
Post by sage on Jul 12, 2023 5:53:18 GMT
Ok, what I was planning to do was finish up all my work, write a long paper, and submitted it here for review. The only problem is the more I learn the more problems I run into. So here is what I plan to do. I will submit what I got so far, and continue to work on it, while submitting update on where I am at the time. Instead of a complete work, you will be able to see my thought and work progress, as I work thought the problem. It will be much like my work on SpaceX Starship.



Post by sage on Jul 12, 2023 5:55:32 GMT
One of the biggest debates in relation to real warfare in space, is how far can I find the enemy, how far I can lock on to my enemy with my weapons, and what effects these two values. It is especially important to us in the Children of a Dead Earth community as we can set the laser range up to 1 Million meters (Mm) and the missile launch range in real time action up to 10 million meters (Mm). Beyond that we can hit targets with missiles and drones as long as we have deltaV to vector them into an interception trajectory. The reason why real time action ends at 10 Mm is because the force from gravity from Nbodies has an effect on trajectory of their interceptions. Now normally this question is framed as “is there stealth in space” or “what range we can find enemy space assets”. Now when I first started to look up equations to use to find the real range of my missiles and drones, I first went Atomic Rocket ( Detection  Atomic Rockets). The problem was that there was wide range of equations to detecting enemy space Assets. With no agreement on the equations, I asked the founder of Attack Vector Tactical for what equation he used. What I found was that the many people were using the radar equation, with thermal noise added in. For those who don’t know, thermal noise is the generated by the senor itself, as it generates heat by being powered. In fact, this was a problem with many heat seeking missiles. The heat form the IR missiles own sensor would obscure the missiles' ability to see the IR signature of the enemy aircraft. The only way to get a lock on was to have them look in the UV spectrum or to have the missile be a “tailchaser”. In which the IR signature of the enemy craft was higher than the thermal noise. The only way to get rid of the thermal noise was to cool the sensor of the missile. Keep this in mind.



Post by sage on Jul 12, 2023 6:04:10 GMT
The following pdf “The Radar Equation – MIT Lincoln Laboratory” , gives two final radar equations with noise on page 14. Search Radar Equation (What is need to find an enemy space craft with radar)S/N = (Pav * Ae* ts * σ ) / (4*π* Ω * R^4 * k * Ts * L)  S/N = signaltonoise ratio
 Pav =average power
 R = distance to target
 σ = Cross section (meter^2)
 Ae = effective area of receiving antenna
 Ω = Solid angle searched
 ts = Scan time for Ω
 k = Boltmann’s constant (1.38*10^23 J * K ^1)
 Ts = System Noise Temp
 Bn = Bandwidth of the receiver (in Hz)
 L =Total system losses.
Track Radar equation ( What is used to target an enemy space craft with radar)S/N =( Pt * Gt*Ga * λ^2 * σ ) / ((4*π)^3 * R^4 * k * Ts * Bn* L)  S/N = signaltonoise ratio
 Pt =peak transmitter power
 R = distance to target
 Gt = Transmit gain
 Ga = Antenna gain
 λ = transmitted wavelength
 σ = Cross section (meter^2)
 k = Boltmann’s constant (1.38*10^23 J * K ^1)
 Ts = System Noise Temp
 Bn = Bandwidth of the receiver (in Hz)



Post by sage on Jul 12, 2023 21:18:31 GMT
The only problem is that IR sensor are not transmitting and receiving, they are only receiving the IR signature transmitted by an enemy craft. It could be said that the enemy craft is transmitting a signal and the only thing you have to do is just receive it. This is why radar warring receivers have a larger range then the radar that are looking for them. Or in other words we need to remove the Reflected energy part of the equation we get from page 7 of “The Radar Equation – MIT Lincoln Laboratory”
Which would be σ / (4* π* R^2) from both equations. This would make the new equation IR Search Equation (What is need to find an enemy space craft from its own waste heat)
S/N = (Pav * Ae* ts ) / ( Ω * R^2 * k * Ts * L)  S/N = signaltonoise ratio
 Pav =average power
 R = distance to target
 Ae = effective area of receiving antenna
 Ω = Solid angle searched
 ts = Scan time for Ω
 k = Boltmann’s constant (1.38*10^23 J * K ^1)
 Ts = System Noise Temp
 Bn = Bandwidth of the receiver (in Hz)
 L =Total system losses.
IR Track equation (What is used to target an enemy space craft from its own waste heat)S/N =( Pt * Gt*Ga * λ^2 ) / ((4*π)^2 * R^2 * k * Ts * Bn* L)  S/N = signaltonoise ratio
 Pt =peak transmitter power
 R = distance to target
 Gt = Transmit gain
 Ga = Antenna gain
 λ = transmitted wavelength
 k = Boltmann’s constant (1.38*10^23 J * K ^1)
 Ts = System Noise Temp
 Bn = Bandwidth of the receiver (in Hz)



