ballistic missile defense (Nike Zeus) system, and as the Soviet adversary was believed to be rapidly increasing their nuclear stockpile, the efficacy of both would begin to enter a diminishing returns trend. When more became known about the cost and limitations of the Nike Zeus system, in the early 1960s the head of the department of defense under president John F. Kennedy, Robert McNamara, determined the ineffectiveness of the Nike-Zeus system, especially in its benefit-cost ratio compared to other options. For instance, fallout shelters would save more Americans for far less money. Efficacy during a nuclear explosion Within a considerable radius from the surface of the nuclear fireball, 0–3 kilometers—largely depending on the explosion's height, yield and position of personnel—ducking and covering would offer negligible protection against the intense heat, blast and prompt ionizing radiation following a nuclear explosion. Beyond that range, however, many lives would be saved by following the simple advice, especially since at that range the main hazard is not from ionizing radiation but from blast injuries and sustaining thermal flash burns to unprotected skin. Furthermore, following the bright flash of light of the nuclear fireball, the explosion's blast wave would take from first light, 7 to 10 seconds to reach a person standing 3 km from the surface of the nuclear fireball, with the exact time of arrival being dependent on the speed of sound in air in their area. The time delay between the moment of an explosion's flash and the arrival of the slower moving blast wave is analogous to the commonly experienced time delay between the observation of a flash of lightning and the arrival of thunder during a lightning storm, thus at the distances that the advice would be most effective, there would be more than ample amounts of time to take the prompt countermeasure of 'duck and cover' against the blast's direct effects and flying debris. For very large explosions it can take 30 seconds or more, after the silent moment of flash, for a potentially dangerous blast wave over-pressure to arrive at, or hit, one's position. It is also worth noting that the graphs of lethal ranges of weapon effects as a function of yield, that are commonly encountered, are the unobstructed "open air", or "free air" ranges that assume among other things, a perfectly level target area, no passive shielding such as attenuating effects from urban terrain masking, e.g.