## **KITES PRINCIPLES & SHAPES**

An excellent way for students to gain a feel for aerodynamic forces is to fly a kite. Kite flying is fun when done safely and you can learn many of the fundamentals of airplane aerodynamics because a kite is very much like an airplane. In fact, the Wright brothers used kites and gliders to learn the fundamentals before their first successful airplane flight.

Like an airplane, a kite is a

Kite flying is a delicate balance between aerodynamic forces, the weight of the parts of the kite, and the distribution of these forces. In flight, the kite is connected to the flyer by the control line and the flyer can feel the tension in the line created by the aerodynamic forces on the kite. The line is connected to the kite by a string bridle. The place where the bridle connects to the line is called the bridle point and the kite pivots about this point in flight. The bridle point can be adjusted to change the flight characteristics of the kite. The

If we remove the covering, we can see the structure which transmits the aerodynamic forces to the bridle. A box kite structure is made from several sticks and some string. The sticks can be made of a light but strong piece of wood such as balsa or bamboo, or a light but strong plastic tube. In the box kite, there are four main "leg" pieces of equal length and four "cross" pieces which are made from two sticks. The structure is held together with strings wrapped around the legs at the location of the cross members. The surface covering is attached to the strings. Notice that the structure is small, light and strong. It must be made strong to withstand the forces of the wind and weight, but it must also be light to keep the weight low. To save weight, only two "cross" pieces are used on some box kites. The trade of strength and weight must be considered in every flying thing from a kite to a large airliner. Compare the structure and coverings of this box kite with the Wright brother's 1900 aircraft and note how similar they are.

Like an airplane, a kite is a

**heavier than air**craft. Kites depend on surfaces to generate the aerodynamic forces necessary for flight and use rigid structures to support the surfaces and transmit the forces. Differen kites. have different types of surfaces and structures; on this slide we show a simple box kite. The left side of the figure shows the kite as it would appear in flight and the right side shows the inner structure.Kite flying is a delicate balance between aerodynamic forces, the weight of the parts of the kite, and the distribution of these forces. In flight, the kite is connected to the flyer by the control line and the flyer can feel the tension in the line created by the aerodynamic forces on the kite. The line is connected to the kite by a string bridle. The place where the bridle connects to the line is called the bridle point and the kite pivots about this point in flight. The bridle point can be adjusted to change the flight characteristics of the kite. The

**surfaces**of the kite are covered by a thin covering of paper, plastic, or cloth, which deflects the wind downward and creates the aerodynamic forces of lift and drag on the kite.If we remove the covering, we can see the structure which transmits the aerodynamic forces to the bridle. A box kite structure is made from several sticks and some string. The sticks can be made of a light but strong piece of wood such as balsa or bamboo, or a light but strong plastic tube. In the box kite, there are four main "leg" pieces of equal length and four "cross" pieces which are made from two sticks. The structure is held together with strings wrapped around the legs at the location of the cross members. The surface covering is attached to the strings. Notice that the structure is small, light and strong. It must be made strong to withstand the forces of the wind and weight, but it must also be light to keep the weight low. To save weight, only two "cross" pieces are used on some box kites. The trade of strength and weight must be considered in every flying thing from a kite to a large airliner. Compare the structure and coverings of this box kite with the Wright brother's 1900 aircraft and note how similar they are.

Newton's first law of motion specifies that when all the external forces on an object are balanced, there is no net external force and it moves at a constant velocity or remain at rest (velocity equals zero). This law holds for both linear motion and forces and for twisting motion and twisting forces. Twisting forces are called torques, or moments. The twisting motion occurs about some point called the

An excellent way for students to gain a feel for the action of torques and forces is to fly a kite. Kites can fly because of the forces acting on the parts of the kite. Though kites come in many shapes and sizes, the forces which act on a kite are the same for all kites. You can compare the forces to the forces acting on an airliner in flight and you will find that, with the exception of thrust, they are exactly the same. The similarity in forces allowed the Wright brothers to test their theories of flight by flying their aircraft as kites form 1900 to 1902.

