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Defense and Aerospace

10 Posts tagged with the avionics tag
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(video via BAE Systems)

 

Today's modern wars are fought with a severe technology disparity between the factions. One side is making improvised explosive devices while the other uses augmented reality to call in air strikes. Despite the differences, the modern countries continue to innovate against a possible war with its hi-tech peers. BAE Systems has just released its "Adaptiv" vehicle camouflage that mimics the heat signatures in its surroundings.

 

The Adaptiv technology consists of hexagonal "pixels." An onboard camera samples the background and displays the IR-image on the pixels accordingly. The process happens fast enough for a moving vehicle to not even make an impression under IR surveillance. The pixels can also be arranged to make the vehicle look like another. In the video example, a tank is make to look like a Jeep.  The pixels could also be used to display words or a message, if need be.

 

The project is funded by the Swedish Defense Materiel Administration, who wanted a focus on IR cloaking. However, the BAE engineers combined the Adaptiv pixels with other electro-magnetic spectrum cloaking devices to provide further stealth coverage.

 

BAE plans on adapting the technology for warships and buildings. For this application, larger panels will be used.

 

I would like to see similar technology for use on soldiers. Seeing soldiers get taken out by UAVs at night, via infrared cameras, is disturbing. Again, the battles are usually one sided anyway. I have never heard of a drone on drone battle in any war.

 

Eavesdropper

 

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Printable UAV Aircraft

Posted by Eavesdropper Jul 29, 2011

A team from the University of Southampton has used 3D printing techniques to build a working UAV from the ground up in just under a week. The team, led by Andy Keane and Jim Scanlan, demonstrated their effort at an air strip just a little down the road from Stonehenge. The 1.5 meter wing span, ultra-low-drag, aircraft successfully flew showing it is possible to build for each individual application.


At 100 micrometers (4 thousands) at a time, a laser traces out the 2D cross section of the design. The laser can "print" with many different types of materials, from polyamide plastic to stainless steel or titanium powder. When forming parts with the metallic powder, the team stated that it is as strong as if the parts were machined from raw/bare metal. To create a stronger formed part, an electron laser sintering is used, instead of the conventional laser, to melt the powder completely.


Of course, the electronics in the craft are not printed. At least not yet. http://www.element14.com/community/community/doittogetherblog/blog/2011/07/14/grow-electronics-by-the-molecule


Eavesdropper

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Airbus A320neo (left). AA branded Boeing 737 (right)  (images via each respective company)

 

The news has hit the airwaves, American Airlines (AA) wants 460 new jets for their fleet. United States based Boeing will build 200, while France based Airbus will get 260 orders.

 

Currently, AA has an entire fleet of Boeing built aircraft. With a previous order of 207 jets, Boeing still has 52 to produce on that request along with the 200 more. Not to over strip Boeing's capability, American Chairman and CEO Gerard Arpey said, "No single manufacturer could provide the number and variety of aircraft we need to fulfill our vision for the future." Now, some of the burden is placed on Airbus.

 

What AA will ultimately get are not all new aircraft, but slightly modified existing planes. From Boeing, they will get 100 regular 737s, with an option for 40 more. Also from Boeing, AA will get 100 "re-engined" 737s, with an option for 60 additional. Re-engined planes are existing platforms with new, modern engines.

From Airbus, AA will receive 130 A320 Family planes with 130 re-engined A320neos, with an option for 365 more.

 

The engine options are LEAP-X from CFM International and the Pratt & Whitney Pure Power PW1100G. These engines will give the jets they are used on better fuel efficiency and less of a carbon foot print.

 

AA plans to replace all of their mid-80s purchased 757 and 767-200 airplanes. Aprey wrote, "These new aircraft will enable us to reduce our operating and fuel costs and deliver state-of-the-art amenities to our customers, while maximizing our financial flexibility. ... These new deliveries are expected to pave the way for us to operate the youngest and most fuel-efficient fleet among our U.S. airline peers in approximately five years."

 

Having flown on an AA 767-200 recently, the upgrade could not come fast enough. Hopefully, AA will start introducing biofuels to their new fleet. At the average of 1.2 miles per gallon on previous generation jets, anything improvement is worth it.

