Cynthia ButheleziFACTORS AFFECTING TAKE OFF ROLL

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Table of contentsIntroduction

Propwash

P-factor

Assymetric thrust (corkscrew effect)

Corkscrew slipstream

Factors affecting take off distance

Screen height Speed Newton's second law of motion Mass Wind Runway slope Temperature Flaps

Factors affecting tail draggers

Torque

Gyroscope effect

Density altitude

Conclusion

FACTORS AFFECTING TAKE-OFF ROLLDedicated scholars and engineers have been monitoring the performance of aircrafts, especially during critical phases of flight, to find contributors that dictates

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the fundamental operation and safety of flying. certain conditions have proven to be attributes and major influences that play different roles in this industry. over the years these factors have been identified as prop wash, gyroscope effect, p-factor, torque effect, and a whole lot of others. This paper will not only outline the "action-reaction" due to the aircrafts motion, but how nature contributes and physical surfaces the aircrafts depart from. This paper looks at the general overview of these different factors involved in flying and how they affect take-off roll in particular.

Prop wash

A slipstream is a region behind a moving object in which a wake of fluid (typically air or water) is moving at velocities comparable to the moving object, relative to the ambient fluid through which the object is moving.[1] The term slipstream also applies to the similar region adjacent to an object with a fluid moving around it. "Slipstreaming" or "drafting" works because of the relative motion of the fluid in the slipstream.

A slipstream created by turbulent flow has a slightly lower pressure than the ambient fluid around the object. When the flow is laminar, the pressure behind the object is higher than the surrounding fluid.

The shape of an object determines how strong the effect is. In general, the more aerodynamic an object is, the smaller and weaker its slipstream will be. For example, a box-like front (relative to the object's motion) will collide with the medium's particles at a high rate, transferring more momentum from the object to the fluid than a more aerodynamic object. A bullet-like profile will cause less turbulence and create a more laminar flow.

A tapered rear will permit the particles of the medium to rejoin more easily and quickly than a truncated rear. This reduces lower-pressure effect in the slipstream, but also increases skin friction (in engineering designs, these effects must be balanced)

The term "slipstreaming" describes an object traveling inside the slipstream of another object (most often objects moving through the air though not necessarily flying). If an object is inside the slipstream behind another object, moving at the same speed, the rear object will require less power to maintain its speed than if it were moving independently. In addition, the leading object will be able to move

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faster than it could independently, because the rear object reduces the effect of the low-pressure region on the leading object.

Spiral slipstream (also known as spiraling slipstream, propwash in the US, or just slipstream in the UK) is a spiral-shaped slipstream formed behind a rotating propeller on an aircraft. The most noticeable effect resulting from the formation of a spiral slipstream is the tendency to yaw nose-left at low speed and full throttle (in centerline tractor aircraft with a clockwise-rotating propeller.) This effect is caused by the slipstream acting upon the tail fin of the aircraft: the slipstream causes the air to rotate around the forward-aft axis of the aircraft, and this air flow exerts a force on the tail fin, pushing it to the right. To counteract this, some aircraft have the front of the fin (vertical stabilizer) slightly offset from the centreline so as to provide an opposing force that cancels out the one produced by the slipstream, albeit only at one particular (usually cruising) speed,

A propeller pushes air not just horizontally to the back, but more in a twisting helix around the fuselage (clockwise as seen from the cockpit). As the air whirls around the fuselage it pushes against the left side of the vertical tail (assuming it is located above the propeller's axis), causing the plane to yaw to the left. The prop wash effect is at its greatest when the airflow is flowing more around the fuselage than along it, i.e., at high power and low airspeed, which is the situation when starting the takeoff run. Same applies when rolling down the runway and having to constantly apply right rudder to maintain centerline.

Propeller torque effect

The torque effect experienced in helicopters and single propeller-powered aircraft is a result of Isaac Newton's third law of motion that "for every action there is an equal and opposite reaction"

In helicopters, the result of the torque effect is a tendency of the main rotor to want to turn the fuselage in the opposite direction from the rotor.

In a single-propeller plane, the result of the torque effect is a tendency of the plane to want to turn upwards and left in response to the propeller wanting to turn (bank) the plane in the opposite direction of the propeller spin.

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Torque effect is the influence of engine torque on aircraft movement and control. It is generally exhibited as a left turning tendency in piston single engine propeller driven aircraft.