There are, however, some important differences in the response of a kite to external forces that do not occur in an airplane. An airplane in flight rotates about its center of gravity. The center of gravity for any object is the average location of the weight of all the parts of the object. A kite in flight does not rotate about its center of gravity because it is pinned by the bridle to the control line. A kite in flight is more closely related to a hinged door than to an airplane in flight. The center of gravity of a hinged door is in the center of the^M door, but the door rotates about the hinges. A kite in flight rotates about the bridle point which is the place where the line is attached to the bridle as shown by the red dot on the slide.

There are three main forces which act on a kite; the weight, the aerodynamics, and the tension in the line. Because the bridle point is the pivot about which the kite rotates, the tension does not contribute to the torques on the system (the distance is zero). As shown on the figure, the weight produces a clockwise torque

TW = W * g

The aerodynamic force produces a counterclockwise torque

TF = F * p

Notice that the distances are measured perpendicular to the forces and not just directly to the center of pressure and center of gravity. Also notice that the direction of the force determines the direction of the torque. Forces and torques are vector quantities having a magnitude and a direction. The direction is as important as the magnitude.

In equilibrium, these torques are balanced and there is no rotation of the kite about the bridle point. This is called a trimmed flight condition.

W * g = F * p

In flight, a kite can rotate about the bridle point. As the kite rotates, the inclination angle between the kite and the wind changes. The magnitude and direction of the aerodynamic force depends on this angle and the ratio of the lift and dragwhich depends on the design of the kite. So as the kite rotates, the aerodynamic force changes and this changes the aerodynamic torque about the bridle point as discussed above. If the changing aerodynamic torque balances the weight torque, the kite reaches an equilibrium condition and sits at a fixed inclination angle with no further rotation about the bridle point. But if the aerodynamic torque does not equal the weight torque, the kite continues to rotate under the action of the unequal torques. It is possible that the aerodynamic torque never equals the weight torque which causes the kite to continually rotate.

In equilibrium the kite is inclined to the wind (and to the ground) at a fixed angle and the magnitude of the lift force depends directly on this angle. Since the weight of the kite is constant, the difference between the lift and the weight is an indication of how well the kite flies. If the lift is greater, the kite climbs faster, flies higher, and is able to lift more string. If the lift is less, the kite climbs slowly or maybe not at all! Since the flight angle depends on the balance of torques, and the torques depend on the location of the bridle point relative to the cg and cp, the location of the bridle point has a major effect on the performance of the kite. The location of the bridle point can be changed by the flyer before launch by moving the knot that holds the line to the bridle.

The mathematical equations involved with the forces and torques on a kite can be solved by using a computer program. You can use the KiteModeler program to further study how kites work and to design your own kites.

**pivot**. A torque is related to a linear force;**the torque about a point is equal to the force times the perpendicular distance to the point**. In equilibrium, there are no net torques about the pivot and the angular velocity is constant (or zero).__Fundamentals__An excellent way for students to gain a feel for the action of torques and forces is to fly a kite. Kites can fly because of the forces acting on the parts of the kite. Though kites come in many shapes and sizes, the forces which act on a kite are the same for all kites. You can compare the forces to the forces acting on an airliner in flight and you will find that, with the exception of thrust, they are exactly the same. The similarity in forces allowed the Wright brothers to test their theories of flight by flying their aircraft as kites form 1900 to 1902.

There are, however, some important differences in the response of a kite to external forces that do not occur in an airplane. An airplane in flight rotates about its center of gravity. The center of gravity for any object is the average location of the weight of all the parts of the object. A kite in flight does not rotate about its center of gravity because it is pinned by the bridle to the control line. A kite in flight is more closely related to a hinged door than to an airplane in flight. The center of gravity of a hinged door is in the center of the^M door, but the door rotates about the hinges. A kite in flight rotates about the bridle point which is the place where the line is attached to the bridle as shown by the red dot on the slide.

