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Intro To Technology

Intro To Technology

2009-2010

Hover Craft Guide

Name:

Pages #

Chapter

Experiment(s)

(page #)

3-4

1:What is a Hovercraft & How Does it Work?

1.1(74)

5-8

2: Velocity &Acceleration

9-12

3: Newton's Laws of Motion

3.1(76) 3.2(77)

13-16

4: Why a Hovercraft Hovers: Pressure &Lift

4.1(78)

17-19

5: Why a Hovercraft Works: Buoyancy

5.1(86)

20-22

6: Drag

23-34

7: Thrust

7.1(91)

25-30

8: Bernoulli's Principle & the Coanda Effect

8.1(93) 8.2(94) 8.5(96) 8.4(97)

31-32

9: Torque

9.1(98)

33-38

10: Gear Ratio

10.1(102)

39-43

11: Torque, Work, and Power

44-45

12: Control

46-48

13: Momentum

49-52

14: Kinetic & Potential Energy

53-56

15: Electric Charges and Forces

15.1(105) 15.2(107)

57-71

Vocabulary List

72-73

Unit Conversion Sheet

WHAT IS A HOVERCRAFT AND HOW DOES IT WORK?

NAME

DATE

Sometimes called an air-cushion vehicle or ACV, a hovercraft rides on a cushion of air instead of wheels to go over many surfaces. A multi-blade fan forces air under the hull of the hovercraft, creating a high-pressure region called the lift air cushion and making the craft float. The hovercraft lifts off the surface it's resting on when the lift air pressure is greater than the total weight of the hovercraft divided by the area of the lift air cushion. It then hovers just above the surface. Because most surfaces are uneven, additional height is needed so the craft can travel without getting the bottom of the hull caught on anything.

To increase the clearance between the bottom of the hovercraft and any uneven surfaces, a flexible fabric skirt is attached to the bottom outside edge of the hull. This creates a wall that traps the lift air, forcing the hovercraft to rise higher above the surface, 6-9 inches [15.24 22.86 cm] in most cases, giving the hovercraft a smooth ride and allowing it to clear obstacles.

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Because the hovercraft only puts a very small pressure on the surface its riding over, it can easily be flown over mud, short grass, sand, water, ice, snow, or pavement. Hovercraft also use air to move forward. Many hovercraft use an engine with an airplane-type propeller or multi-blade axial fan to push air behind the hovercraft, creating forward thrust. Often, a circular enclosure called a thrust duct is built around the propeller. By using a thrust duct built so the tips of the propeller travel within 1/8 inch [0.3175 cm] of the inside face of the duct, the thrust output of the propeller can be increased by 10-15%. (Fowler. Circa: 1993) The thrust determines how fast the hovercraft can go and how steep a grade (like a boat ramp) it can climb.


Steering a hovercraft is accomplished using rudders, similar to those on an airplane. The rudders are mounted behind the thrust duct to put them directly in the flow of the thrust air. Their position also gives them a mechanical advantage in turning the hovercraft, similar to the effect that moving a long lever is easier than moving a short lever. As the rudders turn, the thrust air is deflected left or right, forcing the hovercraft to change direction. Rudders are made with a symmetrical airfoil profile to minimize air drag and increase their efficiency. Most hovercraft use at least 2 rudders, some as many as 5. In the following handouts we will investigate the science behind what makes a hovercraft work.


VELOCITY AND ACCELERATION

NAME

DATE

Before beginning to discuss how hovercraft and other objects move, we need a way to measure motion. Terms like speed, velocity, and acceleration are all familiar, but lets investigate exactly how they are related and how they are measured.

Speed is a change in an objects position with respect to time. This can be found by measuring how far an object travels in a certain amount of time. For example, if a hovercraft traveling at a constant speed goes 100 miles [161 km] in two hours, its speed was 50 mph (miles per hour) [80.5 km/h]. Just divide how far the hovercraft went by how long it took to get there. Often the term velocity is used instead of speed, but these two terms are a little different. Velocity is a measure of both speed and direction of an object. Imagine one hovercraft traveling 60 mph [96.6 km/h] north on a river, and another hovercraft traveling 60 mph [96.6 km/h] south on a river. These two hovercraft would have the same speed, but different velocities because they are traveling in different directions. As you can see, velocity is a more detailed description of how fast something is traveling. An equation for calculating velocity is given below.

Velocity =

change in position

change in time

Acceleration measures the change in velocity with respect to time. Its pretty clear that speeding up and slowing down are both forms of acceleration, but remember that acceleration is change in velocity, not necessarily speed. When a hovercraft turns, even if its speed isnt changing, its accelerating because its direction, and therefore velocity, is changing.

Acceleration =

change in velocity

change in time

In our world, objects are constantly accelerating and decelerating, and this can become quite difficult to test with a model. If we only look at cases in which the acceleration is constant, it becomes much easier to model and to calculate. In fact, we can model any motion along a straight line using only 4 formulas as long as we assume acceleration is always constant.

Formulas for Motion when Acceleration isnt Changing

v = v0 + at

x = x0 + (v + v0)t

v = v0 + 2a(x x0)

x = x0 + v0t + at

In these formulas, x refers to the position of the object, v refers to its velocity, a gives its acceleration, and t gives the time at which these variables are measured. You can see that some of the variables have little zeros next to them. For example, x0 is pronounced x naught (sounds like not). These are used to represent initial conditions, so x0 represents the position of the object initially (at time t =0), while x represents the position of the object at time, t. Well do a few examples to see how these formulas work.

Example 1: (Using Imperial units)Starting from a stop, a hovercraft accelerates at 5 feet per second squared. How fast will the hovercraft be traveling when it reaches 500 ft from where it started?

Solution:Lets begin by listing the variables that were given and the ones we need to find. We are given the acceleration, and since the hovercraft starts from a stop, we know that the initial velocity is zero. Since we know the hovercraft travels 500 ft, we can say the initial position is 0 ft and the final position is 500 ft. We need to solve for the final velocity.

a = 5 ft/s v0 = 0 ft/s x0 = 0 ft x = 500 ft v = ? ft/s

Now we need to find one of the formulas just mentioned that has the one variable were looking for as well as variables that we have values for. It looks like formula (3) has everything we need and nothing we dont. Now we can put in all the values and calculate the final velocity.

v = v0 + 2a(x x0)v = (0 ft/s) + 2 (5 ft/s) (500 ft 0 ft)v = 2 (5 ft/s) (500 ft)v = 5000 ft/sv = 70.7 ft/s

500 ft from where it started, the hovercraft will be traveling 70.7 ft/s [48.2 mph].

Example 2: (Using Imperial units)The same hovercraft accelerates from a stop at 5 ft/s. How far will it travel and how fast will it be going after 10 s?

Solution:Again well start by listing what variables we know and which ones we need to find.

a = 5 ft/s v0 = 0 ft/s x0 = 0 ft t = 10 s x = ? ft v = ? ft/s

If we start by just trying to find x, it looks like equation (4) is the one to use.

x = x0 + v0t + atx = (0 ft) + (0 ft/s) (10 s) + (5 ft/s) (10 s)x = (5 ft/s) (100 s)x = 250 ft

We know that the hovercraft will be 250 ft away after 10 s, now we need to find how fast it will be going when it gets there. We can find this with equation (1).

v = v0 + atv = (0 ft/s) + (5 ft/s) (10 s)v = 50 ft/s

After 10 s, this hovercraft will be 250 ft away from where it started, traveling 50 ft/s.

The first two examples we calculated using Imperial units. Now well try one using System International(SI) units.

Example 3: (Using SI units)A hovercraft drives past a bush traveling at 15 m/s and continues traveling towards a tree standing 200 m away from the bush. The hovercraft passes the tree 10 s after it passed the bush. Assuming the hovercraft maintained a constant acceleration, how fast was it traveling when it passed the tree?

Solution:This problem is a little harder, but if we stick to the same strategy we can figure it out.

v0 = 15 m/s x0 = 0 m x = 200 m t = 10 s v = ? m/s

For this one were going to use equation (2), but v is buried inside the equation so we have to get it out.

x = x0 + (v + v0)t(200 m) = (0 m) + (v + 15 m/s) (10 s)(200 m) = (5 s) (v + 15 m/s)(40 m/s) = (v + 15 m/s)v = 25 m/s

Our calculation shows that the speed of the hovercraft increases from 15 m/s to 25 m/s by the time it reaches the tree.

As you can see in the examples, the trick to figuring out which formula to use for these problems is to list all the variables you have values for and the

NEWTONS LAWS OF MOTION

NAME

DATE

Now that we have ways to measure the motion of a hovercraft, we can begin to investigate why they move the way they do. A good start is to introduce three of the most fundamental laws of motion. These three laws have been named Newtons Laws of Motion, after Sir Isaac Newton. Although they were formulated hundreds of years ago, they work so well that they are still widely used to calculate the motion of everything from pool balls colliding to planets traveling through space.

