# Snowdonia Trail Ultra

## Introduction

The Snowdonia Trail Marathon has four distances; 10k, half-marathon, marathon and ultra. I entered the ultra.

I knew some of the route and it seemed like a good race so I was pleased to be doing it. It starts and finishes in Llanberis in Snowdonia and loops south, anti-clockwise, going to Rhyd Ddu, Beddgelert Forest and Beddgelert, then north east to Nant Gwynant, before continuing north up the valley and round to the west to Pen Y Pass. From there, up Snowdon via the Pig Track and down the Llanberis Path to Llanberis.

I stayed overnight in the Llanberis YHA which was about half a mile outside the town.

## Race Start

It was an early start but the YHA was only a 10 minute walk from the start so that was convenient. I got there just after 6am and the race brief was at 6:15am.

As I stood at the start line, I noticed that one of my water bottles had sprung a small leak. This was annoying but the leak was only minor so I resolved to drink from that one first and just see how things went.

The race started at 6:30am and we set off through Llanberis, then past the YHA and up onto the hill.

It was a cool day with some lowish cloud but the visibility was OK, perfect running conditions as it was not particularly hot and there was not much wind.

The path was very good and the first couple of miles quickly passed. The first water stop was at about 2 miles which I didn’t bother stopping at.

We came out to a railway line at Rhyd Ddu.

We were quickly onto the next checkpoint where I topped up with water. They gave me some cling film to wrap up my leaking bottle. I wasn’t very convinced that this would be much use but I gave it a go. It soon became apparent that it wasn’t having any effect; so I would just have to put up with a leaking bottle.

From here we went round a lake headed for Beddgelert Forest.

There were a few miles in the forest and some quite boggy sections along with some less used paths.

We had quit a long climb across some rough ground.

When we got to the top, there was a steep descent that started on rocky, narrow trail, before turning to fire trail. As we descended down into the valley we found the railway line again.

Somewhere around here the ultra and marathon routes merged and there was suddenly a lot more people about.

## Beddgelert to Pen Y Pass

We went through Beddgelert and another checkpoint and from there continued along the valley towards Nant Gwynant. I knew this area quite well.

There was another checkpoint at the far end of Nant Gwynant. It marked the start of the climb upto Pen Y Pass.

I had started to feel quite bad somewhere between Beddgelert and Nant Gwynant. My stomach was not feeling good so I slowed the pace down and waited for it to pass.

It was walking upto Pen Y Pass. It seemed to take a while to get there but I eventually did. I topped up with water at the checkpoint there and started out on the Pyg Track. As it was a Sunday there were plenty of people going up as well as coming down.

## Pen Y Pass to Llanberis

I was feeling a bit better but still not great so I just took it steadily here and reached the top.

The actual summit of Snowdon was in cloud but the top of the Pyg Track was clear so we had great views. We picked up the Llanberis Path which follows the Snowdon Mountain Railway and started jogging down.

Initially my legs weren’t intereted in jogging but they eventually began to play. There was one more checkpoint part way down the path. After a quick stop I continued on, past the stone cafe and down towards Llanberis.

As we came off the hill, onto road, I could hear the sound system at the finish in the town. We levelled out and at a junction turned right, away from town. We had a small loop past Dolbadarn Castle before looping around and back to the finish.

## Summary

The race was 37miles and took me 8 hours 54 minutes. I was 82nd of 155 starters / 147 finishers.

There was a nice medal and tee-shirt at the end.

# Granfondo Stelvio Santini

The Granfondo Stelio Santini takes place in the Italian Dolomites around the town of Bormio. In 2019 it was held on the 2nd June. The profile of the race is as follows:

There are three major climbs in the race: the Teglio (400m+ over 6km) which is the least well known as well as being the shortest and easiest; the Mortirolo (1,200m over 12km) which has the reputation of being one of the most difficult climbs in road cycling and the Stelvio (1,530m over 21km) which is the biggest and most famous (but not as steep as the Mortirolo).

In the run upto the race the Giro d’Italia had been in the area a couple of weeks earlier, and although the Stelvio was not on this year’s race, one of the nearby high passes, the Gavia was on the route. Unfortunately, there was still plenty of snow around 3,000m and the Giro did not go up the Gavia but did do the slightly lower Mortirolo. So the question was, would the Stelvio Pass be open in time for the race?

## Preparations

I flew to Milan (Malpensa) from Cardiff via Amsterdam. I would have preferred not to change planes when travelling with my bike to minimise the chances of “things happening” but in this case, given the dates, I had no choice.

I was disappointed but not entirely surprised when my bike did not appear in Milan. So, after a while I found the baggage information for KLM and started the process of trying to track it down. It was still in Amsterdam. I decided to wait at the airport for it, although the baggage staff could neither confirm not deny whether it would be on the next plane!

So I went to sort my car hire out. As it turned out my bike was not on the next flight from Amsterdam but may be on the one after that. So I waited around. Eventually (after waiting 5 hours) my bike arrived.

So i packed everything into the hire car and drove to Bormio where I was planning to stay for the race.

## Registration

After breakfast on the Saturday I walked across town to register for Sunday’s race. I got there early and the process was very quick (about 5 mins). So I walked back to the hotel with the intention of assembling my bike and going for a ride.

The organisers had been warming us upto to the idea that the Stelvio Pass may not be open for the race and that another climb may be substituted for it. Then they made the call that we would not be doing the Stelvio and the Cancano climb would be substituted for it. So I thought I would ride up here to check it out and see what the temperature was like at the top.

## Shake-Out Ride

So, back at the hotel I started assembling my bike only to find that the fixing that attaches the rear derailleur to the bike frame had been broken in transit.

So I asked in the hotel for a bike shop and they gave me directions. Obviously the shop was extremely busy with people getting their bikes fixed up for tomorrow’s race. As it happened they did not have an exact match for the broken component but recommended another shop out of town.

This shop did have the part and fitted it for me. I drove back to the hotel with my repaired bike.

So I headed out for the shake-out ride.

The Cancano climb was a steady one and with the sun out it was hot. The climb had a fairly consistent gradient and consisted of a series of switchbacks up the side of a mountain to a plane at the top where the road ran out and there was a couple of lakes.

After descending back towards Bormio I decided to have a look at the base of the Stelvio Pass as it was nearby.

As it was pretty warm at the top of the Cancano I decided to just wear the organisers shirt for the race and not to carry other layers (the forecast for race day was the same as today… hot!).

## Race Day

I wondered down to the start with my bike and found the correct coloured entrance. I hung around towards the back of the pack as I wasn’t particularly bothered about timings.

### The Start to Teglio

Most people were wearing a couple of layers or arm warmers as it was an early start and the sun was not yet shining in the valley. The first 45km were more or less downhill as we descended the valley from Bormio.

I have to say, it was pretty cold on the way down, but we eventually got to the bottom of the Teglio climb.

It started off reasonably gradually and averaged about 9% I think. There were some steep sections that went upto 18%. We made to the town where there was a checkpoint to get some water and something to eat.

It was good to get the first climb done and after a short stop, I was on my way again, rolling down the other side of the hill. It was quite a fast descent and we ended up braking hard at the bottom to cross a busy road.

Then there were about 20km of rolling terrain to the next checkpoint at the base of the Mortirolo.

It was a chance to fill up both water bottles and prepare for what was next.

## The Mortirolo

Setting off again from the checkpoint we soon reached the base of the Mortirolo, indicated by a right turn and a very small sign.

The riders in front soon disappeared into the forest and it was clear that this climb would mostly be hidden. Under the trees it was relatively cool, which was a good thing.

The climb is just under 7 miles at an average gradient of 11%. But there are some sections that are much steeper than this; more on this later.

I settled into the climb and planned to take it steadily. From watching the Giro, I knew that the steepest section was in the middle of the climb and that towards the end the gradient slackened off a bit.

The road was quite narrow, wide enough for a car, or about 3 riders in parallel. The climb was relentless after the first kilometre or so with no flatter parts to take a breather. There were kilometre markers to the top and they ticked away slowly.

The expected ramp up in the middle did not really happen. The road was steep, but not noticeably steeper than before. When we reacher the 6km to go marker I was pleased that things should start to flatten off shortly.

5km to go came and went and on we climbed; then 4km to go. At 3km to go the road flattened off and there was some downhill. I didn’t remember this from the Giro but now there was only 2km to go. I rounded a corner and was back into a steep climb.

I realised afterwards that the Giro had ascended the Mortirolo from a slightly different direction so my knowledge of the profile was completely wrong! Doh!

The way we were going up, they had saved the steepest part till the end.

It says on the above graphic that the max gradient was 22% and over a kilometre or so that is probably accurate but within that there was steeper ramps.

As we hit a very steep ramp, most of the people in front were unclipping and I saw a couple of people fall off.

I knew I didn’t have far to go, but each peddle stroke was a struggle. I managed to keep going and we went through a small group of huts. We were out of the forest so must be near the top.

I rolled over some mud, just at the top of a pedal stroke and as the rear wheel spun on the mud I came to a standstill. Fortunately, I just managed to get moving again before toppling over and shortly after that we were back in the trees. Up ahead I could see a group of stationary riders – the top!

From the summit, it was a long fast descent. The road on the descent was bigger, wider. I think this is the one the Giro normally uses, which makes sense from a support vehicle perspective.

The views were better on the descent as we went through less woodland. At the bottom was another checkpoint which was good as I was getting low on water and it was getting hot now that we were out of the forest.

### Back to Bormio and the Cancano Climb

After the checkpoint the next section was undulating as we made our way back up the valley towards Bormio. It was very hot now, with little breeze, and this was probably the least interesting section of the course.

We arrived back at the town of Bormio and another checkpoint. This was the last one. After this, we set off for the Cancano climb (the replacement for the Stelvio).

I had done this route the previous day so it was familiar. It’s a nice climb, but it was a shame to miss out on the iconic Stelvio. The Cancano is just over 5 miles at an average 7%. So gradient wise it’s quite similar to the Stelvio, but much shorter.

There is a pair of towers at the top of the climb and a small tunnel. From here the sealed road ended and we had a couple of kilometres to travel on a dirt road to the finish.

So it was good to get to the finish.

I had a small break at the top before rolling back to Bormio.