According to Newton's law, "for every action there is an equal and opposite reaction," such that the propeller, if turning clockwise (when viewed from the cockpit), imparts a tendency for the aircraft to rotate counterclockwise. Since most single engine aircraft have propellers rotating clockwise, they rotate to the left, pushing the left wing down.

Typically, the pilot is expected to counter this force through the control inputs. To counter the aircraft roll left, the pilot applies right aileron.

It is important to understand that torque is a movement about the roll axis. Aileron controls roll. Prop torque is not countered by moving the rudder or by setting rudder trim. It is countered by moving or trimming the aileron.

This correction induces adverse yaw, which is corrected by moving or trimming the rudder (right rudder).

On aircraft with contrarotating propellers (propellers that rotate in opposite directions) the torque from the two propellers cancel each other out, so that no compensation is needed.

When the airplane is air born, this force is acting on the longitudinal axis, tending to make the airplane roll. Today's planes are designed with an engine offset to counteract this effect of torque.

When the plane is on the ground during takeoff roll, an additional turning tendency is induced by this torque reaction. As the left side of the plane is forced down, it is

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putting more weight on the left main landing gear. This effect results in more ground friction or drag, more on the left than the right causing even more turning to the left.

P-Factor

P-factor is the term for asymmetric propeller loading, that causes the airplane to yaw to the left when at high angles of attack.

Assuming a clockwise rotating propeller it is caused by the descending right side of the propeller (as seen from the rear) having a higher angle of attack relative to the oncoming air, and thus generating a higher air flow and thrust than the ascending blade on the left side, which at the other hand will generate less airflow and thrust. This will move the propellers aerodynamic centre to the right of the planes centreline, thus inducing an increasing yaw moment to the left with increasing angle of attack or increasing power. With increasing airspeed and decreasing angle of attack less right rudder will be required to maintain coordinated flight.

This occurs only when the propeller is not meeting the oncoming airflow head-on, for example when an aircraft is moving down the runway at a nose-high attitude (in essence at high angle of attack), as is the case with tail-draggers. Aircraft with tricycle landing gear maintain a level attitude on the takeoff roll run, so there is little P-factor during takeoff roll until lift off.

When having a negative angle of attack the yaw moment will instead be to the right and and left rudder will be required to maintain coordinated flight. However negative angles of attack is rarely encountered in normal flight. In all cases, though, the effect is weaker than prop wash.

When an aircraft is flying with a high angle of attack (AOA), the "bite" of the downward moving blade is greater than the "bite" of the upward moving blade. This moves the center of thrust to the right disc area, causing a yawing moment toward the left around a vertical axis.

When the plane is flying at the same high angle of attack (the angle of the plane relative to the wind which is coming in at it), the downward moving blade has a higher resultant velocity, creating more lift than the upward moving blade.

When the plane is at a low AOA the load on upward and downward moving blades are equal. At a high AOA, the load on the downward blade is higher than that of the upward moving blade. Both instances the wind is hitting the propeller from the front.

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Since the propeller is an airfoil, an increased velocity means increased lift. The down swinging blade (viewed from the rear) has more lift and tends to pull (yaw) the aircraft's nose to the left.

Assymetric thrust (corkscrew effect)

One of the very first things that people find out about when they start learning to fly is that it takes right rudder (sometimes a lot of right rudder) to keep the airplane going straight at the beginning of the takeoff roll and often after lift-off while the plane is slow and using a high angle of attack. Three factors are all blamed for this requirement. It depends on who you ask as to the effective importance of each one. The “Corkscrewing slipstream”,

Corkscrewing Slipstream

The high speed rotation of the propeller gives a corkscrew or spiraling rotation to the slipstream, At high propeller speeds and low forward speed or motion of the plane (as in take offs and approaches to power-on stalls), this spiraling rotation is very compact and exerts a strong side ward force on the vertical tail surface.

The propeller causes a slipstream over the plane and it then exerts a force on the left side of the vertical tail

surface. This then pushes the tail surface to the right and the opposite reaction is that

the nose goes to the left or Yaws to the left about the aircraft's vertical axis.

As the forward speed increases, this spiral effect elongated and becomes less effective. This corkscrew flow also causes a rolling motion around the longitudinal axis.

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Notice that this rolling moment caused the corkscrew is to the right, while the rolling effect caused by torque reaction is to the left - in effect one may counteract the other.

