The Wing Surface
The wing provides the primary lifting surface normally for an airplane with the stabilizer providing some lift but exists primarily to keep the wing in a relatively level position. There are planes that do not have a stabilizer but the rear of the wing curves upward to keep the wing level; this would be a “flying wing” configuration.
Calculate Wing Loading for Sample Wing
Wingspan 12” Wing Chord 3” = Wing Area?
Sample Weight 10 Grams Wing Loading = Weight / Wing Area What is the wing loading?
Don Ross in his book Rubber Power Models stated for small airplanes a good wing loading is .33 grams per square inch. Does this sample wing meet this criterion?
Lift
Exactly how lift is created on the wing of an airplane is still a topic that is not agreed upon by all who study aerodynamics. Traditional theory was that because of the curved surface on the top of the wing, this created a longer path than the flat surface of the bottom of the wing creating a lower pressure on the top surface causing the wing to be sucked upward. Lower pressure on the top of the wing is part of the lift components but not because of the shape difference between the upper and lower surfaces. Many shapes of wings will lift an airplane; flat wings, wings curved the same on the top and bottom (symmetrical) or concave bottom surface wings. Flat or symmetrical wings do need the wing surface to be angled upwards (positive angle of attack) while some wing airfoil types will start to lift at zero degrees or less.
More recent theory of lift is that both the air pushing on the bottom of the wing and deflecting downwards and the lower pressure above the wing contribute to the total lift. The most efficient types of wings will create the lift needed to support the airplane weight while creating less drag. For simple model airplanes, a flat wing might be acceptable for ease of construction.
Note: Clark Y is a common airfoil in the type of airfoil that is curved on the top and flat on the bottom. It has been pointed out that the Clark Y is not perfectly flat on the bottom. I am trying to relate a typical airfoil that is curved on the top and flat on the bottom.
Incidence angle is the angle between chord line and longitudinal axis.
It is possible for airplanes to fly with no decalage at all this is the “0 – 0” setting used on some hand launch gliders. This helps in the high-speed launch phase but sometimes the plane will not recover from an upset and crash.
Note: even with no decalage the plane still flies through the air with some positive incidence. Frank Zaic had said that a free flight airplane trimmed for a floating glide will normally fly at around 6 degrees angle of attack. There is also a “downwash” from the wing that changes the effective angle of the stabilizer.
Additional Note: the angles of incidence work together with the balance point of the airplane – Center of Gravity which will be discussed later.
Three Axes of Motion of an Airplane
• Pitch (Lateral Axis) climb and dive motion
• Roll (Longitudinal Axis) bank left or right motion
• Yaw (Normal Axis) nose pivots to the left or right
- It is important to know the three axes that an airplane pivots to be able to analyze the flight path and to perform trim adjustments.
Providing Thrust by Using a Rubber Motor
Mechanical winder is much faster method to wind rubber motor. The motor can be stretched out at least 2 to 3 times the normal length and then more turns can be wound in as you come back to rear motor hook.
Propellers
Propellers are like rotary wings that pull the aircraft through the air, most common is to have two blades but other combinations of blades or even a single blade have been tried.
A propeller has a diameter which is the length from tip to tip but it is called the diameter as the tips are going around a circle.
Normally for the specifications of the airplane the propeller will be matched up in diameter and pitch but for the simple model airplanes we will size the airplane around a pre-made propeller that is 5 1/2” to 6” in diameter.
The Rubber Motor
The wound rubber strip motor supplies an amazing amount of energy for its weight. Plastic propellers assemblies are available that easily slide over the balsa motor stick and should provide sufficient thrust to fly model airplane with wingspans from 10” – 16” provided the airplane is light enough and properly designed. For this tutorial, plastic propellers of 5 1/2 ” to 6” diameter will be considered, rubber strip that is either 3/32” or 1/8” wide.
Some Basics of the Rubber Motor
The thinner the rubber motor is the more turns that can be wound into it but the less energy that will be returned.
Most of the energy will be released in the first few seconds, the power burst and then it will gradually decrease for most of the run.
Descend, Glide, or Dive
When an airplane is not maintaining altitude or climbing it is descending, diving or gliding. If the airplane does not create sufficient lift for the weight or the nose has been pointed downward because some type of an upset such as a stall or elevator surface was deflected down the airplane will fly towards the ground.
Gliding is when there is no thrust propelling the airplane other than the force of gravity that pulls it down the glide angle.
Simple gliders referred to in this article are launched with a gentle hand toss which gives the glider kinetic energy. The glider is also pulled down the glide slope by the force of gravity.
