Maidenhead to Marlow
MAPS
HEIGHTS

CLOG Walk: 8th August 2015


Where ? Map Heights Figures Gradients Extra Timing Track Finally Read Me



Features of Our Walk

Our walk of about 11½ miles or 18⅓ Km largely followed the curve of the River Thames upstream from Maidenhead to Marlow, with the main climb reserved for the afternoon. Cookham of Stanley Spencer fame was on our route, as was Winter Hill, with its "Toad of Toad Hall" connections and its fine views over the southern reaches of Marlow. We gained a maximum height of 109 m (358 ft). Our total ascent for the walk was, to be reasonably precise, 531 feet or 162 m; average rising and falling gradients weighed in at 2.5% over about 4 miles and 3.1% over 3¼ miles - not too strenuous. As the pictures show, we enjoyed sunny August weather and as the heights indicate, it was a relaxed walk.




A peaceful scene on the Thames
before we reach Winter Hill.

Now prepare ye for some plots and graphs. Not too overwhelming, but hopefully quite interesting! You will see here:



How far were we from the Centre of London?

We started our walk at Maidenhead Station (MAI), reaching Marlow Station (MLW) towards the evening. The two stations are both within 28 miles (45 Km) west of the centre of London. The centre of London is officially taken as the intersection of The Strand, Whitehall and Cockspur Street. This intersection is often referred to as Charing Cross, not to be confused with the nearby Victorian Eleanor Cross itself, nor the station in front of which the cross stands. The detailed figures, for the fun of it, are as shown below.


Maidenhead and Marlow Stations are both within 28 miles of the centre of London.

Our "straight line" distances are actually "great circle" distances on the earth's surface. To calculate these we assume here that the earth to be spherical, which is not far off the mark. Assuming the earth to be a sphere gives us a maximum error of about 0.1% in our distance values. Not that much really! Can't complain! Indeed, we can speak of the distances as the "hypothetical crow" (cornix hypothetica) flies.


Cornix Hypothetica, our hypothetical crow,
isn't any old bird, as we should know.
Cornix Hypothetica! Many miles for us you go,
with many a "straight line" o'er Earth to show.

Our walk was within 28 miles of the centre of London (the 3-way road meeting point of Charing X). Maidenhead, the start of our walk, is in easy reach of London, Paddington Station of Great Western Railway fame no less.


Our walk was well within 50 miles of the centre of London
(the 3-way road meeting point of Charing X). On the above map,
Degrees Latitude and Longitude feature on the Y and X axes respectively.


Outline Map of Our Walk

Our walk was topologically linear but was actually shped like the letter "S"! The map grid scales translate to 1.112 Km per 0.01° latitude and a mean of 0.681 Km per 0.01° longitude, all when using 6371.0 Km as the volumetric mean radius of the earth - as per the WGS84 standard! In Scales, in the Lake District, the longitude scale is less (as expected), with a mean of 0.644 Km per 0.01° longitude; in fact, it is 37metres per 0.01° longitude less than in Maidenhead!


Outline Map of Our Walk
Y and X axes are in degrees latitude and longitude respectively.

Our walk has wriggled about a bit, hugging the northern reaches of Berkshire and finally, getting into Buckinghamshire. Here are few numbers. The minus signs for the longitude angles indicate "degrees west of Greenwich". The map grid scales translate to 1.1119 Km per 0.01° latitude and a mean of 0.6914 Km per 0.01° longitude, all when using 6371.0 Km as the volumetric mean radius of the earth - as per the WGS84 standard! It is interesting to compare the present longitude distance-to-degree ratio with that for other walks. It you do this, you will see that the further north you go, the less Km per degree longitude you get. Once you get to the Lake District the reduction in this ratio compared to that for walks in the south-east is quite noticeable. In Scales, in the Lake District, we already have a slightly smaller value of 0.644 Km per 0.01° longitude - a difference of 47 metres per 0.01° longitude compared with our present Berkshire walk.

Because we don't live on a flat earth - unless you are a convinced "flat earther" - maps are inevitably a distortion of what is. In other words, it's all a matter of mapping a curvaceous surface onto a flat surface. We don't want to carry curvaceous representations of the terrain on our walks, do we? In our case, the northern length of our map grid is stretched out by an extra 0.18 %, to make it the same on the page as the length of the southern part of our map grid. Not that much for hiking purposes really! Can't complain.



