doc

WP-SAMs

<h1 id="the-downsides-of-sams">The downsides of SAMs</h1>

<p>A point that I think it’s important to talk about is SAMs and the effectiveness (and cost) thereof. There are some pretty bad SAMs in the game, but the one that I want to focus on is the <a href="https://www.reddit.com/r/worldpowers/comments/3e468y/news_avengers_shield_low_frequency_samads/">Avenger’s Shield</a> system in use by the EF, mostly because I’m in the EF and see a lot of it. I’ll use it as an example of what’s wrong with the common conception of SAM systems in operation, use, and deployment, as well as the physics inherent to the problem.</p>



<h2 id="kinematics">Kinematics</h2>

<p>To understand a lot of the justification for the rest of this, you first have to understand why SAMs have ranges at all. As everyone knows, a missile will stop eventually (mostly, it won’t be able to stay airborne anymore). However, an interesting consequence of this is that as a missile slows down, the amount it can actually turn goes down, as the fins on the missile can’t produce enough force to keep the missile pointing up enough. Also, turning decreases the speed of a missile too. The harder a missile turns, the more speed it loses, turning into a vicious cycle.</p>

<p>This is why those range figures you read about for real missile systems are all lies. That number is how far the missile would go if fired at a 45 degree angle and allowed to fly a ballistic arc, but at the end of that arc, it isn’t going fast enough to keep up with even the slowest maneuvering aircraft. As such, the farther away and faster maneuvering the target, the harder it is for a missile to hit.</p>

<p>There’s only one way to escape from this hole: keep your rocket running for longer. This is the approach the <a href="https://upload.wikimedia.org/wikipedia/commons/7/75/ILA_2010_Samstag_125.JPG">Meteor missile</a> took, integrating a really seriously exotic boron fuelled ramjet (in game: don’t think of building one of these without a decade of work) that keeps running for much much longer than a traditional rocket would. As such, the Meteor doesn’t lose speed as it flies, instead maintaining it, and being lethal for much longer. The problem is that it’s incredibly difficult to build an engine like this, and that the air intake is very drag producing once the rocket burns out.</p>

<p>So, how does Avenger’s Shield run afoul of this? It doesn’t really. The range is similar to that of the S-400’s 40N6 missile. However, this does have implications on the effectiveness of Avenger’s Shield in practice. Let’s take the AMRAAM as an example: in the optimal case, it can hit a target 100nmi away. In the worst case, it can hit a maneuvering mach 2 target at most 12nmi away (this is called the no escape zone, for obvious reasons). If we apply the same numbers to Avenger’s Shield, then the no escape zone is just 30 miles.</p>



<h2 id="sensors">Sensors</h2>

<p>Now, we get to the interesting part. There are two parts to the sensor system, which I’m interpreting as everything needed to detect and guide the missile to the target, the parts on the ground and in the air. Let’s talk about them in order, with missile guidance in general discussed second.</p>

<p>Before we can discuss specifics, we need to talk radio physics for a bit. Everyone knows that radar is like light, but the mechanisms are left unclear beyond that. Light can be described as a wave, with a frequency and amplitude, of which the first is the most important for this discussion. The higher the frequency, the shorter the wavelength, and vice versa. This becomes important for radar because of this thing called the Rayleigh criterion.</p>

<p>What the Rayleigh says is that the lower the frequency, the larger the smallest resolvable thing is. As such, with a high frequency, you can resolve tiny detail (for instance, the millimeter wave scanners that are in US airports now), and with low frequency, you can barely resolve anything. This also means that you can ignore many small things, depending on the frequency. This is why low frequency radars are better against stealth – they simply don’t see the shaping features of the aircraft! <br>
There’s another cost to having low frequency radar too: big antennas. Typical antennas are half the wavelength transmitted, so if you have a 10x10 array of emitters on a 5 meter wavelength, you have quite a big and hard to move device!</p>

<p>As such, you have different radars for different purposes. Lower frequency radars are used to find stuff in a very general sense (because they can’t tell accurately where things are), and high frequency radars are used to get very very accurate fixes on things.</p>

