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Private Pilot Syllabus
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  Maneuvers:
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Normal Takeoff
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Normal Takeoff - Theory
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Below is an excerpt from the FAA's Airplane Flying Handbook - FAA-H-8083-3B
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It should help you understand the underlying "what, why, and how" of this maneuver.
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If you want to read the entire chapter:
Chapter 5: Takeoffs and Departure Climbs
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Normal Takeoff - Defined
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Though it may seem relatively simple, the takeoff often presents the most hazards of any part of a flight. The importance of thorough knowledge of procedures and techniques coupled with proficiency in performance cannot be overemphasized.

A normal takeoff is one in which the airplane is headed into the wind; there are times that a takeoff with a tail wind is necessary. Also, the takeoff surfaces are firm and of sufficient length to permit the airplane to gradually accelerate to normal lift-off and climb-out speed, and there are no obstructions along the takeoff path.

There are two reasons for making a takeoff as nearly into the wind as possible.
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First, since the airplane depends on airspeed, a headwind provides some of that airspeed even before the airplane begins to accelerate into the wind.
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Second, a headwind decreases the ground speed necessary to achieve flying speed. Slower ground speeds yield shorter ground roll distances and allow use of shorter runways while reducing wear and stress on the landing gear.

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Prior to Takeoff
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All run up and pre-takeoff checklist items should be completed before taxiing onto the runway or takeoff area. As a minimum before every takeoff, all engine instruments should be checked for proper and usual indications, and all controls should be checked for full, free, and correct movement. In addition, the pilot must make certain that the approach and takeoff paths are clear of other aircraft.

When operating from a towered airport, pilots must contact the tower operator and receive a takeoff clearance before taxiing onto the active runway.

It is not recommended to take off immediately behind another aircraft, particularly large, heavily loaded transport airplanes, because of the wake turbulence that is generated. Plan to minimize the chances of flying through an aircraft’s wake turbulence by avoiding the other aircraft’s flightpath or rotate prior to the point at which the preceding aircraft rotated.

While taxiing onto the runway, select ground reference points that are aligned with the runway direction to aid in maintaining directional control and alignment with the runway center line during the climb out. These may be runway centerline markings, runway lighting, distant trees, towers, buildings, or mountain peaks.

 
Terms and Definitions
Although the takeoff and climb is one continuous maneuver, it will be divided into three separate steps for purposes of explanation:
   
Takeoff roll (ground roll) - is the portion of the takeoff procedure during which the airplane is accelerated from a standstill to an airspeed that provides sufficient lift for it to become airborne.
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Lift-off - is when the wings are lifting the weight of the airplane off the surface. In most airplanes, this is the result of the pilot rotating the nose up to increase the angle of attack (AOA).
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The initial climb - begins when the airplane leaves the surface and a climb pitch attitude has been established. Normally, it is considered complete when the airplane has reached a safe maneuvering altitude or an en route climb has been established.








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