according to that thread a lid doesn’t save any fuel when boiling based on an experiment inside.  There was a question raised about whether it would make any difference if it was outside and windy
I tried to verify on a 5 day trip. Each day I boiled a pint of water with the lid on, and another pint with the lid off and measured the fuel use. I normalized to 450 g of water raised 150 F degrees. If the water weigh a little more I scaled the result by that much. If I raised it more than 150 F I scaled the result by that amount. etc. I also measured the time and normalized it – I wanted to do a 4 minute boil time. If I did it a little slower then that will reduce fuel use so I wanted to measure that.
results:


Basically, the results varied for reasons other than whether the lid was on or not, but maybe I’m consistent with the gear skeptic who claims there is only a slight improvement when a lid is put on, and the weight of the lid exceeds any fuel weight saved
In run #1 (with lid) it uses 5.5 g of fuel, run #2 (without lid) it uses 6 g of fuel. But run #1 took 4.5 minutes, run #2 took 4 minutes. Since run #2 was done more quickly which results in more fuel used it’s unclear.
Run #3 and #4 were on the second day. #4 was with a lid but it actually used up an extra gram of fuel – the opposite of what I’m trying to prove. For #4 it got breezy which resulted in more fuel used which was greater than any benefit to having a lid on.
Runs #5 and #6 were on the third day. Run #6 without lid was much worse, but again, I think it was because it was windy.
#7, #8, and #9 were on the fourth day. For #7 it was calm, for #8 and #9 it got breezy – maybe 2 MPH. There wasn’t any big difference between lid and no lid, but there was a 1 g increase from calm to breezy.
#10 and #11 were on the last day. Very calm (but even then there were small breezes). They took the same amount of time so the stove was turned up the same for both. #10 with lid took 5.5 g of fuel. #11 without lid took 6.5 g of fuel. The time was about the same so the stove was turned up about the same. I think this is the cleanest measure of lid vs no lid – about 1 g of fuel is saved by putting on the lid. Which is about the same as Gear Skeptic measured.
All of this was with my heat exchanger windscreen. The square aluminum part below is just a windscreen, which also reflects heat to the canister. If the canister has any pressure to light, the reflectors will warm it up more as it burns. The last day I had to use a lighter to warm up the canister. but once it got running the first time, it warmed up enough so I could keep lighting it. The last night the canister was mostly empty and it was 24 F with cheap butane but I could get it to work fine.
My take away is that a lid doesn’t matter but I like having a lid for other reasons, like keeping dirt out. But how windy it is and how much I turn up the stove makes a big difference.




