Hi Nigel,
yes, sparging at a higher temperature by i) draining the bag (equivalent to the conventional lautering), ii) adding hotter water, either by pouring it over or dunking the bag into it is also effecting what's known as a mashout. This combined sparge/ mashout achieves a couple of things, the most important is to rinse the remaining sugars from the mash (that's the sparge), but as you've noted the temperature ends up higher, this is also beneficial as it lowers the viscosity of the now sugary sparge liquor making it more likely to drain away from the grain, while the higher temperature also denatures enzymes and stops them from working and so fixes the proportions of the various sugars. That last point is only significant if the liquor (sparge or mash) is allowed to sit around mash temperatures for some time.
However, the Sparge/ Mashout step in a Maxi-BIAB is really just a rinse, so I only leave it a few minutes, say 10, in which time I'll give it a few good stirs. The water temperature isn't important, however I use water just off the boil, as joshua indicates, around 80C should be the limit that the actual grain reaches to avoid potential astringency problems. It will also be helpful if the water is not alkaline- much town water is so, but a pinch of citric acid (say 1/4 tsp in 4L) will buffer it in that case.

Now, that formula, where is it from? It is not correct, it should be:
Post- boil SG/ Target SG * Volume of Wort in Kettle = Diluted Volume (i.e. what ends up in the fermenter)
The Target SG is from your recipe, it is the SG you want your beer at when it is diluted, also known as Original Gravity, the other two actual values are the volume and SG you've measured. Here's an example, my latest batch was a Schwartzbier with a Target SG was 1.050, there was 17L of 1.070 in the kettle at the end of the boil:
70 / 50 * 17 = 23.8L
Therefore, amount of water to be added:
23.8 - 17 = 6.8L

So it is just a linear scaling based on concentration, initially it took me a while to work this bit out, but it more or less smacked me in the face when I realised how simple it was! You can also incorporate loss to kettle trub in the Volume of Wort in Kettle (i.e. in my case 17L), particularly if it is a non- trivial value, mine is usually <0.5L so I don't bother. As an aside, for my Schwartzbier recipe that's >23L of diluted wort from just 4.3kg of grain, so around 85% efficiency: very nice!
Hope that this helps with the calculations, let me know if it still causes any grief.

WRT recipes, they really don't need any specific modifications for Maxi-BIAB, so any all- grain recipe can be taken as is and just scaled if need be. BeerSmith2, Brewmate, ProMash, StrangeBrew2 etc, all work fine and scale recipes. You can buy a BeerSmith2 licence at the top of the page, its a cheap tool that most brewers should find very useful (pardon the shameless plug!). Initially, set 'efficiency' to around 70%, but you should find with Maxi-BIAB that it is much higher and you can adjust your grainbill to suit.

Many thanks as well for your feedback, we value that very highly. We're very pleased that the guides here on BIABrewer are proving helpful to lots of folks all around the globe. I feel the Stovetop variants have shown dozens if not hundreds of novice brewers a much quicker route to All- Grain with a very simple yet effective, cheap and low- risk method while the quality of their beer has improved out of sight- they would otherwise be still brewing kits or extract and saving up money for a conventional multi- vessel rig. Updates to the Stovetop methods are in the pipeline, but probably not until the southern spring.

I think it would be Top Up Water on the right Nigel. Sorry, I've not had a chance to test this part of BS2 yet, other BS2ers may care to confirm?

Oh, and well spotted! The plain water going into the fermenter certainly does need to be sanitary, everything does for that matter as the yeast is the only organism we want growing in there. Tap water from a reticulated supply (i.e. town water) is usually fine, however if you're using rainwater from a tank it would be advisable to boil it beforehand, then cool it of course, again keeping it sanitary. If I'm topping up with rainwater, I boil and cool it in a stockpot with the lid on, only removing it to pitch.

Here's a few quick notes...

- I've studied BeerSmith2 a fair bit as well Ralph and I actually can't understand the 'Top Up Water for Kettle' and 'Top Up Water'.

-'Tot Water Needed' in BeerSmith2 actually refers to the volume needed as if it were at boiling point. No idea why

- 'Boil volume' means 'start of boil volume at boiling point'.

- Your sparge water can be just off boiling as the addition of even half your liquor at boiling point will fail to raise your mash to 78 -80 C. Even if you did this, having your mash pH correct will protect against tannins - this is just the same for traditional brews.

- Don't trust formulas that you don't understand.

- Total Maxi-BIAB is really a combination of batch-sparging and dilution. Dilution is a known. What is unknown is the sparging effect and this will vary greatly depending on your pot sizes. (IBU's will also vary for a concentrated wort but no one has a definitive IBU formula for any type of brew anyway.)

- I think what Maxi-BIABer's need to do, before they can rely on any figures, is set some standards such as having two pots of equal size. Until this is done, it is really all guesswork for every 'Maxi-BIABer's' set-up. There is no way around this.

- Don't get too hung up on figures. With a good recipe, the end result will always be good.

- Normal water from a town water supply is usually fine as top up water if it tastes okay. If from a tank, as Ralph says, boil it.

Cheers,
PP

If you enter Fermenter Top Up Water into BS2, this will reduce your Boil Volume.

You then need to increase your Top Up Water for Kettle until your total mash volume is less than your mash tun volume.

BS2 should then generate figures for Maxi-BIAB which are a good estimate.

You can then fiddle with the grain and hop quantities to get the OG and IBUs that you want.

BUT once you've cooled your wort and transferred it to your fermenter, only then you should work out how much water to actually add to your fermenter to dilute back to your recipe OG.

The amount of dilution will depend on your actual boil-off rate, absorbtion rate, kettle trub, cooler losses and mash efficiency.

If you take good notes and adjust your equipment profile as you dial in your equipment, you should be able to get some pretty good numbers out of BS2.

Looks OK to me Nigel.
Seeing as it is your first batch I'd err on the side of caution though, so your efficiency should be no more than 70% (as you have done), some additional room for error would increase your grainbill slightly, so I'd order a little more than you need, particularly if you're looking at more ordering more than one batch- worth. If you line the planets up it may yield more wort at the desired SG than you require, but that's probably better than less.
My house beer is an Extra Special/ Strong Bitter (ESB) and that's what I aimed for in the guide, it is slightly stronger than a Standard or Ordinary Bitter and therefore uses more grain. It does demonstrate that 'full' strength beer is chicken feed for the Maxi-BIAB method though.

You should set your mash run specific heat to 0

Bs2 will then correctly calculate your strike temp