Radar Phase 2 update

[Beamscanner]

ED has stated that Phase Two of their radar development will include azimuth/bar settings effecting detection performance.

"Upon Phase 1 release and tuning, we will implement Phase 2 that will include the effect of radar azimuth and bar settings on detection ranges and the inclusion of more accurate look down radar performance."

 

This is not a correct application of radar theory. The radar range equation does not contain azimuth or bar values in it.

Azimuth and bar settings only effect what is has been called Max Range Cumulative detection performance. Which indicates a typical range the radar will first see a target. See my full explanation here. But in short it is a simple way of telling a high ranking officer the typical range he could expect his first detection. Though this does not inform the officer that the detections will be rare/irregular at this range. 

 

Azimuth and bar settings have little to no effect on performance. This is a misnomer told to pilots.

Detection range performance is based on a probability of detecting a RCS at a given range.

ex the APG-66 has a 10% chance of detecting a T-38 at 20 Nmi in a single sweep. (ie the main beam crossed the target once)

 

The benefit of lower ur bar and azimuth isn’t that this performance changes. Rather it’s that you get many more sweeps per second on the target. ie you get more chances to detect the target. Each sweep always being 10% (given the T-38 example).

Said another way, you simply get to roll the dice more often. But the average performance remains the same.

 

ED should instead use single scan probability of detection (not effected by azimuth/bar), rather than max cumulative.

 

For instance, given the APG-66 / T-38 example above. 

Using single scan Pd, the T-38 would only be detected 1/10 sweeps at 20 Nmi. If ED used Max Cumulative, they'd simply make the detection 100% at 20 Nmi.

 

I've made a fully open source/non-ITAR analysis of the APG-63 detailing the math behind all of this.

 

ED should use the SNR figures provided to determine single scan Pd. Id recommend using a 0% Pd for anything lower than a 10% Pd, and a 100% Pd for anything above 95% Pd to simplify the code and because SNR figures get unreliable at these extremes.

 

Note that my math/analysis has been cross checked against the APG-66 as well, with estimates nearly match Westinghouse themselves https://i.imgur.com/cVZSyQf.jpg 

 

Note that this graph is from IEEE, and has no government restrictions: 

"F-16 Pulse Doppler Radar (AN/APG-66) Performance"  IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-19, NO. I JANUARY 1983

APG-63-70 HPRF Basic Analysis.pdf

Edited June 8, 2023 by Beamscanner

[MARLAN_]

Thanks for putting this together. Hopefully the radar update doesn't include more arbitrary performance penalties like the currently existing look down penalty in DCS. Excited to see a well made radar update for the Viper & Hornet.

[Beamscanner]

The biggest difficulty besides finding the Noise Figure for a given radar, was figuring out the SNR for each Pd, per mode.

 

This is key to developing a single scan Pd for a radar. 

 

To save ED the trouble, I'm attaching an excel spread sheet which contains the SNR figures for a swirling case 1 target (fluctuating air target), with a Probability of false alarm of 10^-6 (typical of modern fighter radars). 

 

It calculates the SNR per mode given binomial distribution probability of "M of N detection logic".

 

Examples: 

1. HPRF RWS uses 3 stage FMR for ranging (ie 3 separate coherent processing intervals or CPIs). "Single Burst" (ie single CPI) SNR for 50% Pd = 12.8dB. Given that all 3 CPIs need to detect the target (M of N = 3 of 3), if 12.8dB were used, a single scan Pd would result in a Pd of 12.5%, not 50%. (0.5 * 0.5 * 0.5 = 0.125)

Thus a higher "Single Burst" SNR is require to determine single scan Pd. In this case, a 17.6dB SNR gives about 80% Pd per CPI. given that this mode uses 3 CPIs AND requires target detection in all 3 CPIs, this 17.6 dB SNR results in a single scan SNR of 50%. (0.8 * 0.8 * 0.8 = 0.5)

 

2. MPRF logic is different. Typical M of N detection logic for MPRF is 3 of 8. That is a minimum of 3 detections given a total of 8 CPIs per time on target. What you will see is that because we get 8 chances to 'flip a coin' and we only need 'three chances to get heads' (where 'heads' = detection). The required SNR for a given Pd is less than HPRFs 3 of 3.

 

In truth though, MPRF can almost guarantee that 1 - 2 of its CPIs wont ever see the target due to range and doppler eclipsing. Various sources indicate that on average targets only exist in clear region 57 - 65 % of MPRF CPIs. I've simplified this logic by including a duty cycle input. For example if a MPRF using 8 CPIs has a duty of 15%, Ive made it so that the calculated Pd/SNR treats the M of N logic not as 3 of 8, but as 3 of * (8 * (1 - duty cycle) where duty cycle is indicative of probability of eclipsing. Thus the single scan probability of detection for 3 of 8 MPRF search mode would actually be 3 of 6.8.

