How long is a piece of string?

"How far have we walked?" How long is a track? People have often asked me this. There are several ways of answering the question, and, in approximate order of accuracy:

• Guess
• Buy a pedometer- little better than a guess
• Measure track on map- useful only if track is correctly located
• Use a handheld gps receiver and plot the track on a map- needs some skill plus mapping software- then how far is it really?
• Use surveying equipment to measure the route- impractical.  

Assuming, however, that you have the track plotted on a map as accurately as possible, it is now necessary to find the length as walked, including allowing for ups and downs, winding about and so on. 

The gps receiver will give a figure for the trip but I have not found that satisfactory, especially where, as often happens in bush, lock is lost.

To get some feeling for what allowance should be made for real terrain I plotted three bush tramping tracks with a gps, one in flat and two in hilly terrain, and simultaneously measured the length using a Hip Chain^®. This unreels a cotton thread behind the walker and measures the length of the cotton on a counter. As the hip chain is not precise, depending on how the cotton stretches and goes around obstacles such as vegetation, I also measured one track accurately with a calibrated wheel, and used that data to obtain a calibration factor for the hip chain (about +6%). I then compared the real, measured results with the map distance.

The results can be usefully summarised by using an adjustment factor for the map (plan) distance. This is the distance measured on a map, maybe with a bit of string. Of course, it must be precisely where the track actually goes, and published maps are not at all good at this.

For flat country, add somewhere between 5 and 10%. For rough country, add somewhere between 10 and 20%.

Interestingly, ups and downs actually add very little distance to a route. A cross section through the Urewera using a mapping programme gave a map distance only 3-4% less than the terrain profile, which included gorges and mountain ranges! Of course the profile has a vertical resolution of "only" 20m, but as the examples above show, the real,  measured overall correction, including all sources of error, is not great.

Disclaimer: this is a limited study and there is nothing greatly novel here. I am sure that it has been done before. After all, DoC were supposed to have measured all their "visitor asset" tracks in this way! I did ask....but realised that I was on my own.

Peter

January 2006