Extra distance

There's this, which shows the additional distance people typically add to courses.

https://measure.infopop.cc/eve/...9510622/m/9611072113

And a similar study by Mike Sandford.

https://measure.infopop.cc/eve/...9510622/m/5661053823

The absolute maximum, ignoring weaving and just using the full width or the road, but taking the outside line (30cm from the outside kerb) *see note below* on all bends instead of the inside line can be estimated if one knows the geometry of the course.

Here is an example of the method I use:

Basic course configuration a single lap run anti-clockwise.

Count the number of RIGHT hand 90degree bends.
If the RIGHT hand bend is not 90 degrees count it as a fraction of 90 degrees. ie 45 degree = half a 90 bend or 135 degrees = one and a half 90 bends etc. lets suppose the total righthand 90s is n

Measure the road width and take off 0.6m call this w.

Now use the approx forumula:
extra travelled= (2+n)*pi*w
* NOTE *
One of the approximations made is the outside boundary of the road at each bend lies on a smooth arc distance w+0.6 m from the inner boundary so the runner runs 0w+0.3m from the inner boundary.

Worked example:
I run a one lap course which has a road 8.6m wide. The course map is

How much extra do I travel running 30 cm from the outside boundary of all bends compared with 30 cm from the inside boundary?

Answer (2 + 2)*8*pi= 100 metres approx. Just imagine how it could build up if the course was a lot more twisty!

Without torturing ourselves, imagine that the runner runs about 3 meters wider than he should when rounding the turn.

Geometry tells us that each 90 degree turn run this way will add 5 meters beyond the course distance. Those turns add up.

Different assumptions will lead to different estimates of overage, but I think 5 meters per turn is a simple and useful number.

Let's test your estimate out Pete. The 5k I used in my study is shown here:
http://maps.google.com/maps?f=...e=UTF8&t=k&z=15&om=1

and the average distance people reported was 1.5% over 5000m or 75 meters of extra distance. I counted 15 90-degree turns on the course, which gives 5x15 by Pete's formula, or 75 meters.

For the 10k the course was
http://maps.google.com/maps?f=...e=UTF8&t=k&z=14&om=1

For that one the average over-distance reported by people was 1.13% of 10000m, or 113 meters. I counted 21 90-degree turns, which would give over-distance by Pete's formula of 21x5 = (this is gettin' scary) 105 meters.

All fine and good for city-block courses with 90° turns. How about inside parks, where the roads tend to meander?

I measured a 5k course inside a city park. Generally right-bend turns, but some left-bends, also. City Park course. After my official measurements were complete, I rode the centerline of the roads, just like I see many runners do. (Road is about 7 meters wide throughout.) Over the course of the 5k, the total added distance was 50 meters. Just one example.

For longer courses, one could map the SPR on MapMyRun, then edit the course (or map another one) using the centerline. It would show the difference fairly well. IF one wishes to spend time mapping a marathon twice.