in advance, sorry for my poor language, I´m from Europe, therefore my english is far from perfect and i have to admit I have no experience in bowhunting - which is not allowed in my coutry. But I m a MD, and I will try to enlight this topic from that point of view:
For a lung or double lung hit the following mechanisms will most likely lead to death:
The lung is ventilated (expanded) due to negative intrathoracal pressure: lowering the diaphragm (a muscle) and to a lesser extent expanding an elevating the ribs (intercostal muscles between all neighbouring ribs).
The lung adheres to the inner wall of the thorax (chest) because there is a special fluid between lung and thorax that does not expand due to negative pressure (like gas does). this fluid also provides "gliding properties" for the two moving surfaces of lung and inner thorax wall. This mechanism is called Adhesion.
If you now pierce the thorax(chest) wall, the very narrow fluid filled gap between thorax- wall and lung tissue will fill with air, and this in cosequence will lead to a collaps of the lung,( because the lung itself has a elasticity on its own that enables the expiration as a overall passive action; if the body is in exertion (e.g. an anmal hit by an arrow)also expiration (breathing out) becomes an overall active action.
for making the lung collaps you wont even need to pierce the lung itself.
The collapsing of the lung is called a Pneumothorax (air fills the thoracal gap between lung and inner thorax wall)
If you hit just one lung and no major arteries.
The healthy organism can compensate well with the remaining second lung on the other side.
There are cases where young people suffer from spontaneous pneumothoraxes and walk into the ed with very minor complaints such as little dyspnea only on exertion (seen it myself).
There is one exception which is called a
valvular pneumothorax, a dangerous condition where the entrance wound in the chest forms a valvular mechanism(due to a tissue flap), which enables air to go in but not to flow out. The positive pressure in the hit side of the chest causes the heart to shift on the opposite (healthy) side and compresses the main vessels on the base of the heart which in the worst case leads to death due to a stop of circulation.
A one chest wall or one lung hit without nicking major vessels that causes the lung to completely collapse anyhow will lead to death after days due to the inability of the lung to expand again and the resulting infection(pneumonia)which will affect a non ventilated lung in all cases.
If you pierce the chest wall on both sides (double lung), no hit of major arteries is needed to cause death. if the hole is to big to close itself again in minutes, the organism will lose its ability to reoxygenate the blood, and will fall unconcious in two minutes (maybe faster in a state of exertion, where more o2 is needed)and die within five minutes from oxygen depletion.
Therefore from my point of view the double lunged animal, that dies quickly (minutes), dies in unconciousness because of oxygen depletion mostly.
If you only hit one lung you have to nick major vessels to cause the animal to die quckly (within minutes), if you don´t produce the rare case of a severe valve pneumothorax.
The reason for the Spraying blood through mouth or nose of the animal are the injured bronchi which are all accompanied through veins and arteries.
For the case of a hit of major vessels (heart itself or mainly base of the heart. An adrenaline rush which normally enables the enormous power for the flight reaction will
rise the heart frequency and the blood pressure to the double, which will in case of a nicked artery exponantiate the exsanguination
Ben