I don't have BS on this laptop but I can make a few guesses for you...
Firstly I'm a little confused as to why you have a final bottling volume larger (21L) than your batch volume (20L). Are you planning on topping up in the fermenter with additional water (ie kettle volume + top up water)?
Losses in volume of liquid are typically defined in a few areas:
- loss of liquid due to mashtun deadspace
- loss of liquid due to grain absorption
- loss of liquid through boil off
- loss of liquid through cooling shrinkage
- loss of liquid through trub
The first two are losses form the mashtun, the last three are kettle losses. I'll go through each of these and try and apply it to the numbers you have. You may not need all the info here, but in case someone else stumbles across this topic at a later stage it may be useful.
Mashtun deadspace
I don't know how you make your beer so cant really answer this too well for you unfortunately. I brew in a bag so don't suffer mashtun deadspace. From what I understand, it's the liquid you can't extract from your mashtun due to outlet heights. If the base of your tap sits 2cm above the base of your mashtun, then there is liquid sitting under the tap that cannot get out. If someone who brews with a conventional mashtun can provide some clarification or affirmation it would be good.
From your numbers its hard to say if you have lost some volume to deadspace or not.
Based on your numbers, your strike vol was 12.73 and your sparge vol was 15.37, which totals 28.1L. Your measured pre boil volume was 21.5L, so it looks like you lost 6.6L to the mashtun.
This is accounted for as the combined loss to mashtun deadspace and grain absorption (ie 1L could be extra grain absorption and 0.71L could be deadspace)
Grain absorption
when you add dry grain to liquid it soaks it up. You can't get this liquid back. If you brew in a bag, squeezing will reduce this loss.
I can't remember exactly but I usually loose around 1L of water per kilo of grain.
As your grain bill was 4.8kg, the 6.6 sounds a little high, but nothing to be overly concerned about. This will vary based on your brewery setup. If you have no loss to mashtun deadspace you just need to adjust your beersmith setting for loss to grain to 0.727 L/kg (4.8/6.6) from whatever it was before hand. This option is in the preferences I think rather than an equipment or mash profile.
At this stage in my brew day, when ramping up to the boil, I like to take a gravity reading (calibrated for temp) and check where I should be. I've brewed a few times on my setup that my actual volume is close to spot on to the predicted volume, so if my gravity is higher than expected, I have two options. I can top up with more water to the actual gravity I want, or I can shrug it off and make a slightly stronger (higher abv) beer. If it's too low I can add DME to raise the gravity, boil for longer to lower the volume and raise the gravity or shrug it off and make a slightly lower abv beer.
Hopping schedule can also be tweaked to account for greater final volume or higher/lower OG at this stage too.
Boil off
This will be individual to your brewery. I use a crown urn with a concealed element and typically get around 3.33L/h boil off. I think that is what a few other tassie brewers get with similar setups. My boils usually go for 90 min so it's 5L typically.
your pre boil volume is 21.5L and your post is 15L.
This looks to be the key area here, as you are losing 6.5L here when beersmith only predicted 1.89L so you have not accounted for an additional 4.61L loss here.
Hard to say if 6.5L is too much as you have both a ring burner and an electric one. I have no idea sorry as I've only brewed on my crown with the above mentioned boil off rate.
Are you measuring the post boil volume as soon as you switch off the heat? Or is that 15L the volume you get into the fermenter? I suspect it is the latter.
loss due to cooling
When water is hot it has a greater volume. As it shrinks it contracts which is why the metric system is based on:
1ml of water = 1cm x 1cm x 1cm = 1cm3 @ 1 atmosphere pressure @ 20*C (I think)
The volume you will be measuring in your brew kettle is calibrated (or should be) to volume of water at 20*C.
If your kettle sight tube tells you, you have say 21.5L of water (or wort) at 100*C, then it will shrink in volume to maybe 20.64 L after it has cooled to 20*C. That is based on 4% cooling shrinkage which from memory seems about right.
Loss to trub
This is where I loose a fair bit as I BIAB and crush fairly fine. It doesn't bother me too much as I account for it in beersmith and use extra grain + water to get what I want into the fermenter. Different systems give you different losses to trub.
your numbers give you 0.5L of loss to trub which seems pretty good to me.
Final basic math
Volume should be calculated like this:
Volume into fermeter = (Liquid volume) - (Mashtun losses) - (Brew Kettle losses)
Volume into fermeter = (Strike volume + Sparge volume) - (Grain absorption + mashtun deadspace) - (boil off + cooling shrinkage + loss to trub)
So with your numbers based on 15L into fermenter
Vol into ferm = (12.73 + 15.37) - (6.6) - (6 + 0.5)
Vol into ferm = 15L
Now we need to work backwards a little here.
To work out your kettle losses, you already know your trub loss is 0.5L. So based on your 6.5L kettle loss you know that 6L is due to combined shrinkage and boil off.
Shrinkage = 15.5L x 4% = 0.62L so you may have lost around 0.62L due to cooling wort.
Therefore if kettle loss = 6.5L , and kettle loss = boil off + cooling shrinkage + loss to trub, then:
6.5 = boil off + 0.62 + 0.5
5.38L = boil off. This seems a reasonable amount. In your beersmith profile you need to add this volume for boil off.
Based on your numbers you have allowed for 1.89L boil off when in practice you actually had 5.38L. So there is 3.49L of your missing liquid.
Summary
looks like you have understated both your predicted kettle loss (by 3.49L) and also the mashtun loss (by 1.71L). Combined they make up 5.2L.
Beersmith is great but needs a little time to set up. I would increase your losses to the mashtun to account for mashtun deadspace first (if you have any) and if not just increase your grain absorption. You also need to increase your losses due to boil off as I think beersmith does a pretty good job at estimating shrinkage from memory. You also need to include your trub loss to your equipment profile too if you haven't already.
Making these changes will mean you need to increase your total volume of liquid used by 5.2L. Depending on the size of your brew kettle this may or may not be an issue. if you can't fit any more in, you can add it to your fermenter, and there is a option for entering this top up water in the equipment profile.
If your mashtun and kettle size permit it I would increase your strike volume first, then your sparge water second. If your equipment size wont let you, then go down the topping up of the fermenter route. The reason increasing the mash/sparge volume is better than topping up the fermenter is increased mash efficiency.The additional water coming in contact with the grain helps "wash" more sugar off the grains, meaning you could be topping up your beer with say 1.020 liquid rather than 1.000 liquid.
This equals more beer in your beer, rather than just water.
Once you update beersmith with your numbers, it will recalculate the required volumes for you. Where you add the water is up to you though.
Anyway, hope that all helps. You may know all this already, but I figured I would regurgitate it all in case anyone else stumbles across it at some stage.
Edit: Sorry for the long response