<p>Now, let’s talk about range and stealth. This section is a summary of <a href="http://www.alphalpha.org/radar/intro_e.html">this</a> page (The Radar Equation, specifically). The range of a radar is determined by the maximum distance that a radio return can be detected at – so the signal has to go out, bounce off of, and then fly back from the target, and still have enough energy to be detected in order for the target to be detectable. Stealth works by reducing the amount of energy that is reflected (represented in terms of cross section, the size of the flat plate that would reflect the same amount of energy back) – so no matter how advanced the receiver, it’ll always detect the non-stealth airplane before the stealth one.</p>

<p>Let’s now look at a simplified version of the equation that governs radar range: </p>

<p><code>Range = Power(transmitter) * Cross section / (minimum detectable power)</code></p>

<p>And some example cross sections (high frequency):</p>

<table>
<thead>
<tr>
  <th>Aircraft</th>
  <th>Cross Section</th>
</tr>
</thead>
<tbody><tr>
  <td>B-52</td>
  <td>100m^2</td>
</tr>
<tr>
  <td>Su-27</td>
  <td>25m^2</td>
</tr>
<tr>
  <td>F/A-18E/F</td>
  <td>1m^2</td>
</tr>
<tr>
  <td>Typhoon</td>
  <td>0.5m^2</td>
</tr>
<tr>
  <td>F-35/F-22</td>
  <td>0.0001m^2</td>
</tr>
</tbody></table>


<p>As such, you can detect a F/A-18 at many times the distance that you can an F-35, for instance ( the distance is left as an exercise to the reader).</p>

<p>Now, let’s look at the stats for the Avenger’s Shield system for a second:</p>

<ul>
<li>Range: 235 miles (max)</li>
<li>Range against a stealth aircraft: 210 miles (max)</li>
</ul>

<p>This doesn’t make any sense! There should be a giant gap between the stealth and non-stealth aircraft, which isn’t there. A more realistic detection distance against an F-35 or F-22 would be something like 20 or 30 miles.</p>

<p>What’s more, your range is limited by the radar horizon. This is dictated by the curvature of the earth, so the lower you are the shorter the range you can be detected from. This is why cruise missiles work, and they can leverage both reduced radar cross section (so that it’s hard to figure out what is missile and what is ocean) and flying really low.</p>



<h2 id="missile-guidance">Missile Guidance</h2>

<p>Now, before we can talk about the radars in a battery, we need to talk about missile guidance methodologies. I’ll link to pictures of the radars, to illustrate what I’m saying.</p>

<ul>
<li><p>Command guidance: The most obvious approach. A radar is used to track the missile and the target (usually different physical radars), and the missile is radioed the corrections needed to lead it to the target. This needs a lot of radars on the ground, one to track the missile, one to track the target, and another to find it.</p>

<p>IRL examples: <a href="http://i.imgur.com/zgDMBJu.png">S-75 (SA-2)</a>, <a href="http://i.imgur.com/s128cZf.png">S-125 (SA-3)</a>. </p></li>
<li><p>Semi active radar homing (SARH): The next step up is semi active radar homing. Remember how in most radars the transmitter and receiver are in the same place? Well, SARH puts the transmitter on the ground, and the receiver in the missile. This works like a flashlight, with the ground radar being the lightbulb and the missile flying towards the brightest light. This improves resistance to jamming and enables magic tricks like timesharing and multiple target engagement, and has been the dominant guidance methodology since the late 1970s. SARH reduces the number of radars by one, as you no longer need to track the missile. In Russian/Soviet terminaology, the radar shining on the target is called the <em>illumination</em> radar, and the one that finds the targets is the <em>acqusition</em> radar.</p>