 

Side note: Boeing 737 operators want a newly designed airplane, not re-engined aircraft. U.S. Washington Gov. Chris Gregoire said the 737 is a piece of history. He welcomes a re-engined 737. More on this, in the coming years.

 

Cabe

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klm.jpg

KLM Passenger Jet via KLM

 

The oldest airline with the same name since it started, KLM Royal Dutch Airlines founded in the Netherlands in 1919, is showing off the first use of a biofuel blend on a commercial passenger aircraft. 170 passengers on a Boeing 737-800 flew from Amsterdam to Paris on June 22, 2011. KLM managing director Camiel Eurlings spoke about the use of the fuel, "In November 2009 we demonstrated that it was technically possible to fly on biokerosene. Now, a year and a half after our first demonstration flight on Camelina, a new phase has been entered around the world, that of certification. Authorisation will soon be granted to operate commercial flights on biofuel. I am especially proud to announce that KLM will take this substantial step in September."

 

Biokerosene if a 50/50 blend of kerosene and biofuel made from used cooking oil produced by Dynamic Fuels, a Tyson Foods and Syntroleum Corporation partnership. The Biokerosene met the same specifications of standard kerosene, and required no modification to the aircraft. The end result was a substantial reduction of CO2 emissions and a minimum negative impact on biodiversity and the food supply due to the fuel source.

 

KLM's consortium that is seeking out and developing sustainable aviation biofuel, SkyNRG, supplied the fuel. After seeking the advice of an independent sustainability board consisting of Solidaridad, Copernicus Institute of the University of Utrecht, and the World Wide Fund for Nature, they were given the OK on the mix of Biokerosene.

 

KLM admits that the price of the Biokerosene is very high. To meet true sustainability, the price of the fuel has to "come down substantially and permanently." However, KLM's demonstration is an indicator of big changes on the way. No wonder KLM has been a sector leader of the Dow Jones Sustainability Index for the past six years.

 

Perhaps they should look into algae, as in the recent U.S. Navy's recent biofuel helicopter test fight.

 

Eavesdropper

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BiPod on its test flight and car via Scaled Composites

 

While Terrafugia takes pre-orders on their Airplane Car, and Trek Aerospace consider civilian transport, Burt Rutan tests his last airplane before his retirement. BiPod, the flying car from Scaled Composites. A two seater, dual 15 kW motor driven hybrid-electric airplane that just happens to be drivable on the road. 

 

In just four months from the inception of the BiPod, the craft took its first flight on March 30, 2011. Able to reach a 200mph speed, the BiPod can fly a distance of 530 miles. It also have an "overdrive mode," that lets the user fly 760 miles at a slower 100mph. In ground driving mode it can go 35 miles on battery charge alone, or up to 820 miles on a single tank of gas. Batteries in the nose of the craft privide enough power for takeoff, and a reserve of two possible landing attempts for safety.

 

Two 450CC internal-combustion engines, one in each fuselage, drive generators that in turn power electric motors on the driving wheels and propellers. The driving of a generator by a gasoline motor is also the concept behind the Chevy Volt, under certain conditions. Four propellers, one on each wing and two on the horizontal stabilizer linkage on the tails.

 

Flight and driving controls are separated between the two fuselage sections. Left side are the flight controls, and right side is for driving. When in driving mode, the wings must be removed and stored between the two halves.

 

Scaled Composites announced the ambitious project to gauge the response and viability of the BiPod. All the while Burt Rutan spends most of his time working away on his final legacy. Scaled Composite's President Doug Shane said, "[Rutan] was here all the time - he worked really damned hard - and that was a good lesson to all our young engineers that you don't get something for nothing."

 

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Concept design for the BiPod via Scaled Composites

 

 

You might recognize some of the past eclectic airplane designs from Burt Rutan and the team at Scaled Composites in the below video. Now you know where they all came from.



 

Eavesdropper

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Classification of Radar systems

 

Depending on the desired information, radar sets must have different qualities and technologies.  One reason for these different qualities and techniques radar sets are classified in:

 

schematic.bmp

Imaging Radar / Non-Imaging Radar

An Imaging Radar forms a picture of the observed object or area.  Imaging radars have been used to map the Earth, other planets, asteroids, other celestial objects  and to categorize targets for military systems.

