I claim no credit for the major part of this story, nor any of the photos for that matter. After 44 stories under my belt and having missed a few rides because of some need to be wading through Scottish peat bogs in all weathers I have chosen to mislay my pencil on a Wednesday evening and spend it mentally relaxing.

Please forgive my laziness.

Anyway the ride today was a trip to the Ogmore Vale, led and arranged by Jan Garvey, which I thought would be nice and easy. Now I am not often wrong but this time was one of those rare occasions - we were going there by way of the Bwlch. Now I had heard mention of the Bwlch many times and I had been up there in the car - but cycling? Oh dear.

Worse still I had chosen to cycle the 10 miles to the start point at Briton Ferry.

We had a pleasant ride up the Afan Valley which prepared me for the big climb which turned out to be not as bad as I thought, true it was a long drag but it did not have those sudden steeper bits that really saps my determination and eventually causes me to stop and walk for a while. No, it was just a low gear and a steady plod and a real sense of achievement on reaching the top.

Sorry but here comes John Cardy pushing and shoving as usual desperately trying to get attention. He and David Naylor seem to have struck up a dubious friendship lately, something to do with their science background I think. and he wants me to include a message that he has sent to David.

Judge for yourselves.This is his message:-

David

Let's not tell Bob Evans about these calculations, he might think we are, as they say, off the wall.

But, I have been thinking about our conversation re amount of energy used by us in climbing the Bwlch.

I have split the calculation into three parts and wondered if you could give it some thought

1 the amount of linear distance travelled.
2. The amount of vertical ascent
3. Amount of energy lost by jettisoning warm fluid when having a pee behind the wall.

Following this it would be good to convert the whole lot to something we can all understand ie number of wine gums required for the ascent.

To this end I have researched that one Maynards wine gum = 20calories
The height of the Bwlch above Mc Donalds Baglan is 520m
The linear distance of Bwlch from Mc Donalds is 29Km
Average male bladder capacity is 1 pint at body temp of 37C ie a temperature above ambient of 37 - 8 = 29degrees C

Would it be possible for you to do the calculation given the above values of these variables?

Assuming that you reach a solution in number of wine gums for this specific case, then a simple formula could be derived for any ascent we make in the future given height and time to ascend.

The equation would of course be known as the Naylor/ Cardy wine gum hypothesis, future research would, I feel assured, be sponsored by any of the UKs wine gum manufacturers.

Yours if you can catch me (on the Bwlch)
JC

There, so now you know what I have been up against!

David's reply will, I'm sure, follow. It all seems simple and straightforward.

Well no it wasn't actually and if anyone is interested here it is:-

John,

Well, the cat is out of the bag and although we didn't tell Mr Wennol about our philosophical exchanges unfortunately his computer is not broken down so he has been able to read about them. So now here's a foretaste of Cardy and Naylor (2008) to be published: where? Proceedings of the Royal Society perhaps?

The energy requirements to cross the Bwlch are in three parts, as you say:

1 the amount of linear distance travelled;
2. the amount of vertical ascent;
3. amount of energy lost by jettisoning warm fluid when having a piss behind the wall.

Taking these in the order 2, 1, 3:

The vertical ascent.
This is the easy one: A lower bound on the number of wine gums needed to lift cyclist plus bike 520m is simply their combined weight (kN) times the height ascended (in m). A detail is to convert KN.m (=KiloJoules or kJ) into winegums - of that later. So taking bike plus rider as weighing 1 kN. (I now reach for my slide rule to find 1 kN = 1000/9.81 = 102 kg wt = 102/.454 = 225 lbs = 225/14 = 16.0 stone.) I guess that's a bit on the high side as CTC riders are rarely obese (careful now not to mention names!). But lets suppose we were touring, in which case I think 1 kN (aka 16 stone) would be realistic. Maybe we should weigh Colin and/or Val next time they do one of their trips.

OK, so 1x520 = 520kJ. Now we can do two things, convert directly to wine gums, or to get a better feel for what this means decide how long the climb took, or would have taken if we had been going steadily up from sea level, and figure out our average power expenditure in Watts. (Let's forget about horsepower since we are modern people.) You and I were pedalling along at 6 or 7 mph, say 10kph, for the last mile or so up to the Bwlch. Assuming the gradient to be 1:15 (my guess) then the distance from sea level to the Bwlch would be 7.8, say 8 km. If we didn't stop (for a wine gum, pee or whatever) we would take 8/10 hours or 2880 seconds. Our average power expenditure would then be 520/2880 = 0.181 kW or 181 Watts. Big deal: were we sitting on a stationary bike generating electricity we could have lit up 3, 60W bulbs!

Now lets get really technical. To convert KJ to wine gums we need to invoke the mechanical equivalent of heat. In my youth I used to know the conversion factor but now I need to refer to a cereal packet where I find 455 kJ = 108 kCal or 4.2 kJ/kCal. So 520 kJ = 520/4.2 = 124 kCal. (Incidentally 1 kCal is the heat required to raise 1 litre of water 1 deg. C. - we shall need this later.) So if we were 100% efficient, with 20 kCal coming from a wine gum, we would need six and a bit to fuel us for that climb! But we are not 100% efficient; there are losses as that chain winds it's way round the derailleur (and OK I admit there are some losses in the epi-cyclic gears in my back hub) and that's not to mention the losses in creaking knee joints and the air turbulence in the lungs as one puffs and pants up the hill. Actually we must be very inefficient - see below.

The linear distance travelled
A quick Google search indicates that for moderate cycling such as we do the energy expenditure is in the region of 500 kCal/hour. So for some 6 hours of cycling we would expend 3000kCal, or 150 wine gums. Sounds a lot.

The effect of a pee
The energy expended is that of warming the liquid - essentially water - which is pissed out. Assuming it is 1 litre (= 1kg) and is heated from 17 to 37 deg. C. So the heat required is simply (37-17)x1 = 20 kCal, ie 1 wine gum - pea nuts!

Conclusion
The energy requirement in terms of wine gums to climb the Bwlch has to be much greater than the lower bound of six and a bit wine gums. An energy expenditure in the order of 1000kCal/hour is a round figure for strenuous cycling. So on this basis you or I would require 800 kCal for the climb analysed above, ie 40 wine gums. Our efficiency would be (6.2/40)x100 = 15%. Oh dear!

Overall it appears we used up some 4000 kCal, which means that on future trips you, John, need to bring along I think a pannier full of wine gums to keep us energised.

But I fear that this account doesn't quite meet the criteria for the Proceedings of the Royal Society. Maybe we should try a CTC outlet?

Happy cycling!
David

We had an excellent lunch at the Smithy at Blackmill and I eventually reached home very tired, muscles aching but nevertheless quite elated.

With many thanks to Jan for the excellent ride!

Happy pedalling

Lew Spokes

For the complete Wednesday and Sunday rides programme click on the link at the top of this page, or if that is too much trouble then click here.

Martin reaches the top (photo: John White)		I reach the top (photo: John White)
Jan reaches the top (photo: John White)		So does Phil (photo: John White)
And Val		They were just waiting for me! (photo: John White)
And here I am (photo: John White)		A happy band of climbers (photo: John White)
Martin has a puncture (photo: John Cardy)		And everyone looks on! (photo: John Cardy)