It shouldn't. The same area of the sensor is active and the bitrate is the same in both modes. Processing requirements are probably slightly different. Any differences related to resolution and battery life I imagine would be so small as to be immeasurable compared to all the other ever changing external factors that would affect battery life much more, such as wind.
Any facts to back this up?
Certainly. The fact that you stay at 24mm FOV in both 4K and 1080P means that the entire sensor width is being used for both. Alternatively we can look at the M2P for an example where the entire sensor is not used in certain modes (HQ) which is where the FOV drops to around 40mm equivalent when only the center portion is used. If the Air was using a different sensor portion for different resolutions, the same effect would occur.
As for the bitrate, they are well documented and easily verifiable by any user. I don't think that requires any further explanation as it is so easy for anyone to verify, but here is a link to a full list for those not wanting to test it themselves: DJI Mavic Air Bitrates
As for flight times, again, very easily verifiable by any user. Hover the drone until the battery is low while shooting 1080P and repeat the sane test again in 4K. There will be no noticeable difference in flight times.
I think i read somewhere that the sensor is designed for 4k, and running it at 1080p does it some diservice.
Perhaps it is less efficient at 1080p if anything
Because it's a 4:3 aspect 12MP sensor, it's 4056X3040. If you apply a 16:9 (1.78:1) aspect to that you get 4056X2280, and that is only slightly more than 4K/UHD (3840X2160) which is 8.3MP. So it can pretty much give you full sensor width. If it's doing 1080P, which is only 2MP, it is going to subsample, line skip, or pixel bin to get to 1080P without reducing the FOV. A 1:1 pixel readout of 1080P on that sensor would cause a significant change in FOV (zoomed in). 1080P isn't great on the Air and in my opinion you're probably better off shooting in 4K and outputting 1080p in post if that's what you want your end result to be.
True 4K is actually 4096X2160 at a 1:90 aspect ratio, but that does not match most people's displays. It's interesting because 1080p/FHD is named after it's height (1080), but 4K is most commonly referred to by it's width rather than 2160p. Less marketable I guess!
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