Mathew Newton wrote:
On 14 Mar, 13:09, wrote:
Mathew Newton wrote:
Where did your 7.6m come from?
I'm not one for advocating overdoing things on a ladder however it
sounds to me like the 7.44m will be 'plenty' big enough....
My understanding (based on something I'd read on the net in the last
day or 2) is that a ladder should lean at a ratio of 1:4 (ie ground to
height). So to get 6.1 metres up you need to add roughly 25% to allow
for leaning, hence 7.6m

It's over 20 yrs since I did any geometry / trigonometry & I've got a
feeling that the paragraph above probably demonstrates that clearly...

Michael

They do say if you don't use it you lose it!

Your calculations are (wrongly) assuming that the ladder length is the
sum of the 'ground length' and 'wall height'. That is, 6.1/4 + 6.1 =
7.6m.

However this is not so, the relationship is actually ladder length ^2
(squared) = ground length ^2 + wall height ^2 (Pythagoras rule for
right-angle triangles). However that doesn't really help us
directly...

A more useful function for this case is the trigonometry rule tan
angle = wall height / ground length. For our 4:1 ratio we have tan
angle = 4 / 1 hence Inv tan 4 = 76 degrees. This is the optimium angle
for the ladder.

Also, we know that sin angle = wall height / ladder length. Hence
swapping everything around gives us ladder length = wall height / sin
angle. Using our figures we get 6.1 / sin76 = 6.3m. That is, the
ladder length is actually not all that much more than the height.

Of course these calculations don't take into account the fact that you
want the top of the ladder to extend beyond the working height, and
some spare rung overlap would be also be nice (if only to allow you to
remind yourself 'I could be higher and still be safe'!).

A 7.44m ladder would therefore, in your case, be fine.

Mathew


In practice you often don't have the space for the correct angle, in
which case you tend to hug the ladder rather more