Height Profile of Our Walk

This height profile emphasises that our main climb was in the afternoon. In fact, we visited at least three reasonably distinct "high points", of which, Winter Hill, (at about 96 m) gave us a nice northerly view, and the highest point (at about 109 m) at the top of Cookhamdean Common, allowed us to see the distant Surrey Hills. In the morning we "bobbed along" at about 28 m on the banks of the River Thames. Remember, we were some way up from "Tide End Town", or Teddington as it is now known today.


Height Profile


Some Facts and Figures

Here are some "vital statistics" in metric and imperial units. Start and end elevations are almost the same. Of course, the total ascent (here 162 m) usually exceeds the difference between maximum and minimum elevations (here (109 - 25) m or 84 m); I'd suspect things, if the reverse transpired! The total distance, as always measured on a conceptual "flat" plane at mean sea level, is 11.43 miles or 18.39 Km.


"Walk facts and figures"


Gradients

Here we look at three aspects of the gradients on our walk. There is the issue of assessing gradients and how reliable that assessment can be. Average gradients for calculating the toughness of a walk are also considered. Then there is the gradient profile.

Assessing Gradients

Assessing gradients can be a mathematically noisy activity. Essentially we are dealing with derivatives which unlike integrals (anti-derivatives) can introduce noise. Hence comments made in this "Gradients" section should only be seen as indicative. Repeatibily with a different set "latitude,longitude" pairs, for the same walk map, cannot be assured!

Average Rising and Falling Gradients


Rising and Falling Gradients

And here, for the numerical fun of it, are the average gradients we overcame on our walk. The rising and falling (negative) gradients are both averaged over the distance given, with level stretches having rises and falls of less than ± ½ metre. By comparison, Hertfordshire County Council recommends that its roads should not have longitudinal gradients of more than 5% and one of the steepest adhesion railways in the world, in Austria, has a maximum gradient of 11.6%. By way of further interest, the clockwise route of the Fairfield Horseshoe in the Lake District has a total distance of 15.62 Km (9.71 miles), with the following calculations: an average rising gradient of 14.66% over 6.589 Km, a level part over 0.345 Km, and an average falling gradient of 11.11% over 8.676 Km. This is seen by many as really quite challenging - but then, when you compare it with our Saturday Thames-side walk, it can be said that on our Thames walk we had a more leisurely and less demanding aim compared with Lakeland challenges!

Gradient Profile


Gradient Profile

This graph shows how the gradients vary with the distance into our walk. On this graph, I have really superimposed two plots.

  1. Height. One plot is a repeat of the height (elevation) plot above, but now in pink. The vertical scale does not refer directly to this Gradient Profile graph, except to say that its scale is proportional in magnitude to that required for the height plot, and its vertical zero is correctly positioned.

  2. Gradients. The main (blue) plot represents the gradient (rising - positive, falling - negative) at each measured point of our walk. As some of you know, differentials are notorious for introducing noise. I have done some mild smoothing by looking at the gradient over the two neighbouring points either side of each central reference point on the horizontal distance (x) axis.
As might be expected, the gradients are greater in the hillier area of our walk. Rising gradients reach a maximum of over 11% and the maximum falling gradient reaches over 16%. Interesting if you like that sort of thing - I mean, not in theory but out on your walk!.



Extra, Less Quantifiable, Considerations

On any walk there are considerations which are very real but tantalizingly out of ready reach of those who wish to espouse a numerical approach to many of life's activities. Here are three considerations for starters.



Timing and Speed

It's one thing to discuss the terrain over which we walk. It's quite another to ask how we personally respond to walking over that terrain. There are a number of considerations, of which timing and speed can be taken as starting points.



Track File

If you are keen to see our walk superimposed on an Ordnance Survey® (OS) map, then you can use the following file to do so. The numerical data in this file were recorded on my GPS (Garmin®). The data are based on WGS84. Of course, for copyright reasons, I do not show the OS-based map here. Furthermore, the plot may also include some walkabouts in hostelries and sightseeing places; hence there may be a slight over estimation of the length by perhaps 0.5 Km.

Maidenhead to Marlow



And Finally - a Matter of Practicality

Any map is an approximate representation of what is. Practicality and scale are relevant considerations. We are not dealing with a planning application calling for detailed spatial descriptions of intricate boundaries. For us in the hiking community, the degrees of accuracy and precision should be just enough to give us useable and helpful knowledge of the terrain about us and beneath our feet. I hope my humble endeavours on this page are in this respect interesting for, and useful to, you my reader!