### Conclusions

1. The race was well organised. It isn’t too big and whilst I rode with others most of the time there weren’t so many people that it felt crowded.
2. Bormio itself is a nice town and well suited to cycling and running (from what I could see). The people were very friendly and helpful, and used to outdoor sports.
3. The Mortirolo is very challenging. Its the most challenging hill I’ve ridden by a long way. I used a 34 and probably would not have made it without this.
4. Shame about the Stelvio being absent from this year’s race but that’s how it goes. Maybe I will return to get the full experience!

# The Physics of Tides

## Introduction

Tides turn out to be very interesting. The main patterns are:

• A twice-daily variation
• A difference between the first and second tide of a day
• The spring–neap cycle
• The annual variation

As to how this works at a particular point on the coastline is determined by many factors including the orientation of the coastline, the size of the body of water around it and the characteristics of the sea bed. Although two high and low tides per day are usual, other combinations are not uncommon, as shown below. Of course, other local features like tidal bores also occur.

So what causes tides?

## Rotating Reference Frames

An inertial reference frame is one in which a body with no net force acting on it is not accelerating. This is Newton’s First Law. Newton’s Second Law states for a force, F, causes a body of mass, m to accelerate with acceleration, a :

$\vec{F} = m\vec{a}$

A non-inertial reference frame is one which is accelerating. Consider the following diagram:

So there are two reference frames. Frame A is inertial and the position of a particle at time t is given by $\vec{x_A}$.

Frame B is non-inertial (or accelerating) and the position of the particle at time, t is given by $\vec{x_B}$.

The origins of Frame B from Frame A is given by $\vec{X_{AB}}$.

We know in Frame A, Newton’s Second Law holds so lets see what happens in Frame B.

Let the coordinate axis in B be represented by unit vectors uj with j any of { 1, 2, 3 } for the three coordinate axes, such that:

$\vec{x_B} = \sum\limits_{j=1}^3 x_j.\vec{u_j}$

From Frame A, the equation becomes:

$\vec{x_A} = \vec {X_{AB}} + \sum\limits_{j=1}^3 x_j.\vec{u_j}$

Now, take a derivative with respect to time:

$\frac{d\vec{x_A}} {dt} = \frac{d\vec {X_{AB}}} {dt} + \sum\limits_{j=1}^3 \frac{dx_j} {dt}.\vec{u_j} + \sum\limits_{j=1}^3 x_j.\frac{d\vec{u_j}} {dt}$

So substituting velocity into this equation we get:

$\vec{v_A} = \vec{v_{AB}} + \vec{v_B} + \sum\limits_{j=1}^3 x_j.\frac{d\vec{u_j}} {dt}$

What this equation represents is that the velocity observed in Frame A is the velocity observed in Frame B plus 2 other terms; the first is the relative velocity at which the origin of the two reference frames are moving and the second represents the contribution to velocity due to the rotation of Frame B.

So lets differentiate again with respect to time to get accelerations:

$\frac{d^2\vec{x_A}} {dt^2} = \frac{d^2\vec {X_{AB}}} {dt^2} + \frac{d^2\vec{x_B}} {dt^2} + \sum\limits_{j=1}^3 \frac{d^2x_j} {dt^2}.\vec{u_j} + \sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} + \sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} + \sum\limits_{j=1}^3 x_j.\frac{d^2\vec{u_j}} {dt^2}$

So, on the right the second differential of position is the acceleration in Frame A. On the right, the first term is the acceleration of the origin of Frame B from Frame A. The second term is the acceleration of the particle as observed in Frame B.

$\vec{a_A} = \vec {a_{AB}} + \vec{a_B} + 2.\sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} + \sum\limits_{j=1}^3 x_j.\frac{d^2\vec{u_j}} {dt^2}$

So this equation relates the acceleration observed in Frame A to the acceleration observed in Frame B with these 3 extra terms. The equation can be easily turned into a force equation by using Newton’s Second Law.

$\vec{F_A} = \vec {F_B} + \vec{F_{AB}} + 2.m.\sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} + m.\sum\limits_{j=1}^3 x_j.\frac{d^2\vec{u_j}} {dt^2}$

These 3 additional terms are often called fictitious, pseudo or inertial forces. If we make Frame B the primary frame we are interested in then:

$F_B = F_A + F_{Pseudo}$

and the Pseudo Forces can be equated to:

$F_{Pseudo} = -\vec{F_{AB}} - 2.m.\sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} - m.\sum\limits_{j=1}^3 x_j.\frac{d^2\vec{u_j}} {dt^2}$

The next step is to apply this general result to a B frame of reference of the Earth’s surface.

### A Frame of Reference on the Earth’ Surface

Let $\vec{\omega}$ represent the rotation of the Earth about its axis such that its magnitude is given by:

$\omega = \frac {2.\pi} {1 day} = 0.00007 / sec$

The first time derivative is given by:

$\sum\limits_{j=1}^3 \frac{d.\vec{u_j}} {dt} = \sum\limits_{j=1}^3 \vec{\omega}.\vec{u_j}$

The second time derivative is given by:

$\sum\limits_{j=1}^3 \frac{d^2.\vec{u_j}} {dt^2} = \sum\limits_{j=1}^3 \frac{d.\vec{\omega}} {dt}\times\vec{u_j} + \sum\limits_{j=1}^3 \vec{\omega}\times\frac{d.\vec{u_j}} {dt} = \sum\limits_{j=1}^3 \frac{d.\vec{\omega}} {dt}\times\vec{u_j} + \sum\limits_{j=1}^3 \vec{\omega}\times(\vec{\omega}\times\vec{u_j})$

Where “x” is the vector cross product operator. Substituting this into the earlier equation for acceleration gives:

$\vec{a_A} = \vec {a_{AB}} + \vec{a_B} + 2.\vec{\omega} \times \sum\limits_{j=1}^3 \frac{dx_j} {dt}.\vec{u_j} + \sum\limits_{j=1}^3 x_j.\frac{d.\vec{\omega}} {dt}\times\vec{u_j} + \sum\limits_{j=1}^3 x_j.\vec{\omega}\times(\vec{\omega}\times\vec{u_j})$

Next setting the translation acceleration $\vec {a_{AB}} = 0$ and collecting the terms up:

$\vec{a_A} = \vec{a_B} + 2.\vec{\omega} \times \vec{v_B} + \frac{d.\vec{\omega}} {dt}\times\vec{x_B} + \vec{\omega}\times(\vec{\omega}\times\vec{x_B})$

Lastly, putting this result back into the equation for Pseudo Forces gives:

$F_{Pseudo} = -2.m.\vec{\omega} \times \vec{v_B} -m.\frac{d.\vec{\omega}} {dt}\times\vec{x_B} -m.\vec{\omega}\times(\vec{\omega}\times\vec{x_B})$

The first term is what is called the Coriolis Force, the second the Euler Force and the third term the Centrifugal Force.

### Pseudo Forces

So what are these confusing Pseudo Forces?

So to start off they do not arise in inertial (or non-accelerating frames of reference). When the frame of reference is accelerating (or non-inertial) then these forces are a consequence of being in an accelerating frame of reference. This occurs in everyday life, for example, in a car going around a bend. If the bend is to the left and the speed of the car remains constant then the driver will feel a force pushing him or her to the right. This is called a centrifugal force and is one of the Pseudo Forces. The car seat pushes back on the driver to the left. This is the centripetal force and has the same magnitude but opposite sign to the centrifugal force. The driver therefore has no net force on him or her and follows the line of the corner inside the car.

From the perspective of an observer standing outside the car watching it drive around the corner, the observer sees the car and driver follow a corner to the left. So a net force to the left must be applied (the centripetal force) to make the car change direction. From the standing observer’s perspective, in an inertial frame of reference, the centripetal force exists but the centrifugal force does not.

#### The Euler Force

The Euler Force is given by:

$F_{Euler} = -m.\frac{d.\vec{\omega}} {dt}\times\vec{x_B}$

The first thing to note is that it contains $\frac{d.\vec{\omega}} {dt}$ which is zero for a reference frame spinning at a constant speed (like the Earth), so it plays no part in tides.

An example of the Euler Force would be sitting on a carousel, initially at rest, that starts moving. The force is proportional to the angular acceleration and the distance from the carousel’s centre.

To work out the direction of the force we know the angular acceleration $\frac{d.\vec{\omega}} {dt}$ is vertically upwards and that the position vector $\vec{x_B}$ is outwards from the carousel’s centre. The vector cross product direction is derived from the right hand rule, so would point forwards, in the direction of motion. The force formula, however, has a minus sign which reverses the direction to point backwards.

So back on the carousel, the Euler Force pushes the person back into the seat. As the ride ends, and the carousel decelerates the Euler Force acts to lift the person out of the seat. So it behaves in this case like the real (non-pseudo force) acting on a passenger in a car, initially at rest, that accelerates pushing the passenger back into the seat. When the car decelerates to a stop, the passenger is lifted out of the seat.

#### The Centrifugal Force

The Centrifugal Force is given by:

$F_{Centrifugal} = -m.\vec{\omega}\times(\vec{\omega}\times\vec{x_B})$

Taking the mass away to give the magnitude of the acceleration (where R is the Earth’s radius):

$\omega^2.\rho = \omega^2.R.\cos(\lambda)$

So at the poles, $\cos(\lambda) = 0$ so there is no centrifugal acceleration. At the equator $\cos(\lambda) = 1$ so the centrifugal acceleration becomes:

$\omega^2.R = (\frac{2.pi()} {24.60.60})^2.6,378,000 = 0.034m/s^2$

Note that this is quite small compared to the force of gravity (about 1/3 of 1% of the force of gravity). Note also that the force is independent of the motion of a particle on the Earth’s surface (whether stationary or moving).

The direction of the Centrifugal Force is given by following the right hand rule for the two vector cross products. Firstly, $\vec{\omega}\times\vec{x_B})$ is a vector pointing downwards. Performing the cross product of $\vec{\omega}$ with the previous result is a vector pointing inwards towards the axis of rotation. The minus sign in the equation for Centrifugal force reverses the direction of the force to point away from the axis of rotation.