Typically implementations of a Non-Imaging Radar system are speed gauges and radar altimeters.  These are also called scatterometers since they measure the scattering properties of the object  or region being observed. Non-Imaging Secondary Radar applications are immobilizer systems in some  recent private cars.

Primary Radar

A Primary radar transmits high-frequency signals which are reflected at targets.  The arised echoes are received and evaluated. This means, unlike secondary radar sets  a primary radar unit receive it's own emitted signals as an echo again.

Secondary Radar

At these radar sets the airplane must have a transponder (transmitting responder)  on board and this transponder responds to interrogation by transmitting a coded reply signal. This response  can contain much more information, than a primary radar unit is able to acquire (E.g. an altitude ,  an identification code or also any technical problems on board such as a radiocontact loss ...).

Pulsed Radars

Pulse radar sets transmit a high-frequency impulse signal of high power.  After this impulse signal, a longer break follows in which the echoes can be received,  before a new transmitted signal is sent out. Direction,  distance and sometimes if necessary the height or altitude  of the target can be determined from the measured antenna position and propagation time of the pulse-signal.

Continuous- Wave Radar

CW radar sets transmit a high-frequency signal continuously.  The echo signal is received and processed. The receiver need not to be mounted at the same place  as the transmitter. Every firm civil radio transmitter can work as a radar transmitter at  the same time, if a remote receiver compares the propagation times of the direct signal with  the reflected one. Tests are known that the correct location of an airplane can be calculated  from the evaluation of the signals by three different television stations.

Unmodulated CW- Radar

The transmitted signal of these equipments is constant in amplitude and frequency.  These equipment is specialized in speed measurings. Distances cannot be measured.  E.g. they are used as speed guages  for police. Newest equipments  (LIDAR)  work in the laser frequency range and measure not only the speed.

 

Modulated CW- Radar

The transmitted signal is constant in the amplitude but modulated in the frequency.  This one gets possible after the principle of the propogation time measurement  with that again.   It is an advantage of this equipment that an evaluation is carried out without  reception break and the measurement result is therefore continuously available.  These radar sets are used where the measuring distance isn't too large and it's necessary  a continuous measuring (e.g. an altitude measuring in airplanes or as weather radar/windprofiler).

A similar principle is also used by radar sets whose transmitting impulse is too long to get  a well distance resolution. Often this equipment modulate its transmitting pulse to obtain  a distance resolution within the transmitting pulse with the help of the pulse compression.

Bistatic Radar Sets

A bistatic radar consists of a separated  (by a considerable distance) transmitting and receiving sites.

 

 

Source "http://www.radartutorial.eu/" Copyright (C)  2009  R Colman. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License.
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Radar Technology - Primary RADAR - Height, "the RADAR equation" abnd Reflections

 

RADAR is can be used to track and aircrafts hieght above the gorund while in flight. One the flight decks secondary instruments if often a RAD-Alt, or RADAR Altimeter.

 

The height of a target over the earth's surface is called height or altitude. This is denominated by the letter H (like: Height). The altitude can be calculated with the values of distance R and elevation angle ε.

 

height1.gif

The altitude cannot be so simply calculated on a flying airplane, while refraction is caused when electromagnetic waves cross airlayers at different density and the earth's surface has a bend. The calculation of the targets altitude is not only a trigonometrically calculation. The current location grounding bend must also be taken into consideration.

 

In addtion the propagation of electromagnetic waves is also subject to a refraction and are also dependent on:

 

  • the transmitted wavelength,
  • the barometric pressure,
  • the air temperature and
  • the atmospheric humidity.

 

These variables are one of many reasons why modern aircraft use static pressure and Air Data Computers, rather than RADAR, to calulate their altitude.

 

The RADAR equation

 

The radar equation represents the physical dependences of the transmit power, that is the wave propagation up to the receiving of the echo-signals. Furthermore one can assess the performance of the radar with the radar equation.


Nondirectional power density diminishes as geometric spreading of the beam.

 

Argumentation/Derivation

 

First we assume, that electromagnetic waves propagate under ideal conditions, i.e. without dispersion.

