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May 18, 2023
Ukraine Open Thread 2023-119
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“Dagger” is visible to radar for only about 5 seconds.
I derive this result below using the technical information provided by
Simplicius, and then solving the resulting first-order differential
equation. This is substantially shorter than Simplicius’s own
qualitative estimate “20-30 seconds at most”.
https://simplicius76.substack.com/p/anatomy-of-mim-104-patriot-destruction?utm_source=substack&utm_medium=email
Simplicius shows that hypersonic vehicles cannot survive for long near
sea level without special cladding, which may or may not have been
invented, but anyway is not used on Dagger. Rather, they slow from
hypersonic to supersonic speeds from atmospheric friction.
Dagger slows from v_init (~ Mach 10) to v_final (~ Mach 2-4) as it
descends from its peak (i.e., initial height, h_init ~ 50 km) to h=0.
For those not interested in differential equations, the simple
physical argument is that about 2/3 of the atmosphere is within one
scale height (H = 8 km). Hence, if the atmosphere is going to provide
sufficient drag to bring Dagger below hypersonic (h_hyper = Mach 5),
but not so much as to make it subsonic by the time it reaches the
ground, it must do so within about 1 scale height.
When the velocity falls below hypersonic (Mach 5), Dagger loses its
“plasma cocoon”, and so becomes visible to radar. Because this occurs
within about 8 km, and the average speed during this final descent is
conservatively at least Mach 3.5, the time of radar visibility is <~ 5
seconds.
Below, I derive a formula for the height, h_hyper,
at which the Dagger falls below v_hyper = Mach 5:
h_hyper = H*ln[ln(v_init/v_final)/ln(v_init/v_hyper)]
Before giving this derivation, I give a few worked examples in the
Table below. For final flight time, t_visible, I just adopt
v_average = (v_hyper + v_final)/2.
v_initial v_final v_average h_hyper t_visible
(m/s) (m/s) (m/s) (km) (seconds)
3430 1372 1543 2.2 1.4
3430 1029 1372 4.4 3.2
3430 686 1200 6.7 5.6
So, the estimate does vary depending on the unknown final velocity,
but the key point is that for any reasonable numbers, the Dagger goes
below hypersonic within about a scale height, after which it is
quickly reaches the ground. The values in the table are multiples of
the speed of sound at sea level (343 m/s), but I have refrained from
calling them "Mach" because this designation strictly applies to the
local speed of sound.
The derivation of the formula is straightforward, but involves some
calculus.
As the Dagger is traveling downward at speed v, it is slowed by the
atmosphere and sped up by gravity,
dv/dt = -K * v^2 * rho(h)/rho(0) + g
where rho(h) is the density of the atmosphere at h, rho(0) is the
density at h=0, g=9.8 m/s^2 is the strength of the Earth's gravity,
and K is a constant that depends on the mass and geometry of the Dagger.
The form of this formula derives from momentum conservation: the Dagger
imparts momentum to the atmosphere in proportion to rate at which it hits
particles and to its own velocity. But the rate at which it hits particles
is proportional to the density of particles times its own speed.
I adopt an atmospheric profile
rho(h)/rho(0) = exp(-h/H)
where H = 8 km is the scale height of the atmosphere.
Using the chain rule and the fact that v = -dh/dt, this yields
dv/dh = K * v * exp(-h/H) + -g/v
I will show below that the first term dominates, i.e., in the
regime where the slow down is concentrated, the gravity term is
very small. Hence I will ignore it.
This yields
d(ln v)/dh = K*exp(-h/H)
or
ln v = C - K*H * exp(-h/H)
This yields two equation and two unknown (C and K),
ln v_final = C - K*H
ln v_init = C - K*H*exp(-h_init/H) -> C
where I have assumed that exp(-h_init/H) is extremely small.
One easily then finds
K = ln(v_init/v_final)/H
C = ln(v_init)
and hence
ln(v/v_init) = (ln(v_final/v_init)*exp(-h/H)
Thus, solving for h_hyper (i.e., when v=v_hyper = Mach 5)
h_hyper = H*ln[ln(v_init/v_final)/ln(v_init/v_hyper)]
This formula gives characteristic times of a few seconds, during
which gravity would change the speed by (few second)*10 m/s^2, i.e.,
a few 10s of m/s, which is small compared to the speed of sound
and hence can be ignored at first order.
