f _ mv _ r in which f is centrifugal acceleratory force, m is the mass of the object, v is velocity of travel, and r is radius of curvature of the turn. From this formula, it is obvious that as the velocity increases, the force of centrifugal acceleration increases in proportion to the square of the velocity. It is also obvious that the force of acceleration is directly proportional to the sharpness of the turn (the less the radius).
Measurement of Acceleratory Force—"G." When an aviator is simply sitting in his seat, the force with which he is pressing against the seat results from the pull of gravity and is equal to his weight. The intensity of this force is said to be +1 G because it is equal to the pull of gravity. If the force with which he presses against the seat becomes five times his normal weight during pull-out from a dive, the force acting on the seat is +5 G.
If the airplane goes through an outside loop so that the person is held down by his seat belt, negative G is applied to his body; if the force with which he is held down by his belt is equal to the weight of his body, the negative force is -1 G.
Effects of Centrifugal Acceleratory Force on the Body— (Positive G)
Effects on the Circulatory System. The most important effect of centrifugal acceleration is on the circulatory system, because blood is mobile and can be translocated by centrifugal forces.
When an aviator is subjected to positive G, blood is centrifuged toward the lowermost part of the body. Thus, if the centrifugal acceleratory force is +5 G and the person is in an immobilized standing position, the pressure in the veins of the feet becomes greatly increased (to about 450mmHg). In the sitting position, the pressure becomes nearly 300 mm Hg. And, as pressure in the vessels of the lower body increases, these vessels passively dilate so that a major portion of the blood from the upper body is translocated into the lower vessels. Because the heart cannot pump
Changes in systolic (top of curve) and diastolic (bottom of curve) arterial pressures after abrupt and continuing exposure of a sitting person to an acceleratory force from top to bottom of 3.3. G. (Data from Martin EE, Henry JP: Effects of time and temperature upon tolerance to positive acceleration. J Aviation Med 22:382, 1951.)
unless blood returns to it, the greater the quantity of blood "pooled" in this way in the lower body, the less that is available for the cardiac output.
Figure 43-3 shows the changes in systolic and diastolic arterial pressures (top and bottom curves, respectively) in the upper body when a centrifugal acceleratory force of +3.3 G is suddenly applied to a sitting person. Note that both these pressures fall below 22mmHg for the first few seconds after the acceleration begins but then return to a systolic pressure of about 55 mm Hg and a diastolic pressure of 20 mm Hg within another 10 to 15 seconds. This secondary recovery is caused mainly by activation of the baroreceptor reflexes.
Acceleration greater than 4 to 6 G causes "blackout" of vision within a few seconds and unconsciousness shortly thereafter. If this great degree of acceleration is continued, the person will die.
Effects on the Vertebrae. Extremely high acceleratory forces for even a fraction of a second can fracture the vertebrae. The degree of positive acceleration that the average person can withstand in the sitting position before vertebral fracture occurs is about 20 G.
Negative G. The effects of negative G on the body are less dramatic acutely but possibly more damaging permanently than the effects of positive G. An aviator can usually go through outside loops up to negative accel-eratory forces of -4 to -5 G without causing permanent harm, although causing intense momentary hyperemia of the head. Occasionally, psychotic disturbances lasting for 15 to 20 minutes occur as a result of brain edema.
Occasionally, negative G forces can be so great (-20 G, for instance) and centrifugation of the blood into the head is so great that the cerebral blood pressure reaches 300 to 400 mm Hg, sometimes causing small vessels on the surface of the head and in the brain to rupture. However, the vessels inside the cranium show less tendency for rupture than would be expected for the following reason: The cerebrospinal fluid is centrifuged toward the head at the same time that blood is centrifuged toward the cranial vessels, and the greatly increased pressure of the cerebrospinal fluid acts as a cushioning buffer on the outside of the brain to prevent intracerebral vascular rupture.
Because the eyes are not protected by the cranium, intense hyperemia occurs in them during strong negative G. As a result, the eyes often become temporarily blinded with "red-out."
