How many leaves?

An autumn maths puzzzler

1 to 20 of 31 messages
16/11/2013 at 16:00

So, this afternoon I filled 3x 60x60x60cm bags full of leaves from my front garden,

The garden is about 8x8m square with a mature magnolia in the middle and there is a mature sycamore outside the front gate.

The magnolia has about 20% of its leaves remaining and the sycamore about 10%

How many leaves do you reckon are in the bags?

(FYI - I haven't got a clue I just wondered if anyone fancied a guess )

16/11/2013 at 18:36

About 50% less than if you had filled 6 similar bags?

16/11/2013 at 18:37

All of them ?

 

16/11/2013 at 18:44

Definitely not all of them.

16/11/2013 at 19:06

I'd simply calculate the number. 

Take 100 leaves.

Weigh them. Establish the average weight.

 Weigh the whole lot.

There you go.

16/11/2013 at 20:17

Wet or dry?

16/11/2013 at 20:53

And how many of each type should be included in the sample base ?

 

 

16/11/2013 at 20:58

Ah, good point...

16/11/2013 at 21:27

One.  I read it and now I leaves.  

QED. 

17/11/2013 at 07:10

Ok, just take and weigh a random handful of leaves and count those etc

17/11/2013 at 09:28

You'd need to be careful about where the sample comes from so it doesn't get overly influenced, for instance taking the sample from the ground around the magnolia on the opposite side of the sycamore would likely give a higher ratio of magnolia to sycamore.

whilst we have been given values of the leaves remaining on the branches, we don't know the value remaining the last time they were cleared, this could affect the ratio of any sample. We also don't know the direction of the prevailing wind. Is it blowing the sycamore leaves into the garden, or the magnolia out?

Questions, questions......

 

Is the answer 42?

17/11/2013 at 12:09

Lots.

17/11/2013 at 16:04

There were definitely lots  

Chimney: happy to help. This was the first time they were swept up this autumn so I was dealing with 100% of leaf fall so far. The prevailing wind has been from the SW at varying strengths from gale force to very calm.  Fences on either side and a front wall mean that once they are in the leaves can't get out except in the event of  upward force such as a tornado.

Other that that do you think it's worth asking Brian Cox?

Edited: 17/11/2013 at 16:04
17/11/2013 at 16:12

Hold on Brian Cox for now. RicF may need to reassess this new information first

 

17/11/2013 at 17:37

More than 10. 

17/11/2013 at 17:51

http://wetlandnotes.com/estimating-the-number-of-leaves-on-a-tree

This seemed promising initially but I lost interest when it got to the bit about overlap.

17/11/2013 at 19:20

Thank-you Screamy, that is very helpful. Do I take it a SW wind blows directly into your garden, therefore the leaves from the Sycamore will be mostly blown, and remain, in your garden? Is there evidence of Sycomore leaves on your roof? And any evidence of being blown over your roof? This will of course complicate matters and using LAI values will as a consequence be an inaccurate guess.  Just because a leaf was on the tree, doesn't mean it ended up in one of the bags. There is also the possibility of leaves other than the sycamore and magnolia ending up in your garden.

However, there is a possible solution for you. If your estimation of the amount of leaves left on each is correct, you could count the leaves you have left to extrapolate an answer for how many leaves 100% is. There would still be the matter of the leaves that became dis-attached from the tree but aren't in your garden, but these may have been compensated for by leaves from other trees as noted above, also those that have been consumed by animals, bacteria etc would need to be given a value. there would be an amount that have been partially consumed, would you be counting each partially consumed leaf as a leaf or combining them to count as a whole leaf to reach the number of leaves in your bags?

Still too many variables......    ;-) 

978,654 

 

Am I right?

 

Do I get a prize?

 

make it a Forerunner 620 with new HRM, or a place on the Asics 26.2 team

17/11/2013 at 19:48

The sycamore is to the north of the front wall, so the stronger the wind, the less likely the leaves are to end up in the garden. It is also much taller than the magnolia so there is definitely a higher ratio of magnolia to sycamore leaves.

The partially consumed leaf scenario is interesting at what stage does a leaf officially become compost?

978,64 certainly constitutes "a lot" so you may well be correct within a certain margin of error.

Would you accept a small sapling as a prize?

17/11/2013 at 19:54

It would certainly be easier than it would for you not to be an unutterable twat. Well, anything would.

Edited: 17/11/2013 at 19:56
17/11/2013 at 20:03

Ah, blowing the Sycamore away, umm. That makes a difference to those calculations I have been poring over all afternoon and I shall just have to start again.

The offer of a sapling will indeed come in handy as I can then use it over the years to further refine my model with the sole aim of coming to an exact number of leaves you have in the bags. 

Your thoughts on when a leaf becomes compost weighs heavily on my mind. I accept that it will take some time for me to work through everything so we will need some way to keep your leaves in the state there are. I had thought of simply freezing, but when it comes to defrosting them there could be issues. Perhaps placing them in a vacuum? A Hoover would be fine, or maybe a Dyson. Perhaps a different type of vacuum would be better though.

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