What's the formula used to calculate this?
time / (dist + climb*5)
where climb is the same units as dist.
I've heard various ratios from 5:1 (for many elites) to 10:1 (for the less fit...for some reason hills are relatively harder for the less fit, I guess). In other words, multiply climb by 5 or 10 and add to distance before dividing by time to get pace. I know that my personal ratio has varied. Usually this ratio is used in assessing route choices (usually after the race in my experience, but I can't speak for others). If routes have equal pseudo distance, they'll take the same time to cover physically, ignoring navigation.
Coincidentally, a link posted in the "WOC Long" thread to the IOF's scientific magazine also includes an article that address uphill climbing. Note that 1:10 is considered too much, but I didn't see the alternative (but never saw anything as low as 1:5 in the article). The article points out that the ratio varies widely based on the fitness of the individual athlete. So I suspect 1:10 is probably not even enough for me ;-)
Scientific Publication of the International Orienteering Federation
BOF planning guidance is time / (dist + climb*10)
In practice the multiplier (for any given runner) will also vary according to surface and gradient: shallow climbs on tarmac need a lower mulitplier than steep climbs in terrain - 5 and 10 are probably the range limits for climbs you can actually run up, with higher multipliers needed once you get into walking/scrambling
You can work backwards from real-life data: on a hill run of 600m w 160m climb, a multiplier of 10 suggests an equivalent flat distance of 2200m (which would take El Guerrouj or Mo >5.15), whereas a mulitplier of 5 suggests a equivalent flat distance of 1400m...
I agree the climb factor varies depending on general strength and fitness, but I have always thought people made too much of this, as an excuse for taking the flat route, rather than simply walking the hiller direct route at a similar exertion/HR level.
For WOC '93 I did some crude analysis in this subject as part of the course length homework, that withstood a war of debate, but proved to be amazingly accurate.
I don't pretend that my math was rigorous, but the climb factorr that seemed to fit M21 was 4:1. I can easily believe 5:1 might be more accurate, but I certainly believe the British/Swiss(?) practice of 10:1 to be convenient overestimation, for all but perhaps the weakest category.
As the one responsible for the BOF 1:10 ratio, I feel a word or two of justification is needed!
Some estimates are based on testing athletes on hill climbs and looking at their times for the same distances on the flat. However, my thoughts were that this was artificial and couldn't be compared with O-race conditions for all sorts of reasons ...
* actual distances were used whereas O-courses publish straight line distances
* actual heights were used whereas O-courses have very crude estimates of height climb published
* conditions in an O-race are NOT the same as when athletes are timed on hill climbs - they are not having to navigate as well in an exercise for example
* the terrain in an O-race can vary considerably and can be more of a speed determinating factor than height climb
So I approached this problem from the opposite angle by examining data from real events (32 of them, with some 250 different courses) a few years back.
Of all the variables (apart from course length) which govern winning time (runnability, "wiggle factor", i.e. how much deviation from the straight line there is, weather, etc) the only one you can quantify is height climb. So my task was to find out for each event what value of the height correction ratio minimised the variance of winners' min/km compared with mean min/km for each age class.
The clear "winner" was the 1:10 ratio although, it must be added, taking 1:5 instead didn't make a huge difference.
This analysis was accepted at BOF level and is now entrenched in all BOF Rules, Guidelines, etc, as well as at IOF level where it is used in the WMOC course length ratio tables.
However, since course length and height climb measurements only very approximately represent actual distances run and climbed, there's no need to get hot under the collar about what ratio is used ... within reason, using any sensible ratio is better than using none!
5:1 is definitely too much on tarmac - I ran a hilly 10k last year and the 'climb adjusted' km rate was faster than any of my kilometre splits, even the downhill ones.
I can't see that there can be one ratio that fits for all surfaces and all gradients. I think there would be an inverse proportion depending on the steepness of the climb ie the shorter the distance covered to climb a set elevation change the longer it will take proportional to the distance.
But funny enough just yesterday before seeing this discussion I set up and sent off some route choice exercises using the old Burnt Mountain (NAOC Long) map. I suggested the students use the 5:1 formula so it must be well ingrained somewhere.
I measured this (in spreadsheets) for every control split time over a number of years, for me the best average (in Norwegian terrain) was a 1:7 factor, i.e. with that adjustment my mistake-less running speed was close to constant for all legs (in white forest) independent of climb.
Steep downhills can of course take just as long as steep uphill, so those legs where I had to slide down between multiple cliffs tended to come out the worst.
Anyway, that factor of 7 is the geometric mean of 5 and 10 so obviously in the right ball park. :-)
In reality it must depend on how steep you take the climb? I was just trying to see how my training would convert to flat miles. 1:5 seems a good rough full of thumb for a strong climber
@Nixon: For me personally (I was H45 when I measured this) I've found that I need to take as much climb as possible on paths or other harder surfaces:
When I have to climb up hills covered with deep heather or blueberry bushes I have to walk these days. :-(
In other words there are too many variables to consider for there to be a 'one size fits all' answer.
But fortunately the question was what formula does AP use, for which there was an answer!!! :)