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Assuming that the craft’s engine is capable of any amount of acceleration, how much g-force would prevent the pilot from being able to move their limbs in order to control the space craft?

There is an article about John Stapp surviving stopping at 46g, but that does not appear to document his ability to move during the test.

Also I am assuming that the craft is not fully computerized and needs some pilot input of some kind.

If there are better more technically correct words to describe what I am asking, please feel free to let me know and I can learn and edit the question.

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    $\begingroup$ John Paul Stapp survived 46g for a very short time, probably much less than a second. A longer exposition to G-forces of this strength would cause unconsciousness by reduction of blood flow through the brain. A pilot without conscion would be unable to control the spacecraft anyway. See Wikipedia. $\endgroup$ – Uwe Feb 19 '18 at 10:22
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According to the book Human Engineering guide for Equipment Designers, authored by Wesley E. Woodson and Donald W. Conover and published by the University of California Press, suggests the following effects at various levels of g-force for Transverse, positive and negative g-forces.

                             Effects of prolonged G
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                             Transverse G forces
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             2 g - visual acuity is reduced
             4 g - gross body movement is difficult
             8 g - respiration becomes difficult
            10 g - difficult to hold head up, can't move limbs
            12 g - breathing difficult without mechanical help
            14 g - vision begins to fail
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                              Positive G forces
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             2 g - visual acuity is reduced
             4 g - peripheral blindness, limb movement difficult
             5 g - temporary blindness and loss of body control
             6 g - unconsciousness
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                              Negative G forces
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             2 g - diminished vision and head pains
             3 g - conjunctival haemorrhage, red-out, and mental confusion 
             4 g - probably haemorrhage and retinal bleeding

With transverse g-forces being in the forwards directions from the chest (forcing a person into the back of their seat, positive being an upwards direction (driving the person into the floor) and negative being in a downwards direction (lifting a person off their seat).

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how much g-force would prevent the pilot from being able to move their limbs in order to control the space craft?

How many times do they have to lift their arms? How much control of the limb do they need?

Your arm weighs about 5% of your total body weight -- ~4kg for an 80kg male. The weight is evenly distributed across the musculature of the arm, so it's probably easier to lift an extra-heavy arm than to lift a dumbbell of equivalent mass. At 4g you're lifting an extra 12kg (~26 lbs) of arm -- doable for anyone in good physical condition, but your hand is going to be shaky and you will tire of it quickly. Much more than that and you won't reliably be able to hit a small switch, particularly as your perception is suffering from the g-force at the same time. At 10g you're looking at 36kg of extra weight across your arm, which I would guess most people can't hold up if they aren't dedicated weight trainers.

(Do not give me a hard time about using mass vs weight/force units here.)

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