of weight, which we are accustomed to, plus the affects of other accelerations.

Figure 1 - Classic Four Forces of Flight

Weight = mass x acceleration. Our normal notion of weight is noted as we exist on earth. You may not think of yourself as accelerating but you would be accelerating if the solid earth didn’t stop you. The gravitational pull of the earth produces an acceleration of 32 feet per second, each second. If earth had no atmosphere to produce drag and you jumped from an aircraft, after one second you would have accelerated to 32 feet per second. After two seconds you would have accelerated to 64 feet per second. After three seconds you would be traveling at 96 feet per second …. And so on.

While you are floating down to earth, you would not feel any force. You’d feel weightless. When you are on the ground, you feel the force pulling you toward earth’s center at 32 feet per second, each second.

An aircraft’s weight, caused by the gravitation of earth, acts toward the center of earth. Lift acts perpendicular (at a 90 degree angle) to an aircraft’s relative wind. As discussed in lesson 3, relative wind is approximately opposite to the flight path. If we are in a climb or descent, the lift vector will not point opposite to the weight vector. Figure 2 shows the vectors in a descent.

Figure 2 - Four Forces of Flight in a Descent

Note the “component of weight aiding thrust”. Since the weight vector is tilted forward (relative to the aircraft) we can compute the amount of thrust aid by drawing a line from the dashed lift axis to the point representing the force of weight. Add this “component of weight aiding thrust” to the thrust vector and you would notice that its length equals the length of the drag vector. This balance of forces assumes that you are not accelerating. The thrust line was reduced (the pilot reduced power) during the descent to prevent acceleration. If you are in a car and travel from level ground to a downhill portion of the road, you would accelerate forward unless you reduced power.

An interesting side note to this discussion pertains to gliders. You can see why you don’t need power to go downhill. You can also see how a glider pilot can control his airspeed and descent rate by controlling the up and down pitch of his aircraft.

A similar, opposite analysis, applies to an aircraft in a climb. Figure 3 shows an aircraft in a climb. The “component of weight opposing thrust” plus drag must equal thrust in order to produce steady flight.

Figure 3 - Classic Four Forces of Flight in a Climb

This is a good place to discuss weight’s affect on both, an aircraft’s ability to climb and on its top speed. Thrust in excess of that need to oppose drag is necessary to produce a climb. For analytical purposes lets call this thrust “excess thrust”. In light aircraft of moderate performance, thrust is much more limited than in an average car. Add to this limitation, the fact that unlike a car, if your aircraft is going too slow as well as too fast, drag increases rapidly. Review the power curves/drag curves diagram that was introduced in the last lesson.

Figure 4 (from last lesson) Power curves/Drag curves

At any airspeed you can measure the amount of “excess thrust” available for climb by noting the vertical distance between thrust and total drag. An increase in weight has the same effect on climb performance as lowering the thrust curve. At some point of weight increase, the aircraft would have no excess thrust to produce a climb. This factor of reduced margin of thrust is exaggerated at high altitudes where engines produce less power. In the western United States (at high airport elevations), many aircraft accidents are caused each year, by an overloaded aircraft. The “excess thrust” needed to support a climb is not available. In a car, excess weight causes slower acceleration and a reduced climb ability, however, since you have to oppose only parasitic drag, you can affect a climb up a road at a slower speed.

While a heavy car would accelerate slower, top speed would be affected very little. Aircraft top speed is affected more that a car but not by much. A heavier aircraft must fly at a higher angle of attack to produce more lift. The higher angle of attack causes more induced drag and usually more parasitic drag. Luckily, since the lifting ability of a wing increases by Velocitysquared, The damaging affect of weight on speed is moderated by high cruise speeds. Aircraft manuals often show airspeed reductions of only 1 to 3 percent when comparing light loads vs. maximum gross weight. In contrast, aircraft manuals often show a 30 to 50 percent reduction in climb rate when comparing light loads vs. maximum gross weight.

Perceived Weight

A big factor on aircraft performance is caused by an increase in the weight vector in turns, as well as sudden (accelerated) entries into climbs. Another acceleration is added to earths acceleration. In a turn, force is required to pull an airplane to the center of a circle. This pull [term - centripetal force] increases with bank angle. An increase in the percieved weight vectors require an increase in the offsetting lift vector.

A steeper bank angle is needed to support a faster turn. A classic analogy used to illustrate centripetal force is a person swinging a pail. The faster you swing it, the steeper the angle to the ground as well as the bigger the force felt by your arm.

Figure 5 - Lift Force in a Turn.

Assuming level flight, a 60 degree bank produces a 2G (2 X gravity) acceleration. The perceived weight of the aircraft is twice its normal weight. As you can imagine, climb performance suffers in steep turns.

This article concludes the six part discussion of Simple Aerodynamics. We hope that we touched on knowledge areas which will expand you interest in the physics of flight. You will find good discussion of flight physics in the many texts published for private pilot training.