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Radar Guns & The Doppler Effect Edward G. Lake

Independent Researcher

July 7, 2017

detect@outlook.com

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.