As a fighter pilot makes a tight turn (with his head toward the centre of curvature), the blood drains from his head, leading to loss of brain function. Once the radial acceleration

reaches about 4g, the pilot’s vision switches to black and white and narrows to “tunnel
vision”. If this acceleration is maintained, or increased, the pilot will lose all vision and
will black out. An F-22 Raptor pilot in a dogfight throws his aircraft into a tight turn
(r = 5.80 km) while flying at Mach 2.0. Is he likely to survive?

Type Mach 2 into Google and get back 681 m/s

Ac = v^2/r = (681)^2/5800 = 80 m/s^2

80/9.81 = 8.15 g

Thanks.

To determine if the F-22 Raptor pilot is likely to survive the tight turn, we first need to calculate the radial acceleration experienced by the pilot.

Radial acceleration (ar) can be calculated using the formula:

ar = v^2 / r

Where v is the velocity and r is the radius of curvature.

Given:
v = Mach 2.0 = 2.0 * speed of sound (343 m/s) = 686 m/s
r = 5.80 km = 5800 m

Plugging in these values into the formula, we have:

ar = (686 m/s)^2 / 5800 m
ar ≈ 81.14 m/s^2

Now, we have the value for radial acceleration. Let's compare it with the critical acceleration values at which the pilot starts to experience vision issues.

According to your description, once the radial acceleration reaches about 4g, or about 39.2 m/s^2, the pilot's vision switches to black and white and narrows to "tunnel vision." If the acceleration is maintained or increased further, the pilot will eventually lose all vision and black out.

In this case, the radial acceleration experienced by the F-22 Raptor pilot is significantly higher than the critical acceleration level of 4g. With an acceleration of approximately 81.14 m/s^2, it is highly likely that the pilot will experience vision issues, potentially leading to black-out or loss of consciousness.

Therefore, without any countermeasures or safety precautions, it would be very dangerous for the F-22 Raptor pilot to sustain such a high radial acceleration while performing a tight turn. The pilot's chances of surviving would be extremely low.