2006-07-08

Where did Taepodong-2 land? (ii)

BBC has this chart, showing the Long range missile (TPD-2) landed about 400 km east of Korean coast (launch site musidan-ri).

...and wiki has a similar one


According to wiki, Taepodong-2's full speed is around 8-9km/s, and that the missile landed about 40 seconds after it was launched.

Let's do some simple maths, on the maximum distance the missile travelled. Let's assume the missile reached top speed before it landed (more likely it didn't. it would have started burning the second stage if it did, plus acceleration stopped a few seconds before it reached water surface), and let's assume only the horizontal component of the velocity (the range would be smaller for parabolic trajectory, because the horizontal component is less than 8-9km/s), then the upper bound of the distance traveled is:
  • average speed x 40 sec
  • = (0+8.5)/2 x 40 = 170 km
In reality the distance the missile traveled was at most 50-100km from the launch site. i.e. closer to NK than Russia and it should be to the west end of BBC's green ellipse. More likely it probably landed less than 10 km away from the launch pad, as most of the initial thrust was given to vertical accelerarion. BBC's red ellipse seems to be placed totally wrong.

Update: Globalsecurity confirms my hypothesis here. It also showed that the S Korean claim of 499km is incorrect and "appears to be mixing the other missile flight data observations". In fact, Globalsecurity's estime is only 1.4km, confirming my suspection that a lot of the energy was given to the vertical thrust upward.
  • "[Vick] is reasonably certain it was not aimed at the United States at a much higher inclination as discussed below. It ultimately impacted near the launch site infrastructure just off shore perhaps about 1.4 kilometers from the pad with perhaps 4.4 km altitude gained before collapsing into the Sea of Japan"
Update: An anon commentator (presumably a rocket scientist), posted a table of typical 2-stage rocket trajectory below. Given the known size/weight and nature of the rocket's fuel/propelling mechanism, the actual trajectory should be within the order of magnitude of the 'typical trajectory (i.e. at most a factor of 3-5 away). Vick's estimate was confirmed
"TIME___ ALT___ RNGE ___VEL.
(SEC)___ (KM)____ (KM) ___(KM/SEC)
40.0 ____4.3 _____ 1.2 _____ 0.25
45.0 ____ 5.6 _____ 1.7 _____ 0.29"

4.4km above sea level is like the peak of the highest mountain in Europe/US.
1.4km is slightly less than a mile or some 5 football fields away, just barely into the ocean
0.26km/sec=260m/s = 936km/hr = 585mph, which is sub-sonic and slightly higher than the cruising speed of a 747 airliner
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14 comments:

dylan said...

Not wanting to intrude on your happy fantasies, but Yomiuri says:
"At 4:59 a.m. Wednesday, after a U.S. early-warning satellite indicated the possible launch of a Taepodong-2 at the Musudanri site, the radars of the Aegis-equipped destroyers detected the trail of the ascending missile.

But the missile lost velocity 42 seconds after launch and splashed down in the Sea of Japan about 600 kilometers from the Musudanri site at 5:06 a.m.

According to the Japanese and U.S. governments, the location where the missile fell was approximately 41 degrees north latitude and 135 to 136 degrees east longitude, just dozens of kilometers west of the Kongo destroyer in the Sea of Japan.

The Defense Agency and the U.S. military analyzed the trail of the Taepodong-2 missile on the basis of data collected by Aegis-equipped destroyers and radar sites in Japan.

The data showed that the missile traveled east-northeast from the Musudanri site. "

Now this all might be BS as you would say, but it is pretty elaborate and convincing BS.

Sun Bin said...

600km is a lot of distance for a 42 second flight (accelerating from 0 km/s). is your link in Japanese?

I would be convince if they also show the speed information.

Here is what I find from Yomiuri,

---
"The SDF were informed of the third missile launch immediately after it was fired at 4:59 a.m. Wednesday. The information that the missile was launched from Musudanri in northeastern North Korea, which includes the launch site of the Taepodong-2 long-range missile, came from U.S. forces.

The Maritime Self-Defense Force's Aegis destroyer Kongo, stationed in the Sea of Japan, was ready to track down the ballistic trajectory. However, Kongo's radar did not detect any trace of ballistic missiles.