There are three main forces which act on a kite; the weight, the aerodynamics, and the tension in the line. Because the bridle point is the pivot about which the kite rotates, the tension does not contribute to the torques on the system (the distance is zero). As shown on the figure, the weight produces a clockwise torque

**TW**about the bridle point which is equal to the magnitude of the weight**W**times the perpendicular distance**g**from the bridle point to the center of gravity.TW = W * g

The aerodynamic force produces a counterclockwise torque

**TF**about the bridle point which is equal to the magnitude of the aerodynamic force**F**times the perpendicular distance**p**from the bridle point to the center of pressure.TF = F * p

Notice that the distances are measured perpendicular to the forces and not just directly to the center of pressure and center of gravity. Also notice that the direction of the force determines the direction of the torque. Forces and torques are vector quantities having a magnitude and a direction. The direction is as important as the magnitude.

In equilibrium, these torques are balanced and there is no rotation of the kite about the bridle point. This is called a trimmed flight condition.

W * g = F * p

__The Tricky Part__In flight, a kite can rotate about the bridle point. As the kite rotates, the inclination angle between the kite and the wind changes. The magnitude and direction of the aerodynamic force depends on this angle and the ratio of the lift and dragwhich depends on the design of the kite. So as the kite rotates, the aerodynamic force changes and this changes the aerodynamic torque about the bridle point as discussed above. If the changing aerodynamic torque balances the weight torque, the kite reaches an equilibrium condition and sits at a fixed inclination angle with no further rotation about the bridle point. But if the aerodynamic torque does not equal the weight torque, the kite continues to rotate under the action of the unequal torques. It is possible that the aerodynamic torque never equals the weight torque which causes the kite to continually rotate.

In equilibrium the kite is inclined to the wind (and to the ground) at a fixed angle and the magnitude of the lift force depends directly on this angle. Since the weight of the kite is constant, the difference between the lift and the weight is an indication of how well the kite flies. If the lift is greater, the kite climbs faster, flies higher, and is able to lift more string. If the lift is less, the kite climbs slowly or maybe not at all! Since the flight angle depends on the balance of torques, and the torques depend on the location of the bridle point relative to the cg and cp, the location of the bridle point has a major effect on the performance of the kite. The location of the bridle point can be changed by the flyer before launch by moving the knot that holds the line to the bridle.

The mathematical equations involved with the forces and torques on a kite can be solved by using a computer program. You can use the KiteModeler program to further study how kites work and to design your own kites.

单击此处进行编辑。

An excellent way for students to gain a feel for aerodynamic forces is to fly a kite. Kites fly because of forces acting on theparts of the kite. Though kites come in many shapes and sizes, the forces which act on the kite are the same for all kites. You can compare these forces to the forces that act on an airliner in flight and you will find that, replacing the thrust with the tension in the line, they are exactly the same. The similarity in forces allowed the Wright brothers to test their theories of flight by flying their aircraft as kites from 1900 to 1902.

On this slide we show the aerodynamic equations which would describe the motion of a flying kite. The graphic shows a side view of the flying kite with the aerodynamic lift and drag shown by the blue vectors. The wind is blowing parallel to the ground. The drag is in the direction of the wind, while the lift is perpendicular to the wind. Both aerodynamic forces act through the center of pressure, the black and yellow dot on the kite.

