On 18/05/16 18:24, Chris Hogg wrote:
On Wed, 18 May 2016 18:06:54 +0100, The Natural Philosopher
wrote:

On 18/05/16 17:17, Chris Hogg wrote:
On Wed, 18 May 2016 13:59:31 +0100, Chris Hogg wrote:

On Wed, 18 May 2016 11:45:44 GMT, lid (AnthonyL)
wrote:

Out of curiosity, anyone calculate how many panels
would be needed to lift one ton(ne) in say 6hrs of average light?

To make that question sensible, you'd need to specify the height
you're lifting it to.

Here's a calculation (stepwise, for my benefit, and to allow it to be
torn to shreds by those who can do it better, as I don't believe the
result!).

The upper lake at Dinorwig is a little over 500 metres above the lower
lake, so I'll assume a height of 500 metres.

1 tonne exerts 9806 Newtons of force.

The work done raising 1 tonne by 500 metres is 9806x500 = 4903000
Newton-metres.

A Joule is 1 Newton-metre, so the work done raising 1 tonne by 500
metres is 4903000 Joules.

This is achieved in 6 hrs, or 6x60x60 = 21600 seconds.

Units of power are Joules per second

So the power required is 4903000/21600 = 227 Joules per second.

A Joule per second is a Watt.

So the power required to raise 1 tonne by 500 metres in 6 hours is 227
Watts.

AIUI a typical domestic solar panel delivers 260 Watts at full blast.

So 1 panel should do it, with a little to spare.

I find that hard to believe! Where have I gone wrong?

Seems OK to me. 100 meters an hour is 27mm or a little over an inch a
second.

A human being with a tackle can lift a tonne that fast easy.

In fact an Irish Navvy could shovel and lift 30 tonnes a day back in the
50's.

I think you are encountering the true meaning of 'energy density' - that
a tonne of water up a hill is actually not really that interesting -
maybe a couple of Kwh at best.

Thanks for the confirmation. Reversing the calculation, as it were,
Dinorwig dumps 60 tonnes per second through its turbines, from a head
of 500 metres and for a period of 6 hours. If 1 tonne moving through
500 metres in 6 hours is equivalent to 1 solar panel, Dinorwig is
equivalent to 60x21600 solar panels, i.e. 1,296,000 panels. I'll leave
it to AnthonyL to work out how much of Wales that would cover!

Actually insolation is on average about 100W/sq meter and a solar panel
maybe gets to 25% efficiency, so 25W/sq meter on average. Obviously
midsummer midday peaks are considerably higher - 10 x that.

IIRC Dinorwig can peak at 2GW, but not for 6h, thats less than a GW at
that level.

At 4 sq meters per hundred watts, that's 40 sq meters for a killer-watt
or 40 sq km for a gigawatt?

--
New Socialism consists essentially in being seen to have your heart in
the right place whilst your head is in the clouds and your hand is in
someone else's pocket.