 

nondirectional.png

Nondirectional power density diminishes as geometric spreading of the beam. In the above image Nondirectional power density diminishes as geometric spreading of the beam.

 

If high-frequency energy is emitted by an isotropic radiator, than the energy propagate uniformly in all directions. Areas with the same power density therefore form spheres (A= 4 π R²) around the radiator. The same amount of energy spreads out on an incremented spherical surface at an incremented spherical radius. That means: the power density on the surface of a sphere is inversely proportional to the to the square of the radius of the sphere.

 

Since a spherical segment emits equal radiation in all direction (at constant transmit power),  if the power radiated is redistributed to provide more radiation in one direction,  then this results an increase of the power density in direction of the radiation.  This effect is called antenna gain. This gain is obtained by directional radiation of the power.

 

Of course in reality radar antennas aren't “partially radiating” isotropic radiators. Radar antennas must have a small beam width and an antenna gain up to 30 or 40 dB. (e.g. parabolic dish antenna or phased array antenna).

 

The target detection isn't only dependent on the power density at the target position, but also on how much power is reflected in the direction of the radar. In order to determine the useful reflected power, it is necessary to know the radar cross section σ. This quantity depends on several factors. But it is true to say that a bigger area reflects more power than a smaller area. That means:

 

A Jumbo jet offers more radar cross section than a sporting aircraft at same flight situation. Beyond this the reflecting area depends on design, surface composition and materials used. With this in mind we can say: The reflected power Pr at the radar depends on the power density, the antenna gain.

 

Radar Reflections from Flat Ground

 

The trigonometric representation shows the influence of the Earth's surface. The Earth plane surrounding a radar antenna has a significant impact on the vertical polar diagram.

 

ground1.jpg

 

The combination of the direct and re-reflected ground echo changes the transmitting and receiving patterns of the antenna. This is substantial in the VHF range and decreases with increasing frequency. For the detection of targets at low heights, a reflection at the Earth's surface is necessary. This is possible only if the ripples of the area within the first Fresnel zone do not exceed the value 0.001 R (i.e.: Within a radius of 1000 m no obstacle may be larger than 1 m!).

 

Specialized Radars at lower (VHF) frequency band make use of the reflections at the Earth's surface and lobing to maximize cover at low levels. At higher frequencies these reflections are more disturbing. The following picture shows the lobe structure caused by ground reflections. Normally this is highly undesirable as it introduces intermittent cover as aircraft fly through the lobes. The technique has been used in ATC ground mounted radars to extend the range but is only successful at low frequencies where the broad lobe structure permits adequate cover at higher elevations.

 

lobe.gif

Raising the height of the antenna has the effect of making the lobbing pattern finer.  A fine grained lobing structure is often filled in by irregularities in the ground plane.  Specifically, if the ground plane deviates from a flat surface then the reinforcement and  destruction pattern resulting from the ground reflections breaks down.  Avoidance of lobe effects is one of the prime considerations when selecting a radar location  and the height of the antenna.

 

Source "http://www.radartutorial.eu/" Copyright (C)  2009  R Colman. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License.
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Radar Technology - Primary RADAR - Ranging and Elevation Angles

 

The maximum measuring distance Rmax of a radar unit  isn't only orientated by the RADARs transmitting power/performance but also on the duration of the receiving time.

 

range max 1.gif

 

The radar timing system must be reset to zero each time a pulse is radiated.  This is to ensure that the range detected is measured from time zero each time.   Echo signals arriving after the reception time are placed either into the:

 

  • following transmit time where they remain unconsidered since the radar equipment       isn't ready to receive during this time, or
  • into the following reception time where they lead to measuring failures (ambiguous returns).

 

The pulse repetition frequency  (PRF) determines the maximum unambiguous range  of a given radar before ambiguities start to occur.

 

The pulse repetition time (PRT) of the radar is important when determining the maximum  range because target return-times that exceed the PRT of the radar system appear  at incorrect locations (ranges) on the radar screen.  Returns that appear at these incorrect ranges are referred as ambiguous returns or second-sweep echoes.