Sir Isaac Newton

1642 1727

Newtons first law, often called the Law of Inertia states the following:

An object in motion tends to stay in motion, and an object at rest tends to stay at rest unless acted upon by an outside force.

- or -

An object with no net force acting on it will move at a constant velocity (which may be zero).

This means that when an object is moving, it should keep on moving at the same speed and in the same direction unless some outside force is acting on it. It also means that an object at rest ( not moving ) will stay at rest until some force causes it to start moving. If youve ever seen a video of astronauts in space, this law makes more sense. The astronauts can float without moving because there is no net force acting on them. If they push off the wall of the space ship, they will float away at a constant speed and direction and wont stop until they collide or push off something else.

In order to understand how an object will move, you just need to know what forces are acting on it. Lets describe some of the most common forces. The first is one that has been acting on you your entire life: gravity. Earths gravity is constantly pulling you down towards the center of the earth. When you jump into the air, you exert a force that pushes you up from the ground. Since this force is greater than gravity, you go up. Once youre in the air, gravity becomes the only force acting on you and pulls you back down.

A second familiar force is called contact force. When two objects are touching each other, they are exerting a contact force. When you push or throw something, you exert a contact force on it. Go back to the jumping example. After you jump into the air and begin to fall back down due to gravity, the Law of Inertia says that you should continue that downward motion. If gravity had its way youd keep falling towards the center of the earth, but you stop when you hit the ground because the ground exerts a contact force on you. When youre standing on the ground, Earths gravitational force is pulling you down, but the ground is exerting a contact force pushing you up. These two forces have the same magnitude, or strength, but act in opposite directions, so they cancel each other out. Even though both of these forces continue to act on you, we say there is no net force because they cancel each other out. The term net force refers to the directional sum of all the forces. When two forces act in the same direction, they add together. When they act in the opposite direction, one is subtracted from the other. If two forces that are equal in strength act in the opposite directions, they cancel each other out completely.

A third force you encounter all the time but may not realize it is friction. Friction is a force that opposes motion between two objects in contact. If you push a box across a floor and then stop pushing, it will slide for a while but soon come to a stop because friction opposes the motion between the box and the floor. If you go to a skating rink and push that box across the ice, it will slide further because there is less friction between the box and the ice. It will still eventually come to a stop. Hovercraft, in fact, were invented as a way of reducing this sliding friction! Another form of friction is called wind resistance. If you stick your hand out of the window of a fast moving car, you feel a force pushing your hand back. This is caused by friction between your hand and the air its moving through. If you stick your hand out of a moving hovercraft, you will also feel the wind resistance, but something interesting happens. Hovercraft are designed to have so little friction as they move that the small amount of wind resistance that occurs when you stick your hand out to the side of the hovercraft is enough to make the hovercraft turn in that direction!

We now have a better concept of what forces are, and we know from Newtons first law that if there is no net force on an object, its velocity doesnt change. Exactly how the velocity changes if there is a net force acting on the object is described by Newtons Second Law. It is most easily stated with the following formula:

F = m a

- or -

Force = Mass Acceleration

This means that anytime a net force acts on an object, that object will accelerate. It also states that more massive objects require more force to achieve the same acceleration as less massive objects. This is why you have to push harder to move a big desk than a small chair.

Given what we know about velocity and acceleration, this second law really agrees with the first law. The equation for the second law states that a force leads to an acceleration, so if no net force is acting on an object, it will not be accelerated. No acceleration means that the velocity doesnt change, so no force equals constant velocity just like the first law states!

Knowing the relationship between force and acceleration means we can clear up one of the most common misconceptions in all of science: the relationship between mass and weight. Its very common to believe that kilograms are just the SI (System International) equivalent of pounds and vice versa, but this isnt true. The pound is a measure of weight in the Imperial unit system, and its equivalent in SI is the Newton, named after Sir Isaac Newton. Weight is actually a measure of the force that gravity exerts on an object. The kilogram is a unit of mass in SI. Although practically never used, the unit for mass in the Imperial system is called a slug. Refer to the unit conversion sheet to see exactly how these units are related.

The pound is therefore a measure of force exerted by gravity while the kilogram is a measure of the mass of an object. When you convert between pounds and kilograms, youre essentially using Newtons second law. The reason we can convert so easily is because of the way gravity acts. On earth, gravity acts to accelerate all objects the same, regardless of the mass. If you drop a bowling ball and a pebble from a bridge, they will hit the bottom at the same time because gravity accelerates them the same. If acceleration is constant for all masses and forces, then you can easily interchange between the two. Keep in mind, however, that mass and weight are different concepts. If youve seen a video of astronauts on the moon you would have noticed that they seem to weigh very little as they almost float around on the surface of the moon. This is because they really do weigh less on the moon than on the earth. Their mass, on the other hand, stays exactly the same.

We can now finish up with Newtons Third Law, which states:

For every action there is an opposite and equal reaction.

This means that for every force that is exerted on an object, the object exerts back an equal force in the opposite direction. This can be demonstrated with two pool balls. If the cue ball runs into the eight ball, it will exert a force on the eight ball, causing it to accelerate away. At the exact same time, the eight ball will exert the exact same amount of force on the cue ball in the opposite direction, which causes the cue ball to decelerate. Essentially this means that all forces exist in pairs. You push against a wall, it pushes back. If you bang your head against a wall, youre exerting a force on the wall. Keep doing this and the headache youll get will demonstrate the walls force exerting back on you! When a rifle is shot it forces the bullet forward, but the bullet, in turn, pushes back on the rifle. You can see this in the way the gun recoils after a shot, and you can feel it in your shoulder. It may be hard to believe, but this also works for gravity. The earth is pulling you with a force due to your mass, but you are also gravitationally pulling back on the earth with the same force. The earth doesnt really notice this however, because its mass is so huge that the earths acceleration caused by you is very small according to Newtons second law.

Continue to Experiment 3.1

Why a Hovercraft Hovers: Pressure and Lift

NAME

DATE

Lift air, like other gasses, is considered to be a fluid because it takes the shape of the container surrounding it. In the case of a hovercraft, the air takes the shape of the bottom of the hovercraft, the inside edges of the skirt, and the surface it's hovering above. The fan that blows air under the bottom of the hovercraft keeps pushing more and more air below the hovercraft, thus increasing the pressure in the air cushion. The pressurized air cushion exerts a force on its container (the bottom of the hovercraft, the skirt, and the surface the hovercraft is resting on). When the force this pressurized air exerts on the surface grows to equal the weight of the hovercraft, it becomes buoyant (like a boat in water) and begins to float on air.

When a hovercraft hovers, it will lift as high as the skirts designed shape will permit. Lift air begins escaping through the gap between the bottom of the skirt and the surface it's over. The size of this gap will be large enough so that the same amount of air escapes through the gap as is pushed in by the fan, keeping the pressure inside the air cushion constant. Usually, this air gap will be 0 to inches [12.7 mm] between the skirt bottom and the surface and is called daylight clearance.

Sketch by J. Benini

Pressure is defined as the force exerted on a surface per unit area of the surface.

Pressure = Force Area

P = F A

In order to calculate the lift force of a hovercraft, we solve this equation for the force.

F = P A

The lift force is therefore the air pressure inside the air cushion multiplied by the area enclosed by the hovercraft skirts.

Example:A typical pressure inside the air cushion of a Discover Hover One hovercraft is roughly 7 pounds per square foot, or 7 lbs / ft2 [335 N / m2]. If the hovercraft is 10 ft [3 m] long and 5 ft [1.5 m] wide, what is the total lift force produced by this hovercraft?

Solution: First we must calculate the area of the hovercraft. This is done by multiplying the length times the width. The solution will be worked out in both Imperial and System International units.

Imperial UnitsArea = Length WidthArea = (10 ft)(5 ft) Area = 50 ft2

S I UnitsArea = Length WidthArea = (3 m)(1.5 m)Area = 4.5 m2

Now we can find the lift force by multiplying the pressure times the area.

Lift force = Pressure AreaLift force = (7 lbs / ft2)(50 ft2)Lift force = 350 lb

Lift force = Pressure AreaLift force = (335 N / m2)(4.5 m2)Lift force = 1508 N

This hovercraft produces 350 lb [1508 N] of lift force and will therefore be able to support up to 350 lb [1508 N] of total weight and still hover. This means if the actual hovercraft weighed 100 lb [444.8 N], then it could carry 250 lb [1112 N] of people and cargo.

In the case of hovercraft, there are two forms of pressure that can be measured: static pressure and dynamic pressure. Static pressure is the pressure of a stationary region of air, while dynamic pressure is the pressure of air that is in motion. Static pressure is what lifts the hovercraft. If you measure the pressure of the lift air cushion by placing a manometer (a device that measures pressure) just under the skirt, you will obtain a different value than if you were to measure the pressure further inside the cushion. This is because the air is moving rapidly out of the bottom of the skirt, so you could be measuring dynamic and static pressure at the same time. At the cushion center, the lift air is more static.