<p>IRL examples: S-200 (SA-5) <a href="http://www.ausairpower.net/PVO-S/Square-Pair-K-1M_Hungary_Kecel_MiroslavGyurosi-1S.jpg">(illumination radar)</a> <a href="http://www.ausairpower.net/PVO-S/5N84A-Big-Back-1S.jpg">(acquisition radar)</a>, S-300 (SA-10) <a href="http://www.ausairpower.net/PVO-S/92N6-Grave-Stone-MiroslavGyurosi-1S.jpg">(illumination radar)</a> <a href="http://www.ausairpower.net/PVO-S/5N63-Flap-Lid-A-Aminov-2009-5S.jpg">(acquisition radar 1)</a> <a href="http://www.ausairpower.net/PVO-S/5N64SBig-Bird-A-S.jpg">(acquisition radar 2)</a>.</p></li>
<li><p>Active radar homing (ARH): A very recent invention, it puts an entire radar unit in the missile, transmitter and receiver. This allows the ground component to get even simpler (you don’t need anything beyond the search radar), but makes the missiles much more expensive (a Patriot PAC-2 costs about <span>$</span>1.45m, with SARH, a PAC-3 with ARH costs <span>$</span>4.5 million).</p>

<p>IRL examples: <a href="http://www.radartutorial.eu/19.kartei/pic/img4232.jpg">Patriot PAC-3</a>, MEADS <a href="http://www.lockheedmartin.com/content/dam/lockheed/data/mfc/photo/medium-extended-air-defense-system-meads/press-release-photos/mfc-meads-pr-092314-h.jpg">(radar 1)</a> <a href="http://meads-amd.com/wp-content/uploads/2014/05/MEADS-SR-0570a.jpg">(radar 2)</a>.</p></li>
</ul>

<p>Now, it isn’t specified which of these techniques Avenger’s Shield uses, but given the price of the missiles, it has to be a SARH system. This is a problem, since this is the (only) radar it uses, which doesn’t make sense with SARH. As such, it needs to use much more expensive missiles.</p>

<h2 id="deployment">Deployment</h2>

<p>We’ll talk about prices and about how these systems are used in practice here. A single S-400 battery costs in <a href="https://russiandefpolicy.wordpress.com/2014/11/29/whats-it-cost-addendum/">excess of <span>$</span>500 million for each battalion</a>. Patriot costs about <span>$</span>200 million. MEADS costs about as much as S-400. Most of this cost is concentrated in the radars, which cost a lot. The Avenger’s Shield radar picture is of a Thales Ground Master 4 radar (S-band), which is $25 million alone, and the Ground Master 4 is an “affordable” unit. S-400 and MEADS both have 3, much more complex, radars for every battalion, which is why they cost so much.</p>

<p>So, SAMs cost a lot, and they can’t protect a lot of airspace. We’re still not done, though. A SAM all alone is useless – the aircraft will find the battery before it can find the aircraft on its own. You need an early warning (EW) network, as well as computerized command and control (C3) systems in order to make it work. To get this working, you need more radars for early warning (let’s say you need 8 to cover your country, each costing $50 million a pop), thousands and thousands of miles of fiber optics and new roads, a few thousand fortifications, and massive command facilities.</p>

<p>What’s more, you can swamp SAMs. An S-300 can control (through SARH) 16 missiles engaging 8 targets. If you fire a few dozen cruise missiles, who are detected 1-2min before impact (because of the radar horizon again), there aren’t enough guidance channels (each of which controls a missile) to engage all of them in time, even though enough missiles are available. <br>
To prevent this, you need defense in depth. One SAM can’t protect a radius of 50nmi or so, but 3-4 can. As such, to protect a single target, you’re spending <span>$</span>2-3 billion. This is really serious money, and why SAMs aren’t very cost effective.</p>

<p>If you want to get more in depth, I’d suggest starting with Sean O’Connor’s analyses of IRL SAM networks, <a href="http://geimint.blogspot.com/2007/09/iranian-sam-network.html">which can be found here</a>. Also, pick up <a href="https://sites.google.com/site/samsimulator1972/home">SAM Simulator</a> (free, provides a unmatched simulation of the details of Soviet SAM sysetms), and <a href="http://www.warfaresims.com/">Command: Modern Air/Naval Operations</a>,(<span>$</span>79 and worth every penny - large scale simulations of modern air and naval combat).</p>