WATER TOWER

[Foureyes]

Does anyone know the height of the water tower?
This question was posed once before, but while it generated many remarks and reminiscences, not one answered the question!
So, to be specific, what is the height of the water tower (answers in feet or metres, don't mind which)?
David

[brian walling]

In my day it was clearly known as being 120 feet high. In a Maths class with I R McConnell we once did some trig exercises and surveyed the tower with some rudimentary surveyor's tools, so I remember the 'official' height clearly. Not sure whether the quoted height of 120 feet was to the peak of the roof or to the top of the flagpole.

[LongGone]

In my day it was clearly known as being 120 feet high. In a Maths class with I R McConnell we once did some trig exercises and surveyed the tower with some rudimentary surveyor's tools, so I remember the 'official' height clearly. Not sure whether the quoted height of 120 feet was to the peak of the roof or to the top of the flagpole.

That was my precise recollection also. I remember the entire class measuring the angle to the top from points in the Quad. Presumably we were told the horizontal distance so we could calculate the height.

[Foureyes]

Thank you both. That is really useful for some research I am conducting.
David

[brian walling]

An interesting ‘aside’ from the underlying topic:

Quite coincidentally, the CH Water Tower and its height were fresh in my mind yesterday when I answered the original post. My wife’s family in UK has ancestral links to a small town in central Germany and just the day before yesterday we unearthed a new fact about the German family in the 1800s. They held the position of town watchman and resided in a small house built on top of the town’s fortified medieval church tower. The tower is listed as being 36 metres or 120 feet high. This immediately struck me as being exactly the height of CH’s tower. Imagine living that high up (300+steps) and even being born up there, as the children were, including the one who subsequently emigrated to England. The ‘live-in’ arrangement ended in the 1840s, but the tower-house survived and you can now have your wedding up there if you want something unusual.

[LongGone]

In my day it was clearly known as being 120 feet high. In a Maths class with I R McConnell we once did some trig exercises and surveyed the tower with some rudimentary surveyor's tools, so I remember the 'official' height clearly. Not sure whether the quoted height of 120 feet was to the peak of the roof or to the top of the flagpole.

That was my precise recollection also. I remember the entire class measuring the angle to the top from points in the Quad. Presumably we were told the horizontal distance so we could calculate the height.

In an unusual flash of memory, I believe we didn't need to know how far we were from the tower. An initial location is noted when the angle is 45o and a peg is placed. Since tan45 =1, we are now the tower's height away from it. We then moved directly away until the angle is ~27o, at which point the tangent is 0.5 and we are now twice the height away. Measure from here to the peg and multiply by two. QED

[William]

LongGone is totally correct. But what if you could not approach close enough to the tower to find that it subtended the angle 45 (or 27) degrees? Any two angles will do, not only 45 and 27 degrees, say A & B. Measure one (it’s A). Then walk a measured distance y directly away from the tower. Then remeasure the angle to the top of the tower. It’s now B. The height is H, so

H = y.TanA.TanB / (TanA – TanB) You know A, B, and y, so Bob's your uncle and QED.

I’ll leave it to a genius to prove I’m right (or wrong). And I’ll leave it to a greater genius to decide if the tower’s height can be measured, using this method, if the ground slopes away from its base, for miles and miles and miles (and if so how). Enjoy.

[loringa]

LongGone is totally correct. But what if you could not approach close enough to the tower to find that it subtended the angle 45 (or 27) degrees? Any two angles will do, not only 45 and 27 degrees, say A & B. Measure one (it’s A). Then walk a measured distance y directly away from the tower. Then remeasure the angle to the top of the tower. It’s now B. The height is H, so

H = y.TanA.TanB / (TanA – TanB) You know A, B, and y, so Bob's your uncle and QED.

I’ll leave it to a genius to prove I’m right (or wrong). And I’ll leave it to a greater genius to decide if the tower’s height can be measured, using this method, if the ground slopes away from its base, for miles and miles and miles (and if so how). Enjoy.

Good point and only one thing: I make the calculation H = y.Tan A.Tan B / (Tan B - Tan A)

If Angle A is less than Angle B (which it is in this case) then Tan A - Tan B will be negative in which case H will be negative. OTOH I am not a genius, not even much of a mathematician, so I could easily have made a mistake but I did enjoy trying to prove (confirm?) your supposition.

QED or, as Bob Rae would have said, Quite Easily Done. As an aside, when I did my teacher training just a few years ago, I was advised that we didn't use QED any more but no-one could tell me why. Perhaps they thought it was elitist as most schools don't offer Latin nowadays but they could hardly object to Bob's explanation.

[Katharine]

In days long gone by, I used to set such example for classes, now I have to THINK about it!

I thought A was nearer the tower, so the angle bigger there, which makes gives h = (ytanA.tanB)/(tanA -tanB) the problem changes if the land isn’t level.

[loringa]

I thought A was nearer the tower, so the angle bigger there, which makes gives h = (ytanA.tanB)/(tanA -tanB) the problem changes if the land isn’t level.

Yes indeed - read the b****y question Andrew! Thanks Katharine - I'd better not tell my dd who is now not about to sit her GCSE in maths and further maths but is moving on to the A Level with me coaching her from 3000 miles away!

[J.R.]

I never really did like maths !

[Katharine]

I never really did like maths !

It would have been different had I taught you, John!!! I loved the challenges!

[jhopgood]

How did you know the location of the base of the tower?

[AMP]

An interesting ‘aside’ from the underlying topic:

Quite coincidentally, the CH Water Tower and its height were fresh in my mind yesterday when I answered the original post. My wife’s family in UK has ancestral links to a small town in central Germany and just the day before yesterday we unearthed a new fact about the German family in the 1800s. They held the position of town watchman and resided in a small house built on top of the town’s fortified medieval church tower. The tower is listed as being 36 metres or 120 feet high. This immediately struck me as being exactly the height of CH’s tower. Imagine living that high up (300+steps) and even being born up there, as the children were, including the one who subsequently emigrated to England. The ‘live-in’ arrangement ended in the 1840s, but the tower-house survived and you can now have your wedding up there if you want something unusual.

I would be interested to know the name of that place - worth a visit if I am ever in the vicinity

[Great Plum]

Is it not something like 6 feet lower than Sharpenhurst to balance the water from the reservoir there?