Authors: Derek Mahaffey, Susan Burkett, John Tyler
Suggested Courses: Physics II, E-M I
Level: Freshman & Sophomore
On a very cold dry winter morning in West Germany a group of American servicemen were
removing a solid-state-fueled missile from its packing case, using a hoist. They had some
difficulty with the hoist and had to raise the missile from its cradle several times and
lower it back in before they were finally successful. Shortly after the missile was
finally lifted from its cradle it was moved close to a grounded metal antenna. The fuel in
the missile ignited, burned through the side of the rocket motor and killed several of the
Subsequent analysis and testing pointed to electrostatic charge build-up and sparks
resulting from that charging as the culprit.
The course of events was probably as follows. When the missile was lifted from the
cradle, the friction caused tribo-electric charging of both the cradle which was grounded,
and the surface of the motor casing. The casing was not grounded, moreover, a very good
insulator. The charge on the casing was not able to spread out because of the insulating
nature of the casing and was not able to bleed off through the air because the air was so
dry. (You must have noticed how much more aggravating sparks from your fingers are during
cold, dry weather.)
As the missile was lifted, the cradle and the missile casing acted like the plates of a
capacitor. Because the separation of the plates was increasing, the value of the
capacitance decreased. The total charge on the plates remained unchanged, as discussed
above, so that the voltage on the capacitor increased. The voltage became greater than the
break-down voltage of the air and a spark was drawn from the missile casing to the
grounded metal antenna. ( The exact mechanism by which the spark ignited the fuel is
complicated and involves the removal of polarization electric fields produced inside the
fuel by the charge on the casing.)
II. Numerical and Design Problems
Problem 1. Calculate the separation d between the missile and the antenna when the
spark occurred. See figure.
Assume that the missile and the cradle formed a parallel plate capacitor
with an effective area of 4.0 square feet and a plate separation of 6.0 inches. The
average surface charge density s is 1.0 x10-9 Coulombs per square meter. The
breakdown electric field strength of cold dry air is 3.0 x106 V/m.
Problem 2. What modification to the missile and/or cradle would prevent electrostatic
discharge in the future?
III. Questions on Ethics and Professionalism
Consider the following scenario:
A few years before the accident occurred, and before the missile went into production,
an engineer, who was working on the project, conceived the idea that a missile might be
ignited by just the mechanism we have been discussing. He approached his supervisor and
raised his concern.
The supervisor said that he thought, (a) that electrical breakdown of the air was
unlikely and (b) that even if it did occur, there was only a very remote possibility that
it would cause any problem. They both agreed that there was no data that would help them
evaluate the probability that an accident could occur. Although there was nothing in the
specifications about the matter, they decided to approach the military procurement officer
about the issue.
The military officer agreed with them that the mechanism was possible, but unlikely.
Moreover, he said that any design changes then would seriously delay the deployment of the
missile. Anyway, he added, the people working with the missile would be military
personnel, and they couldn't expect everything they had to do to be absolutely safe.
Question 1. What professional and ethical responsibilities do you think the engineer
and his supervisor had in this case?
Question 2. Does it make any difference to your views that no accident of this type had
been recorded at the time they thought of the problem? Why?
Question 3. What do you think of the procurement officer's views about the deployment
delay? What about his views on safety and military personnel? What alternative views would
Problem 1. Model the system as a pair of parallel-plate capacitors as follows. Let C1 be the capacitor formed by the missile and the cradle, and let C2 be the capacitor formed by the missile and the antenna. The two
capacitors are in parallel as suggested by the figure. Calculate Q, the charge on C1:
Now the two parallel plate capacitors values can be calculated from
The effective area A of C2 is much smaller than that of C1, so the parallel combination of C1 + C2 can be approximated as just C1 alone.
Now express the charge Q in terms of the breakdown voltage and the unknown separation d
between the missile and the antenna, then solve for d.
The missile was about 2 cm away from the antenna when the spark occurred.
Problem 2. No technical design is provided. This is an open ended design problem
involving the addition of grounding.