Resolving the centripetal acceleration into a component parallel to the centre of the Earth gives: $\omega^2.R.\cos^2(\lambda)$. So that gravity on the Earth’s surface is effectively reduced by this factor.

There is also a component parallel to the Earth’s surface in the north south direction of: $\omega^2.R.\cos(\lambda).\sin(\lambda)$

This parallel component is zero at the equator and poles and acts elsewhere in the direction of the equator. Its maximum is at:

$\frac{d.\cos(\lambda).\sin(\lambda)} {d\lambda} = 0$

Which is at +/-45 degrees latitude.

So one of the theories is that this force, small that it is, acting towards the equator is responsible over the lifetime of the Earth for producing the oblate nature of the Earth. That is, it is not quite spherical, but fatter at the equator than at the poles.

#### The Coriolis Force

The Coriolis Force is given by:

$F_{Coriolis} = -2.m.\vec{\omega} \times \vec{v_B}$

So the first thing to note is that the Coriolis Force is proportional to a particle’s mass and to its speed in Frame B, so for stationary particles the force is zero. It has an acceleration magnitude of:

$2.\omega.v = 2.\frac{2.pi()} {24.60.60} = 0.00015.v.m/s^2$

The next thing to note is that the direction of the force is given by the vector cross product of angular velocity and velocity by the right hand rule:

• If the velocity is parallel to the axis of rotation then the cross product and therefore the Coriolis Force is zero.
• If a ball is dropped at the equator, the cross product points west. So the Coriolis Force’s negative sign reverses the direction, and the Coriolis Force on the ball is to the east (in the direction of rotation of the Earth).
• For a ball thrown vertically upwards the Coriolis Force is to west (opposite to the direction of rotation of the Earth).

A major impact of the Coriolis Force is on the atmosphere and oceans. In the atmosphere, when an area of low pressure develops, air would flow towards the area of low pressure from surrounding areas of high pressure. On the revolving Earth, these flows of air are subject to the Coriolis Force, perpendicular to the direction of motion of high to low pressure air flow.

In the northern hemisphere, air flowing towards an area of low pressure (blue arrows) is subject to the Coriolis Force (red arrows) and is deflected as shown in the diagram. This leads to an anticlockwise rotating mass of air, or anticyclone.

In the Southern Hemisphere, the forces act in the opposite direction and lead to clockwise rotating air masses, or cyclones.

In fact, the existence of the Coriolis Force was used as evidence that the Earth rotates; rather than the sun, moon and stars rotating about the Earth. Faucault’s Pendulum is a good example of this, where a swinging pendulum can be seen to precess indicating a force other than just gravity is acting on it.

## Orbiting Reference Frames

So, lets park rotating reference frames for a while and look at the case of an orbiting reference frame.

Lets keep things simple and assume a particle is following orbiting a central point. We know the general equation for acceleration is given by:

$\frac{d^2\vec{x_A}} {dt^2} = \frac{d^2\vec {X_{AB}}} {dt^2} + \frac{d^2\vec{x_B}} {dt^2} + \sum\limits_{j=1}^3 \frac{d^2x_j} {dt^2}.\vec{u_j} + \sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} + \sum\limits_{j=1}^3 \frac{dx_j} {dt}.\frac{d\vec{u_j}} {dt} + \sum\limits_{j=1}^3 x_j.\frac{d^2\vec{u_j}} {dt^2}$

The rotational components are zero (by definition as there is no rotation is Fame B in this example), so the equation simplifies to:

$\frac{d^2\vec{x_A}} {dt^2} = \frac{d^2\vec {X_{AB}}} {dt^2} + \frac{d^2\vec{x_B}} {dt^2}$

Now if the origin of frame A is at the centre of the circle orbited by the particle then:

$\vec{X_{AB}} = R.(\cos(\omega.t), \sin(\omega.t))$

$\vec{V_{AB}} = \frac{d\vec{X_{AB}}} {dt} = \vec{\omega} \times \vec{X_{AB}}$

And the acceleration is given by (remembering that $\omega$ is constant with respect to time:

$\vec{a_{AB}} = \frac{d\vec{V_{AB}}} {dt} = \vec{\omega} \times (\vec{\omega} \times \vec{X_{AB}})$

Lastly, turning this into a Pseudo Force in the orbiting reference frame B:

$F_{Pseudo} = -m.\vec{\omega} \times (\vec{\omega} \times \vec{X_{AB}})$

So we can see that the format is the same as the format of the centrifugal force in the rotating Earth example, and that the magnitude of the acceleration is:

$\omega^2.R = (\frac{2.pi()} {365.24.60.60})^2.149,600,000,000 = 0.0059m/s^2$

The direction of the force using the right hand rule again, gives the force in the orbital plane, pointing outwards from the centre of the orbit.

## The Earth’s Motion around the Sun

In the above diagram we can see Earth orbiting the sun in an anticlockwise direction. Lets assume a circular (rather than elliptic) orbit for now. More on that later. The rotation of the Earth is anticlockwise and inclined at 23.5 degrees to the sun / Earth orbital plane.

In addition, of course, the moon orbits the Earth. The plane of the moon’s orbit is inclined at about 5 degrees to the earth / sun orbital plane.

Technically, the moon does not orbit the Earth, but rather, both the moon and the Earth both orbit their centre of mass (or barycentre). Because the Earth is much more massive than the moon, the barycentre is located within the Earth so the effect on the Earth is for it to appear to wobble, as it orbits the sun, as shown below:

### Pseudo Forces

Thinking about the major Pseudo Forces involved from the perspective of a non-inertial reference frame on the Earth’s surface (Frame B) in relation to an inertial reference frame in deep space (Frame A). The Earth’s rotation contains the following components:

• Centrifugal Force. Acts outwards from the Earth’s axis of rotation $F_{Centrifugal} = -m.\vec{\omega}\times(\vec{\omega}\times\vec{x_B})$. Has an acceleration magnitude of $0.034m/s^2$
• Coriolis Force. Is speed dependent so will be quite small for slow moving things like water currents, but has an acceleration magnitude of $0.00015.v.m/s^2$
• Euler Force. Assuming a constant rate of rotation this will be zero.

The Earth’s orbit around the sun generates the following components.

• A Centrifugal Force like component. Acts outwards from a line joining the Sun and Earth, in the Sun / Earth plane. Has an acceleration magnitude of $\omega^2.R = (\frac{2.pi()} {365.24.60.60})^2.149,600,000,000 = 0.0059m/s^2$

The Earth’s orbit around the moon (or rather the Earth / moon barycentre) generates the following components:

• A Centrifugal Force like component. Acts outwards from a line joining the Earth and moon, in the Earth / moon plane. Has an acceleration magnitude of $\omega^2.R = (\frac{2.pi()} {27.24.60.60})^2.4,600,000 = 0.000033m/s^2$

### Gravity

Now lets look at gravity. The acceleration due to gravity of a mass M at distance R is given by:

$a_g = \frac{G.M} {R^2}$ where G = 6.674×10−11 m3⋅kg−1⋅s−2

So, plugging the numbers for the mass (5.97e24 kg) and radius of the Earth (6.371e6 m) into this equation gives the acceleration on the surface of the Earth due to gravity = 9.82 ms−2

Plugging the numbers for the mass of the sun (1.99e30 kg) and the distance between the Earth and the sun (1.50e11 m) gives an acceleration on the surface of the Earth towards the sun of 0.0059 ms−2

Hang on you are thinking, I’ve seen that number before! Yep, it’s the value of the Pseudo Centrifugal Force on the Earth due to the Earth orbiting the sun. This makes complete sense that these forces are of equal size (gravity acts towards the sun; the Pseudo Force acts away from the Sun). So in the reference frame of the Earth, the Sun’s gravitational pull is offset by the Pseudo force with no net resultant force so we never move any nearer to the sun.

Plugging the numbers in for the mass of the moon (7.35e22 kg) and the distance between the Earth and the moon (3.84e8 m) gives an acceleration on the surface of the Earth towards the moon of 0.000033 ms−2. Bingo, this matches the centrifugal like Pseudo Force calculated above, but acting in the opposite direction so as to cancel out.

## Tide Generating Forces

So now we know a little about the forces acting on the surface of the Earth we can start to think about how tides might be created. Firstly, the Earth’s gravity and Pseudo Forces produced by the Earth’s rotation are clearly not involved in producing the observed tidal patterns simply because these forces are constant with respect to time and therefore would not lead to the observed periodic properties. Although the forces change over the surface of the Earth, they are constant at any point on the surface.

So this leaves the impact of Sun and the Moon. To avoid having to deal with a 3-body problem, lets take the impact of the Sun and the Moon separately, starting with the Sun.

So lets look more carefully at the forces acting at different points on the Earth’s surface. As already stated we can discard the Earth’s own gravitational force and the Pseudo Forces produced by the Earth’s rotation and concentrate on the gravitational force towards the Sun, $F_{gr}$ and the Pseudo Force produced by the Earth’s orbit around the Sun, $F_{in}$.

At points A and B, you can see that there is a net downward force towards the centre of the Earth. At point Z, where the Sun is overhead, the force of gravity will be a little higher than elsewhere on Earth because the point is nearer the Sun so will be a little larger than the Pseudo Force acting away from the Sun, resulting in a net force towards the Sun. At point N, the force of gravity from the Sun will be a little less than elsewhere on Earth due to this point being further from Sun, so the net force at this point will be pointing away from the Sun.

The above diagram shows the direction of the net force of gravity and pseudo force due to the Sun. The thing to note is that there is a tendency to create a tidal force at the point nearest the Sun, and also at the point furthest from the Sun. As the Earth spins about its axis, so the points affected by these maximal tidal forces rotate, and a point on the Earth’s surface will have these maximal tidal forces twice per day.

This is about as far as a static analysis of tides can usefully go. The next step is to consider a dynamic analysis, by thinking about the net, tide producing forces at a point on the Earth as periodic, for example, as the Earth rotates about the Sun, or as the Moon rotates about the Earth.

## Harmonic Analysis

The starting point here is that the tide at a given point rises and falls in a periodic way and that this can be expressed as a Fourier series of periodic terms related to astronomical conditions. So, a general equation for the height, h of the tide at time, t, would be:

$h = H_0 + A.\cos(a.t + \alpha) + B.\cos(b.t + \beta) + C.\cos(c.t + \gamma) +...$

where $H_0$ is the mean tide level. The A, B, C, etc are the amplitudes of each component, the a, b, c, etc are the speed of the component and the $\alpha, \beta, \gamma$, etc are the phase offset of each component.

