How does Strava calculate calories?

[si_c]

No, it is exactly correct, assuming air resistance dominates as I said. Read the formulae, it's just algebra.

At 10mph air resistance will not dominate, rolling resistance will.

On the bike calc numbers, using defaults in there (I suspect you may have used kmh).

20 miles at 10mph= 834 calories, 29 W
20 miles at 20 mph = 1182 calories, 82 W
20 miles at 40 mph = 2577 calories, 358W
20 miles at 80 mph = 8147 calories, 2263W
20 miles at 160 mph = 30433 calories, 16907W

Note how the increase in calories approaches the square as velocity increases, and the increase in watts approaches the cube. It's almost exact at the ludicrously high final step.

The rolling resistance from bike calc is a greater proportion at sensible cycling speeds than I would have guessed, but the principles remain.

The increase in watts should be proportional to the square of the velocity not the cube. I used my own values for the bike and rider weight, and a fixed distance of 20miles for the values.

Rider weight: 210lbs
Bike weight 24lbs

Using a fixed distance of 20miles, I set the speed to ~10mph, giving
Time: 119.7mins, 46W average power, 316kcal

Setting the speed to ~20mph gives
Time: 59.9mins, 220W ave power, 756kcal

Which doesn't track with your estimates.

 

[roubaixtuesday]

The increase in watts should be proportional to the square of the velocity not the cube. I used my own values for the bike and rider weight, and a fixed distance of 20miles for the values.

Rider weight: 210lbs
Bike weight 24lbs

Using a fixed distance of 20miles, I set the speed to ~10mph, giving
Time: 119.7mins, 46W average power, 316kcal

Setting the speed to ~20mph gives
Time: 59.9mins, 220W ave power, 756kcal

Which doesn't track with your estimates.

Yes, as I have explained, because rolling resistance will dominate at low speeds.

Note every single post I have made has included the caveat assuming air resistance dominates.

Also, even moving from 10 to 20mph the change far exceeds your "So for a doubling of speed you might see a quadruple of effort, but a half the time, so calorific burn to be around double. " As you go to higher speeds, the relationship tends to what I've posted.

 

[Dogtrousers]

Here's another fun wattage calculating thingy.
https://www.gribble.org/cycling/power_v_speed.html

 

[Twilkes]

Not calories but power - I know Strava power is an estimate but when I change the bike setting from my 10kg bike to my 14kg bike the power estimate for most rides almost doubles, from 137 watts to 268 watts in one particular case. Surely 4kg can't make that much difference? Rider weight is 100kg in both cases.

Apart from that I've found power estimates fairly consistent for similar conditions, no idea how accurate they are though as I don't have a power meter.