Naval Operations Analysis, Additional Problems for Chapter 7
1. A ship is searching for a raft. Its sensor has an
instantaneous detection rate of 
where r is the range from the sensor to the
target in nm. The ship starts its search 2 nm from the raft and
approaches the raft on a direct course at a speed of 10 knots.
a. Find Pd(t), the instantaneous detection rate
as a function of time.
b. What is the probability that detection occurs within the first mile of
the search?
2. An area 250 by 500 nm is to be completely searched one time by means of parallel sweeps. The sweep width for this particular search is assumed to be 30 nm. Use the inverse cube law to determine the track spacing, s, which would be needed in order that the probability of detection would be 0.90.
3.
An aircraft is to conduct a search for a stationary target that is known to be
in a region that is 280 nm by 280 nm. No other information about the
location of the target is known. The aircraft's search speed is 480 knots
and its sensor sweep width is 30 nm. Estimate the probability of
detecting the target during the search by each of the two following methods.
a.
Assume
a random search for 6 hours.
b.
Assume
the inverse cube law, using parallel tracks to bring the target to within 20 nm
of the searching aircraft, and using a search time that allows the aircraft to
cover the entire region.
a.
What
is the minimum time needed for the search?
4.
Suppose that three sensors are to be used to monitor traffic in a channel that
is 100 nm wide. The sensors are placed on a line across the
channel. Measuring from the west side of the channel, sensor 1 is at 25,
sensor 2 is at 50, and sensor 3 is at 75. The lateral range of the sensor
is given by 
.
a.
If a
target passes at a distance of 30 nm from the west side of the channel,
estimate the probability that it will be detected by at least one of the three
sensors.
b.
Estimate
the probability that any target transiting the channel will be detected.
5. An airborne early warning (AEW) aircraft is searching for any aircraft
that may pose a threat to a carrier battle group (CBG). The instantaneous
detection rate for the radar being used has been estimated to be 
where r is the range in nm from the AEW
to the threat aircraft. Estimate the probability that the AEW will detect
a radially inbound threat before it reaches a range of 200 nm.
ANSWERS
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last update: 05 January 2000