The Discover Hover One hovercraft is an integrated hovercraft. Only one propeller is used to provide both lift and thrust air. Other hovercraft designs have separate lift and thrust systems. The sole purpose of the fan is to maintain the pressure inside the air cushion under the hovercraft. A multi-bladed fan is used for lift because it's better (more efficient) at pumping pressure than a propeller with just two blades. A separate propeller mounted on the back of the hovercraft is responsible for driving the hovercraft forward.

Integrated type Separate lift and thrust systems

Sketch by J. Benini

In the integrated hovercraft, the lift air is divided by a splitter usually located at the bottom of the thrust duct, as shown above. By placing this splitter just after the propeller, a portion (usually 1/3 of the total air supply) is forced by the propeller and directed down into the air cushion by the splitter in order to maintain the pressure inside the cushion. The rest of the air is forced behind the hovercraft, propelling the hovercraft forward. A diagram of the various paths the intake air travels in an integrated type of hovercraft is shown below.


WHY A HOVERCRAFT WORKS: BUOYANCY

NAME

DATE

In the previous handout we discussed how the air pressure in the lift air cushion lifts the hovercraft off the ground. We assumed that the hovercraft was hovering above solid ground. Now lets investigate what happens when the hovercraft travels over water. In order to lift the hovercraft, the pressurized air must now push against the surface of the water. If you tried pushing your hand into a sink full of water, your hand would sink into the water. What keeps the hovercraft from sinking as well? The answer to this comes from one of the oldest established principles in the history of science: Archimedes Principle or the Law of Buoyancy.

Archimedes of Syracuse(287 BC - 212 BC)

According to legend Archimedes was struck by this principle while taking a bath when he noticed that the volume of water displaced was equal to the volume of his body. Overjoyed by his discovery, he jumped out of the bathtub and ran through the streets naked shouting, Eureka! Eureka! (Greek for Ive found it! Ive found it!) Developed in 250 BC, this principal explains why some objects float in water while others sink. The principle states the following:

When a body is immersed in fluid at rest it experiences an upward force or buoyant force equal to the weight of the fluid displaced by the body.

Notice when you get into a bathtub, the level of the water rises. This is because your body is now taking up some of the space where the water used to be. The water has to go somewhere else when it is pushed out of the way, so it goes up, making the water level rise. Youve just displaced that amount of water. Archimedes Principle says that a buoyant force will push upwards on you when youre in the water, and the strength of the force will be equal to the weight of the water that you pushed out of the way when you got in.

The same thing happens with boats. When a boat is placed in water, part of the boat goes beneath the surface of the water and pushes the water out of the way. According to Archimedes Principle, this results in a buoyant force that pushes up on the boat. The magnitude, or strength, of the force is equal to the weight of the water that would have filled the space that is now taken up by the boat. The boat floats in the water because this upward buoyant force is equal to the downward weight of the boat.

In order to do calculations using this principle, we need to know the weight of a certain volume of water that is displaced, or the weight density of water.

Weight Density = Weight Volume

The weight density of water is about 62.42 pounds per cubic foot ( lb/ft3). A cubic foot is a unit of volume equal to the volume inside a box whose sides are 1 ft long. In SI units (System International), the weight density of water is about 9806 Newtons per cubic meter ( N/m3).

Example:A boat is floating in the water and has 0.5 m3 of its volume below the surface of the water. What is the weight of the boat?

Solution:From Archimedes Principle, we know that the weight of the boat must be equal to the weight of the water that is displaced, or pushed out of the way. Since 0.5 m3 of the boat is below the surface of the water, its displacing 0.5 m3 of water. We can use the formula for density to determine what the weight of that much water will be. The weight density of water is 9806 N/m3

Weight Density = Weight VolumeWeight = Weight Density VolumeWeight = (9806 N/m3) (0.5 m3)Weight = 4903 N

A boat that displaces 0.5 m3 of water weighs 4903 N [1102 lb].

When a hovercraft travels over water, it acts a little differently than a boat, because the hovercraft itself doesnt actually displace any water. It is the pressurized air inside the lift air cushion that pushes down on the water, causing some of the water to be displaced. If you blow into a sink full of water, you can see that you create a small dimple in the water. Hovercraft do the same thing, except they create a larger depression in the water. In fact, we know that for every 5.2 lb/ft2 [24.9 N/m2] of pressure in the lift air cushion, the water underneath the hovercraft is depressed one inch [2.54 cm]. In the previous handout, we discussed how the pressurized air in the lift air cushion pushes the hovercraft up and causes it to hover. Now we see that not only does the pressurized air push up on the hovercraft, it also pushes down on the water.


DRAG

NAME

DATE

A hovercraft is able to glide or slide easily because there is so little contact friction with the surface it's hovering over. Still, there are forms of friction which come into play, and these frictional forces are usually called drag. Drag occurs in several forms, the most familiar being wind resistance, or form drag, which is created by the hovercraft having to push aside air as it moves forward. This effect increases more and more as the hovercrafts speed increases. Streamlining the shape of the hovercraft decreases the wind resistance, resulting in higher top speeds. While wind resistance is always present, it becomes much more of a problem at speeds of 30 mph [48.3 km/h] and above. Since Discover Hover hovercraft usually don't travel faster than 30 mph [48.3 km/h], wind resistance is not as noticeable as on other light hovercraft.

A hovercraft operating over water is subject to three other forms of drag not experienced on solid surfaces: wave drag, skirt drag, and impact drag. Wave drag (called hump drag at low speeds) occurs when lift air under the hovercraft pushes down on the surface of the water. Some of the water is displaced from under the hovercraft, creating a depression in the water. The total weight of the water displaced is equal to the weight of the hovercraft and pilot, according to Archimedes Principle. As the hovercraft starts moving forward, the depression moves with it and forms a small wave in front of the bow. This causes the bow (front of hovercraft) to rise and the stern (back of hovercraft) to sink a little. The hovercraft is, in effect, trying to fly "uphill". As the hovercraft increases speed, the bow wave increases in size. Eventually, the hovercraft will reach a speed where it's moving faster than the wave and "climbs" over it. Called planing speed, it is commonly referred to as "getting over the hump". At this point the hovercraft will accelerate rapidly. The moment before planing speed is reached, wave drag is at its greatest. When traveling above planing speed, the lift air under the hovercraft doesn't have enough time to depress the surface of the water and the wave drag decreases dramatically.

Wave drag caused by depression in the waters surface by the air cushion

Skirt drag occurs when the skirt contacts the surface of the water. This is worse when running over small waves.

Sketch by J. Benini

Impact drag happens when the skirt or hull strikes large waves on turbulent water or other objects, such as ice flows or ridges.

THRUST

NAME

DATE

So far weve discussed how pressurized air beneath the hovercraft causes it to hover, and we investigated what happens when hovering over water. We also looked into some of the drag forces encountered when moving through water. Lets examine how a hovercrafts forward motion is produced. A hovercraft moves by using air to create forward thrust. The propeller on the back of the Discover Hover One forces air towards the rear. How does forcing air behind the hovercraft produce forward thrust? Remember Newtons third law: Every action has an opposite and equal reaction. The propeller exerts a force on the air when it pushes it behind the hovercraft. The air, in turn, exerts a force back on the propeller in the opposite direction. This causes the propeller, as well as the rest of the hovercraft, to be accelerated forward.

When designing propeller systems for hovercraft, efficiency is a big concern. Efficiency is the ratio of how much work is produced divided by how much work is put into the system. In order to produce forward thrust (the output), we must power the propeller with a fuel-driven engine (the input). Engineers try to get as much output work as possible for the least amount of input work. Unfortunately, you can never get out as much work as you put in. The heat produced by the engine, the noise produced by both the engine and the propeller, and the vibrations you can feel in the hull are just some examples of wasted energy that isnt being used to produce thrust.

One way to increase the efficiency of a propeller is by surrounding it with a circular enclosure called a thrust duct. In a small hovercraft, a properly built thrust duct can add a 10%-15% increase to the total thrust output, compared to a non-ducted propeller.

Example of a hovercraft thrust duct

To function properly, a thrust duct must be of an aerodynamic shape and smooth on the inside. The propeller tips should be no more than 1/8 of an inch [0.3175 cm] away from the inside wall. If there is too much space between the thrust duct and the propeller tips, the air will move from the back of the blade (higher pressure) to the front of the blade (lower pressure). This reduces the fan or propeller efficiency because it causes turbulence. The closer the propeller tips are to the wall of the duct, the more efficient they become. A typical propeller can produce 4 - 6 lb [17.79 26.69 N] of thrust per horsepower, or 23.8 35.8 N/kW. The length of a thrust duct is also important. Air resistance caused by the air dragging against the walls of the thrust duct as it is blown back will increase as the length of the thrust duct increases, causing the thrust output to decrease. A typical duct is 18 inches [45.7 cm] long, with the propeller positioned 7-8 inches [17.8-20.3 cm] behind the front bell mouth edge of the duct. This allows the propeller or fan to pull air into the thrust duct, compress it, and push it out of the rear of the duct.