The more accurate you want the analysis to be the more components you can add in. Doodson did the pioneering work on this which was published in 1921. He identified 6 orbital attributes (3 for Sun and 3 for the Moon) that described their elliptical orbits and constructed 388 periodic components from this.

By measuring the height of the tide using a tidal gauge at regular intervals over an extended period of time, it is possible to calculate the amplitudes (A, B, C, etc) and phase offsets ($\alpha, \beta, \gamma$, etc) of each component and then use the above equation to predict forward in time the tide height. This is the basis of tide tables.

The main components can be understood in terms of their frequencies: semi-diurnal, diurnal, longer periods, and shorter periods.

### Semi-Diurnal Components

The most significant component is due to the Moon and, by convention, is called $M_2$. “M” for Moon and “2” for approximately twice per day. A lunar day is 24hrs and 50minutes (not 24hrs) as the Earth / Moon combination are orbiting the Sun so the Moon needs to travel a bit more than 24hrs to get to the same spot relative to the Earth (which has moved over the 24hrs). So $M_2$ has a period of 12hrs 25mins and explains why, for example, high tides in tide tables are usually separated by 12hrs 25mins.

The next most significant component is due to the Sun, $S_2$, and the radiation difference between night and day leading to different atmospheric pressure. By definition this occurs at a period of 12hrs.

Then comes, $N_2$, which accounts for the Moon’s elliptical (rather than circular) orbit.

There are potentially many more components all with slightly different periods, but their amplitudes, and therefore their contribution, is smaller.

### Diurnal Components

The most important components are $K_1$ and $O_1$, that both relate to the moon but have slightly different periods.

Again there are potentially many more components, this time with a period around 24hrs.

### Longer Periods

These relate to things like the monthly Moon orbit and the annual orbit of the Earth about the Sun. These components are usually small.

### Shorter Periods

The effect of shallow water causes interaction with the bottom to generate harmonics of the larger components already discussed. For example, $M_4$ with a period of 6hrs 13mins, $M_6$ and $S_4$ with a period of 6hrs.

## Putting it all Together

The US use 37 components and publish data for these components. For example, for The Battery in New York, so you could use this to calculate your own Tide Tables.

Obviously, these calculations are pretty simple for a computer to do now, but back in the days before computers, mechanical computers were built to do this.

Lord Kelvin had one built in 1872 to use 26 components. It was used by Doodson to calculate Tide Tables for the Normandy Landings in the Second World War.

The landings had to be at low water as the beeches had been booby-trapped, and low tide had to be first light so the troops could cross the channel under the cover of darkness, so the Moon had to rise late.

A note was sent to Doodson with 11 harmonics.

Its unclear where these came from, but crunching the numbers Doodson worked out that 5th-7th June would be the most suitable dates for D-Day.

# Exodus

## About the Race

The Exodus Race is a 100 mile single-stage race in the Brecon Beacons. It starts on the west of the Beacons in Llangadog and travels east along the Beacons Way to Abergavenny.

The timetable for the event was as below:

I drove to the finish at Abergavenny and left my car in the car park there and took a coach, laid on by the race organisers, to the start in Llangadog.

The race allows each competitor to leave a drop-bag at each checkpoint. The important point to remember is that after the drop-bag have been accessed at the checkpoint it is then moved to the finish, not to the next checkpoint like in some races. So, this means you potentially need more drop-bags and maybe more kit.

## Beacons Way

The route was along the Beacons Way, west to east, except for the checkpoints that were in buildings like Youth Hostels, just off the route.

I know the Brecon Beacons quite well but have not been on all the route. I probably know the central section the best, then the western side and have not spent much time on the eastern side.

## The Plan

My plan was to take this race fairly steadily and not to push things too hard. I knew that the weather was forecast to be bad; very wet and windy, so I was prepared for this. I assembled all the kit and food according to the plan I had produced.

My checkpoint strategy was to try to minimise time in the checkpoints. I would just get something to eat, change batteries in my electronics, change socks (and possibly shoes), reload food and water for the next leg and set off.

## Check-In

Check-in was a simple process in Llangadog. I deposited my various bags with the race organisers and got my race number, GPS tracker, map and a hi-viz jacket! Then there was a race briefing before we walked outside to the start of the race.

## Leg 1 – Llangadog to Llanddeusant, 22 miles

The start was at 7pm on Friday evening. Given it was December it was dark and the forecast was for wet and windy weather. As we walked to the start I fired up my GPS unit and my watch.

For some reason my GPS was playing up and would not load the route. As I fiddled with it, the race started and everyone ran off.

So I was jogging along fiddling with my GPS whilst watching the line of head torches disappear up the hill in front. I then realised that my watch’s GPS did not appear to be working either. This was not good!

So I decided to reboot all electronics.

I think I must have loaded the wrong segment on my watch (I had loaded each segment as a separate track on my watch) as this time all seemed good. I have no idea what was wrong with my GPS unit, but the reboot seemed to fix things and it was working normally now.

The first section was muddy footpaths through farmland. We were climbing as well. Llangadog is in a valley, and we were climbing up into the Beacons towards the Black Mountain.

There was some road and paths before we got into the Beacons park proper. The weather was still OK and there were a few people around. We went past the village of Bethlehem and continued south towards Trap. As I got near to Carreg Cennen Castle I past a farmer walking with his three sheep dogs. I got a nip from one of the dogs which was not good.

From here it was climbing up onto the Black Mountain. There is not much path here and it was eyes down onto the GPS for much of this section. The rain had started by now and as we got higher so the wind picked up.

After a while we came off the hills onto road and started descending. It was a few miles of undulating tarmac to the first checkpoint at Llandeusant. As is always the case the first checkpoint was quite busy but I found a seat, got something to eat and changed the batteries in my head torch and GPS.

I went to change my socks only to discover a packing failure. I was wearing toe socks where left and right is very important as you simply cannot wear a right sock on the left foot and vice versa. I pulled out the pair of socks from the drop bag to find two right socks. So, all I could do was change the right sock.

I was not finding the poles I was carrying very useful so I left them in my drop bag.

# Leg 2 – Llanddeusant to Brecon Beacons YHA (near Storey Arms), 25 miles

I did not stay long at Llandeusant and was soon out of the door onto the second leg. I was with a younger guy who was not very confident with navigation so we were moving together.

We had a small amount of tarmac at first, out of Llanddeusant, before some muddy paths over farmland before we were back into the Beacons proper. The route was staying low around the northern side of Llyn Y Fan Fach and Llyn Y Fan Fawr, avoiding the higher ground of Banau Sir Gaer and Fan Brycheiniog.

We could just about see the water in Llyn Y Fan Fach as we crossed the northern shore and headed over to Llyn Y Fan Fawr, skirting the northern shore before following the water’s edge south, along the eastern side.

Then it was south off the hill into the Swansea Valley and across the A4067 just north of Pen Y Cae and the caves at Dan Yr Ogof. I made a slight navigation error here and missed the turn off through the graveyard, but soon corrected the mistake.

There were some reasonable paths here as we first traversed some lowland areas along the Swansea Valley, before starting to climb again. Eventually we joined the old Roman Road, Sarn Helen, that took us northeast.

It was starting to get light now and along the Sarn Helen we passed the Maen Madoc burial stone.

We had caught up with Iain who I knew from other races like Cape Wrath and Dragon’s Back. So we talked about these races a bit, as well as races we had coming up in the future.

We dropped down to cross a small road and then climbed back up to Fan Llia. It had been raining hard all morning and my waterproof gortex gloves were now waterlogged. The wind was strong causing my fingers to go numb with the windchill, so I took the gloves off which did improve things.

I was on my own again as I circled around towards the A470. I know this area quite well but had never seen the underpass beneath the road near the Storey Arms. But it was there!

Checkpoint 2 was off the Beacons Way in a youth hostel back towards Libanus. Initially the path was good but there were some seriously muddy fields to cross to get the CP!

I did the usual at the CP; got something to eat and drink, replaced batteries and loaded up my rucksack with food and water for the next stage.

As I pulled a pair of socks from my drop bag I found, unsurprisingly, two left socks. So I changed my left sock. At least at the next checkpoint the socks in the drop bag should be a left and a right.

# Leg 3 – Brecon Beacons YHA to Crickhowell, 26 miles

I left the checkpoint fairly promptly and slithered back the way I had come across the muddy fields until I was back on the path. Feet were soaked again so changing sock was a bit of a waste of time.

From here we climbed up to near the summit of Corn Du, before breaking away and going up Pen Y Fan. It was very windy now, so when I got to the summit, I quickly got across to Jacob’s Ladder on the far side to start descending.

There where two routes advertised. A normal route summiting Fan Y Big and a bad weather route keeping to the Roman Road along the Neuadd Reservoirs. We were advised at the last Checkpoint to follow the bad weather route.

From the Roman Road I headed round to the eastern side of the Talybont Reservoir before heading east towards Llangynidr. From here Crickhowell is not too far away to the east, but the route we were following took us on a big detour to the north before swinging around south and back to Crickhowell.

It had got dark again long before I got to the Checkpoint. I did the usual checkpoint admin process and then closed my eyes and put my head on a table for a few minutes cat-nap. This didn’t work, so I found some camp beds behind a screen so I laid down for a few minutes. I did not sleep for very long, just a few minutes I think, but I was dawdling at the checkpoint.

My feet were starting to show a few signs of becoming waterlogged, which was not too surprising at they had been constantly wet since the start. My shoes were starting to hurt as well. I did think of changing from the Scotts to Hokas. I knew the Hokas would offer a little more cushioning but would not be as grippy as the Scotts on the mud. So I stayed with the Scotts.

After that, I got ready, changed both socks, and set off into the darkness again.

# Leg 4 – Crickhowell to Abergavenny, 27 miles

This section was a big loop, firstly north, then east and then south back to Abergavenny. I was not very familiar with the majority of this section although I did know the final hill.