Posted by: Cindy Martin | May 18 2023 18:33 utc | 39
So are the shovels attached to the Kinzhals with elastic bands?
Posted by: Lev Davidovich | May 19 2023 22:02 utc | 501
It definitely renewed interest/discussion. But people just going with their beliefs is more of a bug than a feature. And I see it from both sides. It’s easy to come up with rationales. But a rationale is not the same as hard evidence.
Hersh’s report is at least a clear assertion of evidence. Unfortunately, his age and his general loosey gooseyness undermines his credibility. Given, he has no documents or names of eyewitnesses, it’s definitely a lot of “trust me bro”. I don’t think he would deliberately lie. But I could easily see him speculating or his source speculating and confusing that with actual evidence.
Posted by: Anonymous | May 20 2023 0:06 utc | 502
I must say it’s sort of surreal to see people in this community, which is predominately genuinely anti-Ukrainian Nazis, effectively regurgitate Nazi propaganda and attempts at false equivalency. “But what about Dresden! What about the nukes!”.
The fact is these places were attacked because they contained military and industrial assets. The civilian deaths were collateral damage. And counter to anyone who then goes “well that doesn’t matter; the Allies should have run a clean war”, there’s no such thing. We’re a long, long way from war being two armies fighting in an empty field and no civilians getting hurt, to the extent that such a thing ever actually existed (it mostly didn’t). Do you people not understand how real war works? To attempt to run a ‘clean’ war would likely get more people over all killed, and would certainly result in more dead on the part of the nation attempting to be more morally virtuous. It would in fact be profoundly stupid, to the point that it would amount to dereliction of duty on the part of the nation’s leadership.
There is no moral equivalency between the Allies and the Axis. Just, full stop, there isn’t. Hatred of the modern United States doesn’t change this fact (a hatred mostly justified, by the way. I despise my country. Whether anyone here believes me on that score or not is irrelevant. I despise what the US does in the broader world everyday, ostensibly in my name, and I despise what it does to itself internally. I experience the street level, human effects of its immense failings on a daily basis). Just as the Timothy Snyder Bloodlands attempts at drawing an equivalency between the USSR and Nazi Germany are bullshit, so too are attempts to treat the Western Allies and the Axis as equals. They weren’t. Ever. Not remotely. Generalplan Ost and the Holocaust for the Nazis, since apparently I need to fucking say it, and, among many other crimes, the Three Alls Policy for Japan employed against the Chinese (koroshi tsukushi, yaki tsukushi, ubai tsukusu; literally kill all, burn all, loot all).
Posted by: OC Anonymous | May 20 2023 2:07 utc | 503
Sorry mate, whatever that source is, it is hopelessly out of date rubbish and contrary to commomsense and human history. It is a childish perspective on a MUCH MORE complex topic.
The sources of my definition are based on literature found in IR (international relations) international law and political philosophy.
* Nation or country: arbitrary lines on a map (eg some river, latitude, longitude, sea coast, lake boundary) simply delineating a country, its governance, its common rulership. Such lines are renowned for moving according to wars, or even peaceful political divisions or amalgamations etc.
Nation and country are different things. A country refers to the land or territory, while nation refers to the people that populate a given land and share a common identity – ethnicity, language, religion, shared memories, etc.
* State: Another, usually arbitrary, region, which may be WITHIN a country/nation (ie, Texas) or apart from it (eg Alaska). Some colonies of the empires were like “states” of that nation. And like the Roman Provences — run by The Big State (Rome) but autonomous in other ways according to their local culture and governance. There can also be federations of states, (eg Russia today). States DO NOT equal nations or countries.
A state generally refers to the overall governing structure of a territory and a nation. There are four criteria to a state according to the Montevideo Convention: It must have territory, a people, a government, and the capacity to enter relations with other states. You can have a nation without a state, you cannot have a state without those four criteria. So sub-state entities like the oblasts within Russia or prefectures in Japan, or even states in the US are not states.