According to Newton's second law, thrust can be calculated by multiplying the mass of the hovercraft by its acceleration. We can determine the acceleration of the hovercraft using the formulas we learned in Curriculum Guide #2. Remember that a hovercraft is affected by different drag forces depending on the surface it's flying over. When you calculate a particular thrust, it is for that particular situation you tested the craft in. Remember that for a fan or propeller, the thrust force decreases as forward speed increases! This is because as the speed of the hovercraft increases, so does the speed of the air that enters the thrust duct. Its harder for the propeller to accelerate air thats already moving fast, so it is unable to produce as much thrust at higher speeds.


BERNOULLIS PRINCIPLE AND THE COANDA EFFECT

NAME

DATE

A closer look at how propellers cause forward thrust will reveal that the hovercraft moves forward by pushing air behind it. Exactly how does the propeller push air behind it? To understand this we turn to a principle that was discovered about 300 years ago, Bernoullis Principle.

Daniel Bernoulli1700-1782

Bernoulli's Principle: An increase in the velocity of any fluid is always accompanied by a decrease in pressure.

Since air behaves exactly like a fluid, Bernoullis principle applies. Any time the wind is blowing or a fan blows air, the pressure of the moving air becomes less than it would be if the air wasn't moving. As an aside, this characteristic plays a huge role in how weather systems work! If you can cause air to move faster on one side of a surface than the other, the pressure on that side of the surface will be less than the pressure on its other side.

One of the most widely used applications of Bernoulli's principle is in the airplane wing. Wings are shaped so that the top side of the wing is curved while the bottom side is relatively flat. In motion, the front edge of the wing hits the air, and some of the air moves downward below the wing, while some moves upward over the top. Since the top of the wing is curved, the air above the wing must move up and down to follow the curve around the wing, while the air below the wing moves very little. The air moving on the top of the curved wing must travel farther before it reaches the back of the wing; consequently it must travel faster than the air moving under the wing, to reach the back edge at the same time. The air pressure on the top of the wing is therefore less than that on the bottom of the wing, according to Bernoullis principle. The higher pressure air on the bottom of the wing pushes up on the wing with more force than the lower pressure air above the wing pushes down. This results in a net force acting upwards called lift. Lift pushes the wings upwards and keeps the airplane in the air.

Though Bernoulli's principle is a major source of lift in an aircraft wing, a French engineer by the name of Henri Coanda discovered another effect that plays an even larger role in producing lift.

Henri Coanda1886 - 1972

Although generally unrecognized, Coanda was actually the first person to build and fly a jet powered aircraft. It is commonly believed that the first jet engines were developed during World War II. Dr. Hans Von Ohain designed the first German jet aircraft, which made its first flight on August 27, 1939. Unaware of Dr. Von Ohain's work, A British engineer named Sir Frank Whittle also independently designed a jet aircraft, which first flew on May 15, 1941.

Although these two men are generally thought of as the fathers of jet aircraft, Henri Coanda built and "flew" the first recorded jet aircraft about 30 years earlier. The somewhat amusing first flight is best described in Coanda's own words:

"It was on 16 December 1910. I had no intention of flying on that day. My plan was to check the operation of the engine on the ground but the heat of the jet blast coming back at me was greater than I expected and I was worried in case I set the aeroplane on fire. For this reason I concentrated on adjusting the jet and did not realize that the aircraft was rapidly gaining speed. Then I looked up and saw the walls of Paris approaching rapidly. There was no time to stop or turn round and I decided to try and fly instead. Unfortunately I had no experience of flying and was not used to the controls of the aeroplane. The aeroplane seemed to make a sudden steep climb and then landed with a bump. First the left wing hit the ground and then the aircraft crumpled up. I was not strapped in and so was fortunately thrown clear of the burning machine."

The Coanda- 1910, the world's first jet aircraft

Unfortunately Coanda couldnt obtain funding to continue his research after the wreck, and so his contribution to jet propulsion never became widespread. If he had been able to continue his work, France could have had a jet-powered air force before WW II began. Even though he didn't build another jet aircraft, he did make a very important contribution to how the aircraft wings produce lift when he discovered what is now called the Coanda Effect.

Coanda Effect: A moving stream of fluid in contact with a curved surface will tend to follow the curvature of the surface rather than continue traveling in a straight line.

To perform a simple demonstration of this effect, grab a spoon and find a sink. Get a small stream of water coming down from the sink, then place the bottom of the spoon next to the stream. Notice how the water curves along the surface of the spoon. If you hold the spoon so that it is free to swing, you should be able to notice that the spoon is actually being pulled towards the stream of water.

The same effect occurs with an airplane wing. If the wing is curved, the airflow will follow the curvature of the wing. In order to use this to produce lift, we need to understand something called angle of attack. This gives the angle between the wing and the direction of the air flow, as shown in the following diagram.

The angle of attack indicates how tilted the wing is with respect to the oncoming air. In order to produce lift, or an upward force acting on the wing, Newton's third law says that there must be an equal force acting in the opposite direction. If we can exert a force on the air so that it is directed down, the air will exert an upward force back on the wing. Look at how the Coanda effect directs the airflow for different angles of attack in the diagrams below.

This diagram shows that increasing the angle of attack increases how much the air is deflected downwards. If the angle of attack is too great, the air flow will no longer follow the curve of the wing. As shown in the bottom of the diagram, this creates a small vacuum just behind the wing. As the air rushes in to fill this space, called cavitation, it causes heavy vibrations on the wing and greatly decreases the efficiency of the wing. For this reason, aircraft wings are generally angled like the middle wing in the diagram. This wing efficiently directs the airflow downward, which in turn pushes up on the wing, producing lift.

This method of determining lift is called momentum change. Other methods to calculate the same lift utilize the difference in pressure fields above and below the wing. Either method is accurate on its own, but never add the two methods together.

In addition to producing lift on an aircraft, Bernoulli's principle and the Coanda effect play an important role in the operation of a propeller. Examine a propeller closely and you will find that the blades of the propeller look like an airfoil, or wing. Essentially, a propeller blade is a wing turned on its side. Just as wings traveling forward are lifted upward, a rotating propeller blade is sucked or pushed forward. A propeller blade also has something that wings don't: they are twisted. Watch a propeller turn very slowly, and you will see how the twist of the blade causes it to move the air evenly and push it backwards. Additionally, the propeller blades are set at an angle. This is called propeller pitch. The greater the pitch of the propeller, the more air it can push. Blades of common household fans are also slightly angled to help move air for cooling. Ideally an equal quantity of air will pass the blade at its root (the hub of the propeller) and its tip, but the tip travels much faster than the root. To maintain an even flow rate as much as possible, the hub pitch (pitch at the root of the propeller) has to be very steep while the propeller tips have to be almost flat! This will help insure an even flow of air through the duct.


TORQUE

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Torque is rotational mechanical force. Screws, bolts, engines, electric motors, flywheels, fans, and propellers all turn or rotate. The amount of force applied at a point on a rotating object, multiplied by the distance from the point of rotation determines the amount of torque. Torque forces are classified as causing either clockwise (cw) or counterclockwise (ccw) , sometimes called anticlockwise, rotation, determined by observing the rotation of the object as it faces you.

Torque = Force Length of lever arm

Length of lever arm is a way of saying the distance between where the force is applied and the point of rotation. In order to tighten or loosen a bolt, you have to exert a torque on it. Using a wrench, the torque applied is equal to the amount of force used to pull the wrench multiplied by the distance between your hand and the center of the bolt. If youve ever used a wrench you probably know that its easier to tighten a bolt when holding the wrench at its end and harder to pull when you move your hand closer to the bolt. This is because the further your hand is from the bolt, the longer the lever arm, and the larger the torque.

Example: You and a friend are on a see-saw trying to balance on either side. Your friend weighs 200 lbs [889.6 N] and is sitting 3 ft [0.914 m] from the see-saws point of rotation. You weigh 150 lbs [667.2 N]. How far from the point of rotation do you have to sit in order to balance the two torques on the see-saw?

Solution:In order for the see-saw to be balanced, the torque exerted by you has to be equal to the torque exerted by your friend. We must first calculate the torque produced by your friend, then use that to calculate the distance you have to sit from the center of the see-saw.

Imperial UnitsFriends Torque = Length of lever arm ForceFriends Torque = (3 ft) (200 lbs)Friends torque = 600 ft lbs

SI UnitsFriends Torque = Force Length of lever arm Friends Torque = (889.6 N) (0.914 m)Friends Torque = 813.1 N m

We know that the torque you exert must be equal to 600 ft lbs [813.1 N m] and we know your weight, so we can plug those values into the torque formula and calculate the length of the lever arm.

