How do tthe air sacs of birds help make the body lighter?

air in the bones lighten the wholww skeleton:
http://www.backyardnature.net/birdbone.htm

But the 9 breathing air sacs do not really lighten the bird except to possibly allow smaller lungs:

http://www.people.eku.edu/ritchisong/birdrespiration.html

The air sacs in birds play an important role in their respiratory system and are not directly responsible for making the body lighter. Instead, they assist in facilitating efficient oxygen exchange during respiration.

To understand how air sacs work, let's start with the basic anatomy of a bird's respiratory system. Birds have a complex system that involves both lungs and air sacs. Unlike mammals, who have a two-way system of breathing, birds have a one-way system.

When a bird inhales, air enters through the trachea and flows into the posterior air sacs. From there, it moves into the lungs for oxygen exchange. When the bird exhales, the air from the lungs is pushed into the anterior air sacs. Then, during the next inhalation, the air from the anterior air sacs passes through the lungs, while fresh air is simultaneously drawn into the posterior air sacs.

This unidirectional airflow allows a constant supply of fresh oxygen to be inhaled and a continuous removal of carbon dioxide from the body. The air sacs act as reservoirs, storing and moving air throughout the respiratory system.

While the air sacs themselves do not directly contribute to making the bird lighter, they do help with efficient respiration. By constantly supplying fresh oxygen, the bird's muscles receive an adequate amount of oxygen to function properly. This is important for birds' high activity levels and their ability to sustain flight for long periods.

Additionally, the air sacs can play a role in assisting with flight by providing a more efficient exchange of gases. Although the air-filled bones do help reduce the overall weight of the bird, it is not primarily due to the air sacs.

In summary, while the air sacs in birds do not directly lighten their body, they play a crucial role in facilitating efficient respiration, providing oxygen to the body's muscles, and allowing birds to maintain their high activity levels.