Effect of Wind

A headwind will always reduce the ground roll distance required for an airplane to attain a desired airspeed. Although the headwind increases the drag and decreases the thrust for a given ground speed, it increases the lift and adds directly to the ground speed to increase the airspeed so that the net effect on takeoff distance is favorable.

The effect of jthe wind is most easily determined by using the ap­proximation of Equation 7.4, keeping in mind that Г, Д and L depend on the airspeed and not the ground speed.

If Va denotes the ground speed and Vw the headwind then, for this case, Equation 7.4 becomes

The factor к is presented graphically in Figure 7.8.

Suppose, in the previous example, that the 747 was taking off into a 30-kt (50.7-fps) headwind. Using the same lift-off velocity of 274.5 fps gives a ratio s of headwind to airspeed of 0.185. From Figure 7.8, к equals 0.0753. Thus the average acceleration should be evaluated at an airspeed of 207 fps. At this speed,

T = 153,7001b D= 12,736 lb L = 280,200 lb

Therefore, a = 5.79ft/sec2.

The ground roll distance is thus determined to be

(274.5 – 50.7)2
2(5.79)

= 4325 ft (7.9)

Compared to the no-headwind case, the 30-kt headwind decreases the ground roll distance by more than 30%.

It should be noted that FAR Part 25 requires a conservative estimate of

headwind effects. Takeoff and landing distances must be calculated on the basis of 50% of reported headwinds and 150% of reported tailwinds. Since the wind can vary from one instant to another, the intent of FAR Part 25 is to use only half of any wind that improves performance but 150% of the opposite.