How long is a piece of string?

This time in 3 weeks I will have finished running the inaugural Piece of String Fun Run. Well, I hope so anyway. There is every possibility that I may still be going - who knows! For indeed, this is the concept of the run, and the reason for the otherwise confusing name; we don't know how far it is going to be! There will be multiple potential routes, ranging anywhere from 100 meters to 1000 miles (and beyond?!), one of which will be chosen on the day. We'll be given a section to run. We'll run. We'll return to the start. We'll be given the next section. We'll run. We'll return to the start. You get the picture. And we'll do this until the Race Director lays his hand on our shoulder and tells us "well done, you've finished". Or until we collapse in a heap and wait for the paramedics to rescue our battered corpses. Whichever occurs first I guess.

Well, that answers that question then. Sorted. From http://relationshipocd.wordpress.com/2012/09/11/tip-8-how-long-is-a-piece-of-string/

The concept was thought up by the fevered evil minds of James Adams and James Elson. On paper, it doesn't sound so tough. It's in Oxfordshire, so the terrain won't exactly be up to Hardrock standards. We know the start time (despite their best efforts to lose some of us through the use of the ambiguous term "midnight Friday"), so there won't be any of the anticipation waiting for the conch shell to blow at Berkley. But the question is; if we don't know where the end lies, how can we mentally prepare for what's to come? When you inevitably feel like crap at mile 80 in a 100 miler, the fact that you only have 20 miles to go is a great mental boost. So how do you pull yourself out of the funk when you could be running for another 200 miles for all you know? Pacing is right out of the window, so this may end up as the slowest 10k of all time. Or I may be sprinting a 300 miler. The point is, it's going to be a bit of a mindf*ck, and I guess I'm just going to have to see how I get on. My saving grace is that I figure that mind games don't work so well on idiots like me!

But this got me thinking: how far can a person actually run without stopping? By not stopping I mean running with no obvious rests like stopping to sleep, whilst toilet stops, walking breaks and aid station stops are all part of the game and are going to be difficult to avoid. Obviously it is not possible to run forever, but history has certainly shown that we humans can run a really, really long way. From persistence hunting (essentially chasing your prey all day until it can't run any further) of the !Xo San bushmen of the Kalahari desert in Southern Africa and the Tarahumara Indians of Mexico, through Pheidippides' running 150 miles from Athens to Sparta to request help against the attacking Persians, to Pam Reed running 300 miles with no sleep in under 80 hours (narrowly pipping Dean Karnazes to the 300 mile record), there are plenty of feats throughout the ages that make "only" running 26.2 miles look like a walk in the park (of course  I'm talking purely distance here - the marathon is a much faster event, but let's not get into that debate here).

But is there something special about these people that allows them to run such "superhuman" distances? Well, some of the elite runners probably do have some gifts in the genetics department that allow them to run faster for longer (Kilian Jornet's VO2 max is a frankly incredible 92 ml/kg/min, mostly through training, but there is likely a genetic predisposition), but I maintain that anybody can run 100 miles. It may take a lot of work to prepare your body and build up a base of endurance, and certainly requires mental fortitude to push through the low points (which you will have). But anyone who wants to do it can. In fact, modern research suggests that our evolution as the dominant species on earth may have been predicated on our ability to run long distances.

So let's ignore these genetic factors and ask what other things are likely to affect how far we can go before our body gives up:

1. Energy: As every good dieter knows, we get the energy that we need to function from metabolising food. The basic unit of dietary energy is the Calorie (or kcal - the energy required to increase the temperature of 1kg of water by 1 degree C). In order to keep functioning, we need to make sure that we take in as many Calories as we are using. The typical person can absorb about 350 Calories per hour, but running even at a moderate pace will burn at least twice that. Awkward. Your body has energy stores in the form of glycogen and fat that will be tapped to account for the deficit, but this is limited. We only have about 2,000 Calories stored as glycogen which will get used up pretty quickly before we start metabolising fat instead (this is where the feeling of "hitting the wall" comes from). Fat stores are much more abundant (about 3,500 Calories per pound of body fat) so are an ultrarunner's friend. So as we run, we are eventually going to eat into our stores and will eventually be scraping the barrel of our energy supplies. This is therefore going to be a limiting factor if we don't keep on top of our nutrition.
2. Fatigue: One obvious problem that we are going to face is tiredness. Running is tiring. The longer you go, the more knackered you're going to get. If we also factor in the need for sleep which is only going to get worse once bedtime comes and goes, this is going to be a big factor in grinding us to a halt.
3. Deterioration: It's fair to say that, no matter how good our running style is, running long distances is gradually going to cause muscle deterioration. In the worst case, the gradual sloughing off of myoglobin into the blood stream can cause rhabdomyolysis if the kidneys are unable to filter them out, and this may cause acute renal failure. But otherwise muscles will gradually become sore and inflamed, and running will become more difficult. Many people use NSAIDs such as Ibuprofen ("vitamin I") to relieve this, but this has been shown to be linked to the onset of exercise induced hyponatremia and rhabdomyolysis so isn't recommended. Also, there are more acute issues that might occur, such as falls and sprains, which will have a large effect on running speed. 

So I decided to have a bit of a play, and modelled how my speed might develop over time if I were to factor these three effects into the equations. As a quick caveat, I have absolutely no basis whatsoever for the models that I have used here, other than the fact that they seem to be about what I would expect to happen over time. But it gives a rough idea of how things might proceed over time. Here are some of the facets of the model that I ran:

1. I factored in my bodyweight and body fat for calculating my energy store size and energy use, and modelled my energy intake assuming a maximum of 350 Calories per hour, but slowly decreasing over time (to account for difficulties eating later in the race)
2. I modelled my fatigue as a scaled exponential function, getting worse and worse as time goes on particularly after about 18 hours of running (bedtime!)
3. I modelled my deterioration as a quadratic function, but also included a random term to account for injuries that occur along the way
4. At each time point, I scaled my running speed (starting at a nice leisurely 8.5 mins per mile pace) based on the energy deficit, fatigue and deterioration

Change in speed (miles per hour) and distance (miles) over time when running continuously in a stupid and pointless race

As I say, this model has absolutely no basis in reality but it does look quite convincing doesn't it! As a side note, the first 100 miles fits in quite well with my last 100 miler at the South Downs Way race (although whether I'll be starting out that fast this time is debatable). The speed quickly drops after about 20 hours, which makes sense as this is where the fatigue is really going to be kicking in (note that this model doesn't account for second winds - or third, fourth or fifth winds either for that matter). As time goes on, the speed will continue to drop until I am barely crawling along as I approach 200 miles in about 40-45 hours. Realistically, I think that this is about right - not that I think I can run for that long without stopping (I don't really), but that I don't honestly believe that I could possibly run any longer. Time will tell I suppose.

I have pretty much resigned myself to be running all weekend so this hasn't really changed anything with regards to my preparation, but it will be interesting to see how this model fits in with the reality of the race afterwards. Now I just have to hope that the race is at least 200 miles long. Fingers crossed!