 

By employing staggered PRT the target ambiguous return isn't represented any more by small arc.  This movement or instability of the ambiguous return is represented typically as a collection  of points in certain equipment because of the change in reception times from impulse to impulse.  With this distinction, a computer controlled signal processing can calculate the actual distance.

 

range max 2.gif

 

More modern 3D- radar sets with a phased array antenna  don't have this problem with an ambiguous range. The system computer steers the transmitted beams so that  ambiguous returns from the previous pulses are not received while the antenna beam points in another direction.

 

Figure 3 shows a target return by the primary radar (thick shorter arc) and an IFF answer reply  of the IFF interrogator (thin longer arc) and a second sweep answer of the IFF by using staggered PRT  on an PPI-scope.

 

range max 3.jpg

 

Here you can see as well, that the interrogator doesn't use every primary synchronous-pulse.  (The appearance of too many ambiguous IFF-returns can be reduced by using a decreased Tx-power  of the interrogator.)  Now by using fixed PRT one would expect to see ambiguous returns confusably  similar to the unambiguous returns (arcs).

 

A monostatic pulse radar uses the same antenna for transmitting and receiving.  During the transmitting time the radar cannot receive:  the radar receiver is switched off using an electronic switch, called duplexer.  The minimal measuring range Rmin („blind range”)  is the minimum distance which the target must have to be detect. Therein, it is necessary that the transmitting pulse  leaves the antenna completely and the radar unit must switch on the receiver. The transmitting time tPW and the recovery time trecovery should are as short as possible, if targets shall be detected in the local area.

 

Targets at a range equivalent to the pulse width from the radar are not detected.  A typical value of 1 µs pulse width of a short range radar corresponds  to a minimum range of about 150 m, which is generally acceptable. However, radars  with longer pulse width suffer a relatively large minimum range, notably pulse compression  radars, which can use pulse lengths of the order of tens or even hundreds of microseconds.  Targets at ranges closer than this minimum are said to be eclipsed.

 

Elevation Angle

 

Altitude-  or height-finding search radars use a very narrow beam in the vertical plane.  The beam is mechanically or electronically scanned in elevation to pinpoint targets.  Height-finding radar systems that also determine bearing must have a narrow beam in the horizontal plane  in addition to the one in the vertical plane.

 

height.gif

 

The elevation angle is the angle between the horizontal plane and the line of sight,  measured in the vertical plane. The Greek letter Epsilon (ε) describes the elevation angle.  The elevation angle is positive above the horizon (0° elevation angle), but negative below the horizon.

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Radar Technology - Primary RADAR - Detecting and Ranging

 

The electronic principle on which radar operates is very similar to the principle of sound-wave reflection.  If you shout in the direction of a sound-reflecting object (like a rocky canyon or cave),  you will hear an echo. If you know the speed of sound in air, you can then estimate the  distance and general direction of the object. The time required for an echo to return  can be roughly converted to distance if the speed of sound is known.

Radar uses electromagnetic energy pulses in much the same way, as shown in the below.

 

radar RF.gif

 

The radio-frequency (rf) energy is transmitted to and reflected from the reflecting object.  A small portion of the reflected energy returns to the radar set.  This returned energy is called an ECHO, just as it is in sound terminology.  Radar sets use the echo to determine the direction and distance of the reflecting object.

 

Radar is an acronym for RAdio (Aim)* Detecting And Ranging. Modern radar can extract widely more information from a target's echo signal than its range.  But the calculating of the range by measuring the delay time is one of its most important functions. The distance is determined from the running time of the high-frequency transmitted signal  and the propagation c0.  The actual range of a target from the radar is known as slant range.  Slant range is the line of sight distance between the radar and the object illuminated.  While ground range is the horizontal distance between the emitter and its target and  its calculation requires knowledge of the target's elevation.  Since the waves travel to a target and back, the round trip time is dividing by two  in order to obtain the time the wave took to reach the target.


The angular determination of the target is determined by the directivity of the antenna.  Directivity, sometimes known as the directive gain, is the ability of the antenna to concentrate  the transmitted energy in a particular direction.  An antenna with high directivity is also called a directive antenna.  By measuring the direction in which the antenna is pointing when the echo is received,  both the azimuth and elevation angles from the radar to the object or target can be determined.  The accuracy of angular measurement is determined by the directivity,  which is a function of the size of the antenna.