Since the forces on a kite are the same as the forces on an airplane, we can use the mathematical equations developed to predict airplane performance to predict the aerodynamic performance of a kite. In particular, the lift equation and the drag equation, shown on the upper right side of the slide, have been developed to determine the magnitude of the aircraft forces. The lift

L = Cl * A * r * .5 * V^2

Similarly, the drag

D = Cd * A * r * .5 * V^2

The magnitude of these forces depend on the lift coefficient, Cl, and the drag coefficient, Cd, which depend on geometric properties of the kite and the angle between the kite surfaces and the wind. The coefficients are usually determined experimentally for aircraft. But the aerodynamic surfaces for most kites are simple, thin, flat plates. So we can use some experimental values of the lift and drag coefficients for flat plates to get a first order idea of our kite performance. The values of these coefficients are given on separate slides for lift and drag.

The aerodynamic forces on your kite depend directly on the surface area of the kite. You first learn how to compute thearea for a geometric shape while you are in middle school. The surface area depends on the particular design of your kite.

The aerodynamic forces also depend on the air velocity and density. In general, the density depends on your location on the earth. The higher the elevation, the lower the density. The standard value for air density

r = 1.229 kg/m^3 or .00237 slug/ft^3.

The variation with altitude is described on a separate page. The air velocity is the relative speed between the kite and the air. Since the kite is held fixed by the control line, this reduces to the wind speed. The aerodynamic forces change with thesquare of the velocity.

The mathematical equations involved with the forces and torques on a kite can be solved by using a computer program. You can use the KiteModeler program to further study how kites work and to design your own kites.

On this slide we show the aerodynamic equations which would describe the motion of a flying kite. The graphic shows a side view of the flying kite with the aerodynamic lift and drag shown by the blue vectors. The wind is blowing parallel to the ground. The drag is in the direction of the wind, while the lift is perpendicular to the wind. Both aerodynamic forces act through the center of pressure, the black and yellow dot on the kite.

Since the forces on a kite are the same as the forces on an airplane, we can use the mathematical equations developed to predict airplane performance to predict the aerodynamic performance of a kite. In particular, the lift equation and the drag equation, shown on the upper right side of the slide, have been developed to determine the magnitude of the aircraft forces. The lift

**L**is equal to a lift coefficient**Cl**times the projected surface area**A**times the air density**r**times one half the square of the wind velocity**V**.L = Cl * A * r * .5 * V^2

Similarly, the drag

**D**is equal to a drag coefficient**Cd**times the projected surface area**A**times the air density**r**times one half the square of the wind velocity**V**.D = Cd * A * r * .5 * V^2

The magnitude of these forces depend on the lift coefficient, Cl, and the drag coefficient, Cd, which depend on geometric properties of the kite and the angle between the kite surfaces and the wind. The coefficients are usually determined experimentally for aircraft. But the aerodynamic surfaces for most kites are simple, thin, flat plates. So we can use some experimental values of the lift and drag coefficients for flat plates to get a first order idea of our kite performance. The values of these coefficients are given on separate slides for lift and drag.

The aerodynamic forces on your kite depend directly on the surface area of the kite. You first learn how to compute thearea for a geometric shape while you are in middle school. The surface area depends on the particular design of your kite.

The aerodynamic forces also depend on the air velocity and density. In general, the density depends on your location on the earth. The higher the elevation, the lower the density. The standard value for air density

**r**at sea level conditions is given as:r = 1.229 kg/m^3 or .00237 slug/ft^3.

The variation with altitude is described on a separate page. The air velocity is the relative speed between the kite and the air. Since the kite is held fixed by the control line, this reduces to the wind speed. The aerodynamic forces change with thesquare of the velocity.

The mathematical equations involved with the forces and torques on a kite can be solved by using a computer program. You can use the KiteModeler program to further study how kites work and to design your own kites.

An excellent way for students to gain a feel for aerodynamic forces is to fly a kite. Kites can fly because of the forces acting on the parts of the kite. Though kites come in many shapes and sizes, the forces which act on a kite are the same for all kites and are shown on this slide. You can compare these forces to the forces acting on an airliner in flight and you will find that, with the tension substituting for thrust, they are exactly the same. The similarity in forces allowed the Wright brothers to test their theories of flight by flying their aircraft as kites from 1900 to 1902.