Post by sage on Jul 12, 2023 21:34:50 GMT
Now what we have to do is solve for R or range with these equations and then find out a way for use to relate each of the variables' thing we can find in CoaDE. Let's first solve for range. What I did was first divided both sides by S/N (which is the signaltonoise ratio). Then multiplied both sides by r^2 to move it to being by itself on the other side of the equation. Then I took the square root of both sides to range by itself. This produced the following equation: IR Range Search Equation (What is need to find an enemy space craft from its own waste heat)
R = ((Pav * Ae* ts ) / ( Ω * S/N * k * Ts * L))^(1/2)  S/N = signaltonoise ratio
 Pav =average power
 R = distance to target
 Ae = effective area of receiving antenna
 Ω = Solid angle searched
 ts = Scan time for Ω
 k = Boltmann’s constant (1.38*10^23 J * K ^1)
 Ts = System Noise Temp
 Bn = Bandwidth of the receiver (in Hz)
 L =Total system losses.
IR Range Track equation (What is used to target an enemy space craft from its own waste heat)
R =(( Pt * Gt*Ga * λ^2 ) / ((4*π)^2 * S/N * k * Ts * Bn* L))^(1/2)  S/N = signaltonoise ratio
 Pt =peak transmitter power
 R = distance to target
 Gt = Transmit gain
 Ga = Antenna gain
 λ = transmitted wavelength
 k = Boltmann’s constant (1.38*10^23 J * K ^1)
 Ts = System Noise Temp
 Bn = Bandwidth of the receiver (in Hz)



Post by sage on Jul 12, 2023 21:49:47 GMT
Now the part that I'm still working on which is find the Values in CoADE that we can use for these equations. Then we will double check the work and ask ourselves if the numbers make sense. As well as ask ourselves what is the result of our numbers.
Here the parts we need to find:
S/N = signaltonoise ratio Pt =peak transmitter power Pav =average power Gt = Transmit gain Ga = Antenna gain λ = transmitted wavelength Ae = effective area of receiving antenna Ω = Solid angle searched ts = Scan time for Ω Ts = System Noise Temp Bn = Bandwidth of the receiver (in Hz) L =Total system losses.



Post by sage on Jul 12, 2023 21:51:08 GMT
Here is information on signaltonoise ratio for imaging. What is important form this info is that: image quality  signaltonoise ratio  excellent  40:1  acceptable  10:1 
From this we know that S/N needs to be 40 if the image quality is excellent and 10 if it acceptable. What does this really mean than? Well after talking to someone from the field, he told me that humans can tell what an image is a long time before image processing software or AI can. I take it to mean that a computer can Identify an enemy space craft if the image has a S/N of 40, but humans only need 10. This is a better reason why we have manned spacecraft in CoADE and AV:T then what those game creators came up with.



Post by sage on Jul 12, 2023 21:59:26 GMT
"Peak Transmitter power" and "Average power" would be based on the waste heat coming of the ship. There is a breakdown of each part of the waste heat in the left side of the ship build screen in CoaDE. It is between "Power" and "Mass".
One of my problems and the one that keeps me form posting this as a paper, is what to use as "Peak Waste Power" and "Average Waste Power". Or the waste heat be transmitted by the space radiators.



Post by sage on Jul 12, 2023 22:23:20 GMT
So, what would the gains be for an IR sensor and not a radar? Will I have looked into it and found the following definition with relation to optics. The first one is was called emissivity, which was talked about in this post called "Thermal Imaging Cameras and Temperature" from "Talking Physics". You see there are different emissivity for each type of material. It why the thermal camera gives back different temperatures for different items in the room that are at the same temperature. The Stefan–Boltzmann law is what is used to tell how much power is being transmitted by the radiators on our space craft: Power = Area * emissivity of the material * the StefanBoltzmann constant(5.670374419...×10^−8 (W /((m^2)*(K^4)))) * temperature^4 It why the area we need to get rid of waste heat goes down exponentially, with small increase in temperature of the radiators. This Emissivity table pdf point out that emissivity is a product of "material and surface finish", which explains why we see it with our radiators. Material  emissivity  Aluminum Nitride  .8  Silicon Carbide  .83.96  Silicon Nitride  .88  Titanium Carbide  .9 
The second gain or that of the camera is defined by it quantum efficiency or the ability of the camera to converter the waste heat that is in the form of light photons to electrons that can be detected by it detector. This IR camera from Thor labs has both Raw data and graph that we could use for find values at a chosen wavelength of light. Wavelength (nm)  Standard Mode QE  NIR enhanced (Boost) Mode QE  200  0  0  250  0  0  300  3  3  350  22  22  400  43  43  450  57  57  500  60  61  550  51  59  600  42  56  650  33  49  700  24  41  750  16  32  800  10  23  850  8  17  900  4  10  950  2  6  1000  1  2  1050  0  1  1100  0  0 
Gt = Transmit gain = emissivity of the material Ga = Antenna gain = Quantum efficiency of the camera at that wavelength.