Torque = Distance to center Weight Distance to center = Torque WeightDistance to center = (600 ft lbs) (150 lbs)Distance to center = 4 ft

Torque = Weight Distance to centerDistance to center = Torque WeightDistance to center =(813.1 N m) (667.2 N)Distance to center = 1.22 m

Since you weigh less than your friend, you must sit further away from the see-saws point of rotation in order to produce the same torque as your friend. This will keep the see-saw balanced.


GEAR RATIO

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To make the concept of gear ratio easier to understand, lets first review some properties of circles. The radius of a circle is defined as the length from the center of the circle to the outside of the circle. If we draw a line that starts at one side of the circle, goes through the center, and then stops at the opposite side of the circle, we would have the diameter of the circle. The diameter is twice as long as the radius. Finally, if we measured the distance around the circle, wed get the circumference. It turns out that the circumference is equal to the diameter multiplied by Pi. Pi is often represented by the Greek symbol, , and is equal to 3.1415927 or a very strange ratio of 22 / 7 !

Now we can apply these concepts to look at how gears work. Look at the gears in the diagram. The radius of the gear is the distance from the center of the gear (where it rotates) to the outside of the gear. If gear A measures 10 in [25.4 cm] in radius and gear B measures 5 in [12.7 cm] in radius, then the radius of gear A is twice as large as gear B. We say that the gear ratio of gear A to gear B is 2:1. Additionally, we know that the diameter is twice the radius, and the circumference is times the diameter, so if the radius of gear A is twice the radius of gear B, then the circumference of gear A is also twice that of gear B. In the diagram of the two gears you can see that twice the circumference means that the gear has twice the number of teeth.

Imagine gear A starts to rotate. As its teeth touch the teeth of gear B a force is exerted. In the diagram this is shown as FA. If gear A rotates clockwise, the teeth of gear A push downwards on the teeth of gear B. This will cause gear B to move counter-clockwise. In this case, gear A is called the driving gear, and gear B is called the driven gear. If the gear ratio of A to B is 2:1, then there are twice as many teeth on gear A as on gear B. If you look where the two gears connect, you can see that the gear teeth alternate, that is a tooth from gear A is followed by a tooth from gear B, then one from gear A, then one from gear B, and so on. Since we said that gear A has twice as many teeth as gear B, then it will take twice as long for gear A to rotate once all the way around. This means that the gear A will rotate two times slower than gear B. This is very useful because we now have a way of speeding up and slowing down torque rotation!

We said that a gear that is half the size of another will rotate twice as fast. A gear that is one fourth the size of another will rotate four times as fast. This relationship is called a reciprocal. is the reciprocal of 2, and is the reciprocal of 4. To find the reciprocal of a number, you take one divided by the number.

Reciprocal of number = 1 number

We say that the gear ratio of two gears is the reciprocal of the ratio of their rotation speeds.

To calculate torque on two gears, use the formula for torque.

Torque = Force Length of lever arm

Gear A is exerting a force on gear B, but remember Newtons third law states gear B will, in turn, exert an equal force back on gear A. This means that the force on each gear is the same. The force applied to each gear occurs where the gear teeth are in contact on the outside of each gear, so the length of the lever arm for each gear is equal to the radius of the gear. Since the radius of gear A is twice the radius of gear B, the torque on gear A will be twice the torque on gear B. This is very useful because we now have a way of enlarging or reducing torque!

Lets review what gear ratio means. If the gear ratio of gear A to gear B is 4:1, we know the following. The radius, diameter, and circumference of gear A are all four times larger than gear B. We know that the torque on gear A will be four times greater than the torque on gear B. Finally we know that gear A will rotate at one fourth the speed of gear B. A larger gear will rotate slower than a smaller gear and have a greater torque, and the two gears will rotate in opposite directions.

When working with pulleys connected by a belt, the principles behind gear ratio, rotation speed, and torque are exactly the same. In the diagram, the pulley on the left has a radius equal to half the radius of the pulley on the right. This means that the pulley on the left will rotate twice as fast, but will have only half the torque.

Torque and gear ratios are important in designing what is called the hovercrafts transmission. Lightweight engines produce most of their horsepower at high rpm (revolutions per minute). Unfortunately, this would spin a propeller too fast for safety. To get maximum thrust from a propeller, the tips of the blades should rotate between 683.4 and 714.5 mph [1100 1150 km/h]. At speeds above this, the flow of air begins to detach itself from the propeller, decreasing efficiency and increasing noise. Propeller tip speed on a hovercraft should never run higher than 460 mph [641 km/h] tip speed for safety. It's often necessary to use a belt or gear driven system to slow the propeller but still let the engine reach its maximum horsepower. Using a small pulley on the engine and a larger pulley on the propeller will allow the propeller to turn more slowly than the engine. This is ideal for a two or four-bladed propeller, since they produce more thrust at slower speeds. They also produce less noise and develop more thrust per horsepower than fans with many blades.

Recall that the pitch of a propeller refers to the angle at which it is set, and a greater pitch means that the propeller can push more air and produce more thrust. Pushing greater amounts of air, however, requires more torque. If the pitch of the propeller is too great, it will strain the engine, making it unable to reach its maximum rpm. Too great a pitch can also cause the blade to "stall" where upon it will push almost no air. Choosing the right propeller pitch to maximize thrust while still allowing the engine to reach its maximum rpm is a very important step in designing a hovercraft.

The graph below is an example of what the characteristics of an engine and propeller could look like. The red curve shows the power output of the engine. Notice how it increases as rpm increases until it reaches a maximum at about 3400 rpm. It then quickly decreases as the speed continues to increase. The green curve represents how much power needs to be supplied to the propeller in order to keep it turning at the given speed. Notice how the faster the propeller spins, the more power is required. At lower rpms the red curve is higher than the green curve, meaning that the engine produces more power than is needed to keep the propeller spinning. At about 3700 rpm, the two curves intersect, meaning that the engine produces just enough power to keep the propeller spinning at that rpm. This is the most efficient engine speed to run at because no engine power is being wasted. Notice that at higher rpms the engine cannot produce the horsepower necessary to power the propeller.

This is only an example power profile. In fact, this graph could change drastically depending on the conditions the hovercraft is operating in. For example, the propellers curve can change quite a bit depending on if wind is blowing, and on what direction its blowing. No matter how the propeller or engine power profile changes, the engine speed at which the two curves intersect will indicate the point of maximum efficiency and maximum static thrust.


TORQUE, WORK, AND POWER

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Before taking a closer look at how torque, work, and power are involved in an engine, we need formal definitions of work and power. When we think of the words, work and power, many different meanings may come to mind. Work is often thought of as physical labor or something we get paid to do. Common meanings for power include the amount of energy something can produce, the electricity that we get out of electrical sockets, or a synonym for strength. According to physics, work and power have specific definitions, and were about to learn what those are.

When a force acts to move an object, work is done. This is written as

Work = Force Distance force acts

When you push something, how much work you do on it depends both on how hard you push it and how far you push it. In the Imperial system, work is measured in foot pounds (ft lb). The equivalent unit in the SI system is the Newton meter (N m), also known as the Joule (J). This is named after James Prescott Joule, a scientist who lived in the 1800s and made important discoveries in the field of thermodynamics, or the study of heat, work, and other forms of energy.

Example 1: (Using SI units)You pull a hovercraft with a force of 50 N along a sandbar that is 5 m long. How much work is done on the hovercraft?

Solution:The work done is equal to the force applied times the distance it acts across.

Work = Force DistanceWork = (50 N) (5 m)Work = 250 N mWork = 250 J

In pulling the hovercraft along the sandbar, you performed 250 J [184.4 ft lb] of work on the hovercraft.

Example 2: (Using Imperial units)Your hovercraft weighs 60 lb and is sitting on the floor. You need to lift it up onto two 3 ft high workhorses so the skirts can be changed. How much work is required to lift the craft?

Solution:In this case, we are lifting the craft up, so the force required is the weight of the craft. The calculation, however, is exactly the same.

Work = Force DistanceWork = (60 lb) (3 ft)Work = 180 ft lb

It will take 180 ft lb [244 J] of work to lift the hovercraft onto the horses.

Remember that torque can be thought of as a turning or twisting force. When we talk about work done by a torque, we multiply the torque by how much it turns, or the angle it rotates through.

Work = Torque Angle torque acts through

To turn an object, you exert a torque on it. How much it turns is given by the angle it turns through. For example, if you tighten a screw so that the screw twists one full revolution (360), you exerted a torque on that screw through an angle of 360.