There was a sharp climb out of the checkpoint through farmland, before I dropped down to cross a couple of small roads. Then a repeat as we continued to travel north. We dropped off the hill into the village of Llanthony. Somewhere around here was an unmanned checkpoint. We were advised we did not have to dib into it, as it had some sort of proximity device to record us passing.

It was getting light and the weather was improving.

The next climb was up to Hatterrall Hill. I was now moving south towards the finish. I dropped off the hill and there was a bit of a lowland road section to traverse.

I was somewhat familiar with this area. The last hill was Skirrid, which I knew. In the past, I had taken a wrong turn off the road onto the hill and for some reason (tiredness probably) I did the same again. This was annoying and it took me some time to retrace my steps to sort it out.

Skirrid is quite steep so it took a while to get to the top. There was the second unmanned checkpoint somewhere at the top. I did not see it. I came off the hill through a wood and was now on the outskirts of Abergavenny.

There was a couple of miles still to go. This was a combination of roads and a golf course. And then I was at the finish!

I made it 107 miles in 41 hours 17 minutes. I did make a couple of navigation errors that may have added an extra mile or two.

Statistics for the race were: 55 signed up; 43 showed up at the start; 19 finished. I came 10th.

# Things I Learned

1. Its Wales in December so its going to be wet and muddy. We had pretty bad weather with a lot of rain and high winds.
2. Take as much kit as you can, its good to change into fresh kit at the checkpoints (all my waterproof gear leaked to some degree).
3. The Beacons Way is sign-posted but in places not that well. Most of the route has a reasonable path to follow but there are some less used section like the Black Mountain where there is not much of a path on the ground.
4. Terrain is undulating and generally not technically difficult. It is mainly hilly rather than mountainous.
5. There are not many places outside Checkpoints to buy things so you have to support yourself between CPs.
6. Pair up toe-socks carefully to ensure a pair really is a pair!

# How did the Kit Perform?

1. Shoe choice of Scott Kinabalu was good at these perform well on mud. Feet were quite painful at the end though.
2. Injinji mid-level toe socks were fine. I’ve used these many times.
3. UD Fastpack 15L backpack worked well and was plenty big enough.
4. Waterproofs. Montane Ajax jacket and Montane Trailblazer trousers. Wore the jacket for the whole race and the trousers for the second half. Both leaked to some extent but given the amount of heavy rain I was happy with both.
5. Sealskinz hat. Worked fine.
6. Trekmates gortex gloves. Became waterlogged and useless. Changed to Sealskinz gloves and the same thing happened. Simply need multiple pairs.
7. Garmin eTrex 30x. Worked fine after the initial problems at the start.
8. Garmin Fenix 3 HR watch. Worked well.
9. Organiser map. I had a couple of looks at the map inside at the checkpoint to get an overview of what was coming up but did not look at the map on the course. Navigating by map and compass would have been very difficult given the weather and the fact that a lot of this race occurs at night.
10. Headtorch Ledlenser H14.2. Heavy so need to get used to it but worked well in the conditions. The light beam is big and bright and the batteries last all night.

# Introduction

I love maps. But how do they work? This blog post examines some of the physics behind maps and how they work.

# Representing the Earth on a Piece of Paper

If we assume the Earth is a sphere for now. Its not really, its quite a complex shape but for now we will keep things simple. More on its non-spherical nature later.

So a globe can be made to be quite a good approximation of the Earth. However, its not possible to represent the 3-D Earth on a 2-D piece of paper without distortion. You can see how this is the case by taking something spherical like an orange or an old football and trying to flatten out the surface layer (the peel in the case of the orange, or the football once deflated). The only way to flatten the surface layer is to tear it and / or stretch or deform it.

So, to get a representation of the globe on a sheet of paper a projection is required that will cause some sort of distortion. So compromises need to be made. The distorted properties are:

• Distances
• Directions
• Shapes
• Areas

There are many ways that a map projection can be done. These can be visualised as wrapping the Earth with a piece of paper in some way to mark all the detail on the piece of paper and then flattening out the piece of paper.

## Mercator Projection

Gerardus Mercator, 1512 – 1594, was a Dutch Cartographer who came up with a world map in 1569.

The Mercator projection is a conical projection. Conical projections preserve angles (this is called conformality) but distort other properties like areas. The cone touches the Earth, for example, at the Equator. Nearer the point where the cone touches the earth, the distortion is smallest; further away it gets progressively bigger. So, typically on World maps the distortion gets bigger nearer the poles.
Here is a typical Mercator projection map of the world. The classic distortion is the size of Greenland being much bigger than Australia where in reality, Australia is more than 3.5 times the size of Greenland!

This graphic flips between the Mercator projection and actual areas of countries.

The reason Mercator would have chosen this projection is because of navigation. With a conformal (equal angles) map, if you traverse a straight line from point A to point B, you will traverse a course of equal angle to the meridians on the Earth. A line of equal angles is called a Rhumb Line or Loxodrome. So, to sail from one side of an ocean to another, draw a line on the map and measure the angle, then sail that constant angle and you will reach your desired destination. This is obviously easy to do from a navigation perspective.

With a projection that is not conformal, Rhumb lines are not straight lines. Or, put another way, if you follow a straight line on a non-conformal map, you will need to constantly change your bearing as you get nearer to your destination. Possible, but far harder from a navigation perspective.

So for a standard Mercator projection centred on the Equator, the map is very useful around the equator but less so nearer the poles. Lambert realised that if you rotated the piece of paper relative so the Earth, so it touched a meridian of longitude then you could produce a map accurate around that meridian. This is the Transverse Mercator Projection and is useful for mapping areas with a north south extend, like for instance South America.

## Gnomic Projection

Marine maps are often Mercator projections. But to travel large distances it is usually better to take the shortest route. The shortest route between two points is a straight line, right? Well, not if you are travelling on the Earth (unless you plan to tunnel through the Earth to your destination). To travel from A to B on the Earth’s surface, you will travel a curved line along the Earth’s surface. The shortest curved surface route would be the Great Circle going through the start and end points. A great circle is any circle on the surface of the Earth centred at the centre of the Earth (assuming the Earth to be a sphere for a moment).

Rhumb lines on a Mercator projection map are not Great Circles so are not the shortest way to travel from any given start point to an end point. A “planar” projection map called a Gnomic projection is defined to represent all Great Circles as straight lines and so drawing a straight line from start point to end point will result in following a Great Circle on the Earth’s surface which is the shortest distance between the start and end points (on the Earth’s surface). Note, to steer this course will require constant bearing adjustments.

## Lambert Conformal Conic Projection

The Lambert Conformal Conic projection is similar to the Mercator projection but is a conic, rather than cylindrical, projection. The imaginary cone touches the Earth twice. Being conformal, angles are preserved so Rhumb lines are straight lines on this projection (like Mercator).

However, by touching the cone on the two extremities of the area to be mapped, distortion within the mapped area is less than with a Mercator projection, and the Rhumb lines are nearer Great Circles than on a Mercator projection.

The Lambert Conformal Conic projection is often used for Aeronautical charts (as above).

## More Projections

Many projections have been produced for specific purposes. A large list is here.

## Globe

A globe, of course, suffers none of the distortions of a 2-dimensional map, but is obviously more difficult to carry about and impractical at a more detailed level.

# The Shape of the Earth

The Earth is obviously a complex shape with mountains and valleys, land and sea. It is best approximated by an oblate ellipsoid, that is a sphere that has been squashed slightly at the poles, so it is wider at the equator.

So a point on the equator is approximately 21km (13 miles) further from the Earth’s centre than the North or South Pole.

By convention, mountains are measured as height above sea level (even if they are nowhere near the sea). An alternative would be to measure their distance from the centre of the Earth. Everest is 28º North, so clearly at a disadvantage compared to mountains near the equator. In fact, Chimborazo, a peak near the equator in the Andes turns out to be the furthest point from the centre of the Earth (even though it is not the highest peak in the Andes!). Everest does not make the top 20 mountains using this method of height calculation.

## Ellipsoids

So the best simple shape to use to model the Earth is an ellipsoid but it is only an approximation. Depending on the intended use it may make sense to use one ellipsoid over another. For example, the best fit global ellipsoid may be a relatively good fit in some areas but relatively poor in others so typically country or regional maps will use an ellipsoid that makes sense for that country or region.

Globally, the most common ellipsoid in use is the World Geodetic System 1984, WGS-84. GPS uses this. In the UK, it is common to use the Airy ellipsoid (calculated by George Airy in 1830), for example, this is what Ordnance Survey uses.

Here are some common ellipsoids:

## Geoid

By convention, “height” is measured with respect to sea level. But what sea level? Tides rise and fall, the moon influences the height of the high tides at different times of the year, etc. So some conventions are required?

Typically, an average sea level is chosen as height = zero. The shape of the Geoid is defined as a surface perpendicular to the Earth’s field of gravity, having a constant gravitational potential. Gravity generally acts towards the centre of the Earth but due to differences in the composition of the Earth there are variations on both small and large scales meaning that gravity does not always point at the centre of the Earth. The shape of the Geoid is therefore as complex as that of the Earth’s surface, but usually approximated by an ellipsoid.

### Global Geoid

The Global Geoid is usually defined with height relative to the average sea level across all the world’s oceans. This leads to an ellipsoid accurate to about 200m across the whole world, quite good but not that accurate.

### Local Geoid

In the UK, the Local Geoid height is measured relative to a tide-gauge at Newlyn in Cornwall. The seas around the UK are below the global average and the Newlyn gauge measures about 80cm below the Global Geoid! The seas are not all at the same level, due to temperature variation, tides, winds and water impurities.

This also means that measuring sea level at Newlyn from year to year will give different results (and that is before global warming comes into play!). The Ordnance Survey defines Ordnance Datum Newlyn as the mean sea level at Newlyn between 1915 and 1921. It is still used on maps and marked as ODN, and all heights on Ordnance Survey maps are relative to ODN.

## Datum

A datum is a convention used to define a coordinate system and reference points in order to describe a point on the Earth. So a datum would typically reference an ellipsoid, a coordinate system and an origin of that coordinate system. It is a little confusing because sometimes the datum and its ellipsoid have been given the same name, e.g. WGS84.

The datum may refer to a globe, which is unprojected or to a particular map projection that specifies how to translate from the 3D ellipsoid to a 2D map, e.g. a Mercator projection.