 

Simply plug in your duty cycle and choose the mode of interest and use that SNR on the far left to determine the single scan Pd when applied to the radar range equation.

 

Edit: I've added the reference for Single Burst SNR (Swirling Case 1). Again, this is not the Single Scan SNR that SHOULD be used for actual detection. Single Scan SNR can be found in my attached excel. 

 

SNR Figures.xlsx

Edited June 8, 2023 by Beamscanner

[Krippz]

Nice write up. 

[funkyfranky]

Thanks for the write up @Beamscanner. I'm trying to understand your max detection range equation and the values of the parameters you quote in the table.

What does not make sense to me is the area constant

You write 4π^3 but you the number you calculate (1984) is actually (4π)^3. That might be just missing parentheses but I still don't quite get where a factor of (4π)^3 comes from and why that should be an area? (I assume you take a sphere of radius = 1 m so the radius is not "visible" in the equation but still).

[H7142]

On 6/5/2023 at 8:59 PM, Beamscanner said:

ED has stated that Phase Two of their radar development will include azimuth/bar settings effecting detection performance.

"Upon Phase 1 release and tuning, we will implement Phase 2 that will include the effect of radar azimuth and bar settings on detection ranges and the inclusion of more accurate look down radar performance."

 

This is not a correct application of radar theory. The radar range equation does not contain azimuth or bar values in it.

 

Azimuth and bar settings only effect what is has been called Max Range Cumulative detection performance. Which indicates a typical range the radar will first see a target. See my full explanation here. But in short it is a simple way of telling a high ranking officer the typical range he could expect his first detection. Though this does not inform the officer that the detections will be rare/irregular at this range. 

 

Azimuth and bar settings have little to no effect on performance. This is a misnomer told to pilots.

Detection range performance is based on a probability of detecting a RCS at a given range.

ex the APG-66 has a 10% chance of detecting a T-38 at 20 Nmi in a single sweep. (ie the main beam crossed the target once)

 

The benefit of lower ur bar and azimuth isn’t that this performance changes. Rather it’s that you get many more sweeps per second on the target. ie you get more chances to detect the target. Each sweep always being 10%.

Said another way, you simply get to roll the dice more often. But the average performance remains the same.

 

ED should instead use single scan probability of detection (not effected by azimuth/bar), rather than max cumulative.

 

For instance, given the APG-66 / T-38 example above. 

Using single scan Pd, the T-38 would only be detected 1/10 sweeps at 20 Nmi. If ED used Max Cumulative, they'd simply make the detection 100% at 20 Nmi.

 

I've made a fully open source/non-ITAR analysis of the APG-63 detailing the math behind all of this.

 

ED should use the SNR figures provided to determine single scan Pd. Id recommend using a 0% Pd for anything lower than a 10% Pd, and a 100% Pd for anything above 95% Pd to simplify the code and because SNR figures get unreliable at these extremes.

 

Note that my math/analysis has been cross checked against the APG-66 as well, with estimates nearly match Westinghouse themselves https://i.imgur.com/cVZSyQf.jpg 

 

Note that this graph is from IEEE, and has no government restrictions: 

"F-16 Pulse Doppler Radar (AN/APG-66) Performance"  IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-19, NO. I JANUARY 1983

APG-63-70 HPRF Basic Analysis.pdf 1.36 MB · 54 downloads

Excellent work thanks for taking the time and doing this!

[Beamscanner]

On 6/7/2023 at 12:59 PM, funkyfranky said:

Thanks for the write up @Beamscanner. I'm trying to understand your max detection range equation and the values of the parameters you quote in the table.

What does not make sense to me is the area constant

You write 4π^3 but you the number you calculate (1984) is actually (4π)^3. That might be just missing parentheses but I still don't quite get where a factor of (4π)^3 comes from and why that should be an area? (I assume you take a sphere of radius = 1 m so the radius is not "visible" in the equation but still).

Yes, that was a typo. It is as you assumed. I meant to say (4pi)^3. The excel formula has it correct, its just the adjacent text that has the typo. 

(4pi)^2 relates to the area of a sphere, in which the transmitted signal propagates outward and expands spherically. 

I'm not sure how (4pi)^2 becomes (4pi)^3 in the radar range equation. Yes, this all assumes meters.

I will have to do some research on why it is cubed. 

 

The source for this equation is depicted in equation (20.8): 

Edited June 8, 2023 by Beamscanner

[funkyfranky]

23 minutes ago, Beamscanner said:

Yes, that was a typo. It is as you assumed. I meant to say (4pi)^3. The excel formula has it correct, its just the adjacent text that has the typo. 