Before we can do some examples, we need to know what units the angles are in. We are most familiar with angles in terms of degrees. When doing calculations with angles, however, we need to use a unit called radians. 1 radian is equal to about 57.3. Why would anyone want to make a new unit for angles which is equal to 57.3? Look at the figure of the circle. It shows both an angle of 1 and of 1 rad (short for radian). You can see that the angles cut out triangular pieces of the circle. The length of the portion of the circle contained in that triangular section is called the arc length. It turns out when the angle is 1 rad, the arc length is equal to the radius of the circle! Another interesting fact is that 1 full revolution (360) is equal to 2 radians. Half of a revolution (180) is therefore equal to radians. Remember that is equal to 22/7.

Example 3:It takes 10 ft lb [13.56 N m] of torque to turn a hovercraft propeller. If we turn the propeller so that it rotates 3 revolutions, how much work did we do on the propeller?

Solution:First we must determine the angle of rotation in the right units. This means converting 3 revolutions into radians. Remember that 1 revolution is equal to 2 radians, so 3 revolutions would be equal to 6 radians. Now we can calculate the work done.

Work = Torque AngleWork = (10 ft lb) (6)Work = (10 ft lb) (6) (22 / 7)Work = 188.5 ft lb

Turning the propeller 3 revolutions will require 188.5 ft lb [255.6 N m] of work.

Now we need a way to define power. Power is the rate at which work is performed, or the amount of work done per unit time.

Power = Work Time

Go back to the example where you pull the hovercraft along the sandbar. You could take 10 seconds to pull the craft that far, or you could pull really slowly and take 10 minutes. Either way, youre still doing the same amount of work. Your power, however, is greater the faster you pull it. In the Imperial system, power is usually measured in horsepower (hp). In the metric system, Joules per second (J/s) has another name, the Watt (W). This was named after James Watt, an engineer who made important contributions to the development of the steam engine. Interestingly, James Watt invented the term horsepower. It is said that he measured a pony producing 22,000 foot pounds of work in a minute while pulling buckets of coal out of a mine. He thought that horses were about 50% more powerful than a pony, so he increased it to 33,000 foot pounds per minute, or 550 foot pounds per second. This is also equal to 746 Watts in SI units.

To get power from torque, multiply torque by the angle it acts through, then divide by the amount of time it takes. This angle per unit time is called an angular velocity. With engines, this is commonly called revolutions per minute (rpm). If we multiply torque by angular velocity, we get power. Often we know the horsepower of an engine, but want to know how much torque it can produce. We now have a simple formula for this.

Power = Torque Angular velocity- or -Torque = Power Angular velocity

When doing these calculations, it is essential that all the values are in similar units. This often leads to some unit conversions to ensure they are similar.

Example 4:The Discover Hover Ones engine operates at 12.5 horsepower (hp) [9325 W]. How much torque is being produced when the engine is running at 2500 rpm?

Solution:Before solving this problem, convert some units. Convert the angular velocity from rpm to rad /s. There are 2 rad in a revolution and 60 seconds in a minute, so we must multiply by 2 and divide by 60

(2500 revolution/min) (2 rad/revolution) (60 sec/min) = 261.8 rad/s

Convert horsepower to either foot pounds per second or watts, depending on if were using Imperial or SI units. For this example, well use Imperial units.

(12.5 hp) (550 ft lb/s / hp) = 6875 ft lb/s

With power in foot pounds per second and angular velocity in radians per second, calculate the torque produced.

Torque = Power Angular velocityTorque = (6875 ft lb/s) (261.8 rad/s)Torque = 26.3 ft lb

When Discover Hover Ones engine runs at 2500 rpm, it will produce 26.3 ft lb [35.7 N m] of torque.

CONTROL

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When driving a car, friction of the rubber tires on the road allows almost instant change in direction when the steering wheel is turned. Piloting a hovercraft, however, is like driving a wet bar of soap, partly because you slide over most surfaces with little friction. Because ground contact friction is limited, they are easily affected by wind and surface slope. To maintain directional control of a conventional hovercraft, rudders at the rear of the craft are used to direct the flow of thrust air from the propeller. This causes a change in the directional force of the thrust air, which will turn the rear of the craft either left or right. Initially, when the rudders are turned the body of the hovercraft turns, but maintains the same direction of travel. Remember from Newtons first law that objects in motion tend to stay in motion, so even when the rudders are turned, the hovercraft will want to continue traveling in the old direction. Gradually, the new thrust direction overcomes the momentum of the hovercraft and the direction of travel changes.

Sketch by J. Benini

The more thrust air you can redirect, the faster the hovercraft will respond to directional changes. This is why hovercraft usually have at least 2 rudders. Some models may have as many as 5 rudders to change the direction of nearly all the thrust air. To be effective at low speeds, rudders must also turn at least 60 degrees in each direction. Rudders are usually shaped like a symmetrical airfoil to minimize drag (air resistance) and to maintain smooth airflow as the angle increases.

Sketch by J. Benini

In the above diagram you can see how the rudders cause the hovercraft to turn. By redirecting the flow of air in one direction, the air pushes back on the rudders (Newtons third law). The rudders, as well as the entire backside of the hovercraft, turn. The hovercraft rotates so that it is heading in a new direction.

On many light hovercraft, such as the Discover Hover One, you can also turn the hovercraft by leaning in that direction. If you shift all your body weight to one side, you can cause the skirt and edge of the hull on that side to drag along the ground. This added friction will cause the hovercraft to turn. Combining this with the rudders can lead to sharper turns!

MOMENTUM

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When a hovercraft turns, it continues to travel in the same direction for a while before it finally changes direction. This is due to its momentum. Momentum is defined as the mass of an object multiplied by its velocity.

Momentum = Mass Velocity

Newtons first law states that an object in motion tends to stay in motion. The momentum of an object is a sort of way to describe just how much the object tries to stay in motion. Lets say there are three objects coming toward you, and you have to try to stop them. The first is an empty shopping cart rolling at 5 mph [8 km/h], the second is a small car traveling at 5 mph [8 km/h], and the third is an identical small car traveling at 50 mph [80 km/h]. If we calculate the momentum of each one, the shopping cart would have the least momentum because it has the lowest mass times velocity. The 5 mph car would be second, and the car going 50 mph would have the greatest momentum. We can probably imagine that the shopping cart would be easy to stop. Stopping the car going 5 mph would be much harder, but we could probably get it stopped after pushing it for a while. Its safe to say that the car going 50 mph, however, would push you out of its way!

Newtons first law can now be rewritten to say the following: An objects momentum tends to stay the same. Remember that velocity is a measure of both speed and direction, so when the objects momentum tries to stay the same, its velocity tries to stay the same. This means that the direction of travel also tries to stay the same. This explains why the hovercraft initially keeps going in the old direction when you try to turn it. Its momentum is carrying it in the old direction and wants to keep going in the old direction. Only after exerting enough thrust to push it in the new direction will the momentum finally change.

Rewrite Newtons second law using momentum. Remember that Newtons second law states that:

Force = Mass Acceleration.

It was stated earlier that acceleration can be defined as a change in velocity, so we restate Newtons second law:

Force = Mass Change in Velocity

Since momentum is mass times velocity, lets go one step further:

Force = Change in Momentum

Any time we want to change an objects momentum, we have to exert a force on it. The greater the change, the more force is required.

So far weve rewritten Newtons first and second laws to include momentum. If we do the same with Newtons third law, the result is known as the Law of Conservation of Momentum. Remember that Newtons third law states that for any action there is an equal and opposite reaction. This also means that for any force, there is an equal force acting in the opposite direction. Since we know that forces lead to changes in momentum, we can also say that changing the momentum of one object means that the momentum of a neighboring object will change by an opposite amount.

Imagine a game of billiards in which you shoot at the eight ball. Right after you shoot, the cue ball has momentum as it travels towards the eight ball, but the eight ball isnt moving and so has no momentum. After they collide, the momentum of the eight ball is increased as it rolls away, but the momentum of the cue ball is decreased as it slows down or even stops. During the collision, the momentum of both balls change. If you add the momentum of the two balls before and after the collision, youll find that the total momentum doesnt change during the collision. The eight balls momentum increases by the same amount that the cue balls momentum decreases. The momentum of the system, or everything involved in the collision, remains the same. This is what is meant by Conservation of Momentum.

Returning to the hovercraft turning, the momentum of the hovercraft is changing. The law of conservation of momentum says that the total momentum of everything involved in the system stays constant. Can you think of what else is changing its momentum in order to balance the hovercrafts change in momentum? Remember that in a turn, the rudders change the direction of the airflow blowing out behind the hovercraft. The rudders are essentially changing the momentum of the air. When you add the change in momentum of the air to the change in momentum of the hovercraft, the total momentum again stays the same.

