From what I can see for A: it's fairly accurate (give or take a hundreth of a mile or so). I have a map from a local park with the trails marked out. I did the best that I could to copy it to make a map for this site and compared it to the markers on the actual trail. At most, I'm about .04 of a mile off. This could either be the way I marked it here on the site or the trail markers/map from the park are estimated/rounded off.
For B: From my experience, this can affect your time by probably a few minutes at most over the long haul of your run. That is of course, if you are trying to keep the pace consistent for the majority of the time. In the short term, you would probably see your mile pace time go up anywhere from 5 to 15 seconds if you have to slow down because of mud/slippery conditions and shortening your stride a bit for up hills. I could even out though by about 3 to 5 seconds with the downsides depending if you can open up your stride fully again and keep your balance. The only downfall to both of these is if there are obstacles on the slopes as they can slow your pace down considerably.
Hope these answer your questions!
The accuracy of the horizontal distance provided by Google maps is dependant on the accruacy of the underlying data. All of the mapping data for Google maps comes from public sources ultimately. Those sources vary in accuracy depending on the scale at which they were compiled. The smaller the sacle of the map, the bigger the area covered by the map and the less accurate it will be. A 1:100,000 USGS map is less accurate than a 1:24,000 USGS map which is less accurate than a municpal map at a scale of 1:100. So, if you are running through a forested part of Central park, the distance is as good as you can map it out, same as if you were running down Fifth Avenue. If, on the other hand, you are running through a wilderness area back of beyond in Montana, your accuracy will be less due to the less accurate underlying data.
So much for the horizontal accuracy. I don't think that the vertical component is taken into account at all. If there are significant changes in elevation on your route, then you are actually running/biking farther than what the map shows. Significant would be either a few very high hill/mountains or several smaller ones. Let's assume we have two towns A & B that are one mile apart as the crow flies, but there is a half mile high ridge in between and no way around it. The minimum distance between the two towns as the turtle crawls is at least 1.4142 miles. And that assumes a consistent 1:1 slope up and down. Change that to 2 quarter mile high ridges or four 1/8 mile high ridges and you get the same result. Keep cutting the ridge height in half and doubling the number and the true travel distance remains the same until the ridges are close enough together to step from one to the next. Swap out some of the ridges for flat stretches or reduce the slopes and the discrepancy between the horizontal, mapped distance and the actual travelled distance becomes less.
45 degree slopes are not common, certainly not on trails, so the difference between what you map and what you ran will probably not be as great as my example by a long shot. But if your mapping does not take into account the switchbacks that get you up that steep hill, your mapping distance isn't accurate either.
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