(4pi)^2 relates to the area of a sphere, in which the transmitted signal propagates outward and expands spherically. 

I'm not sure how (4pi)^2 becomes (4pi)^3 in the radar range equation. Yes, this all assumes meters.

I will have to do some research on why it is cubed. 

 

The source for this equation is depicted in equation (20.8): 

 

 

Cool, thanks for the source! Think I already found why it's cubed  (for R=1 m)

[Beamscanner]

A mathematically gifted friend of mine found the reason for the extra 4pi. 

(4pi)^2 is in relation to expansion of light spherically as I stated earlier. 

 

The extra 4pi comes from effective area ("Ae"; not depicted in the formula). 

You can see in the top that Gain is squared. In truth it would be Gain * Ae. Where Ae = (lamda^2/4pi)*Gain

Ae refers to the effective receiving area of the antenna aperture. 

So the author altered the formula for simplicity sake. 

[DSplayer]

How would something like the APG-68 and APG-73 fair with your analysis compared to the current Phase 1 radar changes?

[Hobel]

vor einer Stunde schrieb DSplayer:

How would something like the APG-68 and APG-73 fair with your analysis compared to the current Phase 1 radar changes?

so currently there is no probability of detection, the target is either in range or not. for F16/18

 

What Beamscanner shows us is very comparable to the DCS M2000 radar.

As far as you can observe it ingame
each swipe has a certain possibility to detect the target, the farther away it is the lower the probability to detect it.

If you now set the azimuth/bar in the M2000 radar tighter, the probability of detecting targets earlier is greater because a very small area is scanned very often,
and from the possible more frequent "blips" a track can be created

[DSplayer]

15 minutes ago, Hobel said:

so currently there is no probability of detection, the target is either in range or not. for F16/18

 

What Beamscanner shows us is very comparable to the DCS M2000 radar.

As far as you can observe it ingame
each swipe has a certain possibility to detect the target, the farther away it is the lower the probability to detect it.

If you now set the azimuth/bar in the M2000 radar tighter, the probability of detecting targets earlier is greater because a very small area is scanned very often,
and from the possible more frequent "blips" a track can be created

Yeah, the lack of probability of detection was what I expected since Quaggles' graph showed a hard number. I was more interested in perhaps how his analysis could translate in terms of maximum detection and STT ranges compared to our new Phase 1 values.

Edited June 9, 2023 by DSplayer

[Маэстро]

On 6/6/2023 at 5:59 AM, Beamscanner said:

ED has stated that Phase Two of their radar development will include azimuth/bar settings effecting detection performance.

"Upon Phase 1 release and tuning, we will implement Phase 2 that will include the effect of radar azimuth and bar settings on detection ranges and the inclusion of more accurate look down radar performance."

 

This is not a correct application of radar theory. The radar range equation does not contain azimuth or bar values in it.

Azimuth and bar settings only effect what is has been called Max Range Cumulative detection performance. Which indicates a typical range the radar will first see a target. See my full explanation here. But in short it is a simple way of telling a high ranking officer the typical range he could expect his first detection. Though this does not inform the officer that the detections will be rare/irregular at this range. 

 

Azimuth and bar settings have little to no effect on performance. This is a misnomer told to pilots.

Detection range performance is based on a probability of detecting a RCS at a given range.

ex the APG-66 has a 10% chance of detecting a T-38 at 20 Nmi in a single sweep. (ie the main beam crossed the target once)

 

The benefit of lower ur bar and azimuth isn’t that this performance changes. Rather it’s that you get many more sweeps per second on the target. ie you get more chances to detect the target. Each sweep always being 10% (given the T-38 example).

Said another way, you simply get to roll the dice more often. But the average performance remains the same.

 

ED should instead use single scan probability of detection (not effected by azimuth/bar), rather than max cumulative.

 

For instance, given the APG-66 / T-38 example above. 

Using single scan Pd, the T-38 would only be detected 1/10 sweeps at 20 Nmi. If ED used Max Cumulative, they'd simply make the detection 100% at 20 Nmi.

 

I've made a fully open source/non-ITAR analysis of the APG-63 detailing the math behind all of this.

 

ED should use the SNR figures provided to determine single scan Pd. Id recommend using a 0% Pd for anything lower than a 10% Pd, and a 100% Pd for anything above 95% Pd to simplify the code and because SNR figures get unreliable at these extremes.