This page shows a

On the page, there are three principle forces acting on the kite; the weight, the tension in the line, and the aerodynamic force. The weight

When the kite is in stable flight the forces remain constant and there is no net external force acting on the kite, from Newton's first law of motion. In the vertical direction, the sum of the forces is zero. So, the vertical pull plus the weight minus the lift is equal to zero.

Pv + W - L = 0

In the horizontal direction, the sum of the horizontal pull and the drag must also equal zero.

Ph - D = 0

With some knowledge of the kite geometry and the velocity of the wind, we can determine the value of the lift and drag. And with knowledge of the kite geometry and the materials used to make the kite we can determine the weight. We can then solve the two equations given above for the horizontal and vertical components of the tension in the line.

Near the bridle point, the line is inclined at an angle called the bridle angle

tan b = Pv / Ph

where

The relative strength of the forces determines the motion of the kite as described by Newton's laws of motion. If a gust of wind strikes the kite, the lift and drag increase. The kite then moves vertically because the lift now exceeds the weight and the vertical pull, and the tension force increases because of increased drag. Eventually a new balance point is established and the kite achieves a different stable condition. Because of the change in relative strength of the aerodynamic and weight forces, the kite also rotates about the bridle point to balance the torques.

This page shows a

**free body diagram**of the kite. In a free body diagram, we draw a single object and all of the forces which act on that object. Forces are vectors having both a magnitude and a direction, so we draw each force as an arrow with the length proportional to the magnitude and the head of the arrow pointing in the direction of the force. An important property of vectors is that they can be broken down into perpendicular components, and we can develop scalar equations in each component direction.On the page, there are three principle forces acting on the kite; the weight, the tension in the line, and the aerodynamic force. The weight

**W**always acts from the center of gravity toward the center of the earth. The aerodynamic force is usually broken into two components (shown in blue); the lift**L**, which acts perpendicular to the wind, and the drag**D**, which acts in the direction of the wind. The aerodynamic force acts through the center of pressure. Near the ground, the wind may swirl and gust because of turbulence in the earth's boundary layer. But away from the ground, the wind is fairly constant and parallel to the surface of the earth. In this case, the lift is directly opposed to the weight of the kite, as shown in the figure. The tension in the line acts through the bridle point where the line is attached to the kite bridle. We break the tension into two components, the vertical pull**Pv**, and the horizontal pull**Ph**.When the kite is in stable flight the forces remain constant and there is no net external force acting on the kite, from Newton's first law of motion. In the vertical direction, the sum of the forces is zero. So, the vertical pull plus the weight minus the lift is equal to zero.

Pv + W - L = 0

In the horizontal direction, the sum of the horizontal pull and the drag must also equal zero.

Ph - D = 0

With some knowledge of the kite geometry and the velocity of the wind, we can determine the value of the lift and drag. And with knowledge of the kite geometry and the materials used to make the kite we can determine the weight. We can then solve the two equations given above for the horizontal and vertical components of the tension in the line.

Near the bridle point, the line is inclined at an angle called the bridle angle

**b**. The magnitude of this angle is related to the relative magnitude of the components of the tension.tan b = Pv / Ph

where

**tan**is the trigonometric tangent function. Knowing the bridle angle, the length of line, and the weight per length of line, you can predict the height at which the kite flies. You can use the KiteModeler program to solve all the equations shown on this slide.The relative strength of the forces determines the motion of the kite as described by Newton's laws of motion. If a gust of wind strikes the kite, the lift and drag increase. The kite then moves vertically because the lift now exceeds the weight and the vertical pull, and the tension force increases because of increased drag. Eventually a new balance point is established and the kite achieves a different stable condition. Because of the change in relative strength of the aerodynamic and weight forces, the kite also rotates about the bridle point to balance the torques.

Please read the chapter " IMPORTANT kite design parameters"