Lets look at a couple of examples:

### World Geodetic System 1984, WGS84

GPS uses WGS84 as it is a global system with the satellites orbiting the centre of the Earth on elliptical paths, so basing measurements from the centre of the Earth is quite convenient. This datum is unprojected. WGS84 is defined by the following:

• The WGS84 Cartesian axes and ellipsoid are geocentric; that is, their origin is the centre of mass of the Earth including oceans and atmosphere.
• Their orientation (that is, the directions of the axes, and hence the orientation of the ellipsoid equator and prime meridian of zero longitude) coincided with the equator and prime meridian of the Bureau Internationale de l’Heure at the moment in time midnight on New Year’s Eve 1983.
• Since this time, the orientation of the axes and ellipsoid has changed such that the average motion of the crustal plates relative to the ellipsoid is zero. This ensures that the Z-axis of the WGS84 datum coincides with the International Reference Pole, and that the prime meridian of the ellipsoid (that is, the plane containing the Z and X Cartesian axes) coincides with the International Reference Meridian.
• The shape and size of the WGS84 biaxial ellipsoid is defined by the semi-major axis length a = 6378137.000 metres, and the reciprocal of flattening 1/f = 298.257223563.

### UK Datum OSGB36

The National Grid defines the UK into a series of 100km x 100km squares each given a 2 letter code. The datum specifies a Transverse Mercator Projection. The origin (called True Origin) is defined at 49°N 2°W. To remove the need for negative values west of the origin, a False Origin is defined 400km west and 100km north of the True Origin.

Any point in the UK can be defined to a 1 square metre accuracy as:

• 2 character grid square
• 5 digit “easting”. Number of metres east of the southwest corner of the square
• 5 digit “northing”. Number of metres north of the southwest corner of the square.

# GPS

Following a map on a GPS is relatively straightforward. If you need to take a position reference from a GPS and compare it to, say, a map, then it is important that the GPS is configured in the same way as the map. Typically, this would involve configuring:

• Datum
• Ellipsoid
• Grid System

So, in the UK you would set the OSGB36 datum, Airy ellipsoid and UK National Grid system.

# What is a Glory?

A Glory is an optical effect, not unlike a rainbow, where an object appears to have a halo of light broken into individual colours. Usually, the object is a shadow of a person but, if flying, the object would be the aeroplane the person is flying in. Interestingly, you can tell where the person taking the photo is sat in the aeroplane by where the centre of the Glory intersects the aeroplane. In the photo, below the photographer is sat in the middle of the plane just ahead of the wings.

When the object is the distorted shadow of the person viewing the Glory, it is called a Brocken Spectre. The Brocken is a mountain in the Harz Mountains in Germany whose geometry and meteorological conditions lend themselves to the formation of these Glories.

# How does it Work?

So the basics behind the Glory are that a light source, like the Sun, is directly behind the person seeing the Glory. In front of the person would be cloud or fog that reflects some of the light back to the person.

So, when out walking, you need a particular geometry to see this. You need the sun behind you and in front you need a cloud or fog bank. So you need to be on, for example, a ridge looking down, and the sun cannot be too high.

The spectre appears deformed because of the long shadow that is cast, but is really just you blocking out the sunlight.

# The Glory Itself

The Glory itself is a set of concentric rings with blue at the centre and red further out. This is opposite to a rainbow where red is the lowest arc and blue the highest. It is also possible to see higher order rings following the same pattern as the innermost ring, but with reduced intensity.

Rainbows (more here) are an effect of refraction, “2” in the below diagram; whilst Glories have the characteristics of a diffraction phenomena, “1” in the below diagram.

The exact mathematics required to produce the Glory need a computer to calculate the light intensities based on Mie Scattering. The parameters are water droplet size, refractive index and angle on incidence. One thing that does seem to be required for a Glory is a fairly uniform droplet size.

Whilst Mie Scattering gives the right answer in terms of computer simulations it does not explain what is actually happening. Several theories have been tried:

Internal reflection of the light ray inside the water droplet. The issue with this is that water does not have a high enough refractive index to bend the light ray enough to return it to starting point. The best water can do comes up about 14º short.

Maybe there could be multiple internal reflections before the light ray returns to the observer. The issue here is that intensity is lost at each reflection so light reflected multiple times would be very faint; much fainter than is actually observed in Glories.

Next way an idea that light rays incident with the edge of the water droplet could propagate a short distance along the surface before being refracted and reflected off the back wall, thus making up the missing 14º. The issue with this is that the surface propagation, though possible, would result in a significant reduction in intensity of the light eventually reflected back.

The current theory is that the largest contribution to the formation of a Glory is from waves near (within 1 wavelength) of the surface of the water droplet. These waves are able to “tunnel” into the water droplet, and eventually after several shallow reflections (where energy is not lost) are able to tunnel out and return to the observer. This tunnelling effect has been observed in many areas of physics and quantum mechanical tunnelling is well known (for example in alpha particle radioactivity). However, it is a wave phenomenon and light is a wave.

So the conclusion is the Glory effect is a light tunnelling phenomena.

# What is The Spine?

The Spine is a point to point traverse of the Penine Way, starting in Edale in Derbyshire and travelling north to Kirk Yetholm in the Scottish Borders, 268 miles away.

There are 5 checkpoints along the way at: Hebden, Hawes, Middleton, Alston and Bellingham. There are three x.5 checkpoints which are not really checkpoints but timing points where you can stay 30minutes and get water. No food nor access to your drop bag is allowed. In addition, there are several other small villages and points of interest that the route passes through.

# Race Format

Its a single stage race with five checkpoints where competitors have access to a 20kg drop bag as well food, water, sleeping and medical facilities.

There is a 168 hour time limit (7 days) with corresponding cut-offs at checkpoints along the way. You can sleep at the checkpoints and along the route. The race starts 8am Sunday so you have until 8am the following Sunday to get to Kirk Yetholm.

The route is not marked by the race (except near checkpoints which are off the Pennine Way). The Pennine way itself is a national trail and is marked although not well enough to navigate by these marking alone.

# Preparation

Preparation for the race had not been ideal. I did a 100 mile race in November with the aim of taking it steadily and using it to test out some new kit. Shortly after the race, however, I developed very painful sciatica which significantly impacted my running. So I did very little training in November and December.

I pulled together all the info I thought I’d need in a spreadsheet. The mandatory kit was the most extensive of any race I’d done before. Not only were the kit items listed but extensive guidance on each item of kit was provided, e.g. sleeping bag ratings, mat sizes. I had not put much effort into reducing kit size of weight and consequently my pack was about 9kg without water so I was due to spend the week carrying between 10 and 11kg along the Pennines.

The organisers had supplied several GPX files of the route. I loaded them as sections between checkpoints and added a few waypoints for interesting items along the way. The race is a little unique in that competitors need to be self sufficient between checkpoints but can use shops, cafes, pubs, etc. along the way. It is quite difficult for newcomers to get a complete list of these unofficial aid points; folks who have done the race before seem to  build their own list. Anyway, I added waypoints for aid points that I managed to scavenge from discussion on the facebook forum.

One thing was clear though, distances between CPs is very large so I would need to carry a lot of stuff. My strategy was to try and sleep only at the CPs and eat the food provided at the CPs and just eat snacks in between. I decided to minimise sleep as much as possible.

# Registration

I arrived in Edale on Saturday morning and checked in, picking up race number 140. I had the privilege of a “full kit check” because of my race number, whatever that meant.

I chatted with a few other competitors that I knew and then decided to have a look around Buxton in the afternoon.

In the evening I checked into the Edale YHA and arranged to have dinner with Gwynn and Marcus. Back in the YHA it turned out that I was rooming with Steve who I knew from other races such as the Rebellion.

# Section 1, Edale to Hebden. 45.9miles 2,442m.

We got up at 6am and had breakfast at the YHA. I gave Steve a lift down to the start in Edale and we got our trackers fitted and waited around until just before 8am when we walked down to the start in a field next to the car park.

At 8am we setoff. It was windy and had started to rain.

We climbed out of Edale and soon hit Jacob’s Ladder on the way up onto Kinder Scout. There were plenty of people around and I settled into a pace set by those in front. It was very windy up on top and quite cold. Past Kinder Downfall and eventually onto Bleaklow Moor. In the main the navigation here was quite straightforward as I was just following people.

I saw someone in front of me slip over and sit on one of his poles; which of course broke.

We started to descend to Torside and the water station next to the reservoir.

I noticed that I was feeling lethargic. I put this down to the 100 miler I had done a few weeks before. The felling persisted for the first 48 hours of the race then I did not notice it after that.

This was also the first race I have ever done in glasses; I usually wear contact lenses. Going into the strong headwind with heavy rain it was really difficult to see where I was going. With all the water on the lenses of my glasses I could just about make out where to put my feet but following the path was difficult and navigation very difficult. I fell into just following the person in front. This is not the best idea but did work until the rain lessened.

After that we rounded the reservoir and tracked along the far side for a bit before starting to climb back onto the moors, coming out onto Wassenden Moor. There was a good path of flagstones here so progress was good.

We crossed the A62 where I was expecting at least some water but it got confusing with an aid station for another race that had setup at the road junction. The marshals were not keen to give us any water with “nothing for you here, move along”. I was not particularly bothered as I had enough water.

Next up was another moor section ahead of the M62 crossing. Here I was expecting a burger van. Unfortunately I think I was too late and there was no burger van. There were some folks offering water so I took some.

So, on we went across the very windy footbridge across the M62 and across another moor. There is a pub called the White House Pub which was closed but some folks had setup a small tent with some supplies, tea, coffee, water and snacks. It was nice to stand out of the wind for 5 minutes and resupply.

After a while the lights of Hebden Bridge came into view. The first checkpoint was a little past the town and slightly off the Pennine way.

The detour off the Pennine way is quite narrow and with all the traffic, very muddy and slippery. But we eventually arrived at CP1.

I got my drop bag given to me, handed in my running shoes and poles and sorted out some kit. The CP was very busy and there was not much space to spread anything out and my top opening rucksack and drop bag were not the best in this confined situation.