 

Note that my math/analysis has been cross checked against the APG-66 as well, with estimates nearly match Westinghouse themselves https://i.imgur.com/cVZSyQf.jpg 

 

Note that this graph is from IEEE, and has no government restrictions: 

"F-16 Pulse Doppler Radar (AN/APG-66) Performance"  IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. AES-19, NO. I JANUARY 1983

APG-63-70 HPRF Basic Analysis.pdf 1.36 MB · 77 downloads

 

Hi! First of all thanks for your feedback and SNR figures.

I should clarify things a bit because phrase about azimuth/bar settings caused a misleading. 

This does not mean we are going to use cumulative detection probability in our radar model. This only means that we have plans to introdice realstic detection probabilitiy calculations based on SNR. Indeed, in general case azimuth/bar setting may affect detection range only because of more frequent sweeps. 

BTW

Today will be published a new paper about our approach to APG-65/73 detection range estimation. It will be interesting to hear your thoughts on that. Perhaps this paper is a bit sketchy, but we still gathering information and refining our estimation.

[Beamscanner]

8 hours ago, DSplayer said:

How would something like the APG-68 and APG-73 fair with your analysis compared to the current Phase 1 radar changes?

Its much closer to reality in general performance. But I think the APG-68 RWS (ie MPRF) is still too high. I will do an analysis of my own on it since its figures exist to the public. 

[Beamscanner]

3 hours ago, Маэстро said:

Hi! First of all thanks for your feedback and SNR figures.

I should clarify things a bit because phrase about azimuth/bar settings caused a misleading. 

This does not mean we are going to use cumulative detection probability in our radar model. This only means that we have plans to introdice realstic detection probabilitiy calculations based on SNR. Indeed, in general case azimuth/bar setting may affect detection range only because of more frequent sweeps. 

BTW

Today will be published a new paper about our approach to APG-65/73 detection range estimation. It will be interesting to hear your thoughts on that. Perhaps this paper is a bit sketchy, but we still gathering information and refining our estimation.

First off, I really like the mathematical approach ED is taking. So kudos to you and the team. 

2. My APG-63 analysis has the figures you were missing (Pavg, (S/N)req, and L).

Pavg is calculated from Ppeak (found in the CP-140 document) * duty cycle (Intro to airborne radar 1st edition mentions that the APG-63 in HPRF uses 1 range bin (ie 50% duty cycle; which I made 45% to account for receiver recovery time).

SNR was difficult, but I calculated everything you would need here. SNR is key to understanding Probability of detection. Scroll to the bottom of that excel I made, you will see a chart I made that shows SNR per mode for any given pulse doppler Air radar. 

In my APG-63 analysis, you can see my losses chart. Using generic information from various radar sources I estimated about 10.5dB of losses in the APG-63 for HPRF. (ex radome losses are typically 0.5 dB per path, ie 1dB of loss to the radome in total)

3. Without seeing your full equation, the SNR and losses you chose, I cannot fully compare our two papers.

4. I suspect you may be using the full time on target (tot) in your equation. Keep in mind that in HPRF RWS/TWS, 3 stage FMR is used to range doppler targets. Thus the integration time for the equation is actually ToT/3. In MPRF, 7-9 PRFs may be used (radar dependent), in which case integration time would actually be ToT/8.

 

I look forward to continued discussion on this. 

 

EDIT: I am willing to share my google sheets that I've built up over a year or so. However, I'd like to share it in a way so that each individual gets a copy without effecting someone else's copy (ie I don't want a single shared copy/link). If anyone knows google sheets, please PM me the correct way to do this. 

Converting to excel disrupts my graphs.. I already tried that. 

Edited June 9, 2023 by Beamscanner

[falcon_120]

Great discussion, I hope it can keep up to get the best existing simulation in a consumer product.

2 things strike my mind after reading ED whitepaper:

1-According to the graph the Apg73 has better detection range that the Apg63 all things considered? (diff. in Antenna diameter, peak power...), as far as I remember the ranges are lower to some known as the public data
2-I see no reference 8n the paper to difference in detection range in look down and look up situations close to the ground, coming from side lobe interference, is that a phase 2 feature? what should we expect for the time being?

Enviado desde mi ELE-L29 mediante Tapatalk

[Маэстро]

On 6/9/2023 at 8:49 PM, Beamscanner said:

2. My APG-63 analysis has the figures you were missing (Pavg, (S/N)req, and L).

Pavg is calculated from Ppeak (found in the CP-140 document) * duty cycle (Intro to airborne radar 1st edition mentions that the APG-63 in HPRF uses 1 range bin (ie 50% duty cycle; which I made 45% to account for receiver recovery time).

SNR was difficult, but I calculated everything you would need here. SNR is key to understanding Probability of detection. Scroll to the bottom of that excel I made, you will see a chart I made that shows SNR per mode for any given pulse doppler Air radar. 