Post by sage on Jul 12, 2023 22:23:44 GMT
λ = transmitted wavelength
So, while looking into blackbody radiation, I came across something called Wien's displacement law. What it means it that the blackbody radiation, or the power given off by our radiators in an ideal world, will have its peak intensity change with temperature. The equation is λpeck = b/T b = 2,897,771 nm*K or 2,897,000 nm*K round up T = absolute temperature Radiator temperature  Peak Wavelength  500 K  5796 nm  1000 K  2898 nm  1500 K  1932 nm  2000 K  1449 nm  2500 K  1159 nm 
As you can see form this table the nm goes down as T goes up. Note that this is the peck and not the total amount of energy. That is spread out over a large bandwidth. With archetypal Bandwidth being the Full width at half Maximum, which we will come back to latter. Now for some time I have been using inefficient lasers as stand ins for depth space telescopes. Gain Medium  Wavelength  Alexandrite  750 nm  Ce:LLF  308 nm  CTH:YAG  2100 nm  Erbium: Silica Fiber  1550 nm  Ho:YAG  2010 nm  Nd:GGG  1060 nm  Nd:YAG  1060 nm  Nd:YLF  1050 nm  Ruby  694 nm  Thulium: Silica Fiber  1900 nm  Titanium Sapphire  790 nm  Tm:YAG  2010 nm  Ytterbium Silica Fiber  1030 nm 
Ae = effective area of receiving antennaList of current Large Space telescopesSpace Telescope  Effective Aperture  James Webb  650 cm  Herschel Obs.  350 cm  Hubble WFC3  240 cm  Euclid NISP  120 cm  Spitzer  85 cm  Akari  68.5 cm  ISO  60 cm  IRAS  57 cm  NEO Surveyor  50 cm  WISE/NEOWISE  40 cm  MSX  33 cm  SpaceLab IRT  15 cm 



Post by sage on Jul 12, 2023 22:24:12 GMT



Post by sage on Jul 12, 2023 22:24:30 GMT
Ts = System Noise TempOk I found two different equations for noise for these systems. One is from the “The Radar Equation – MIT Lincoln Laboratory” that we I was using before. Ts = Ta (Temperature Noise of Antenna) + Tr (RF components Noise) + Lr(loss of input RF)*Te(Temperature of Receiver Noise) The other came form Assessing CCD Camera SensitivityTs = (Readout Noise ^{2} + Dark Noise ^{2} +Clock Induced Charge Noise ^{2} ) ^{0.5} Readout Noise is forming the readout electronics before the digitized signal is sent.
 Dark Noise is thermally generated "dark current". Which can be reduced by cooling of the sensor.
 Clock Induced Charge Noise is noise generated during the clocking of the pixels.
SPACE COMMUNICATION CALCULATIONSBn = Bandwidth of the receiver (in Hz)This link on Photometric system was the only place where I could find a link between astronomy, wavelength and Bandwidth. Type of light  Effective Wavelength midpoint  archetypal Bandwidth  Ultraviolet  365 nm  66 nm  Visible  445 nm  94 nm  Visible  464 nm  128 nm  Visible  551 nm  88 nm  Visible  658 nm  138 nm  NearInfrared  806 nm  149 nm  NearInfrared  900 nm  152 nm  NearInfrared  1020 nm  120 nm  NearInfrared  1220 nm  213 nm  NearInfrared  1630 nm  307 nm  NearInfrared  2190 nm  390 nm  NearInfrared  3450 nm  472 nm  MidInfrared  4750 nm  460 nm  MidInfrared  10500 nm  2500 nm  MidInfrared  21000 nm  5800 nm 
Formulae for AstrophotographyL =Total system losses.L= 1/Fm Where Fm = Focusing Mirror



Post by sage on Jul 13, 2023 1:41:09 GMT
Final equations and real world examples



Post by sage on Jul 13, 2023 1:41:27 GMT
Final data and results



Post by sage on Aug 3, 2023 0:33:17 GMT
As you can see, I have been updating the information thought editing to make these post cleaner. Right now, I'm still held up with "Bandwidth of the receiver" and "Scan time for Solid angle searched". I will let you know that I still working on it.

