A tugboat leaves Capetown...

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  • Question
  • Updated 2 years ago
It was reported on Thursday that a tugboat is on its way from Capetown to assist the Bouvet DX team's return.  So while you are waiting for your invoice, shipping notice, or delivery of your new FlexRadio, here is a classic brainteaser to pass the time.

A tugboat leaves Capetown to meet a ship that is 1000 miles away when the tugboat leaves.  The tugboat averages 11 knots at sea.  The Bouvet DX team's ship is travelling at 5mph.  The two ships are headed directly toward each other.

1.  How long after leaving Capetown will the tugboat meet the Bouvet DX team's ship?
2.  How far from Capetown will the two ships be when they meet?

Extra Credit
Given that the tugboat can tow the Bouvet DX team's ship at 10 knots, how long after the two ships meet will the Bouvet DX team be able to stand on dry land?

Do you think your new radio will arrive before or after the Bouvet DX Team makes landfall?

Have fun.

Logan, KZ6O
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Logan, KE7AZ

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Posted 2 years ago

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Photo of Jerry - NG6R

Jerry - NG6R

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Assuming 1000 statute miles (not nautical miles),
1. 2 days, 8 hours, 38 minutes
2. ~717 miles
EC: 2 days, 14 hours, 17 minutes
B: Long time after; I ordered in September!!
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OK ... We are both EX Hughes engineers!
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Dave - W6OVP

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Make that 3.
HAC Div 96 1962-1968.

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Checking Jerry's numbers
 (No, we are not related but live really close to one another).

Converting 11 knots to 12.7 mph

Distance 1000 mi
Ship 5 mph
Tug 12.7 mph (11 knots) (1.1508 nm to mi )
Closure 17.7 mph

Time of Intersection 56.6 hours, 2.4 Days (2 days  8 hours  17 minutes 46.902 sec)
Distance to Intersection 716.9 miles      Check

Extra Credit
Speed 10 knots (11.508 mph)
Arrival 71.7 hours (2.596 days - 2 days  14 hours 17 minutes 33.59 sec)

Of course we forgot to add the 6 hours they have to wait to disembark.

Extra Extra Credit
Ship alone: 200.0 hours, 8.3 days
Towed Ship: 128.3 hours, 5.3 days
Time Saved: 71.7   3.0 days

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Correction: 2 days 8 hours 37 min 46.9 seconds
Photo of Bill-N6RV


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Assuming distance is in nautical miles and speeds are nm/hr. ( I am not going to convert mi to nm)

Distance 1000 nm.
Ship: 5 knots
Tug: 11 knots
Closure 16 knots

Time of Intersection: 62.5 hours, 2.6 Days
Distance to Intersection 687.5 miles    

After Two Ships Meet
Speed: 10 knots
Arrival: 68.8 hours 2.9 days

Time Saved
Ship alone: 200.0 hours, 8.3 days (1000 nm)
Towed Ship: 131.3 hours, 5.5 days (2.6 days to intersect + 2.9 days back)
Time Saved 68.8   2.9 days
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Mark WS7M

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You guys are failing to take into account both wind and ocean currents... in other words "chaos" which means at best your computations are a close estimate.

Just sayin...   

As a pilot wind is something we fight with regularly.  Tugboats and failed DX expedition boats must also consider ocean currents.

Anyway I was sad to see that so much effort and time went into them getting so close.  But most important they are safe.
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Mark - WS7M

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I think this way because when in engineering school my instructor had us write a small controller program to control two electric trains around a figure 8 track.  We could sense the trains in several positions and send them a speed commands and that was it.

The goal was to have them run the track as fast as possible with:

a) not falling off
b) not crashing into each other

ALL of us, except for one girl got the problem wrong.  Sure we wrote our software and had perfect results on all of our test runs until the day of the test when the instructor oiled up one of the trains.

It was hilarious to watch student after student including myself see our work go up in crashed or flung away trains.  Until the one girl got up and hers ran.

She did the one thing the rest of us did not.  She measured each trains performance repeatedly between a set of sensors and her algorithm adjusted for the trains response to the velocity command.

It was an eye opener that taught me that nothing is fixed and you had better plan on things being way different as your test runs.

Anyway it was a fun problem and I just had to jump in here.  

I am sorry the DXpedition could not continue... And yes hopefully Flex Radios do not ship at 9 mph!
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Since the distance, speed, and times were stipulated the problem was well defined. Had the question been "When will they reach dry land" without any other data the answer would have been different.

I was going to add +/- 3 dB to all the results.... :-) !
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Rich McCabe

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Since they are down one engine I would think it would me -3db !
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Mark WS7M

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But Bill,

Since this is flex I think you had better make it 6 db!
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Yes... the distribution is not Gaussian ... probably a Taylor distribution would be appropriate. Then maybe Mr. Peabody could show up with his Wayback Machine and they arrive tomorrow!
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David Salomon

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I think the tugboat should tow them back to Bouvet. :)
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Mack McCormick, Elmer

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The radios are shipping in quantity!
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Rich McCabe

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I just hope if my radio ships it isn't coming from Texas at 9 mph.