In my APG-63 analysis, you can see my losses chart. Using generic information from various radar sources I estimated about 10.5dB of losses in the APG-63 for HPRF. (ex radome losses are typically 0.5 dB per path, ie 1dB of loss to the radome in total)

 

Yes, I have already read your paper, thanks. But Pavg seems to high to me. From that I know, typical fighter radar has Pavg about 1-2kw. Much of that is due to relatively low TWT efficiency(only 25-30%). For example from Introduction To Airborne Radar book we know that APG-73 transmitter input power is 4.5kw. Suppose electronics consume 500w and 4kw consumes TWT, than average output transmitter power is 4kw * 0.3 = 1.2kw.
It would be nice to have some info on APG-63 power consumption or alternative source to double-check transmitter peak power.

On 6/9/2023 at 8:49 PM, Beamscanner said:

3. Without seeing your full equation, the SNR and losses you chose, I cannot fully compare our two papers.

4. I suspect you may be using the full time on target (tot) in your equation. Keep in mind that in HPRF RWS/TWS, 3 stage FMR is used to range doppler targets. Thus the integration time for the equation is actually ToT/3. In MPRF, 7-9 PRFs may be used (radar dependent), in which case integration time would actually be ToT/8.

No, I know what CPI is. BTW, assuming Tint = ToT/3 when 3 stage FMR used is not quite correct. We also should account for number of PRFs used to minimize eclipsing. If 2 PRFs are used, then we need 4 CPIs to guarantee successful ranging. If target eclipsed during first CPI it will be detected on second and 2 remaining CPIs will be used for ranging. If we have 3 PRFs then at least 5 CPIs per ToT are needed.

Unfortunately, I can not make our model public, but we can continue discussion to make things clear, and maybe combine our approaches.

[Маэстро]

On 6/9/2023 at 10:20 PM, falcon_120 said:

Great discussion, I hope it can keep up to get the best existing simulation in a consumer product.

2 things strike my mind after reading ED whitepaper:

1-According to the graph the Apg73 has better detection range that the Apg63 all things considered? (diff. in Antenna diameter, peak power...), as far as I remember the ranges are lower to some known as the public data

Please note that data in the whitepaper is for original APG-63 from early 70s, updated APG-63v(1) may have range grater than APG-73.

On 6/9/2023 at 10:20 PM, falcon_120 said:

2-I see no reference 8n the paper to difference in detection range in look down and look up situations close to the ground, coming from side lobe interference, is that a phase 2 feature? what should we expect for the time being?

In look-down situations main limitation is receiver dynamic range which depends on the number of ADC amplitude bits. It's already in our model. However, there is no big impact on detection range of medium size targets.

[H7142]

5 hours ago, Маэстро said:

Please note that data in the whitepaper is for original APG-63 from early 70s, updated APG-63v(1) may have range grater than APG-73.

In look-down situations main limitation is receiver dynamic range which depends on the number of ADC amplitude bits. It's already in our model. However, there is no big impact on detection range of medium size targets.

I have a few issues with the current radar model and want to know the plans and reasons for certain decisions.

1-HPRF rear aspect detection

HPRF can see objects that are cold even through the SLC however this is not the case for HPRF in the hornet anymore.  In the Hornet it is essentially nill at sub 4-5nmi over open ocean at 15K feet.  SLC and the MLC should not be major issues in this scenario.  The M2K in the same scenario sees the target at ~60nmi (+-5nmi) its max head on detection range, and the APG63 report that ed has in lookdown it was 20-30nmi over land. 

*Opening rate was 115kts to get out of MLC fliter for both hornet and M2K. Target was a hornet.

^Intro To Airborne Radar https://www.amazon.com/Stimsons-Introduction-Airborne-Radar-Electromagnetics/dp/1613530226/?_encoding=UTF8&pd_rd_w=87xHA&content-id=amzn1.sym.bc5f3394-3b4c-4031-8ac0-18107ac75816&pf_rd_p=bc5f3394-3b4c-4031-8ac0-18107ac75816&pf_rd_r=PVYJ1V3ZD01C7NGMW1VA&pd_rd_wg=n71wx&pd_rd_r=577c209e-68dd-46ba-93f9-d97806329953&ref_=pd_gw_ci_mcx_mr_hp_atf_m

2-MPRF STT track stability
https://cdn.discordapp.com/attachments/1030876724415709184/1116398606648352840/2023-06-08_19-07-32_Trim.mp4

 

Target was in an orbit it did not try to stay in the notch.  Yet its a guaranteed loss of lock every time, lets also note that this is over ocean in a level scenario i'm not even sure the MLC would be strong enough to actually cause a break lock...  I've tested it an had the ai in a 7G break turn it should have come out of the MLC (if there was a strong enough spike even) in a mater of seconds.  Yet it was always a loss of lock, target was f18 at 15K feet over water.  Range was 30nmi.

