Core answer: battery energy Wh=mAh×voltage÷1000, runtime=energy÷power×efficiency; every 3 seconds between lightning and thunder ≈ 1 km; surface distance uses the Haversine great-circle formula (Earth radius 6371km); depth of field is set by aperture, focal length and focus distance — f/8 gives roughly 4× the DoF of f/2.
Estimating battery runtime
Chain: mAh → Wh → hours.
- Energy: Wh = mAh × 3.7V ÷ 1000 (10000mAh ≈ 37Wh)
- Runtime: h = Wh ÷ device W × efficiency (~0.85)
- Flight rule: ≤100Wh carry-on freely; 100-160Wh needs airline approval
| Device | Typical power | 37Wh lasts |
|---|---|---|
| Phone (screen on) | 3W | ~10 h |
| Tablet | 8W | ~4 h |
| Ultrabook | 20W | ~1.6 h |
| Drone | 60W+ | ~30 min |
Lightning distance and 30-30
Light arrives instantly; sound crawls at ~343m/s — gap ÷3 ≈ km (÷5 for miles). The 30-30 rule: under 30 seconds (~10km), go indoors; wait 30 minutes after the last thunder before going back out.
Great-circle distance
Earth is a sphere, so “straight-line” distance is a great-circle arc: Haversine takes two lat/lon pairs and returns the shortest arc on R=6371.0088km.
| Route | Distance |
|---|---|
| Beijing–Shanghai | 1068 km |
| Beijing–Guangzhou | 1889 km |
| Shanghai–Tokyo | 1763 km |
| Beijing–New York | 10990 km |
Flat maps distort badly — Beijing-New York is shortest over the Arctic, the classic great-circle surprise.
The three DoF factors
- Aperture: larger f-number → deeper field; f/8 ≈ 4× f/2
- Focal length: wider lens → deeper field
- Focus distance: farther → deeper
Hyperfocal trick: focus at the hyperfocal distance and everything from half that distance to infinity is sharp — the landscape photographer’s core formula. In-focus range splits roughly 1/3 front, 2/3 behind.
Example: drone flight time
A 3850mAh/15.4V drone pack: energy = 3850×15.4÷1000 = 59.3Wh; hover draw ~55W at 0.85 efficiency → 59.3÷55×0.85 ≈ 0.92h ≈ 55 min. The spec sheet says 46 — it reserves 20% for return-to-home and cold. At -10℃ lithium capacity drops another ~20%.
Example: portrait vs landscape aperture
50mm at 2m: f/1.8 DoF ≈ 0.2m — nose-tip sharp, ears melting (the creamy look you want); f/8 widens it to ~0.9m. Switch to landscape: 24mm, f/11, focus at hyperfocal ~1.7m → sharp from 0.85m to infinity, rocks and peaks together.
Common pitfalls
- “More mAh always lasts longer”: compare Wh — 10000mAh/3.7V (37Wh) loses to 8000mAh/7.6V (60.8Wh).
- “Distant thunder means safety”: bolts can strike 15km out (“bolt from the blue”); treat 45s gaps with respect too.
- “DoF is always 1/3-2/3”: macro approaches 1:1; at hyperfocal the rear zone runs to infinity.
- “Map ruler equals flight distance”: projections distort; great-circle math on lat/lon is the honest number.