I ordered and ate some food and prepared to get some sleep. I went into the sleep area with a sleeping bag from my drop bag (which is lighter and more suitable to sleeping indoors that the one i carried in my rucksack). The sleeping area was very hot so I lay on the sleeping bag.

I set my phone to alarm in 2 hours and charged both my watch and phone.

I didn’t sleep much and remember being awake. I estimate I only slept 30-45 minutes of the 2 hours.

When my alarm sounded I got up and ordered some breakfast. I changed the batteries in my GPS and head torch, packed up my kit, reclaimed my shoes and poles and set off on section 2.

# Section 2, Hebden to Hawes, 61 miles 3,195m

This is a tough section. Its long and hilly, but there are some unofficial aid stations along the way. Also, there is the official CP 1.5 at Malham Tarn. The x.5 CPs are not really checkpoints. You have a max stay of 30 minutes before you are asked to move along and whilst water is available there is no food, you have to eat your own.

So we setoff from Hebden and retraced our way back up the narrow, muddy path. I was travelling with Colin who was reasonably familiar with the area which helped. I can’t quite remember when but Will joined us and we moved as a three.

We kept climbing and Colin kept mentioning Top Withens. On Wadsworth Moor we came across a deserted farmhouse, Top Withens, which is said to have been the inspiration for the location of the Earnshaw family house in Emily Brontë’s Wuthering Heights.

We went inside and sat down for a 5 minute catnap.

We descended off the moor and saw a sign for a cafe just off the Pennine Way, so we decided to see if it was open. The night had passed and it was now morning so we were hopeful. And yes, it was open! So we had breakfast.

After breakfast, we went back to the Pennine Way and continued onto Ickornshaw Moor.

The sun came out periodically and the rain had stopped. The wind has lessened a bit as well so this section was quite pleasant.

From here we dropped down to Cowling but there was not much there for us so we continued onto Lothersdale. The pub in Lothersdale was closed but a local triathlon club has setup an aid station so we sat there for a while and ate and drank their fayre – which was very nice of them.

After Lothersdale we joined the Leeds and Liverpool Canal for a bit. This is an interesting bridge. Looks like they built the bridge then needed to raise the road and build another bridge on top of the first.

it was a few miles cross-country to the village of Gargrave which had a Co-op. We bought a supply of ready to eat food and drink and sat outside eating it. It was getting dark and with it, getting quite cold. I was pleased to get moving again.

Next up was Airton, then Malham, but we did not stop. We were aiming for the CP 1.5 at Malham Tarn, north of Malham. This was a checkpoint that was not a checkpoint.

It was dark by the time we arrived at Malham Tarn. Will and Colin were unsure whether to try and sleep at Malham Tarn or continue. I was keen to continue. We thought we’d see how long we could stay at the CP, but they were onto us and after half an hour someone came round to point out we had to move on.

Colin and I decided to carry on. Will needed some sleep so he decided to bivvy down outside the CP on a verandah.

As soon as we left the checkpoint that was not a checkpoint, at Malham Tarn, it was obvious that the weather had changed. The wind had strengthened and it started raining. We started climbing towards Pen Y Ghent.

Pen Y Ghent is a well known hill in the area. Most people seem to translate it as Hill of the Wind or something similar. In modern welsh this would be Pen Y Gwynt. Apparently it could also mean Hill of the Border or refer to a particular tribe.

As we climbed so the wind and rain increased and so our group of 2 grew bigger and bigger numbering about a dozen. People  were becoming concerned about traversing Pen Y Ghent in these conditions. I did not have much of a view not having been up before. In the end Colin decided to try and call race HQ and see what they thought, but neither he nor anyone could get a phone signal.

So there was a lot of indecision. Colin went off to try and get a phone signal, the rest of the group continued on thinking the decision was to avoid and the summit and skirt around the lower ground.

I waited for Colin for a bit then went off to try and find him. The visibility was very low and I did not find him. So I set off on the route again. After a short while I came across the rest of the group sheltering in a farm building.

The group decision was to avoid the summit so I thought I would stick with the group. After a while, however, it became clear that folks doing the navigation were not clear on the route to avoid the summit so we passed up and down the same path a few times. Eventually, we found the path to descend the other side of Pen Y Ghent and after a while came out in Horton in Ribblesdale.

There is a cafe here (the Pen Y Ghent or PYG Cafe) that stays open 24hrs during the Spine race so we took the opportunity to order some food and drink and rest a while. I had only been in the PYG Cafe 5 minutes when Colin walked in. So he had eventually got through to Race HQ who said Pen Y Ghent was fine so he had gone over it. I picked up a 1 hour penalty for missing the summit.

After the PYG Cafe, we set off again. The weather was improving as we moved along Cam Fell. Eventually we started to drop down to Hawes. It was a long and muddy descent into the town and CP2.

We were all very tired when we arrived at the CP.

I handed in my shoes and poles and had some food and drink. Then I sorted some kit out and prepared for a sleep. There were bunk beds here so no need for a sleeping bag.

I planned for a 2 hour sleep here and found an empty bunk. As I was drifting off, it became apparent that one of my fellow Spiners had the loudest snore that I have ever heard. In both the human and animal kingdom. This snore was not just loud; it was deafeningly laud. I have no idea how this guy was not waking himself up with each breath; but unfortunately he was not.

After a couple of minutes it became apparent that I was not going to be able to ignore this noise. I was just about to get up and go find another room to sleep in when someone else had the same idea and noisily got up, moved about and left the room, slamming the door behind him. This seemed to wake snory guy up as the snoring stopped. I fell asleep.

My alarm went off after 2 hours. My estimation is that I had slept for about 1.5 hours.

I got up and had some breakfast. I also thought I would get a medic to have a look at my feet as I was having trouble with blisters on the little toes of both feet. I was wearing toe socks which I am normally OK with but the very wet underfoot conditions I think were causing more wear and tear than normal. I think if I were to do the race again, waterproof socks would be the way to go.

The medics did a good job of dealing with the blisters and taping up my feet a bit.

I sorted out some more kit, packed it all up and prepared to set off. I had arranged with Colin to set off at 3pm and had got up at 2:25 but had not seem him. I asked a couple of folks but nobody had seen him. So either he could not sleep and had already left, or was still sleeping. I decided to set off on my own to make use of the hour or so of daylight.

# Section 3, Hawes to Middleton, 33.7 miles 1,871m

The first section was a big anti-clockwise loop over Thwaite Common to the village of Thwaite. There is a cafe here, but it was dark when I arrived and the cafe was closed. So I continued on with a steep climb before starting to contour along a river valley. Somewhere along here I missed the path and found myself too high and had to shimmy down and a steep bank. Back on the path I went up onto Stonesdale Moor. It was raining hard again now.

I was moving well on this section which was slabbed in the main. The moor was quite bleak but eventually the lights of the Tan Hill Pub came into view (the highest pub in England).

The kitchen was closed but they did me tomato soup, cake and 1 pint of coke.

My feet were beginning to swell and getting going after the Tan Hill Pub was a little difficult. Not helped by getting a few hundred meters out of the pub before discovering I had left my poles there!

I don’t remember much about the next section except that the flag stones ran out and the ground was very boggy and therefore progress was slower. Eventually, I arrived at Middleton and CP3.

It was the usual checkpoint process but I decided to go for 3 hours sleep rather than 2.

On waking up, I had breakfast, did the necessary admin and prepared to setoff again. I then saw Colin just arriving at the CP. He said he had overslept at Hawes. I also saw Will who said we had slept at Malham Tarn for an hour or two and felt fine so had continued and was obviously doing very well.

# Section 4, Middleton to Alston, 38.5 miles 2,002m

Setting off from Middleton, the Pennine Way heads west towards Dufton. The first part of the route is quite straightforward along the River Tees and some rapids.

The weather had improved again and the sun was out, so all was well. As I followed the River Tees so the terrain became more and more remote. Some quite long scrambling sections followed that were slow going. The light was fading so I was keen to get as far as I could before night settled in.

After quite a while I came to Cauldron Snout which is scramble next to a cataract upto the Cow Green Reservoir. At this point I got out my head torch and prepared for nighttime.

The next section was fairly easy to travel and then we arrived at High Cup which, by daylight is supposed to be a spectacular view. Visibility was low when I got there and staying on the path at the top not easy. The path got easier further down, though, and was easy to follow to Dufton. I met up with Carlos and Ken and we started travelling together.

Checkpoint 3.5 was in Dufton. It was another of the x.5 checkpoints, that are not really checkpoints. Just before the CP, was a cafe that was open. We jumped in for a meal which was great.

They were just closing up so one more Spiner got in before the cafe closed.

After the cafe we moved along to the checkpoint. We only stopped there a few minutes.

After Dufton the path is very muddy as it heads north and starts to climb. The is the climb to Cross Fell the highest point on the Pennine Way, at 893m. The weather was getting worse and we were told in Dufton to expect high winds, snow and -18C at the top. It did not disappoint. I was struggling to get moving after the stop at the cafe and Carlos and Ken pulled away from me.

At the top I saw a head torch and headed over thinking I was near Gregg’s Hut. It turned out to be a guy called Javed who was camping out there for some reason. He gave me a biscuit and a piece of cheese which was very nice, and pointed me in the direction of Gregg’s Hut.

Gregg’s Hut is not a checkpoint but a welcome aid station on the Spine. There is an entrance porch that leads to an outer room which itself leads to an inner room. In the inner room, John Bamber cooked us chilli noodles and hot chocolate. Perfect!

Carlos and Ken were in the hut so we determined to set off again together.

It was good to get over Cross Fell and as we descended so the wind eased. It was very cold though and we hurried along to stay warm. The descent is quite easy to navigate and we soon picked up a road that took us down to the village of Garrigill.

I thought we were close to the checkpoint here and refused the offer of some refreshment that a Filipino lady was making. Probably a mistake as it took forever to travel the last few miles. The navigation across fields was awkward and slow. Ken had disappeared by this point and Carlos and I trudged on slowly.

Eventually we arrived at CP4!

Usual checkpoint procedure with a 3 hour sleep. Again, as usual, on awakening I sorted out and packed up kit, ate breakfast and set off.

# Section 5, Alston to Bellingham, 40 miles 1,674m

Andy suggested we travel together and this sounded good so we set off from the Checkpoint.