 

Is track memory broken/not implemented?  Will there be a more accurate simulation of MLC strength and width in the future?  How are tracking gates currently modeled? How is range folding currently modeled?

3- RCS differences

I think a big issue impacting the radar model that needs worked on is the RCS values.  They need to be more varied and larger for larger aircraft.  5m^2 for a flanker/eagle is just not accurate a minimum of 15 to represent the average frontal/rear would make faaaar more sense.  And they need at a minimum a side on RCS increase multiplier.  Razbam has this in their own model added, will ED be adding this as well.

^ work by https://basicsaboutaerodynamicsandavionics.wordpress.com/2016/04/12/radar-electronic-countermeasure/

4 - Terrain impact on MLC and SLC

Is this going to be modeled?

^Intro To Airborne Radar https://www.amazon.com/Stimsons-Introduction-Airborne-Radar-Electromagnetics/dp/1613530226/?_encoding=UTF8&pd_rd_w=87xHA&content-id=amzn1.sym.bc5f3394-3b4c-4031-8ac0-18107ac75816&pf_rd_p=bc5f3394-3b4c-4031-8ac0-18107ac75816&pf_rd_r=PVYJ1V3ZD01C7NGMW1VA&pd_rd_wg=n71wx&pd_rd_r=577c209e-68dd-46ba-93f9-d97806329953&ref_=pd_gw_ci_mcx_mr_hp_atf_m

[Beamscanner]

On 6/11/2023 at 8:39 AM, Маэстро said:

Yes, I have already read your paper, thanks. But Pavg seems to high to me. From that I know, typical fighter radar has Pavg about 1-2kw. Much of that is due to relatively low TWT efficiency(only 25-30%). For example from Introduction To Airborne Radar book we know that APG-73 transmitter input power is 4.5kw. Suppose electronics consume 500w and 4kw consumes TWT, than average output transmitter power is 4kw * 0.3 = 1.2kw.
It would be nice to have some info on APG-63 power consumption or alternative source to double-check transmitter peak power.

No, I know what CPI is. BTW, assuming Tint = ToT/3 when 3 stage FMR used is not quite correct. We also should account for number of PRFs used to minimize eclipsing. If 2 PRFs are used, then we need 4 CPIs to guarantee successful ranging. If target eclipsed during first CPI it will be detected on second and 2 remaining CPIs will be used for ranging. If we have 3 PRFs then at least 5 CPIs per ToT are needed.

Unfortunately, I can not make our model public, but we can continue discussion to make things clear, and maybe combine our approaches.

For Pavg: 

The CP-140 document indicates that the APG-63 GTWT amp has a peak power of ~12900 Watts. This seems correct for a GTWT amplifier built for high duty cycle. A public Tennessee.edu doc indicates that the GTWT amplifier from the APG-66 (built for low duty cycle, and high peak power) has an output power of 21000 Watts. A non controlled hughes aircraft doc (F-15 Radar BIT) indicates that the GTWT output power check requires a minimum power of 1360 Watts and says that this represents the MPRF waveform (page 68 in that doc). If we assume both the CP-140 doc and the F-15 Radar Bit doc are correct, this would indicate that the 1360 Watt (Pavg) figure is only the 10% duty cycle for the GTWT. This duty cycle is in fact typical for MPRF modes. In HPRF, the typical duty cycle is 30 - 50%. Thus I believe my estimated Pavg for high PRF of 5850 Watts to be accurate (13000 * 0.45 = 5850). 

 

I think you are locked into input vs output power. The problem is that you are forgetting physics. Just like a microwave oven, energy is built up over time due to resonance within the cavity (or tube in the case of the GTWT). A 1000 Watt beam of 2.4GHz microwaves would not cook food in free space. But in a resonant cavity, that energy builds up over time can increase that internal power to tens of thousands of Watts. This is how a 1000 Watt microwave oven can actually cook food within. 

 

HPRF FMR CPI:

I believe you're wrong. Many HPRF radars simply change PRF bar to bar. No need to guess though. The CPI time is exactly 8.6 milliseconds per FMR stage. This is described in the non-ITAR / Not controlled Hughes 'F-15 Radar Bit' document. Page 66 shows that there are 3 CPIs (a 4th stage exists at the beginning, but this is not processed and thus not a "CPI"), each CPI being 8.6 milliseconds long. 

Edited June 13, 2023 by Beamscanner

[F-2]

https://www.scribd.com/document/639334350/kuchinski1984
 

paper on apg-66 and 68 from 1984, possibly of use.