When turning in a vehicle, you often feel a force that pulls you towards the outside of the turn. Although this outward pull is often called centrifugal force, its actually not a force at all. It is the Law of Inertia at work. Remember that an object in motion tends to stay in motion. When the vehicle turns, your body wants to keep going straight. Refer to the diagram of the ball on a string that is spinning around in a circle. The inertia of the ball tries to make the ball travel in a straight line, but the string pulls on the ball, making it travel in a circle. The inward force on the ball due to the tension in the string is called centripetal force. A constant centripetal force keeps the ball traveling in a circle. If the string were to break, the ball would instantly start to travel in a straight line according to the Law of Inertia.

The same thing occurs when riding in a car as it goes around a curve. Instead of the tension in the string, friction between the tires and the road provides the centripetal force that pulls the car around the curve. Your body, however, wants to continue traveling in a straight line. Although it seems like your body is being pulled to the outside of the car, it is actually the car being pulled inward while you try to continue traveling straight. This is why the outward centrifugal force doesnt really exist. Your seat belt or the wall of the car must push against you in order to accelerate you around the turn with the car.

In a hovercraft, there isnt enough friction between the craft and the surface its hovering over to provide the centripetal force necessary to turn in the same way a car does. The centripetal force must instead be provided by directing the hovercrafts thrust partially towards the inside of the curve. This is why in the pictures of the turning hovercraft, they appear to be moving sideways. The hovercraft must turn towards the inside of the curve and use its thrust to provide the centripetal force necessary to pull it around a curve. This is called vector thrust. Some of the thrust is used to keep the hovercraft moving while the remainder is used to turn the craft or to overcome the crafts tendency to continue in a straight line.

KINETIC AND POTENTIAL ENERGY

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The term energy seems to be a very common word. Everyone has used the word, but do you really know exactly what it means? If not, youre not alone. Even scientists arent sure exactly what energy is; they just know what it does and how it works. Energy is often defined as the ability or capacity for doing work. Remember that work is a force moving an object a certain distance. Energy is used to do work. In fact, the units for energy are the same as the units for work: Joules (Newton-meters) in the SI system and foot-pounds in the Imperial system.

Energy is the capacity for doing work; that means that energy doesnt always have to be doing work on an object. It can also be stored in an object, ready to do work once released. These two forms of energy are called kinetic and potential energy. Kinetic energy is energy of motion. The more massive an object is or the faster its moving, the more kinetic energy it has. This may sound like momentum, which was defined as the mass of an object times its velocity. Kinetic energy has a slightly different formula, however.

KE = m v2Kinetic Energy = (mass) (velocity)2

Potential energy can be thought of as stored energy. When discussing work, we did an example in which the work required to lift a hovercraft onto workhorses was calculated. Energy was used to do that work. That energy is now stored in the hovercraft as gravitational potential energy. When sitting on the workhorses, the hovercraft is not moving, but it has the potential to move. If the workhorses were taken out from under it, the hovercraft would fall due to gravity. As the hovercraft began to move downwards, its potential energy would be converted into kinetic energy, or energy of motion. The following formula is used to calculate how much gravitational potential energy an object has.

PE = mghPotential Energy = (Mass) (Acceleration due to Earths gravity) (Height)

Increasing the mass of an object, or raising the height of the object will increase its potential energy. Remember in the example of dropping a pebble and a bowling ball from the same height at the same time, both objects hit the ground at the same time. This is because the force of gravity tries to accelerate all objects by the same amount. The acceleration due to Earths gravity used in the formula above is equal to 32.15 ft/s2 [9.8 m/s2]. Any object lifted above the ground has potential energy. When allowed to fall, the potential energy is then converted into kinetic energy.

Example 1:A 50 kg hovercraft is hovering at the top of a steep hill that is 20 m high. Without using the propeller to produce any forward thrust, the hovercraft is nudged so that it begins to slip down the hill. How fast will it be going when it reaches the bottom of the hill?

Solution:In order to find the speed of the hovercraft at the bottom of the hill, we need to find its kinetic energy at that point. Remember that the gravitational potential energy of the hovercraft at the top of the hill will be converted to kinetic energy as the hovercraft slips down the hill, so begin by calculating the potential energy at the top of the hill.

PE = mghPE = (50 kg) (9.8 m/s2) (20 m)PE = 9800 J

If the hovercraft has 9800 Joules of potential energy at the top of the hill, it will have 9800 Joules of kinetic energy at the bottom of the hill. Using the formula for kinetic energy, we can find the speed of the hovercraft.

KE = m v29800 J = (50 kg) v2v2 = 392 m2/s2v = 19.8 m/s

When the hovercraft reaches the bottom of the hill, it will be traveling 19.8 m/s, or 44.3 mph.

Example 2:How fast will the hovercraft be traveling when it is of the way down the hill? How much potential energy will the hovercraft still have at this point?

Solution:The method for solving this problem is the same as the first example. When the hovercraft is of the way down the hill, however, the hovercraft has both potential and kinetic energy. It still has potential energy because it is 5 m above the bottom of the hill, and it has kinetic energy because it has slid down 15 m. First calculate how much potential energy was converted to kinetic energy when the hovercraft slid down 15 m.


KE = m v27350 J = (50 kg) v2v2 = 294 m2/s2v = 17.1 m/s

When the hovercraft is still 5 m from the bottom of the hill, it is traveling at 17.1 m/s [38.4 mph].To find out how much potential energy the hovercraft still has, it would make sense to simply subtract how much energy was converted to kinetic energy from the total amount of potential energy it originally had.

PE(at 5 m) = PE(at top) KE(at 5 m)PE(at 5 m) = 9800 J 7350 JPE(at 5 m) = 2450 J

Just to make sure this is right, use the formula for potential energy to check the potential energy when the hovercraft is 5 m above the bottom of the hill.


Not only did we find the potential energy 5 m up the hill in the last example, we just demonstrated an extremely important law of physics: Conservation of Energy.

Law of Conservation of Energy: Within a system, energy can never be created or destroyed.

This states that although energy can be converted from potential to kinetic and vice versa, the total amount of energy always stays the same. This is why we were able to simply subtract the two energies in Example #2. Potential energy was converted into kinetic energy, but the total amount of energy always stayed the same.

Potential energy is converted into kinetic energy as the hovercraft travels down the drop

The hovercraft works best in the example because there is very little friction between a hovercraft and the ground. If a car was used, the calculations wouldnt be accurate because friction would slow the car down as it rolled down the hill. At first glance this seems to violate the law of conservation of energy. Slowing the car means kinetic energy is lost, so where does that energy go? Quickly rub your hands together for a while and notice that they begin to warm up. Friction converts kinetic energy into heat, another form of energy. Heat is actually a form of kinetic energy. The atoms and molecules that make up all matter vibrate and move around very tiny distances. What we measure as temperature is simply a measurement of how quickly the atoms and molecules are moving about.

Besides gravitational potential energy, there are other forms of potential energy. One is called elastic potential energy. This is observed in springs or anything else that stretches and compresses. There is a certain relaxed length that a spring wants to be at. If it is compressed or stretched from this length, potential energy is added to the spring. Releasing it causes the spring to bounce back to its relaxed length, releasing its potential energy as kinetic energy.

Another form of energy is chemical potential energy. This is potential energy located within the atomic bonds of molecules. This form of energy is most commonly put to use in gasoline. When gas is burned, its atomic bonds are broken, releasing its potential energy, usually in the form of heat. Engines are designed to use this release of energy to do useful work, such as powering a hovercraft fan or propeller.

ELECTRIC CHARGES AND FORCES

NAME

DATE

Although we often think of gravity as a fairly strong force, on the scale of tiny things such as atoms and molecules, gravity becomes insignificant. Remember that the strength of the gravitational force depends on the mass of an object, so extremely light objects like atoms feel practically no gravitational force. Instead, other forces begin to play a large role in how atoms act. One is the electric force. While gravity is an attractive force based on the mass of objects, the electric force can be either attractive or repulsive, and is dependant on something called charge. There are two types of charges: positive and negative. When two charges are near each other, they create a force that can either try to pull them together or push them away, depending on the charges. In order to determine whether the force between the charges will be attractive or repulsive, remember the following rule:

Like charges repel each other, while unlike charges attract each other.

Two positive charges or two negative charges will repel each other, but a positive and a negative charge attract one another.

Where exactly does charge come from? The answer to this lies in the microscopic world of atoms. Atoms are made of three basic particles: protons, neutrons, and electrons. Protons are tiny, positively charged particles. Neutrons have about the same size and mass as protons, but carry no charge. Together these particles are found in the nucleus of an atom. This is the small but very dense core of every atom. Similar to how the moon orbits Earth, electrons orbit around the nucleus. Electrons are much smaller than protons and neutrons, and they carry a negative charge. Since protons and electrons have opposite charges, they attract each other. This force holds the electrons in orbit around the nucleus, just like gravity holds the moon in orbit. The atom as a whole, however, has no net charge because the negative charge of the electrons and the positive charge of the protons cancel each other out.