It would be nice if the propeller would just take the air and throw it straight backwards, but it doesn't. The propeller airfoil necessarily has some drag, so it drags the air in the direction of rotation to some extent. Therefore the slipstream follows a corkscrew-like trajectory, rotating as it flows back over the craft.

The next thing to notice is that on practically all aircraft, the vertical fin and rudder stick up, not down, projecting well above the centerline of the slipstream. That means the corkscrewing slipstream will strike the left side of the rudder, knocking the tail to the right, which makes the nose go to the left, which means you need right rudder to compensate.

You don't notice the effect of the corkscrewing slipstream in cruise, because the aircraft designers have anticipated the situation. The vertical fin and rudder have been installed at a slight angle, so they are aligned with the actual airflow, not with the axis of the aircraft.

In a high-airspeed, low-power situation (such as a power-off descent) the built-in compensation is more than you need, so you need to apply explicit left rudder (or dial in left-rudder trim) to undo the compensation and get the rudder lined up with the actual airflow.

Conversely, in a high-power, low-airspeed situation (such as initial takeoff roll, or slow flight) the corkscrew is extra-tightly wound, so you have to apply explicit right rudder.

Factors Affecting the Takeoff Distance

The takeoff distance that an airplane needs is influenced by several factors. Most you can easily think of yourselves, while some are perhaps less obvious. To be able to talk about the influence of a variable on the required distance we must first agree on where the takeoff ends.

The takeoff, and then we mean a successful one that ends in you flying, ends in the air at a certain height AND at a certain speed. The height and speed are closely linked.

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When you reach the height but not the speed that belongs to it, then that was not the end of the takeoff. A takeoff, the TakeOff Distance Required or TODR, is always calculated in such a way that it ends at both the height and speed that are required. If you can not comply to that then you are probably too heavy for the available runway (TODA) or the runway is too short for that weight.

4.1. The height that you must reach: Screen height

Screen height

The height that must be reached is called the screen height.

• Class A: 35 feet.

• Class B: 50 feet.

When landing, the landing distance required is also determined from screen height, which is 50 feet for both Class A and B.

Exception: For class A on a wet runway a screen height of only 15 feet is allowed!

See chapter 7 for details.

4.2. The speed that you must reach

The speed has two different names and is not defined in knots but as a percentage above the stalling speed. Just the names first:

• Class A: V2.

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• Class B: Clear 50 speed.

Class A (top) vs. Class B

4.3. Formulas that can describe the takeoff distance

To find the factors that affect the takeoff distance you may want to begin by looking at Newton's second law of motion:

F = m x a

a = F / m

Formula 1

Then you can continue with:

t = V / a

Formula 2

On top of that we have the relationship between time and speed:

s= ½ a x t2

Formula 3

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Units:

F [N]

m [kg]

a [m/s2]

t [sec]

s [m]

F = m x a

a = F / m

Actually it is quite simple. If you want to take off you must have a certain speed and to accelerate to that speed you must apply a force. So basically the only thing we must find out is: What is the influence of a given variable on the acceleration that we get, or on the final velocity (V) that we need. The final velocity must be in TAS and not in IAS because IAS is TAS combined with air density. We will look at density as one of the variables.

4.4. The mass of the airplane

A heavy airplane needs a longer runway because:

a = F / m : If you are heavy a is small and

t = V / a: it takes you longer reach the speed V.

s= ½ a x t2: If it takes longer, you use more distance.

4.5. The wind

In a headwind your initial velocity not zero because there is wind already blowing over your wings. This headwind you can deduct from your final ground speed. Now it is simple.

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With head wind you need a shorter runway because:

T = V / a: The speed is lower, it takes less time to reach that lower speed and

s= ½ a x t2: if it takes less time you need less distance.

4.6. The slope of the runway

Suppose you have a runway with a down slope. You then roll easier because you travel along the slope. Your acceleration a is larger.

With down slope distance becomes shorter because:

a = F / m : The acceleration a is larger and thus

t = V / a: it takes less time to reach the speed V.

s= ½ a x t2: If it takes less time you need less distance.

4.7. The surface of the runway; paved / unpaved

If the runway is a grass runway then you have much more rolling resistance when compared to a concrete runway. The acceleration now is smaller.