The section after the CP at Alston is low lying farmland which is muddy and moreland and quite boggy. Blenkinsopp Common eventually leads to the village of Greenhead. There is a pub and cafe in Greenhead off route but we were not confident they would be open when we got there so we passed on by.

Instead, there is a museum as the Pennine Way leaves Greenhead. And associated with the museum are some public toilets which are unlocked at night. So in we piled. There were already some other Spiners there and inside the building was much warmer than it was outside.

So this was time to use my stove (with a urinal providing a water feature in the background) and try a freeze dried meal.

After our meal some people wanted to bivvy down for an hour or two but I decided to push on. Andy came with me.

The next section was quite hard as it followed the undulating ground of Hadrian’s Wall. Navigation is, of course, quite easy as we just followed the Wall but the terrain is quite hilly so progress was slow. The weather had improved and the moon was out which was quite spectacular. I attempted to take some photographs but for some inexplicable reason failed to take any!

Andy was getting tired by now and kept sitting down for a catnap. I would head on and then he would catch me up. This happened a few times then I think I pulled away.

I eventually headed north through the wall. I went through some wooded areas and some moorland. It was very cold.

I had used up the water in my soft flask and then realised that my bladder had frozen up. Initially I thought it would just be the outflow pipe that had frozen but after removing it from my backpack I realised that the screw cap fill had also frozen.

Although there was some ice in the bladder most of it was liquid. I just could not get at it. It would have been easy to make a hole in the bladder and decant the water to my soft flask but that would have been a bit destructive. I tried warming the bladder on me but that did not seem to work.

So i decided to pee on the frozen inflow cap. That worked and thawed the ice sufficiently for me to be able to remove the cap and decant water to the soft flask.

I started noticing hallucinations at about this point. They seemed to follow the following format:

• In the distance I would see African animals (elephants, rhinos, lions) or cartoon characters or zombies.
• If I looked away and back again the original hallucination would be replaced by a European type animal; horse, dog, etc.
• When I got nearer the secondary hallucination would disappear and I would see a bush.

Sometimes the cartoon characters would laugh and point at me. The zombies would try and chase me. The African animals never took any notice of me.

Next up after a few miles was a farm called Horneystead which acts as an impromptu aid station.

The farmer seems to like walkers and has kitted out one of his outbuildings into a little den with food and drink. Perfectly possible to sleep there and top up on supplies. He even has some spare kit. I make a coffee and had a couple of snacks. I put some money in the honesty box and was on my way.

My feet were very painful by this point and each step hurt. A lot. They were very swollen and being crushed by my shoes. This seemed to be the major source of pain. I was thinking about cutting open my shoes to relieve the pressure but was concerned that on the boggy terrain this would lead to other problems.

In the end I left the shoes as they were.

It was not too far to Bellingham and CP5, but a miserable few miles just the same. I was very tired when I arrived just as the daylight began to fade.

I thought I would maintain the same checkpoint routine, eat, sort kit out, sleep 3 hours, get up, sort more kit out, pack up kit, get feet sorted and re-taped, eat breakfast and leave.

# Section 6, Bellingham to Kirk Yetholm, 41.9 miles 2,146m

I got up and started on the painkillers straight away. The recommendation from the medics was for paracetamol and to avoid ibuprofen. I thought I’d start with paracetamol and keep the ibuprofen in reserve. My feet were not quite as swollen as before I went to sleep so that was a good thing.

I took my flask out of the drop bag for the first time at this checkpoint and it filled with sweet, milky coffee.

Setting off out of Bellingham, I was soon onto moorland. The next milestone was another x.5 checkpoint, CP 5.5 at Bryness so I was motivated to get there.

After the moorland there was a long section of road and then forrest fire track. Progress was quite reasonable. A couple of miles before Bryness I met two Mountain Rescue folks marching straight towards me. They asked me how I was before marching off the way I had come.

I continued on towards the x.5 checkpoint (that is not a checkpoint).

I got there and Chris, Carlos and Ken were already there. They make us a drink and I got my flask refilled with coffee. Then there was talk of the “casualty” which did not sound very good.

A few minutes later the two Mountain Rescue folks burst into the CP matching a competitor who was shivering badly. They went straight into a small room next to where we were, that evidently had been warmed considerably to reheat the guy suffering from hypothermia. Apparently he was bivvying outside and had become hypothermic and pressed his emergency beacon.

Then we got the nod that our half hour at the CP was up and we had to move on. Chris, Carlos, Ken and I decided to move on together to the Cheviots.

We were told it was going to be very cold and very windy.

Next up was a steep climb through a forest up Byrness Hill. There was no wind and we were all overdressed and sweating. As we came out onto the moor the breeze picked up and the temperature dropped. It was now cold!

The next section was, for me, the worst of the race. The sleep monster was calling to each of us and our pace was very slow. Not only that, we were lurching along in a zig zag pattern rather than staying on the path. We would each fall half asleep then trip on a rock or tussock which brought us back into the world of the conscious only to slowly drift off again.

And on we trudged. We were all quiet; even the normally talkative Carlos.

I was cold because we were moving so slowly. My feet were getting painful again, making progress more difficult.

Had there been anywhere to rest, we would have done. I was certainly concerned to stop after witnessing what we had back at Bryness, and I think the others would have felt the same. I am not sure how we kept going through the night but we did.

As it started getting light so the sleep monster’s grip on us started to wane and the others picked up the pace. I was struggling at the back with my very painful feet. Eventually the others pulled clear.

The hallucinations were back. I remember seeing a field of sheep with an elephant and 2 lions. I wondered way the sheep were not bothered by the lions. Then the lions and the sheep turned into bushes.

Around Lamb Hill we came across Hut 1. Not much had been made of this by the organisers so we were not sure what would be there for us but as I arrived I saw a few sets of poles outside so it was obvious there was something going on.

Inside a couple of folks were making hot drinks and food. Chris, Carlos and Ken were there as well as a couple of folks just leaving. I got a hot drink and made up a freeze dried meal.

Chris, Carlos and Ken were keen to move on so left. By the time I packed everything up they were out of sight.

The next section along the Cheviots was relatively easy to navigate. The Pennine Way follows a fence marking the boundary between England and Scotland and the path is reasonable. Everything was frozen so it was nice not to have negotiate bog.

As usual getting going after a stop was very painful and slow.

I trudged on alone for several hours before the ground starting rising sharply. After a while there was a sharp left handed bend and we started descending towards Hut 2, the last timing point on the course before the finish.

I caught up with Carlos.

It had been foggy for some some time and as we descended so the fog came and went. Then the sun appeared on the left and over to my right I saw an apparition. It was not an average hallucination! I knew what it was, as I had seen photos but have never seen one in real life before; a Glorie or Brocken Spectre. I got my phone out to take a picture but it disappeared!

I walked on a bit and suddenly it reappeared. Wow!

So the figure is my shadow (the sun is behind me) distorted by perspective and the halo of light is the sun reflected by the mist. The “white” light of the sun is broken into constituent colours like a rainbow. But there are some interesting things here:

• Blue light is nearest the centre, red furthest away. This is opposite to a rainbow where red is nearer the ground, blue furthest away.
• There is a fainter set of rings outside the primary blue to red set of rings.

If you are interested I did a bit more research on Glories here.

A little bit further along we came to Hut 2 and had a chat with the folks there.

It was mid afternoon and I thought it would be good to see if we could finish before dark. Carlos was not too keen so we separated.

It is mainly downhill from Hut 2, but there are a couple of hills before the descent proper starts. They told us it was about 7 miles down to the finish.

I hobbled on as fast as I could; which was not very fast.

It was dusk when I saw Kirk Yetholm in the distance after climbing the last hill. A short jog later I was at the Border Hotel, touching the wall to finish my Spine race.

Colin, Carlos, Ken and Andy all finished. Hypothermia guy was at the Border Hotel as well looking pretty chipper!

# Race Statistics

The race distance is 268 miles long with 36,000ft of elevation.

There were 123 starters and 70 finishers. I came 46th. I took 153 hours to complete the course. I tried to sleep for 13 hours, and probably did sleep for 11 hours 15 minutes during the race.

# Lessons Learned

1. My backpack weight just under 9kg without water so would have been between 10 and 11kg during the race. If I really tried I could probably cut this in half.
2. My strategy of sleeping only in the CPs worked but was inefficient. It would be more efficient to sleep along the route as you can sleep when you want and without disturbance. I would practice this before doing it though.
3. My backpack (UDFP35) was big enough but only openable from the top so not possible to take the bottom items out without taking everything out.
4. I think cat-napping for 10 minutes when really tired, for example, at Bryness would have helped.
5. Shoe / sock combination did not work very well. I think waterproof socks would have really helped in the first 3 days when it was very wet. My feet got waterlogged which I think contributed to my blister problems. Feet also swelled up significantly which I think was due to lack of training in the run up to the race due to injury. A bigger size of shoe in the drop bag would have been good.
6. Hokas were OK (not so much grip on the muddy sections) but gentler on the feet.
7. I carried poles but did not feel I really needed them. They are useful on very steep ground (not much on the Pennine Way) or when very slippery. The rest of the time I did not find them very useful.
8. My primary headlamp (LedLenser H14R2) stopped working, due I think to water ingress. Good to carry 2 headlamps.
9. Navigation is generally quite easy with a GPS on the Pennine Way. I used my watch and a Garmin Etrex 30x. This combo worked well. I did hear of people’s GPS units freezing in the cold weather so it is worth having a backup unit. Going to map in high winds, low visibility is not very practical unless you are a hardcore map user.
10. Good waterproofs are vital. Use many clothing layers to allow for large temperature variations.
11. The goggles on the mandatory kit list got quite a bit of use. The winds were for the most part side winds with the occasional head wind. Some people did have eye issues from the winds.
12. Some folks took a front pack for easier access to things like food. This is worth considering.
13. Waterproof gloves. I’ve never owned a pair despite trying a few pairs that have claimed to be waterproof. I wore a thin pair of liner gloves and a thicker pair of “waterproof” gloves over the top. This was OK except on the wettest sections when my gloves became waterlogged. I saw a few folks with toughened rubber over gloves that would be genuinely waterproof. I would get myself a pair of these if I was to do the race again.