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198 Bu il d Y o ur O w n Q u a d c o p t e r

take about ten years travelling at nearly the speed of light. The other twin will stay on Earth
awaiting the return of his/her sibling. The twin in the space ship will accelerate very close
to light speed and will patiently wait the ten years it will take, according to the clock in the
ship, to make the round trip. According to Professor Einstein, if the travelling twin could
view a clock on Earth he/she would observe time going by more quickly than it did in the
spaceship. This effect is part of the theory of special relativity and, more specifically, is called
time dilation. If the twin on Earth could view the clock in the spaceship, he/she would see it
turning at a much slower rate than the earthbound clock. Imagine what happens when the
travelling twin returns and finds that he/she is only ten years older but that the earthbound
twin is 50 years older due to time dilation. The space twin will have time travelled a net
40 years into Earth’s future by taking the ten-year space trip!
The second effect is more complex than time dilation. I will simply state what it is.
According to Einstein’s theory of general relativity, objects located close to massive objects,
such as the earth, will have their clocks moving slower as compared to objects that are
further away from the massive objects. This effect is due to the curvature of the space-time
continuum predicted and experimentally verified by the general relativity theory.
Now back to the GPS satellites that are orbiting at 14,000 kilometers per hour (km/h),
while the earth is rotating at a placid 1,666 km/h. The relativistic time dilation due to the
speed differences is approximately -7 µsec/day, while the difference due to space-time is
+ 45 µsec/day for a net satellite clock gain of 38 µsec/day. While this error is nearly
infinitesimal on a short-term basis, it would be very noticeable over a day. The total daily,
accumulated error would amount to a position error of 10 km or 6.2 miles (mi), essentially
making GPS useless. That is why the earth ground stations constantly update and synchronize
the GPS satellite atomic clocks.

Note: As a point of interest, the atomic clocks within the GPS satellites are deliberately slowed prior
to being launched to counteract the relativistic effects described earlier. Ground updates are still
needed to ensure that the clocks are synchronized to the desired one nanosecond of accuracy.

Quadcopter GPS Receiver

I selected the Parallax PMB-688 GPS receiver, which is small, lightweight, and very suitable
for use in this project. Figure 8.7 is a picture of this receiver. The PMB-688 GPS receiver will
track up to 20 satellite channels, which provides for both fast acquisition and the continuous
lock of NMEA data from the satellites. Table 8.1 lists key specifications and features for this
receiver.
Several key specifications are worth discussing a bit more. An acquisition sensitivity of
−148 dBm means that the receiver is extremely sensitive to picking up weak GPS signals.

Figure 8.7 Parallax PMB-688 GPS receiver.