 

radar 2.gif

 

Radar units usually work with very high frequencies. Reasons for this are:

 

  • quasi optically propagation of these waves.
  • High resolution (the smaller the wavelength, the smaller the objects the radar is able to detect).
  • Higher the frequency, smaller the antenna size at the same gain.

The True Bearing (referenced to true north) of a radar target is  the angle between true north and a line pointed directly at the target.  This angle is measured in the horizontal plane and in a clockwise direction from true north.


The antennas of most radar systems are designed to radiate energy in a one-directional lobe  or beam that can be moved in bearing simply by moving the antenna. As you can see  the shape of the beam is such that the echo signal strength varies in amplitude as the antenna  beam moves across the target.

 

radar 3.gif

 

In actual practice, search radar antennas move continuously;  the point of maximum echo, determined by the detection circuitry or visually by the operator,  is when the beam points direct at the target. Weapons-control and guidance radar systems  are positioned to the point of maximum signal return and maintained at that position  either manually or by automatic tracking circuits.

In order to have an exact determination of the bearing angle, a survey of the north direction  is necessary. Therefore, older radar sets must expensively be surveyed either with a compass  or with help of known trigonometrically points. More modern radar sets take on this task and with help of the GPS Satellites determine the northdirection independently.

Transfer of Bearing Information

The rapid and accurate transmission of the bearing information between the turntable  with the mounted antenna and the scopes can be carried out for

  • servo systems and
  • counting of Azimth Change Pulses

Servo systems are used in older radar antennas and missile launchers and works with help of devices like  synchro torque transmitters and synchro torque receivers. In newer radar units we find a system of Azimth Change Pulses ACP).  In every rotation of the antenna a coder sends many pulses, these are then counted in the scopes.

 

Newer radar units work completely without or with a partial mechanical motion.  These radars employ electronic phase scanning in bearing and/or in elevation (phased array antennas).

 

Source "http://www.radartutorial.eu/" Copyright (C)  2009  R Colman. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License.

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Radar Technology - Primary RADAR

 

The implementation and operation of primary radars systems involve a wide range of  disciplines. This series of blogs will aim to explain the basic principles of Primary RADAR and it's role for aircraft.

 

Radar measurement of range, or distance, is made possible because of the properties  of radiated electromagnetic energy.

 

Reflection of electromagnetic waves

 

The electromagnetic waves are reflected if they meet an electrically leading  surface. If these reflected waves are received again at the place of their origin,  then that means an obstacle is in the propagation direction.

 

Electromagnetic energy travels through air at a constant speed,  at approximately the speed of light:

 

  • 300,000 kilometers per second or
  • 186,000 statute miles per second or

 

This constant speed allows the determination of the distance between the reflecting objects and the radar site (the aircraft) by measuring the running time  of the transmitted pulses.

 

This energy normally travels through space in a  straight line, and will vary only slightly because of atmospheric and  weather conditions. By using of special radar antennas this energy can be focused  into a desired direction. Thus the direction (in azimuth and elevation) of the reflecting objects can be measured.

 

These principles can basically be implemented in a radar system,  and allow the determination of the distance, the direction and the  height of the reflecting object.

 

The following figure shows the operating principle of a primary radar set.  The radar antenna illuminates the target with a microwave signal, which is then reflected  and picked up by a receiving device. The electrical signal picked up by the receiving  antenna is called echo or return. The radar signal is generated by a powerful transmitter  and received by a highly sensitive receiver.

 

radar path.gif

All targets produce a diffuse reflection i.e. it is reflected in a wide number of directions.  The reflected signal is also called scattering. Backscatter is the term given to  reflections in the opposite direction to the incident rays.

 

Radar signals can be displayed on the traditional plan position indicator (PPI) or other more  advanced radar display systems. A PPI has a rotating vector with the radar at the origin, which  indicates the pointing direction of the antenna and hence the bearing of targets.

 

This is as far as I will go for now - however keep an eye out for my next blog which will follow on from here......


 

Source "http://www.radartutorial.eu/" Copyright (C)  2009  R Colman. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License.