Protection of the Body Against Centrifugal Acceleratory
Forces. Specific procedures and apparatus have been developed to protect aviators against the circulatory collapse that might occur during positive G. First, if the aviator tightens his or her abdominal muscles to an extreme degree and leans forward to compress the abdomen, some of the pooling of blood in the large vessels of the abdomen can be prevented, thereby delaying the onset of blackout. Also, special "anti-G" suits have been devised to prevent pooling of blood in the lower abdomen and legs. The simplest of these applies positive pressure to the legs and abdomen by inflating compression bags as the G increases. Theoretically, a pilot submerged in a tank or suit of water might experience little effect of G forces on the circulation because the pressures developed in the water pressing on the outside of the body during centrifugal acceleration would almost exactly balance the forces acting in the body. However, the presence of air in the lungs still allows displacement of the heart, lung tissues, and diaphragm into seriously abnormal positions despite submersion in water. Therefore, even if this procedure were used, the limit of safety almost certainly would still be less than 10 G.
Acceleratory Forces in Space Travel. Unlike an airplane, a spacecraft cannot make rapid turns; therefore, centrifugal acceleration is of little importance except when the spacecraft goes into abnormal gyrations. However, blast-off acceleration and landing deceleration can be tremendous; both of these are types of linear acceleration, one positive and the other negative.
Figure 43-4 shows an approximate profile of acceleration during blast-off in a three-stage spacecraft, demonstrating that the first-stage booster causes acceleration as high as 9 G, and the second-stage booster as high as 8 G. In the standing position, the human body could not withstand this much acceleration, but in a semireclining position transverse to the axis of acceleration, this amount of acceleration can be withstood with ease despite the fact that the acceleratory forces continue for as long as several minutes at a time. Therefore, we see the reason for the reclining seats used by astronauts.
Acceleratory forces during takeoff of a spacecraft.
Problems also occur during deceleration when the spacecraft re-enters the atmosphere. A person traveling at Mach 1 (the speed of sound and of fast airplanes) can be safely decelerated in a distance of about 0.12 mile, whereas a person traveling at a speed of Mach 100 (a speed possible in interplanetary space travel) would require a distance of about 10,000 miles for safe deceleration. The principal reason for this difference is that the total amount of energy that must be dispelled during deceleration is proportional to the square of the velocity, which alone increases the required distance for decelerations between Mach 1 versus Mach 100 about 10,000-fold. But in addition to this, a human being can withstand far less deceleration if the period of deceleration lasts for a long time than for a short time. Therefore, deceleration must be accomplished much more slowly from high velocities than is necessary at lower velocities.
Deceleratory Forces Associated with Parachute Jumps.
When the parachuting aviator leaves the airplane, his velocity of fall is at first exactly 0 feet per second. However, because of the acceleratory force of gravity, within 1 second his velocity of fall is 32 feet per second (if there is no air resistance); in 2 seconds it is 64 feet per second; and so on. As the velocity of fall increases, the air resistance tending to slow the fall also increases. Finally, the deceleratory force of the air resistance exactly balances the acceleratory force of gravity, so that after falling for about 12 seconds, the person will be falling at a "terminal velocity" of 109 to 119 miles per hour (175 feet per second). If the parachutist has already reached terminal velocity before opening his parachute, an "opening shock load" of up to 1200 pounds can occur on the parachute shrouds.
The usual-sized parachute slows the fall of the parachutist to about one ninth the terminal velocity. In other words, the speed of landing is about 20 feet per second, and the force of impact against the earth is 1/81 the impact force without a parachute. Even so, the force of impact is still great enough to cause considerable damage to the body unless the parachutist is properly trained in landing. Actually, the force of impact with the earth is about the same as that which would be experienced by jumping without a parachute from a height of about 6 feet. Unless forewarned, the parachutist will be tricked by his senses into striking the earth with extended legs, and this will result in tremendous deceleratory forces along the skeletal axis of the body, resulting in fracture of his pelvis, vertebrae, or leg. Consequently, the trained parachutist strikes the earth with knees bent but muscles taut to cushion the shock of landing.
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