The illustration of the trumpet model seems to suggest that the intrathoracic airways remain very narrow until they are near the alveoli. That seems to contradict an illustration, where airway cross-sectional area was shown to increase regularly and more than exponentially. Can we reconcile the two illustrations?
There is a difference between the illustration of cross-sectional area as a function of airway generation and that of the trumpet model. In the latter we have depicted area as a function of distance from the glottis. Obviously the various orders of airways do not have the same length. The trachea accounts for nearly half the distance between glottis and alveoli!
Let us look at this in greater detail. From the relationship between airway diameter versus airway generation we computed the cross-sectional area of each airway, and multiplied this by the number of airways for each generation. This gave us the total cross-sectional area for each generation of airways.
Now consider the total cross-sectional area of each airway generation, depicted as a function of the distance of the airway from the glottis (left). Initially airway area diminishes slightly, but from generation 4 on there is a more than exponential increase. Note that up to about 22 cm deep down the airways from the glottis there has been little change in cross- sectional area. In the last few centimetres near the alveoli the area expands dramatically to nearly 10,000 cm².
You will probably agree that a thumbtack better describes the model than a trumpet.