How many miles? - SailNet Community
 
LinkBack Thread Tools
post #1 of 8 Old 06-21-2014 Thread Starter
Junior Member
 
Join Date: Jun 2014
Posts: 3
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 0
 
How many miles?

Hi Folks,

I'm wondering if any of you expert navigators out there could solve a simple geometry problem for us...

A person sets sail from one side of the Earth to the exact opposite along the equator, aiming for a very small port, but they are off course by just one degree the entire voyage. By how many miles would they miss their precise destination?

Thank you!
Bob
Bob77 is offline  
Quote Quick Reply Share with Facebook
Sponsored Links
Advertisement
 
post #2 of 8 Old 06-21-2014
Senior Member
 
Join Date: Jan 2011
Posts: 765
Thanks: 0
Thanked 19 Times in 19 Posts
Rep Power: 5
 
Re: How many miles?

If I remember my spherical trig correctly, one could use the spherical law of sines.
The angle between the intended course and actual end point will be 90 degrees or pi/2 radians
Spherical law of sines says A/a =B/b=C/c where A, B, C are arc lengths of a triangle and a, b, c are angles in radians.
So, a is 1 degree or .0174 radians (from 2pi radians in a circle) so with a tiny bit of algebra you get:

A=2Ba/pi (B is half the circumference of earth or12000 miles)
A= 2*12000*.0174/3.14=133 miles.
Frogwatch is offline  
Quote Quick Reply Share with Facebook
post #3 of 8 Old 06-21-2014
Senior Member
 
Join Date: Jan 2011
Posts: 765
Thanks: 0
Thanked 19 Times in 19 Posts
Rep Power: 5
 
Re: How many miles?

How close would you be simply using the formula for arc length in planar geometry?
s=r*theta where s is arc length, r is distance(12,000 miles) and Theta is in radians (.0174) gives 12000*.0174 = 208 miles, a diff of about 67 miles.
Frogwatch is offline  
Quote Quick Reply Share with Facebook
post #4 of 8 Old 06-21-2014
Senior Member
 
Join Date: Jan 2011
Posts: 765
Thanks: 0
Thanked 19 Times in 19 Posts
Rep Power: 5
 
Re: How many miles?

Do NOT trust my answer, this is off the top of my head.
Frogwatch is offline  
Quote Quick Reply Share with Facebook
post #5 of 8 Old 06-21-2014 Thread Starter
Junior Member
 
Join Date: Jun 2014
Posts: 3
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 0
 
Re: How many miles?

Frogwatch,

THANKS for taking the time! Great answer.

(I wish I could spin off brilliance like that from the top of my head!)

Bob
Bob77 is offline  
Quote Quick Reply Share with Facebook
post #6 of 8 Old 06-21-2014
Senior Member
 
Join Date: Jan 2011
Posts: 765
Thanks: 0
Thanked 19 Times in 19 Posts
Rep Power: 5
 
Re: How many miles?

No brilliance, simply familiarity. I use this stuff for a living so I remember it.
Frogwatch is offline  
Quote Quick Reply Share with Facebook
post #7 of 8 Old 06-22-2014
Junior Member
 
Join Date: Mar 2014
Posts: 2
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 0
 
Re: How many miles?

And for us simpletons, you could borrow a TLAR Navigation formula that I use in aviation every day. One degree over one mile yields 100 foot difference. So, miles traveled times 100 divided by 6000 (6000 to convert to miles'ish).

12000*100/6000=200 miles off course

For those unfamiliar with TLAR Navigation... That Looks About Right
Panpan is offline  
Quote Quick Reply Share with Facebook
post #8 of 8 Old 06-22-2014 Thread Starter
Junior Member
 
Join Date: Jun 2014
Posts: 3
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 0
 
Re: How many miles?

Thanks, Panpan!
Bob77 is offline  
Quote Quick Reply Share with Facebook
Reply

Tags
compass , navigation

Quick Reply
Message:
Options

By choosing to post the reply above you agree to the rules you agreed to when joining Sailnet.
Click Here to view those rules.

Register Now



In order to be able to post messages on the SailNet Community forums, you must first register.
Please enter your desired user name, your email address and other required details in the form below.
Please note: After entering 3 characters a list of Usernames already in use will appear and the list will disappear once a valid Username is entered.


User Name:
Password
Please enter a password for your user account. Note that passwords are case-sensitive.

Password:


Confirm Password:
Email Address
Please enter a valid email address for yourself.

Email Address:
OR

Log-in









Human Verification

In order to verify that you are a human and not a spam bot, please enter the answer into the following box below based on the instructions contained in the graphic.




Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools
Show Printable Version Show Printable Version
Email this Page Email this Page



Similar Threads
Thread Thread Starter Forum Replies Last Post
Nautical miles per season engineer_sailor Seamanship & Navigation 29 10-23-2013 04:51 PM
One Million Miles of Experience ... killarney_sailor General Discussion (sailing related) 8 07-19-2012 02:40 PM
a measly 80 miles starcresttoo Cruising & Liveaboard Forum 2 10-23-2004 04:17 PM
Miles flint66 Learning to Sail 0 09-28-2001 03:28 PM

Posting Rules  
You may post new threads
You may post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is On
Trackbacks are On
Pingbacks are On
Refbacks are On

 
For the best viewing experience please update your browser to Google Chrome