Just had to show you this take off.....

[Tiger G]

Hope this isn't an oldie ?? Definitely worth a look:

https://www.liveleak.com/view?t=a0fFO_1535553838

[Sam Rutherford]

I think it's relatively recent, but it's definitely everywhere...!

[chevvron]

It must have landed there first.:D

[Lantern10]

I think he's done that more than a few times.

[27/09]

I think he dives quite low to make it look dramatic.

I note there's no sign of any registration markings.

[Jim59]

Similar technique to a glider bungee launch. The dive is necessary.

https://video.search.yahoo.com/search/video?fr=opensearch&p=bungee+launch+video#id=3&vid=f8b3402a9e324bea61274e6cd1b3a600&action=click

[Nurse2Pilot]

The dive is necessary, but not that much, surely? Isn't that aircraft (Piper J-3 Cub) capable of STOL?

[scifi]

There is a formula which relates height loss to speed gained (due to gravity.). At these speeds for every 45ft lost you gain 10 knots, so if he dived 3x45 = 135 ft he would have gained 30 knots. The camera lens is most likely wide angle so the height loss is deceptive.
.

[Pilot DAR]

At these speeds for every 45ft lost you gain 10 knots, so if he dived 3x45 = 135 ft he would have gained 30 knots.

Would the angle of descent affect the applicability of that formula?

[Jan Olieslagers]

I think he dives quite low to make it look dramatic.
Just like he (or she?) does not turn over the river, where a possible crash would be more controllable than in the treetops.

Would the angle of descent affect the applicability of that formula?
It might also depend on the type of aircraft, more specifically on the wing profile.

[27/09]

There is a formula which relates height loss to speed gained (due to gravity.). At these speeds for every 45ft lost you gain 10 knots, so if he dived 3x45 = 135 ft he would have gained 30 knots. The camera lens is most likely wide angle so the height loss is deceptive.
.
I'm guessing that rule of thumb applies to a glide. The speed gained would also be dependent on the thrust being produced or more correctly the amount of excess thrust over the thrust needed to overcome drag.

As an aside, why do people persist in holding their phone in portrait instead of landscape when taking photos or videos that should be taken in landscape?

[abgd]

The easiest way of converting height to speed is potential energy to kinetic energy.

MgH = 0.5MV^2

M = mass, g=9.8,H = altitude in metres, V = velocity.

Mass cancels out so 9.8*height = 0.5V^2

if you drop something 40 metres straight down - which is about 135 feet - it should reach sqrt(2*40*9.8) = 28 m/s which is 54 knots, ignoring losses due to air resistance.

If you are in an X15 (i.e. a flying bullet) then air resistance is negligible and you'd probably be moving at close to 54 knots by the time you'd fallen 40 metres. If you borrowed my old hang glider then you would never get past 30, so the idea that there could be some kind of generalised rule of thumb seems to me to be false.

The other issue is that because kinetic energy increases with the square of speed, if you start off at 30 knots you will end up with a smaller speed increment than if you simply push the aircraft over the edge of the cliff at walking speed.

i.e.
0.5MVs^2 + MgH = 0.5MVe^2
0.5Vs^2 + gH = 0.5Ve^2
2*Vs^2 + 2gH = Ve^2

sqrt(Vs^2 + 2gH) = Ve where Vs is the speed you fly over the cliff edge and Ve is the speed at which you are travelling when you reach 40M below the cliff top.

Putting numbers into it, if you fly over the cliff edge at 30 knots:

sqrt(2*(30*1852/3600)^2 + 2*9.8*40) = 35.5 m/s = 70 knots - an increment of only 16.

All are welcome to pick holes in my maths - a while since I had A levels - but I don't believe any general formula exists.

[Runaway Gun]

Are you separating vertical speed gained due to gravity, and horizontal components?

[Nurse2Pilot]

Short takeoff without the dramatic dive

https://www.youtube.com/watch?v=ucdb0TKu3rk

[abgd]

Are you separating vertical speed gained due to gravity, and horizontal components?
No, why would I?

[Whopity]

You should have seen the fully laden B52s taking off from Guam.