4.8. The field elevation and the pressure altitude

The field elevation is the altitude of the airport above sea level. The pressure altitude is the altitude above 1013 hPa. If the elevation increases then so does the pressure altitude. The pressure then decreases.

That effect has several consequences:

4.9. The end speed in knots TAS

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If the field is a at a high elevation above sea level then the air pressure and the density are less. Skaters and cyclists think that is amazing because then they have less drag.

For the takeoff of an aircraft this is not so amazing since the air density is a variable inside the lift formula which tells you that at a lower air density you need a higher speed (TAS) to develop the same amount of lift.

Formula 4

This higher end speed in TAS will take more time and as a result more runway length.

The speed in IAS will remain the same, that is the advantage of using IAS. This can be explained as follows:

IAS is indicated on the speedometer from the product ½ ρ V2 .

With increasing field elevation ρ decreases and as a result V (TAS) must increase to keep the outcome of the product constant, and that is exactly what happens.

4.10. The power of the engine

Because of the lower air density you need a higher end speed (V) and your engine will also be less powerful. That is because there is less air to create the fuel/air mixture. Lower power results in less Force (F). If you have a propeller airplane then propeller will also perform less and as a result you will have even less Force.

On an elevated runway the required takeoff distance will increase because:

a = F / m: F is less so acceleration (a) is less and then

t = V / a: it takes extra long before you reach the higher speed V.

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s= ½ a x t2: If it takes longer, you use more distance.

4.11. The temperature

A high temperature causes a low air density. The same effects of field elevation apply. Higher end speed, less power from the engine and lower thrust from the propeller. For a fan engine these factors also apply if the temperature is high enough. The "flat rated temperature" of a jet engine is the threshold at which the thrust begins to decrease under the influence of the temperature. Be extra cautious on an elevated field during a hot day. "Hot and high." Your takeoff speed must increase speed while the airplane has less power!

In the Netherlands, Hilversum Airport is notorious for that. It has a grass runway which is not exceedingly long with tress behind it and it can be over 25 degrees Celsius on a summer day.

4.12. The rotation speed

The rotation speed VR is the speed at which the pilot brings the nose wheel off the ground. This speed has a value that depends on the weight of the aircraft. It is important to use correct value of VR and not to rotate too early or too late. Both will cause the takeoff distance to increase.

If you do rotate too late then you have used more runway than necessary. Rotating at a low speed also results in longer runway required because the wings reach an angle of attack too soon in the takeoff roll. Angle of attack causes lift and lift causes drag.

4.13. The use of aircraft systems or their failure

Failure of certain aircraft systems may affect the runway length required.

For example:

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4.13.1. The anti-skid system

In case of an anti-skid system failure in a Class A aircraft, the stopping distance will increase which will result in an increased stopping distance in case of a rejected take-off. As a result you need a longer runway even if you do not intend to stop, because the possibility of stopping must be present.

4.13.2. The anti-icing system

When a jet takes off in icing conditions the use of the anti-icing system results in having less power from the engines because the hot air for the anti-icing system is taken from the engines. That causes significantly longer takeoff distances and reduced climb performance.The relative humidity

The relative humidity is also a factor. The takeoff performance of an airplane is based on a prescribed relative humidity of the air. That influence does not show from the takeoff tables.

Water molecules are lighter than Oxygen and Nitrogen, the main components of dry air. You can now state that where there is water in the air there is no dry air. Because moist air is lighter than dry air the density decreases when the relative humidity increases. The aircraft performance will decrease.

The influences of high humidity are not as important as those from the other variables. For example if you look at a takeoff in a very hot and humid tropical climate, the biggest problem is the high temperature and the resulting lower air density.

4.14. Flaps

The effect of extending the wing flaps is beneficial to the moment of lift-off because the speed at which you can fly is lower than without flaps. The stall speed decreases.

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As a result the ground roll is shorter but the total TODR to screen height is not automatically shorter. The drag of the flaps can cause the advantage to disappear in the (initial) climb.

Extending the flaps beyond the maximum position for take-off makes no sense because the drag increases faster than the lift. The use of flaps can have a clear disadvantage:

Once you are airborne then the extra drag from the flaps will decrease you angle of climb. The use of flaps in a climb to a higher altitude is always a disadvantage and is normally not done. To climb fast you should retract the flaps as soon as possible after the 50 or 35 feet point (screen height).

