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Radar Guns & The Doppler Effect Edward G. Lake
Independent Researcher
July 7, 2017
Abstract: Many mathematicians have a difficult time understanding how radar
guns work because they do not understand how a single photon can produce the Doppler
Effect. A YouTube video illustrates a lot about how radar guns work. This is a step by
step description of what is shown in that video and what it means.
Key words: Radar; photons; wave; Doppler Effect.
The YouTube video at this link https://www.youtube.com/watch?v=XlnYO_G_IxA shows
a “complex” radar gun in use in various situations. At the 55 second mark, it shows the basic
internal parts of a hand-held radar gun:
Figure 1 – Hand-held radar gun interior
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The rest of the video is mostly about a dash-mounted radar gun, but it is important to first
understand that the “antenna” in both types of guns consists of a photon emitter and receiver at
the rear of the cone-shaped antenna, and the front of the cone is covered with a semi-
transparent “radome.” Here’s an illustration of that points out the radome on a hand-held gun:
Figure 2 – A radar gun radome
On a dash-mounted radar gun, the antenna’s also have a radome, as can be seen on the
Front Antenna in Figure 3 below:
Figure 3 – Dash-mounted radar gun components
The gun appears to be a Kustom Signals Golden Eagle K-band Police Radar System. Each
antenna is both a transmitting antenna and a receiving antenna. It is what I call a “complex”
radar, not because it has so many parts but because it measures the speed of the antenna in
addition to measuring the speed of one or more targets. A “basic” radar gun does not measure
the speed of the antenna. It just measures the speed of a target. The primary difference between
the two types of guns is that the radome for a “complex” radar gun is only semi-transparent to
microwave energy, while a “basic” radar gun has a radome that is fully transparent.
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Figure 4 – Semi-transparent radome
Figure 4 illustrates that a “complex” radar gun will transmit photons that travel to the
target and back to the receiver, just as with a “basic” radar gun, but because a “complex” radar
gun has a semi-transparent radome, a few of the photons only travel to tiny metallic obstacles
imbedded in the radome before returning to the receiver.
What this does is allow the radar gun to measure both its own speed AND the speed of
one or more distant targets.
I. How does a radar gun work?
The “complex” radar gun measures its own speed the same way it measures the speed of
the target, via the Doppler Effect.
Every photon oscillates at a specific energy frequency which determines what kind of
photon it is. This NASA link https://imagine.gsfc.nasa.gov/science/toolbox/emspectrum2.html
says, "the only difference between radio waves, visible light and gamma rays is the energy of
the photons. Radio waves have photons with the lowest energies.
Microwaves have a little more energy than radio waves. Infrared has still more, followed by
visible, ultraviolet, X-rays and gamma rays."
Today’s radar guns mostly emit photons which oscillate in the “K-band frequency,” which
is 24.125 GigaHertz (GHz), or 12,125,000,000 Hertz (cycles per second).
When a radar gun emits a photon at that specific frequency, the photon travels to a target
at the speed of light, c., which is 670,616,629 miles per hour. If the target is moving away from
the gun’s emitter at 60 mph, the photon will hit the target at 670,616,569 miles per hour, which
is c-v, where v is the velocity of the target away from the emitter.
The photon is absorbed by an atom in the target as if it had lower energy equal to
670,616,569 miles per hour. The atom cannot hold any additional energy from any photons, so
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it emits a new photon back toward the radar gun. The new photon has the lower energy in the
form of a lower oscillating frequency.
When the gun receives back the photon, it compares the oscillation frequency that it
emitted to the oscillation frequency of the photon that came back. The difference in the
frequencies is converted to miles per hour and provides the speed of the target: -60 mph.
This is also how the gun measures its own speed. The emitter emitted photons at a given
frequency toward the radome of the gun. Since the radome was moving away from the point
where the photons were emitted, the photons have to catch up with the radome. That means
the photons will hit the radome at the speed of light minus 60 mph.
This is a problem for mathematicians who cannot understand how a radar gun can
measure its own speed. They view speed as distance divided by time. And the distance between
the emitter and the radome never physically changes. But it actually does change, because when
the gun is stationary the distance is fixed, but when the gun is moving, the distance between the
emitter and the radome must include the distance the radome traveled between the time of the
photon emission and the time the photon hit the radome. There is no simple way to measure
that extra distance, but due to the Doppler Effect, it isn’t needed. The Doppler Effect gives you
the speed of the radome without the need to measure distances.
And, it must not be forgotten that the radome is semi-transparent, so the vast majority
of the photons passed through the radome and traveled to the distant target and back. That
provides the gun with the speed of the target in addition to the speed of the gun. That is why
there are three speed displays on the dash-mounted radar gun in Figure 3. The display on the
right is for the speed of the gun. The display on the left is for the speed of a distant target. The
display in the center is for the speed of a specific distant target.
Figure 5 – radar gun speed only
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In Figure 5 above, there is no distant target, so the gun only shows the “patrol speed” of
31 mph, which is actually the gun’s speed, since the gun is attached to the patrol car. The gun
is only measuring the speed of its radome. The ground and trees do not provide any
measurable speed for two reasons: First, because none of the displays can show any speed that
is less than 10 mph. Second, the speed of the stationary trees and pavement is not shown
because of Einstein’s Second Postulate:
“light is always propagated in empty space with a definite velocity c which is
independent of the state of motion of the emitting body.”
