Let's say we hike a mile straight up or down a 30 degree slope. I know this is almost dangerously steep, but the numbers work easy.

If I accurately pace my distance. But on the map, I've only moved .87 miles. Which will the GPS show? My impression is it will show the mile.

If I marked the start as a waypoint and I hiked in a straight line, will the distance to the waypoint show as .87 miles or 1 mile?

This only matters over long distances. The Appalacian Trail is 2,187 miles long. Is that according to the map? Or is that according to miles walked. If the average slope is 7 degrees, there is a 10% difference.

Maybe I woke up too early this morning.

I would think horizontal distance. Based on several satallites the GPS should be capable of measuring the distance on the slope, but I am not sure all GPS units are that sophisticated. If it gave you slope distance than that would not match the map that is shown on your GPS screen.

I would be really surprised if the GPS did not give you the full mile. GPS locates you 3-dimensionally. It would be shear laziness on the part of the programmers not to use the info. I would also think reported trail miles are actual miles and typically not numbers measured off a map. What about the topo map tools some people use? It too should also be able to use elevation change to calculate actual miles covered.

But if it does not give you the slope distance, it will not match the distance you hike. With a GPS in a car, the distance traveled matches the odometer with a correction for the percent the odometer is off.

I think I'm going to have to go climb a mountain and see. Yet, as you say, if it does it that way, it will not match the map.

A GPS, does not add elevation profiles to your distance, it measures point to point.

You could climb a ladder that's a mile high and still not have moved a bit from your starting lat/long, and your GPS will tell you that have traveled zero feet, as it should.

The GPS measures what you have traveled. I can go down a series of switchbacks and drop 1,000 feet and it will tell me how far I've gone on the trail - it's more than it would tell me if I had not walked all those switchbacks and just slid down a pole. It leaves breadcrumbs and measures speed as well as time.

I suppose I could do an experiment - throw the GPS off a hill and go get it at the bottom, and see what it tells me, then walk back up the slope and compare the two. But it's not going to short you because the distance is not linear.

To calculate actual distance (d) off of a topo map. Determine the horizontal distance taveresed (x), count up the number of contour lines you cross (n), and the vertical distance between each contour line (h). Plug into this equation:

d = x/sin(arctan(n*h/x))

if you don't like arctan and sin's you can use the alternate formulation:

d = square root(x^2 + (n*h)^2)

With topo map software you could easily develop a cubic spline algorithm to get a more accurate estimate of distance traversed. I would be surprised if commercially available topo software didn't include that feature.

I doubt you have driven your car straight down a 30 degree slope! So that is not a good test.

Switchback vs straight down is not the question. Switchbacks will show up as horizontal variation with associated distance.

The question is the gometry of slope distance (triangle hypotenes) vs horizontal distance (long limb of triangle adjacent to the right angle).

If the "bread crumbs" are recorded as lat/long or equivelent, you get horizontal distance- the shorter distance.

By the way I am not a GPS user, just have done surveying in the past. A GPS seems to have the capability to triangulate and calculate slopes, but I do not think that is necassarily what you get when it tells you the distance. It is NOT what you get if the distance is shown on the screen (flat surface). Does your GPS have an option to give you both? You can probably find out if you read your users manual in detail or call the manufacturer.

GPS most certainly does measure elevation (its not as accurate as longitude and latitude though!). Whether you are delivering bombs to a target or airplanes to a runway, the elevation is very important. See how smooth of a landing a plane would have trying to land at sea level at Denver International Airport. Horizontal distance traversed has very little meaning outside a 2-dimensional map.

WanderingDaisy,

Men do NOT read directions. We fiddle with it until we break something.