Unofficial Christ's Hospital Forum

brian walling wrote: Sun Mar 22, 2020 10:58 am 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 wrote: Sun Mar 22, 2020 7:28 pm

brian walling wrote: Sun Mar 22, 2020 10:58 am 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.

William wrote: Tue Mar 24, 2020 5:01 am 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.

Katharine wrote: Tue Mar 24, 2020 9:33 am 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.

J.R. wrote: Tue Mar 24, 2020 11:59 am I never really did like maths !

brian walling wrote: Mon Mar 23, 2020 2:12 am 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.