4.14.1. Use of flaps in Class B aircraft

For a Class B aircraft (Single Engine Piston) this flap retraction after 50 feet not such a problem. Below you can compare the effect of the use of flaps for Cessna and Piper as stated in the flight manual:

Cessna 172M

Ground roll:

• Flaps 0: 775’

• Flaps 10: 10% shorter

TODR to 50 feet:

• Flaps 0: 1380’

• Flaps 10: No advantage

Piper 28

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Ground roll:

• Flaps 0: 1000’

• Flaps 10: 800’

TODR to 50 feet:

• Flaps 0: 1800’

• Flaps 10: 1600’

The conclusion here is that the flight manual usually requires one single flap position that you use for normal take-off and possibly also a greater flap setting for the soft-field takeoff which allows you to lift off the soft soil earlier. The advantage to 50 feet is not so big and is generally more obvious as the size of the airplane increases. For the climb the flaps should be retracted as soon as possible and allowed after 50 feet.

4.14.2. Use of flaps in Class A aircraft

The bigger the airplane the more choice of flap settings to use for take-off. The use of a high flaps setting seems like a good thing for a large aircraft but it can be also be a disadvantage. All Class A aircraft must first pass over 400 feet height or the nearest obstacle - whichever is higher - before they are allowed to retract the flaps. That is a rule from JAR-OPS 1. The advantage of early lift-off can be lost in this first part of the climb. You may not be able to clear the obstacle with that flap setting.

The use of flaps is especially beneficial for a short runway with no obstacles or only a low obstacle further away. Not using flaps is beneficial for a very long runway with a nearby obstacle. The picture below shows the choices in a somewhat exaggerated way:

Effect of flaps on the TODR of Class A Airplanes

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Without flaps: Late liftoff and good climb

With flaps: Early liftoff and poor climb.

In reality the effect is less dramatic than it seems. It will be discussed in more detail in the section on the Class A take-off where flap settings have more consequences since in those aircraft you are only allowed to retract the flaps at a minimum height above the ground.

Class B aircraft have a very limited choice of flap settings for takeoff and the advantage of that choice is almost non-existent. For large aircraft it can make quite a difference, especially if you must make a decision regarding a takeoff from a challenging runway that also has an obstacle in the departure path.

Factors affecting a tail dragger

A taildragger has its main landing gear ahead of its center of gravity and a steerable tailwheel or skid supporting the aft fuselage, so the airplane's tail appears to rest on the ground, hence the name taildragger. Until World War II, taildraggers reigned supreme. Because this landing gear configuration was so common on early aircraft, taildraggers, or tailwheel airplanes, became known as airplanes with conventional gear.

The biggest difference between taildraggers and aircraft equipped with tricycle gear is that taildraggers have their center of gravity positioned behind the main landing gear while tricycle gear airplanes have their center of gravity in front of the main gear. This doesn't make much difference in the air, but when the airplane is on the ground, things change.

When taxiing, taking off, and landing, tricycle-gear airplanes are easier to control than taildraggers. If you land a taildragger too hard on the main gear with the tailwheel still off the ground, for example, the aircraft will have the tendency to bounce and want to fly again. This is because the angle of attack increases as the tail drops, thus increasing lift unless the plane is moving slower than its stall speed. The opposite is true for nosewheel planes. Because their center of gravity is situated in front of the main gear, after the main gear touches down, the nosewheel wants to touch down, too. This lessens the angle of attack on the wings, and the plane ceases to fly. So, landing a taildragger takes some extra care.

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Also, because most of a taildragger's weight is behind the main gear, the aircraft is more difficult to control or steer on the ground. If the taildragger begins to swerve, it can get out of control as its tail (where most of the plane's weight is) wants to overtake its nose. This happens. It's called a groundloop. In addition to spooking the pilot, ground loops can possibly damage or even wreck the airplane. The worst kind of ground loop is when the gear shears because of the side load, causing the propeller, wing, and fuselage to strike the ground.

And because most of an airplane's surface area is located behind the main landing gear, wind also has a pronounced effect on taildraggers, coaxing them to pivot into the wind and making them difficult to taxi. Moreover, when you taxi in some taildraggers, you must use the side windows to see because the nose is pointed toward the sky, blocking your view.

