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It is not hard to find the limits of tolerance of humans to G forces, but I can't seem to find more detailed graphs for other positions.

Graph showing the limits of tolerance of humans to linear acceleration on sitting position

This one was taken from wikipedia page about G-Forces, but as shown bellow, supposedly, laying down on different positions can help you withstand more G's for longer.

Illustration showing how many G's can a pilot withstand depending on body position

But I couldn't find more detailed graphs such as the first one, I took this picture from this news article talking about the subject.

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As you stated there are no exact plots for human g-force tolerance in laying position readily availlable.

We can, however, use the graph you linked, which is based on work of Dr. Mike Rickards:

The Gemini safe-ejection acceleration criteria we used were based on human tolerance acceleration limits as postulated by Dr. Mike Rickards of Weber Aircraft Corporation and are shown in figure 14

Excerpt from Robert V. Brulle (2008). Engineering the Space Age: A Rocket Scientist Remembers

enter image description here

We can pretty safely assume the "transverse" line in the graph quite well correlates with that of a prone and supine positions. The figure depicts a person sitting down, and at higher transverse (or lateral) g-loadings the normal gravity has only a small effect on g-tolerance of a person. The effect will depend on whether the transverse acceleration is driving blood towards the legs or away from them. The graph is close enough especially when we take into account the vast spread in individual differences when it comes to g-load tolerance.

At high g-loading the tolerance is not simply a matter of maintaining consciousness. Prolonged high acceleration will cause tissue damage, especially in brain tissue, and after passing out, the subject will eventually die if the acceleration keeps the blood pressure in the brain elevated.

On a further note: from the "transverse" line in the figure 14 we can see that the picture in your question depicting pilots in different positions cannot be correct. As per the graph, at best a human body can stand 14 g's shown in the middle position of the picture for several seconds, not minutes.

Note that the time scale in the graph is logarithmic, and by continuing the line we can safely assume that to remain conscious for three minutes, the pilot in the middle position could not pull more than approximately 6 g's. I dare say at this time the pilots visual cortex would most likely be badly swollem from the pressure of blood, so at least temporary blindness would be imminent.

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