Where does the "g" force that pilots experience come from? I understand that it has to do with acceleration. Say a pilot does a quick maneuver and experiences a force of 5g. What exactly is happening here? 
And what is this force relative to? 
If someone can show an example with some calculations that would be really helpful. 
Thank you 
 A: It comes from the wings actually. His body wants to move in a free fall parabola and the wings make the plane move some other way forcing the pilot on a different path. 
NASA's vomit comet plane makes parabolic flights causing 20 seconds of weightlessness. 
The opposite occurs when a fighter pilot does a split-S or barrel rolls, where the control surfaces of the plane force it on a track requiring up to 9g of acceleration being felt through the seat.
A: There are some simple diagrams and definitions here 
The lift action of air on the wings as well as the thrust of the engines or propellers apply a force on the plane. That force will cause the plane to accelerate unless it exactly balances gravity and drag. Since the the pilot is strapped into the plane he or she feels the force caused by the acceleration of the seat and/or straps. That force divided, by the weight of the pilot to make it relative to 1, is the g force. 
A: The g-forces you feel are caused by inertia. Inertia is the basic tendency of all matter to resist any change of motion, whether it be a change of speed or of direction. 
Because of that, when the plane turns, your body still wants to keep going straight ahead. As a result, you feel as if you are being pushed towards the outside of the curve. The plane itself also wants to keep going straight ahead, but it has wings and control surfaces that can apply a force to overcome its inertia and make it curve. As your body does not have such features, it is your seat, seatbelt or the walls of the plane that will apply the force you feel.
The actual force experienced can be positive, zero or negative, depending on the trajectory. During level flight you feel the normal 1 g. If the plane pulls up, your seat pushes you up to follow the plane, and you feel more than 1 g. This is positive g-force. If the plane pulls the other way (down), the g-force you feel will be less than the normal 1 g. It can go to zero, or even go negative (so you're thrown towards the top of the plane), depending on the path of the plane. NASA's Vomit Comet flies on a special path that keeps the g-force at zero for up to 30 seconds.
A: Suppose you jump off a tall building. When you hit the ground you feel a high "g force" for the obvious reason that the ground decelerates you rather rapidly.
Now suppose you put a large balloon on your landing point. This time the compression of the air slows you more gradually, brings you to a stop and eventually you bounce up again. During this time you feel a "g force" that might, for example, be 5g. The force is ultimatwely provided by the Earth as a whole. The air in the balloon pushes on you and the ground pushes on the balloon.
Now consider the aeroplane. When the plane pulls out of the dive it's the air rushing over the wings that brings the dive to a halt and accelerates the plane upwards, and during this time the pilot (and plane) feel a "g force" just as you do when landing on the balloon. The force isn't just compression of the air as in a balloon: it's more complicated as it's the air flow over the wings, but essentially it's the same as you landing on the balloon.
However it's harder to see what is ultimately providing the push. With the balloon it was the ground under the balloon. With the aeroplane the air supporting the plane it's the atmospheric pressure of the air around the plane. The plane's wings compress the air that's supporting them and this generates pressure waves that spread into the surrounding atmosphere.
A: Let me simplify it.
We know that $F=mg$, where $g$ is the acceleration due to gravity.
Weight has the measurement of force (Newton) so if you are 50Kg, that means your mass times 9.8M/Sec^2 gravitational force is acting on you. This force is resisted by us always, and that is why we could stand on the surface of the earth.
Imagine you are freely falling on the earth. In every second you pick up speed of 9.8 m s^-2.
If we are falling at this speed, we feel weightless, because we dont have resist at all.
But when we are quickly climbing up in the sky, and if the acceleration of climbing is higher than gravitational pull (9.8 m s^-2), then you feel more weight than your normal weight. This is because we are moving against acceleration due to gravity. If it is 5 times, then you will feel 5g.
This can be measured easily. Tie a 5KG stone on a weighing scale and drop it from a height of 1.5m. (Drop it on some shock absorbing material,like bed or something). You see the scale reading when it is free falling - it will be 0.
If you quickly lift this weighing scale upwards and see the reading, it will show an increase in the weight - ie more than 5Kg. The reason is we move the object against gravity and so it increases.