Torque

Torque is a major factor acting on the airplane at all times when the engine is running. It's there when you're sitting on the ramp with the engine idling. It's there when you're doing your run-up. It's there when you're in cruise. It's there during takeoff too, and in a taildragger, this is one of the times it's most noticeable. In the average taildragger most of us fly, it is most noticeable early in the takeoff roll. Essentially, torque is the tendency for the propeller to stop and the airplane to turn. The more horsepower an airplane has, the stronger the effect of torque on that airplane. A 65 HP J-3 Cub does not have a lot of torque, but it is (barely) noticeable and cannot be ignored. A 300 HP Cessna 195 has very noticeable torque and must be countered properly during takeoff or you'll end up in the weeds for sure. Imagine what torque must be like in a P-51 Mustang! In these really powerful airplanes, you have to bring in the power incrementally as you pick up speed so you don't introduce more torque than you have available rudder with which to counteract the torque. The bottom line is that when you add power for takeoff, you must get on the right rudder to counteract torque. Torque is trying to turn the airplane to the left.

P-Factor

P-Factor is caused when the plane of the propeller is moving through the air at an angle. With the airplane in a nose-high attitude in relation to the path of the airplane, as is the case in a taildragger starting its takeoff roll, the plane of the propeller is not moving perpendicular through the air. The air is coming at the propeller at an angle from below. This means that the propeller blade moving downward has a higher angle of attack than the blade moving upward. Since the blade on the airplane's right hand side is moving downward it is realizing a higher angle of attack, therefore producing a little more "lift". Since the blade on the airplane's left hand side is moving up, it realizes the slightly lower angle of attack and produces a little less "lift". So, the right hand side of the propeller is pulling a little harder than the left

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hand side. This tends to turn the airplane to the left. If the airplane is not moving, there is no P-Factor at all. As the airplane begins to roll down the runway, P-Factor increases. The bottom line is that this force also requires right rudder to counteract. This force gets stronger as the airplane picks up speed, but the rudder also becomes more effective as you pick up speed. This force is reduced once you have the tail raised, but is still there because you do not raise the tail high enough to completely eliminate this force.

Gyroscope Effect

All applications of a gyroscope are based on two fundamental properties : rigidity in space and precession. We are only interested in precession for this discussion.

Precession is the resultant action of a spinning rotor when a deflecting force is applied to its rim.

Any time a force is applied to deflect a propeller, the resulting force is 90 degrees ahead of and in the direction of the rotation, causing a pitching moment, a yawing moment, or any combination of the two.

It is said that, as a result of this action, any yawing around the vertical axis results in a pitching moment, and any pitching around the lateral axis results in a yawing moment.

To correct for the gyroscopic action effect, it is necessary for the pilot to properly use elevator and rudder to prevent undesired pitching and yawing. This force only acts on the airplane during the moment the tail is moving up. The propeller is a pretty good gyro. When you apply a force to a gyro, it reacts 90 degrees in the direction of rotation. When you are raising the tail, you are essentially changing the plane of the propeller "gyro" as if you were pushing on the top of the propeller arc from behind. Since the propeller is turning clockwise when viewed from behind, and since a "gyro" reacts with a force 90 degrees in the direction of rotation, the reaction comes as if you were pushing from behind on the right side of the propeller arc. This tends to turn the airplane to the left. The more horsepower the engine has, the stronger this gyroscope reaction will be. In airplanes with a lot of power, you will need to be careful not to bring the tail up too soon, before you have enough speed and therefore rudder effectiveness to counteract this force. The bottom line is that while the tail is coming up, an extra dose of right rudder is required to keep the airplane straight. A good taildragger pilot will anticipate the tail coming up and be there an instant before with the right rudder so the nose never moves, rather than waiting to see the nose to start to the left and then kicking it back with the right rudder. Once the tail stops coming up, you let off the right rudder a little because the gyroscope effect stops, and at this time, you have reduced the angle at which the plane of the propeller is moving through the air, so P-

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Factor has also been reduced. Also, when the tail comes up, you lose the traction provided by the tailwheel, so this too causes a little more rudder to be required. Once the tail is up, the airplane is picking up speed, so the rudder is becoming more effective. As the rudder becomes more effective, less rudder is required to do the same job. The typical taildragger takeoff may require a lot of right rudder during the initial moments of takeoff, maybe even sustained doses of full right rudder. During the end of the takeoff, you have pretty much reduced right rudder usage to that normal during a climb. When the airplane flies off the runway, you are essentially in a normal climb, and we all know that a little right rudder is required in the climb, whether in a taildragger or a nose wheel airplane, to counteract torque and P-Factor.