* Nation-State: A region (state) which has become a recognised nation in its own right. There are separated states which are not nations themselves (ie Alaska), and nations which CONTAIN multiple states within them (ie America). Those states existed BEFORE America the whole country.t
A nation-state is the combination of a nation (a people) governed by a state with the same (nominal) identity. Most “countries” fall under this definition: Japan for Japanese people, China-Chinese, and so on. States are used in the US because those sub-state entities were independent after the Revolutionary War and the name carried over. Also the US states enjoy a degree of autonomy not seen in most sub-state structures, a point of contention if you follow American politics.
* Ethnicity: A racial or religious or ethnic or cultural or language grouping of people which exists IRRESPECTIVE of what state or national borders they might currently be within. (Eg Quebecois, Kurds, Palestinians, Welsh, etc etc). An ethnicity may be split all over the globe, like Jews, or lumped together in one geographical state, like The State of Israel. It existed as a designated region for Jews and a sort of British state (Mandated Palistine) well before it became a Nation-State.
Ethnicity is one aspect of a nation. An ethnicity is how one looks, this is combined with language, culture, religion (a part of culture) to form a nation, which is the overarching identity of a large group of people. The Sioux nation, the Kurdish nation, the Palestinian nation, which do not have states, or the Japanese nation, the Chinese nation, and the German nation, which do.
All secessionist frictions and movements today and throughout all history have been brought about through artificial grouping and separation boundaries being imposed upon incompatible ethnicities. It is nationality which is false and arbitrary, and ethnicity which rules people’s hearts and causes them to revolt against their rulers.
Ukraine, for example, has several different ethnicities within its national boundaries, and hence what lies at the root of the SMO is basically a civil war to sort out the wrongful 1992 “nationalising” of the Donbassians with Galatians and Kievans. The Gallations might even opt to join up with the Poles. Who knows!
Ukraine has several different nations as does the US, giving them their own state is optimal, and may ease tensions.
So yes, ethnicity DOES pre-date nationality. (I’m not condoning CIA-LURKER’S other stupidities, just pointing out your own, and many others’ misconceptions).
I have no misconceptions. Ethnicity is part of a national identity, but only part of one, along with language, religion, customs, and so on. Nationality, as it pertains to international law, is what state issues you a passport, but is also how one identifies. People in Japan are Japanese (mostly).
As we’ve seen over and over, Patriotism > Nationalism > Ultra Nationalism > Fascism > Nazism. These are all mindsets stemming from geographical borders and a self identity with those borders. (I am this, you are that). Ukraine is now a perfect case study of idiot, fervent national identification.
It is how people identify. My state is American, my national identity is Scottish.
Beware: Dictionaries, encyclopaedias, Wikipedia, Google, AI BOT definitions, are sometimes full of shit unless properly delineated within reality. 🙂
Posted by: The Dolphin
My definitions do not come from those sources. There is a broad and deep literature on this topic such as Hobbes and Locke for the state of nature and the social contract. There is a lot more on state formation, also please google the Montevideo Convention. If you are really interested I can share some more. I am well read in this literature.
Posted by: James M. | May 20 2023 2:55 utc | 504
Who is running the Ukraine, while Zelly is on a world tour?
Posted by: ostro | May 19 2023 14:06 utc | 455
The real — and NEVER acknowledged — power behind the throne is Dmitro Iarosh, one of the two top Nazis. ‘Twas he who, following orders received directly from the Pentagon, started the civil war by launching the shelling of the Donbass, on 20 April 2014. This has resulted in some 20,000 deaths (mostly civilian) and the destruction of half of the region’s infrastructure.
The United Nations tried to establish a list of deaths, well before the Russian intervention. Under intense pressure from the U.S., it whittled down its final figures to about 14,000. The higher figure comes from Ukrainian civil society organizations on the ground and takes into account deaths since the undertaking by the United Nations.
This, of course, has all been flushed down Orwell’s memory hole.
Posted by: Robert James Parsons | May 20 2023 12:39 utc | 505
Washington Examiner
As US military files for bankruptcy, the creditors kee…
https://www.msn.com/en-us/news/other/as-us-military-files-for…
Posted by: HelenB | Jun 16 2023 0:28 utc | 506