[Beamscanner]

Attached is my recommendation for ED, as well as some of my excel sheets. I've put a lot into these sheets, so if anyone has any questions about the math please ask. 

 

The main equation I think ED should use is the SNR equation. Its in both docs. My PPT explains the benefits of using it. I think ED should use Phase 2 to implement Pd detection (it also effects azimuth/bar settings like they previously mentioned, but not directly). 

 

I think ED should hold off on look-down and altitude loss until Phase 3. 

 

As usual, everything contained within is open-source / non-ITAR / never been classified at any level, ever. Its all just physics and theory from reputable sources. 

 

Its mostly equations derived from:

Intro to air (George Stimson; all 3 editions)

Air and Spaceborne Radar Systems

Radar Handbook V2

 

I'm recommending resolution cells of:

• MPRF
  • Range: 150m
  • Doppler: 10 Knots
• HPRF
  • Range: 4000m
  • Doppler: 3 Knots

Be applied to all radars, when their true values are unknown. These values are generic and typical values one would see from a Pulse Doppler AA Radar. The point isn't to have a specific radars real values. The purpose is to:

1. Show that these radars do not measure targets with perfect accuracy
2. That MPRF and HPRF have pros and cons to resolution
3. That targets within a res cell (must be within all 3 domains at same time; Beamwidth, Range AND Doppler) merge into 'one' large target/RCS.

 

EDIT: Fixed Gain sheet in excel. It was missing the formulas.

 

Beamscanner's Pd Detection recommendation.pptx

 

Beamscanners Basic Radar Equations v1.2.xlsx

Edited June 30, 2023 by Beamscanner

[Маэстро]

On 6/13/2023 at 4:42 AM, Beamscanner said:

HPRF FMR CPI:

I believe you're wrong. Many HPRF radars simply change PRF bar to bar. No need to guess though. The CPI time is exactly 8.6 milliseconds per FMR stage. This is described in the non-ITAR / Not controlled Hughes 'F-15 Radar Bit' document. Page 66 shows that there are 3 CPIs (a 4th stage exists at the beginning, but this is not processed and thus not a "CPI"), each CPI being 8.6 milliseconds long. 

Maybe I'm wrong about F-15, but i know some red radars that work exactly as I have described - alternate 2-3 PRFs until detection occur and then froze PRF for range measurement.
Anyway it would be interesting to make some research on performance of both methods.

On 6/13/2023 at 4:42 AM, Beamscanner said:

I think you are locked into input vs output power. The problem is that you are forgetting physics. Just like a microwave oven, energy is built up over time due to resonance within the cavity (or tube in the case of the GTWT). A 1000 Watt beam of 2.4GHz microwaves would not cook food in free space. But in a resonant cavity, that energy builds up over time can increase that internal power to tens of thousands of Watts. This is how a 1000 Watt microwave oven can actually cook food within.

But that was the point. To lock average power in some bounds using transmitter input power. Energy conservation law is always there. System(GTWT) can not give more energy than it receive => average output power can not exceed consumed power. Otherwise it's a violation of the law of energy conservation.

On 6/13/2023 at 4:42 AM, Beamscanner said:

For Pavg: 

The CP-140 document indicates that the APG-63 GTWT amp has a peak power of ~12900 Watts. This seems correct for a GTWT amplifier built for high duty cycle. A public Tennessee.edu doc indicates that the GTWT amplifier from the APG-66 (built for low duty cycle, and high peak power) has an output power of 21000 Watts. A non controlled hughes aircraft doc (F-15 Radar BIT) indicates that the GTWT output power check requires a minimum power of 1360 Watts and says that this represents the MPRF waveform (page 68 in that doc). If we assume both the CP-140 doc and the F-15 Radar Bit doc are correct, this would indicate that the 1360 Watt (Pavg) figure is only the 10% duty cycle for the GTWT. This duty cycle is in fact typical for MPRF modes. In HPRF, the typical duty cycle is 30 - 50%. Thus I believe my estimated Pavg for high PRF of 5850 Watts to be accurate (13000 * 0.45 = 5850). 

I understand your considerations. But problem there is relatively high(to similar systems) average power. Taking into account low efficiency of TWTs we should expect about 20kW of input power in that case, most part of which will turn into heat(which in turn must be removed by powerful cooling system). Does not look typical.

On 6/30/2023 at 3:34 AM, Beamscanner said:

Attached is my recommendation for ED, as well as some of my excel sheets. I've put a lot into these sheets, so if anyone has any questions about the math please ask. 

 

The main equation I think ED should use is the SNR equation. Its in both docs. My PPT explains the benefits of using it. I think ED should use Phase 2 to implement Pd detection (it also effects azimuth/bar settings like they previously mentioned, but not directly). 