Density Altitude

Density altitude is the altitude relative to the standard atmosphere conditions (ISA) at which the air density would be equal to the indicated air density at the place of observation. In other words, density altitude is air density given as a height above mean sea level. "Density altitude" can also be considered to be the pressure altitude adjusted for non-standard temperature.

Both an increase in temperature, decrease in atmospheric pressure, and, to a much lesser degree, increase in humidity will cause an increase in density altitude. In hot and humid conditions, the density altitude at a particular location may be significantly higher than the true altitude.

In aviation the density altitude is used to assess the aircraft's aerodynamic performance under certain weather conditions. The lift generated by the aircraft's airfoils and the relation between indicated and true airspeed are also subject to air density changes. Furthermore, the power delivered by the aircraft's engine is affected by the air density and air composition.

Air density decreases with altitude. At high elevation airports, an airplane requires more runway to take off. Its rate of climb will be less, its approach will be faster, because the true air speed [TAS] will be faster than the indicated air speed [IAS] and the landing roll will be longer.

Air density also decreases with temperature. Warm air is less dense than cold air because there are fewer air molecules in a given volume of warm air than in the same volume of cooler air. As a result, on a hot day, an airplane will require more runway to take off, will have a poor rate of climb and a faster approach and will experience a longer landing roll.

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In combination, high and hot, a situation exists that can well be disastrous for an unsuspecting, or more accurately, an uninformed pilot. The combination of high temperature and high elevation produces a situation that aerodynamically reduces drastically the performance of the airplane. The horsepower out-put of the engines decrease because its fuel-air mixture is reduced. The propeller develops less thrust because the blades, as airfoils, are less efficient in the thin air. The wings develop less lift because the thin air exerts less force on the airfoils. As a result, the take-off distance is substantially increased, climb performance is substantially reduced and may, in extreme situations, be non-existent.

Humidity also plays a part in this scenario. Although it is not a major factor in computing density altitude, high humidity has an effect on engine power. The high level of water vapor in the air reduces the amount of air available for combustion and results in an enriched mixture and reduced power

Mountain airports are particularly treacherous when temperatures are high, especially for a low performance airplane. The actual elevation of the airport may be near the operational ceiling of the airplane without the disadvantage of density altitude. Under some conditions, the airplane may not be able to lift out of ground effect or to maintain a rate of climb necessary to clear obstacles or surrounding terrain.

Density altitude is pressure altitude corrected for temperature. It is the altitude at which the airplane thinks it is flying based on the density of the surrounding air mass.

Too often, pilots associate density altitude only with high elevation airports. Certainly, the effects of density altitude on airplane performance are increasingly dramatic in operations from such airports, especially when the temperature is also hot. But it is important to remember that density altitude also has a negative effect on performance at low elevation airports when the temperature goes above the standard air value of 15° C at sea level. Remember also that the standard air temperature value decreases with altitude.

In order to compute the density altitude at a particular location, it is necessary to know the pressure altitude. To determine the latter, set the barometric scale of the altimeter to 29.92" Hg and read the altitude.

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Density altitude can be calculated for any given combination of pressure altitude and temperature, by using the circular slide rule portion of a flight computer.

In conclusion, it is identified how different factors affect aircraft performance. These factors are interlinked together, in terms of one can influence the other and alter the performance all together. Not only did this paper show forces, physical surfaces and forces that can't be seen but only their effect can be, but also how the structure of the aircraft reacts to each force. For example tail draggers and tricycle with nose wheels act differently when experiencing factors affecting takeoff roll.

There's a lot of factors that can be identified, but for this study its been limited to prop wash, torque effect, gyroscopic effect, p-factor, density altitude and seen the relationship between newton's second law and flying. How wet runways, muddy or dry affect takeoff in hot weather condition and the slope of the runway limits aircraft performance. Weightnplays a huge role in terms of determining the CG limits as well as ramp weight and landing weight. If the density altitude is high, certain reductions need to be made in order to be able to takeoff within limits, weight reductions and fuel as well.

This paper takes into consideration the fundamental issues involved in flying and carefully explains different effect and how to identify each one. It shows the links of each factor and how they work together to produce certain risks experienced during flying. Over the years there have been aircraft crashes and investigators tried to identify the causes and solutions to avoid accidents in future.

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