G
AIM-9B can pull approximately 10G at sea level and approximately 3.5 G at 50,000 feet. The 10G maximum at sea level extends almost all the way to 30,000 feet. From that altitude upward, the capability decreases until, at 50,000 feet the missile can pull approximately 3.5 G. In other words, Sidewinder can pull 10G from sea level to 30,000 feet and approximately 3.5 G at 50,000 feet. Maximum fighter G, when launching, is approximately 2G below 40,000 feet and 1.6 G above 40,000 feet. The G-capability of the missile determines the G-limit on the fighter at launch. To illustrate: The rate of turn of the fighter in a pursuit curve is dependent on target speed, angle off, and range, as indicated by the following formula:
W = Vt x Sinθ / Range
Where
W = Rate of turn in radians per second
Vt = Target velocity in feet per second
Sinθ = Sine of the angle-off
By examining the formula we can see that the rate of turn (W) increases any time target velocity or angle-off increases, and decreases as range increases. The number of G which the fighter pulls, at a given rate of turn, is directly proportional to fighter speed, and may be represented by the following formula:
W = 32.2 x N / Vf
Where
W = Number of radial G
Vf = Fighter velocity in feet per second
W = Rate of turn in radians per second
We can see from the formula that any time fighter velocity increases, we must also increase G (N), in an effort to maintain a given turn rate. Rate of turn required for the missile to set up a collision course is dependent upon five factors: (1) target speed, (2) angle-off, (3) range, (4) enabling time, and, (5) the navigational constant. The number of G which the missile pulls, for a given rate of turn, is directly proportional to missile speed. The higher the speed, the higher the G. If the missile is launched from a Mach 1 fighter pulling 2G, how many G must the missile pull in order to maintain the same rate of turn as the launching fighter? As shown by the formula:
N = Vf x W / 32.2
since the missile (V) is going 1.7 Mach above the launch aircraft’s velocity, or 2.7 Mach, it must pull 5.4 G, in order to maintain the same rate of turn as the launching fighter. Why, then, are we committed to pull a maximum of 2G when the missile can pull 10G, an amount considerably greater than the 5.4 G which we just computed? AIM-9B does not begin to guide until 1 ∕ 2 second after launch, at which time it receives its first guidance signal to set up a collision course. During this enabling period (1 ∕ 2 second) the missile has the characteristics of an ordinary rocket. Because of this, an additional rate of turn is necessary to set up its collision course. To set up the collision course, Sidewinder turns 3 1 ∕ 2 times the rate of turn of the gyro-seeker – this is a navigational constant. Because of this, the rate of turn generated by the missile, in the first maneuver, is greater than the rate of turn of the launching fighter. Since the number of G pulled by the missile and fighter is equated to rate of turn and velocity, it is obvious that the 2G limitation of the fighter at launch is tied to the 10G limitation of the missile. If more than 2G is pulled, the tracking rate of the gyro-seeker is exceeded by the line-of-sight rate, thus the seeker loses the target.
Another means of exceeding the tracking rate of the gyro-seeker is to launch the missile with an angle-of-attack in excess of 12° (the angle between the missile’s longitudinal axis and the launch aircraft’s flight path). For the F-100, since the missile launcher line is aligned 2° below the fuselage reference line, the maximum aircraft angle of attack is 14°. If launched with a greater angle of attack, Sidewinder will jump toward flight path, causing the tracking rate of the gyro-seeker to be exceeded by the line-of-sight rate, consequently the gyro-seeker will lose the target. When this happens, the missile goes ballistic. To avoid exceeding a 14° angle of attack, the F-100 should not be flown at less than 170 knots in a 1G condition and 230 knots in a 2G condition.