 

I think ED should hold off on look-down and altitude loss until Phase 3. 

 

As usual, everything contained within is open-source / non-ITAR / never been classified at any level, ever. Its all just physics and theory from reputable sources. 

 

Its mostly equations derived from:

Intro to air (George Stimson; all 3 editions)

Air and Spaceborne Radar Systems

Radar Handbook V2

 

I'm recommending resolution cells of:

• MPRF
  • Range: 150m
  • Doppler: 10 Knots
• HPRF
  • Range: 4000m
  • Doppler: 3 Knots

Be applied to all radars, when their true values are unknown. These values are generic and typical values one would see from a Pulse Doppler AA Radar. The point isn't to have a specific radars real values. The purpose is to:

1. Show that these radars do not measure targets with perfect accuracy
2. That MPRF and HPRF have pros and cons to resolution
3. That targets within a res cell (must be within all 3 domains at same time; Beamwidth, Range AND Doppler) merge into 'one' large target/RCS.

 

EDIT: Fixed Gain sheet in excel. It was missing the formulas.

 

Beamscanner's Pd Detection recommendation.pptx 1.92 MB · 21 downloads

 

Beamscanners Basic Radar Equations v1.2.xlsx 686.23 kB · 12 downloads

 

Thank you! I will study your recommendations.

We also have some thoughts on resolution effects implementation, but it will require time - more realistic tracking loops for STT and TWS, and other things are needed in that case.

[Beamscanner]

2 hours ago, Маэстро said:

Maybe I'm wrong about F-15, but i know some red radars that work exactly as I have described - alternate 2-3 PRFs until detection occur and then froze PRF for range measurement.
Anyway it would be interesting to make some research on performance of both methods.

HPRF FMR (HPRF RWS/TWS) 1 vs 2 PRFs 

For this to work, a 3 stage FMR would be required for each PRF. Thus, you have the following options:

1. 1 PRF / 3 FMRs = ToT/3 + Eclipsing loss (1-3 dB of loss)
2. 2 PRFs / 6 FMRs = ToT/6

The math shows use that option 1 gives better range (even with the added 3 dB eclipsing loss) than option 2.

Thus, option is used because we double our integration time over option 2. 

You are correct for VS mode (HPRF no FMR). It typically does use 2 PRFs to reduce eclipsing loss.

 

2 hours ago, Маэстро said:

But that was the point. To lock average power in some bounds using transmitter input power. Energy conservation law is always there. System(GTWT) can not give more energy than it receive => average output power can not exceed consumed power. Otherwise it's a violation of the law of energy conservation.

I understand your considerations. But problem there is relatively high(to similar systems) average power. Taking into account low efficiency of TWTs we should expect about 20kW of input power in that case, most part of which will turn into heat(which in turn must be removed by powerful cooling system). Does not look typical.

IDK where you got your input power figures. 

But as I said before, the hughes aircraft doc (F-15 Radar BIT) indicates that the GTWT output power check requires a minimum power of 1360 Watts and says that this represents the MPRF waveform (page 68 in that doc).

We know that MPRF duty cycle is typically 5 - 15%.

We can extrapolate the usable input power from this very easily.

Best Case (5% Duty Cycle):

Usable input power = 1360 * (1/.05)

Usable input power = 1360 * 20

Usable input power = 27200 Watts

This is unlikely. 

Most probable Case (10% Duty Cycle):

Usable input power = 1360 * (1/.1)

Usable input power = 1360 * 10

Usable input power = 13600 Watts

This is likely.

Worst Case (15% Duty Cycle):

Usable input power = 1360 * (1/.15)

Usable input power = 1360 * 6.67

Usable input power = 9067 Watts

This is unlikely.

 

Even in the worst case scenario, the input power would need to be much higher than your statement: "From that I know, typical fighter radar has Pavg about 1-2kw." 

Its very likely, based on multiple references that the APG-63 TWT peak power is ~13500 Watts. 

I know that you're more concerned about the APG-73. But I dont have any figures on that. 

 

Additionally, TWTs are cavity resonators. Meaning they build energy over time. 

Resonance does not break the law of conservation of energy. 

This video describes how a microwave oven, with an input of say 1000 Watts will generate internal powers of much higher strength. 

 

 

TWTs are not microwave ovens, in that they do not contain standing waves like microwave ovens. 

TWTs are however resonant cavities though, and do add up energy over time because they generate 'slow wave' oscillations where energy is continuously added up over time as that slow wave propagates down the tube. This occurs in a short period of time, and continues for the duration of a single pulse. 

[SOLIDKREATE]

I know some secret squirell RADAR equations from when I flew on P-3C's. Sadly I cannot share that here.