A light aircraft commences a stalled-on landing from a 15.24 � screen height. Just before touchdown of the main landing gear, the pilot decided to perform a touch-and-go maneuver. Thus, at the instant of touchdown, the pilot proceeds to enter a takeoff procedure to a screen height of 15.24 � by applying full throttle. The overall available field length is 2000 � within these screen heights. Determine total distance for this maneuver.
During the course of the landing and takeoff, assume that no weight is applied to the runway at any point (assume airplane gets close to but never contacts the ground), and that there are no delays in pilot actions (i.e., don’t add any extra delay distances).
Three major airborne segments:
- Stalled-on landing,
- Transition from landing to takeoff situation (accelerated level flight close to the ground from touchdown point to liftoff point) by using mean kinetic energy model, and finally
- Takeoff.
Given
| Runway | |||
| Aircraft | |||
| Glideslope angle, flight path descent angle | |||
| Engine | |||
| Single Piston-Prop Engine | |||
| Note: No thrust reverse capability. | |||
| Airfield |
| ISA conditions at 900 m above sea level | |||
| From density ratio | |||
| Zero runway slope. | |||
| Ground effect factors in close proximity to ground | |||
Notes:
- No weight applied to the runway at any point
- No delays in pilot actions
Solution
- Stalled-on Landing
Landing distance (while in air)
=
Deceleration time
Ground distance in consideration of velocity of tailwind
Stall speed:
Approach velocity:
Radius of flare maneuver (landing):
Mean velocity:
Mean thrust:
Lift coefficient:
Mean drag at:
Stalled-on landing airborne transition:
Total ground distance needed for the airborne landing segment:
According to FAR 25 specifications we must use 150% of the predicted tailwind. Therefore, we need to adjust our calculations accordingly.
b. Transition from Landing to Takeoff Situation (Mean Kinetic Energy Model)
From the stalled-on landing we know that the ground speed at touch down would have been approximately equal to the landing stall ground speed.
Using the mean kinetic energy method.
We must first determine the liftoff velocity.
Takeoff stall speed:
Liftoff speed:
Similar to the first part of climb segment #1 on takeoff we need to calculate the mean velocity:
Before we can solve for the distance the mean thrust and drag must be determined.
Mean thrust:
Now we need the lift coefficient to calculate drag. Since we are in straight level flight, we know that:
Assuming a typical Oswald efficiency value of 0.7:
`
Ground effect factor on lift induced drag: =0.95
The drag can be calculated using the standard definition which takes into account both zero-lift drag and induced drag:
We may now calculate the drag:
Now we may solve for the still air distance travelled in the transition segment:
The time taken to accelerate to the liftoff speed can be calculated using the following:
Finally, we may calculate the ground distance of the transition segment using the following relation:
The total distance needed to transition from a landing to a takeoff situation is approximately equal to meters.
Using FAR 25 specification for tailwind:
c. Takeoff
In this segment we begin at the liftoff point and transition into the first climb segment where the goal is to clear the screen set to a height of 15.24 meters.
An approximation model will be used.
We know that the takeoff climb airspeed is equal to the following:
As previously calculated the takeoff stall speed is equal to 40.88 m/s.
Therefore, the climb airspeed is equal to 49.056 m/s.
We may now calculate the airspeed at mean kinetic energy. This will be used to calculate the mean thrust and drag.
Solving for the first part of the climb segment where increases from to. In this part, little height is gained so the ground effect factor will still be used:
The still air ground distance is defined as the following:
Mean thrust:
Lift coefficient:
2
Drag coefficient:
Mean drag:
Solving for still air distance covered in the first part of the first climb segment:
We may now correct for the tailwind by first calculating the time for this part of the climb:
Solving for tail wind corrected ground distance of the first part of climb segment #1:
FAR 25 specifications adjustment for tailwind:
For the second part of climb segment #1 the aircraft is assumed to be climbing at a constant angle. Here, to calculate the climb angle, we will assume it is relatively small:
In the first part we accelerated from to. Therefore, the lift coefficient can be determined using:
Finally, we must calculate the thrust produced by the single engine at:
Solving for the climbing angle:
The still air distance covered in the second part of climb segment #1 can be calculated with the following:
To determine the tail wind corrected distance we must first calculate the time elapsed for this segment:
Tail wind corrected distance for the second part of climb segment #1:
Therefore, the total ground distance covered by the second part of climb segment #1 is approximately
FAR 25 specifications adjustment for tailwind:
Total ground distance covered during the airborne transition component of the takeoff run:
Total ground distance needed according to FAR25 specifications:
We may now calculate the total distance needed to perform the touch-and-go maneuver:
However, using 150% of the predicted tailwind, we will need some additional runway:
The aircraft will need approximately meters to perform the touch-and-go maneuver. A distance of meters is required if the additional 150% is applied to the tailwind as per FAR25 specifications. In either case the pilot can perform this touch-and-go maneuver safely.