"Was the launch a failure, or what?" Defense Agency officials asked each other, according to sources.

The Taepodong-2 missile, which can attain a height of 1,000 kilometers, was supposed to be visible on Kongo's radar when it reached a height of 20 kilometers shortly after the launch. However, the missile never reached that height and, according to U.S. national security adviser Stephen Hadley, splashed down in the Sea of Japan--about 500 kilometers off the Japanese coast--after about 40 seconds. "
---

Are you sure it said 600km from Musudan-ri, or from Hokkaido?

I am interested to compare the yomiuri report you read.

Sun Bin said...

ok, here is a theory closer to your "yomiuri" version. i.e. assuming the allegation (contradicts pentagon and was said as 'conflicting'). TPD-2 actually continued for 7 minutes, and went as far as 499km from the launch site.

1. This is very incredulous and supported by no other evidence
2. if 7 munites goes 499 km. then first 1 min = 70 km at most (since 1st minute started from zero). Therefore, first 42 seconds at most goes 50km.

bobby fletcher said...

I'm shaking my head at all this NK propaganda.

- Taiwan is testing missiles in the Pacific. US is testing missiles to shoot down missiles in the Pacific. India just tested missile too - was it capable of reaching US?

- There's absolutely no info on weither it can carry the supposed nuclear payload.

This reminded me of the anti-China ammo comming out of Pentagon last year right wing Congressman latched on. They accused the Chinese of having multiple war head missiles on nuclear submarines. Never mind the JL missiles can't possibly carry more than one nuclear warhead, given the payload size.

Sun Bin said...

and japan is sending satellites to the space......ability to send satellite (plus retrieving it) means long rang missile ability.

Sun Bin said...

NYT on the "big fuss".

dylan said...

In fact Globalsecurity does no such thing as "confirm" your claims. Vick clearly says the failure occured 40-42 seconds after launch with a piece falling off but the missile first stage kept flying for some minutes after that before impacting in the Sea of Japan. Your critique of BBC proved to be less accurate than BBC.

Sun Bin said...

dylan

1) did you read Vick's report at all? see what i quoted vick above. 1.4km from the launch pad is his estimate. i gave a very generous upper bound of 50km. but usually the first 30 sec were entirely given to upward thrust. that is what Vick has taken into account.
you can use edit/find to locate where it is in its webpage if you don't want to read the whole report.

2) i am still waiting for the link for your 'yomiuri quote'

Anonymous said...

This is a little late, but here is the ascent profile for a generic two-stage, liquid-fueled ICBM during the first two minutes of flight. As can be seen, it mostly ascends vertically early on.

TIME ALT RNGE VEL.
(SEC) (KM) (KM) (KM/SEC)


5.0 0.1 0.0 0.02
10.0 0.2 0.0 0.05
15.0 0.6 0.1 0.08
20.0 1.0 0.1 0.11
25.0 1.6 0.3 0.14
30.0 2.3 0.5 0.17
35.0 3.2 0.8 0.21
40.0 4.3 1.2 0.25
45.0 5.6 1.7 0.29
50.0 7.0 2.4 0.34
55.0 8.6 3.2 0.39
60.0 10.4 4.2 0.44
65.0 12.5 5.4 0.50
70.0 14.7 6.8 0.56
75.0 17.2 8.5 0.63
80.0 19.9 10.4 0.71
85.0 22.9 12.7 0.79
90.0 26.1 15.3 0.87
95.0 29.6 18.3 0.97
100.0 33.4 21.7 1.07
105.0 37.5 25.6 1.19
110.0 42.0 30.0 1.31
115.0 46.8 34.9 1.44
120.0 51.9 40.5 1.58

Sun Bin said...

anon,

thanks very much. this is great info. it is consistent with Vick's 1.4km estimate.

is there some formula (or source link)? i suppose it assumes some typical parameters such as mass ejected per second/etc.

bobby fletcher said...

Here's the source I think:

http://msl1.mit.edu/ESD10/block4/4.5_NMD_01a.pdf

BTW I'm not anon.

Sun Bin said...

that is a great link, thanks!

how did you find it?:)

bobby fletcher said...

pasted the last set of #s into Google...

Sun Bin said...

wow, google, orz!