Most atoms have the same amount of protons and electrons in order to keep a total charge of zero. Since electrons orbit on the outside of the atom, however, it is possible to remove some electrons and give the atom a positive charge, or add some electrons and give the atom a negative charge. Doing this to a large number of atoms in an object causes the object to become charged. Charged objects act in the same way that single charges do: opposite charges attract while like charges repel. When this charge remains on an object and doesnt move, it is called static charge.

A Van de Graaff generator is a device that contains a large metal ball that gains a large negative charge. This is done by adding a lot of extra electrons to the ball. When someone touches the ball, some of the extra electrons pass over onto the person. This makes the persons body (including the hair) negatively charged. Remember that like charges repel each other, so each negatively charged hair on the persons body will repel each other. The hairs stick straight up, trying to separate as far as they can.

This condition can also occur in hovercraft. As the skirt of the hovercraft drags along the ground, it can scrape electrons off of the grass or ground. This can give the entire hovercraft a static charge. This makes designing electronic equipment on the hovercraft difficult since it can be affected by the static charge.

When charges are put into motion, electricity is the result. Scrape your feet across a carpet wearing only socks. This will rub electrons off the carpet and onto you, giving your body a charge. Put your finger close to a metal door knob and youll see a spark and feel a jolt as the excess electrons on you jump onto the doorknob. This is the same electricity that is supplied by batteries and/or wall sockets. Electrons flowing through power wires provide the electricity that powers everything in your home. All electricity is simply charges in motion.

How do electrons move through a wire to create electricity? To solve this question, look to the atomic structure of the metal in the wire. Metals, such as copper, silver, aluminum, and brass are called conductors. Conductors allow charges to easily move through them.

The diagram shows how the atoms in conductors are typically arranged. Each large ball represents the nucleus of an atom. Notice all the space between the nuclei (plural of nucleus). The electrons of each atom are free to roam in this free space, jumping from one atom to another. When extra electrons are placed on a conductor, they are free to move about. This is why electricity flows so easily through conductors.

Plastic, glass, rubber, and wood are all examples of insulators. Insulators do not allow electricity to pass through them. Unlike metals and other conductors, the atoms of insulators do not exchange electrons. When an atom of an insulator gets extra electrons put on it, the electrons stay on that atom rather than spreading out across neighboring atoms. Because of this, when you put a charge on an insulator, the charge stays put and doesnt spread across the material in the way charge does on conductors. Electrical wires always have copper or some sort of conductor on the inside and plastic or another insulator on the outside. This allows electricity to flow through the inside of the wire, but keeps you from getting shocked when you touch the outside of the wire.


GLOSSARY OF TERMS

Acceleration The rate of change of velocity.

ACV Abbreviation for air cushion vehicle(s), a family of vehicles that travel on a cushion of air. The hovercraft belongs to the ACV family.

Air density A measurement of the mass of air per unit volume for a given air temperature.

Airfoil An airfoil or aerofoil is a part or surface, such as a wing, propeller blade, or rudder, whose shape influences control, direction, thrust, lift, or propulsion.

Air gap Also called daylight clearance, air gap refers to the distance between the bottom of the hovercraft skirt and the surface beneath it.

Air pressure Measurement of the force exerted by air above, at, or below atmospheric pressure on a unit of area.

Angle of attack The angle between an airfoil or wing and the direction of the wind relative to it.

Angular speed The rate at which an object rotates or spins.

Angular velocity Angular speed in a certain direction, clockwise or counter-clockwise.

Arc length The length of an arc, or a section of a circle's perimeter.

Archimedes' Principle of Buoyancy The principle stating that when a body is immersed in a fluid at rest it experiences an upward or buoyant force equal to the weight of the fluid displaced by the body.

Atmospheric pressure The pressure exerted by the atmosphere at the surface of the earth due to the weight of the air above.

Bag skirt A type of hovercraft skirt consisting of a flexible fabric tube that surrounds the perimeter of the hovercraft.

Bernoulli's Principle Bernoulli's Principle states that an increase in the velocity of a fluid is always accompanied by a decrease in pressure.

Body The top surface of the hovercraft; usually attached to the hull.

Bow The front of a boat or hovercraft.

Buoyancy The upward force on an object immersed in a fluid; equal to the weight of the fluid displaced by the object (Archimedes' Principle).

Centerline A line of symmetry along the axis of an object.

Centrifugal "force" Not an actual force but, rather, the result of an object's inertia trying to maintain motion along a straight line when the object is forced to travel along a curve.

Centripetal force When traveling in a circle or curve, the force that pulls an object towards the center of the circle or curve.

CFM Abbreviation for "cubic feet per minute," a rate of fluid flow.

Chalk line A tool consisting of an enclosed spool of string with powdered chalk inside, allowing the user to stretch the string to a particular length then pluck or snap the string to create a straight chalk mark on the surface.

Charge An electromagnetic property of matter that can be positive or negative and will cause either an attractive or repulsive force on another charge (Coulomb's Law).

Chemical Potential Energy Energy in the chemical bonds of matter.

Circumference The distance around the outside of a circle.

Clearance The space between two objects, allowing for free movement.

Coanda Effect The Coanda Effect states that a moving stream of fluid in contact with a curved surface will tend to follow the curvature of the surface rather than continue to travel in a straight line.

Cockpit The area where the pilot or passenger(s) sit(s); also called a cabin.

Coefficient of friction A quantity representing the extent to which friction develops between two objects in contact as the normal force changes.

Conductor There are two kinds of conductors: electrical and thermal. An electrical conductor is a material that allows an electric charge to move through it. A thermal conductor is a material that allows heat to flow through it.

Contact force A force between objects in contact with each other. A contact force can be attractive (as in a tension force), repulsive (as in a normal force), resistive (as in friction), restoring (as in a spring force), or arbitrary (someone pushing and pulling on things).

Contact line A theoretical line around the perimeter of a hovercraft where the lower edge of the skirt makes surface contact. Jupe and segmented finger skirts have complicated contact lines. The contact line can move as the skirt flexes and changes shape.

Control surface Any movable surface, usually the rudders, designed to deflect air and cause the resulting force to change the direction of the hovercraft.

Coulomb's Law Coulomb's Law describes the interaction between two objects that have electric charges. It states that the force between two charged bodies is equal to a constant k approximately 8.99109N m2/C2 times the product of the two charges, all divided by the square of the distance between the bodies. If the two charges are both either positive or negative, the force will be positive and the bodies will repel each other. If one is positive and one is negative, the force will be negative and they will attract each other.

Cross-sectional area The area of a two dimensional slice of a three dimensional object.

Cushion pressure Liquid or gas pressure measured between the hull of the hovercraft and the earth's surface.

Daylight clearance Also called air gap, daylight clearance is the distance between the bottom of the hovercraft skirts and the surface beneath it.

Density The ratio of mass to volume of an object.

Diameter The distance across the center of a circle, from one side to the other. The diameter of a circle is equal to twice its radius.

Drag Any force that creates resistance to motion.

Driving gear A gear that rotates while in contact with another gear, causing the other gear to rotate in the opposite direction.

Driven gear A gear in contact with a rotating gear; it will rotate in the opposite direction.

Dynamic friction Friction between two objects in contact that are moving. Dynamic friction is always less than static friction.

Dynamic pressure The pressure of a fluid in motion, measured by the pressure it exerts on a flat surface.

Efficiency The ratio of output work compared to input work. Efficiency is sometimes expressed as a percent, in which case the ratio is multiplied by 100 to give a percentage value.

Elastic potential energy Energy stored in a spring or elastic object due to its being stretched or compressed.

Electric force The force resulting from the difference between existing charges.

Electricity The area of physical phenomena dealing with the behavior of electric charges. There are two main branches of electricity: electrodynamics, the study of charged particles in motion; and electrostatics, the study of charged particles at rest.

Electron A negatively charged particle that is a small part of an atom.

Energy The capacity for doing work. An important property of energy is that in a system with no external influences, the total amount of energy can never change. This is called the Law of Conservation of Energy.

Epoxy A two-part compound of resin and hardener used as a very strong waterproof glue. It is often used in conjunction with fiberglass cloth or tape.

Fan A rotating, multi-bladed device (usually 4 or more blades) for moving volumes of air in ducts with only a small pressure increase.

Fiberglass Fine filaments of glass, usually made into a mat or cloth. When combined with epoxy or polyester resin, fiberglass creates a strong, long-lived, rigid, and waterproof material.

Finger skirt A finger skirt, also called a segmented skirt, is a type of skirt consisting of several segments that press together when inflated.

Fluid A liquid or gas that flows and assumes the shape of its container.

Foot-pound A unit of work equal to the work done by a force of one pound acting through a distance of one foot in the direction of the force. Also a unit of torque equal to the amount of torque exerted by a force of one pound at a distance of one foot.

Form A pattern or mold used to give shape to something else.

Form drag Form drag, also called profile drag or wind resistance, is the drag force created on a hovercraft as it displaces the fluid through which it moves. If moving forward, form drag results in gre

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