Trigonometry can be used to compute the amount lift and the drag amount in a glide. In the Simple Glider Curriculum Gary Hinze created, Gary presented a method of computing these amounts by using ratio. On a NASA website formulas were presented to compute lift and drag in a glide that required solving for several variables, Gary pointed out the formulas are really as simple as this:
Glide Angle = (Height / Distance) Arctangent
Lift = Weight x Cosine (Glide Angle)
Drag= Weight x Sine (Glide Angle)
Note: the calculator built into Windows can do trig functions by changing the View to Scientific. Arctangent function is obtained by pressing Inv button and then using Tan¯ᶦ.
Calculate the glide angle if launched from a height of 1 meter and glider travels over 5 meter distance?
What would the lift be if the weight was 10 grams?
What would the drag be?
The Climb of an Airplane
The climb of an airplane might be more confusing that it would first appear. To start, when lift is greater than the weight of the aircraft the nose begins to pitch upwards. As the thrust, created by the spinning propeller, pulls the airplane at an increasingly steeper angle the amount of lift actually decreases as more of the force is coming from the pull upwards. When the airplane is completely vertical in the hover position there is no lift from the wing.
In the formula for lift, the cosine of the climb angle is multiplied by the weight. As the angle increases, the value returned from the cosine function decreases. The thrust formula contains the sine function which increases as the climb angle increases.
At some angle of attack the air flowing over the rear portion of the top of the wing detaches and becomes turbulent, the wing loses lift.
Pitch – Lateral Stability
The Center of Pressure will move forward and back during flight based on the angle of attack of the wing. Further ahead for greater angle of attack.
Understanding the Moment Arm
The “tail moment arm” length in the pitch axis is defined as the distance between center of gravity of the wing and the aerodynamic center of the stab.
Note: this is the definition given by many sources. Another source defined “the tail moment arm as the distance between the mean aerodynamic chords of the wing and the stab.”
The amount of force needed on the stabilizer varies with length of the moment arm. With a longer moment arm a smaller stabilizer can be used which should create less drag.
Pitching Moment of an Airfoil
With a long moment arm if the tail surface is not lightweight it can take a lot of weight in the nose for proper center of gravity balance. The surface area is more effective with a longer moment arm in stabilizing the airplane so less surface area is needed.
As the plane goes into a dive the speed will increase. This will increase the lift causing the wing to pull up and at the same time the force pushing down on the stabilizer will be greater pushing down with more force causing the nose to pivot upwards.
Controlling the Flight Path
Full-scale aircraft and radio controlled model aircraft adjust the flight path by control surfaces. Free flight model aircraft often use “trim tabs” to adjust the flight path using a set deflection of the control surface. More complicated free flight models can have control surfaces that move in flight but without control from a pilot on the ground.
Control Surfaces Added to Flying Surfaces
Elevator Movement Up and Down as Seen From Side View
Dihedral is the mechanism to level the wing when it pivots on the roll axis into a banked position. When the rudder is deflected starting the yaw with dihedral the side slip will start advancing into a bank.
Turning the Airplane
An airplane normally will be in a bank condition where one wing tip is higher than the other as viewed from the front or the rear. Turning the airplane with the rudder will cause the airplane to turn in the normal axis which is known as “yaw”.
If the airplane does have dihedral, the yaw will start a side slip causing the bank angle needed for a turn.
Yaw – Normal Axis
For a sport rubber model 10% of the wing area is good proportion to try. What would be the area for the vertical fin using the 36 square inches of wing area? After computing the square inches of the vertical fin, what function would you use on this area to get equal length sides?
Turning a Plane with Dihedral with the Rudder
Longitudinal or Roll Axis
Maintaining altitude in a turn the vertical component of the lift must be equal to the weight of the airplane. The amount of lift required will be the vector resultant of the vertical and horizontal components. In physics the horizontal component is known as the “centripetal force”. The confusing part is that centripetal force points towards the inside of the circle. Centrifugal force is the force directed in the opposite direction but this has been called a “false force”.
Centripetal Force
A common example of centripetal force has been to swing a ball around on a string. The force directed outwards 90 degrees from the centripetal force is the labeled as the velocity. Realize that these two forces are constantly moving around the circle with the string and ball. If the string were released it would follow the velocity direction.
Another confusing fact to remember is that even if ball is moving at a constant speed it is always accelerating because the direction is constantly changing. The acceleration is directed towards the center of the circle.
Note: the source of this information is Wikipedia Article Centripetal Force; there has been dispute on the labeling of this diagram. If you know a better source, please send a comment.
Formulas Used in Forces in a Turn
Centripetal Force = mass x velocity ² / radius
Lift = weight / cosine (bank angle)