That postulate says that regardless of how fast the gun is moving, the speed of the
photons it emits will always travel at c or 670,616,629 miles per hour. The speed of the gun (or
of the patrol car) does not change the speed at which the emitted photons travel. So, if the gun
was stationary, the photons would hit the trees and pavement at the same speed the photons
would hit if the gun was moving at 20, 30, 50, 80 or 100 miles per hour.
Figure 6 – target speed only
Figure 6 shows the radar gun as being stationary in a patrol car parked next to a
highway. As before, none of the displays on the display unit shows a number if the gun is
measuring less than 10 mph for an object. The only object moving faster than 10 mph in front
of the radar gun is the vehicle on the highway traveling at 67 mph.
Figure 7 below completes the picture by showing all three display panels with different
speeds.
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Figure 7 – multiple targets and a moving gun
The radar gun (and patrol car) are moving at 35 mph, which shows in the display on the
right. The strongest signal the gun is measuring comes from the pickup truck and trailer behind
the car that is “out of beam” (which appears to be another patrol car). This part of the video
begins at the 3 minute 30 second mark. It begins with only the speed of the radar gun showing.
Then the oncoming police car registers in the left display as traveling at 46 mph. Then the
oncoming patrol car gets out of the signal beam and its speed moves to the center display, while
the 38 mph speed of the pickup truck and trailer are shown in the left display.
Figure 8 – misaligned radar gun
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In Figure 8, which is from the 4:50 mark in the video, the radar gun is deliberately
misaligned. It is no longer pointed straight down the road in the direction the patrol car is
traveling. This clearly demonstrates that the gun is measuring its own speed, not the speed of
the patrol car.
Figure 9 – misaligned radar gun AND second radar gun
Figure 9 confirms this when, at the 7:45 mark the driver picks up a handheld Bushnell
Speedster SPORTS radar gun and points it at the road ahead. The gun has only one display, which
shows the speed of the fastest object, which is the speed of the Bushnell radar gun’s radome.
This is an illustration of the “cosine effect.” The Bushnell is pointed straight ahead in the
direction of movement, and it shows the gun’s speed to be 62 mph. The dash-mounted gun is
pointed off to one side, and it shows that gun’s speed to be 55 mph. In the video they compare
the Bushnell’s speed to the patrol car’s speedometer and it is stated that they agree. Only the
misaligned dash-mounted gun is showing an “incorrect” speed.
In reality, the dash-mounted gun is just as accurate as the Bushnell. They are just
measuring different things. The dash-mounted gun is measuring the speed of the radome as it
moves at less than a zero angle to the receiver and emitter. If the dash-mounted gun was pointed
at a 90 degree angle to the direction of travel, the gun would show its speed to be zero (or less
than 10 mph). It is neither moving toward nor away from the emitter at that angle.
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II. The Key question
The key question that needs to be asked after viewing the video is: How does the gun in
Figure 5 know that the trees and road are not a moving target? How does the gun know it has to
put their “relative speed” into the “Patrol Speed” display window on the left and not into the
“Target Speed” display window on the right?
According to mathematicians, all speeds are relative. So, as they understand things, there
is no difference between a moving tree approaching your stationary car at 31 mph and your
moving car approaching a stationary tree at 31 mph. But the gun puts the speeds on different
displays, so it knows there is a difference. How?
First of all, the gun is designed to measure two things using the Doppler Effect: 1. The
speed of the radome. 2. The speed of an oncoming target.
Secondly, the returned signal from the radome is always the same strength. Since the
radome is a fixed distance from the emitter, and since the radome always contains the same
amount of reflecting material, the signal strength coming back from the radome to the receiver
will always be the same. Only the Doppler Effect on the photons will differ. Meanwhile, the
return signal from targets varies widely in both signal strength and in their Doppler Effects.
So, logically speaking, the gun can distinguish return signals from the radome from return
signals from a target by measuring the return signal strength. It knows what the signal strength
of the radome returned photons will be. Any other frequency strength must be from a target.
If by pure coincidence the signal strengths happen to be the same from both sources, it can just
fail to display both of those speeds.
Mathematicians will argue that the gun cannot possibly measure the speed of the radome
because the radome is part of the gun, and the emitter/receiver and radome are always
stationary relative to one another. But the mathematicians also argue that a target’s speed
toward the radar gun cannot be distinguished from the radar gun’s speed toward a target. Yet,
the gun puts the different speeds in different digital display boxes. The speed of the target goes
into the LEFT display and the speed of the gun goes into the RIGHT display. Mathematicians
probably believe that is impossible, too. That is why radar guns are so terrific for explaining and
demonstrating Einstein’s theories.
III. Summing up
1. A “complex” radar gun can measure its own speed by measuring how fast the radome
moves away from the location of the emitter at the time of photon emission.
2. Radar guns use photons, not waves.
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3. A radar gun can, in theory, measure the speed of a target with one photon. The
reason many photons are used is to verify what would have been measured by one
single perfectly aimed and returned photon.
4. If a “basic” radar gun (with a fully transparent radome) is pointed at a highway sign
from a patrol car traveling at 60 mph, the gun will display the highway sign’s speed as
ZERO (actually “no reading” which means “less than 10 mph”).
5. When a “complex” radar (with a semi-transparent radome) like those in the video is
pointed at a highway sign from a patrol car traveling at 60 mph, the gun will display
the radar gun’s speed.
6. It appears that if the gun shown in the video is placed on the passenger seat and
pointed at the wall under the dashboard, when the car is traveling at 60 mph, the
target speed will show as 60 mph and the gun speed will also show as 60 mph.