Winglet save money by reducing fuel-wasting drag at the wingtips. If you've ever seen a picture of a jet flying through clouds you might remember that there is a swirling pattern at the tips. The air under the wing (high pressure causing the lift) wants to go sideways around the wingtip to get to the top of the wing. That is what causes the swirling pattern coming off the wingtips. The winglets prevent this airflow and the air that used to escape the bottom of the wing is now still down there creating lift. More lift for the same wing area = less drag. Since the Winglet prevents more drag than they cause, they give a net positive effect to the economy of the airplane. That equals fuel savings.
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