walkhighlands

This forum is for general discussion about walking and scrambling... If writing a report or sharing your experiences from a route, please use the other boards.

Straight line walking

Re: Straight line walking

Postby litljortindan » Tue Sep 07, 2021 12:16 pm

litljortindan wrote:Surely in walking a chord length of 78.4km they will have deviated from a straight line by approximately
6371*(1-COS((ACOS((6371*6371*2-78.4*78.4)/(2*6371*6371))/2)))*1000 = 121m at the mid-point?


Or should that be (6371 - SQRT(6371*6371-POWER(6371*SIN(((78.5/40075)*2*PI())/2),2)))*1000 = 120m?
User avatar
litljortindan
Mountaineer
 
Posts: 2060
Munros:123   Corbetts:63
Grahams:28   Donalds:1
Sub 2000:47   Hewitts:12
Wainwrights:10   
Joined: Dec 11, 2011

Re: Straight line walking

Postby ChrisButch » Tue Sep 07, 2021 12:42 pm

Nicholas Crane's 'Two Degrees West' - a N-S walk on the 2% W meridian - is one of the more impressive (if eccentric) examples:

https://www.amazon.co.uk/Two-Degrees-West-English-Journey/dp/0140272364
ChrisButch
 
Posts: 128
Joined: Apr 18, 2016

Re: Straight line walking

Postby litljortindan » Tue Sep 07, 2021 1:39 pm

litljortindan wrote:
litljortindan wrote:Surely in walking a chord length of 78.5km they will have deviated from a straight line by approximately
6371*(1-COS((ACOS((6371*6371*2-78.4*78.4)/(2*6371*6371))/2)))*1000 = 121m at the mid-point?


Or should that be (6371 - SQRT(6371*6371-POWER(6371*SIN(((78.5/40075)*2*PI())/2),2)))*1000 = 120m?


I noticed my error in taking the arc length of 78.5km as the chord length (which is actually 78.4km) so that should have been:

6371*(1-COS((ACOS((6371*6371*2-78.4*78.4)/(2*6371*6371))/2)))*1000 = 120.6m at the mid-point

or (6371 - SQRT(6371*6371-POWER(6371*SIN(((78.5/40075)*2*PI())/2),2)))*1000 = 120.3m
User avatar
litljortindan
Mountaineer
 
Posts: 2060
Munros:123   Corbetts:63
Grahams:28   Donalds:1
Sub 2000:47   Hewitts:12
Wainwrights:10   
Joined: Dec 11, 2011

Re: Straight line walking

Postby jmarkb » Tue Sep 07, 2021 3:16 pm

And how much difference is there in the horizontal between a great circle arc and a straight line on the OS national Grid projection?
User avatar
jmarkb
Mountaineer
 
Posts: 4864
Munros:241   Corbetts:98
Grahams:81   Donalds:31
Sub 2000:46   
Joined: Oct 28, 2011
Location: Edinburgh

Re: Straight line walking

Postby simon-b » Tue Sep 07, 2021 3:27 pm

jmarkb wrote:And how much difference is there in the horizontal between a great circle arc and a straight line on the OS national Grid projection?

Maybe a map like this might help establish that?
Attachments
20210907_152346.jpg
User avatar
simon-b
Munro compleatist
 
Posts: 2078
Munros:282   Corbetts:30
Grahams:7   Donalds:12
Sub 2000:1   Hewitts:155
Wainwrights:214   Islands:4
Joined: Jan 2, 2012
Location: Wakefield, West Yorkshire

Re: Straight line walking

Postby litljortindan » Wed Sep 08, 2021 3:30 pm

jmarkb wrote:And how much difference is there in the horizontal between a great circle arc and a straight line on the OS national Grid projection?


https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf

https://pubs.er.usgs.gov/publication/pp1395

Answer's bound to be in there somewhere.
User avatar
litljortindan
Mountaineer
 
Posts: 2060
Munros:123   Corbetts:63
Grahams:28   Donalds:1
Sub 2000:47   Hewitts:12
Wainwrights:10   
Joined: Dec 11, 2011

Re: Straight line walking

Postby litljortindan » Wed Sep 08, 2021 3:38 pm

https://www.ordnancesurvey.co.uk/documents/resources/guide-coordinate-systems-great-britain.pdf

p10:
"heights in mainland Britain are measured relative to the tide-gauge in Newlyn, Cornwall, giving a reference surface which is about 80 centimetres below the Geoid."

It's a can of worms or possibly a rabbit hole.
User avatar
litljortindan
Mountaineer
 
Posts: 2060
Munros:123   Corbetts:63
Grahams:28   Donalds:1
Sub 2000:47   Hewitts:12
Wainwrights:10   
Joined: Dec 11, 2011

Previous



Walkhighlands community forum is advert free


Your generosity keeps this site running.
Can you help support Walkhighlands and the online community by donating by direct debit?



Return to General discussion

Who is online

Users browsing this forum: No registered users and 33 guests