Lift due curvature of the earth?

[Turbavykas]

Hi,

There is a lot jokes that Russian airplanes use this to get airborne but how does it really effects lift? According my calculations: Schuler period is 84min, lets say jet airplane can go around the world in 40 hours. 1.4/40*100 we get around 3.5% of the lift generated by the curvature of the earth. Is that true? If so is it taken into account calculating lift of the airplanes in cruise?

[BOAC]

Is that true?- if it wasn't, satellites would not stay in orbit and aeroplanes would fall out of the sky if they flew too slowly - wait a minute...........................

If so is it taken into account calculating lift of the airplanes in cruise? - I very much doubt it

[ATCast]

The ratio of the Schuler time to the time that it takes to travel around the world is not the percentage of lift that you get for free.

The centripetal force is given by F = m * V^2 / r
Where:
m - aircraft mass
V - aircraft speed
r - radius of the earth

Lift is given by L = m *g
Where:
g - gravitational acceleration

The percentage of Lift "generated by curvature of the eart"
V^2 / (g*r) * 100

Substituting:
r =~ 6400000 m
V =~ 280 m/s
g =~ 9.81 m/s

Gives 0.12%

My guess is that is within the error margin of most measurements and calculations and therefore it is probably not used.


For validation of the above you can calculate the "Schuler speed" and substitute that:

V =~ 40000000 / (84*60) =~ 7936 m/s

Gives 100.31% ~ 100% Q.E.D.

[Turbavykas]

ATCast (http://www.pprune.org/members/268925-atcast) : It's sad but you are perfectly right. Thank you for formulas. :)

[CliveL]

If so is it taken into account calculating lift of the airplanes in cruise?

Depends on how fast you are flying and in which direction. Concorde performance brochures were calculated for flying north/south so no effect

[Capot]

The effect of rotation is greater than you might think; any artilleryman will tell you that when precision shooting a correction must be applied to take it into account. Shooting North-South and vv the correction is entirely to the azimuth, and East-West and vv it's to the range. As you might guess, on other bearings it's a mixture.

I forget the values of a typical correction; could it have been 10m on a 35 second time of flight when shooting, say, due North?

[Arfur Dent]

The only reason the Sepecat Jaguar ever got airborne.:O

[ATCast]

Depends on how fast you are flying and in which direction. Concorde performance brochures were calculated for flying north/south so no effect

There is an effect, even when flying North - South. But the North - South effect is the same as the South - North effect.

The East - West effect is different from the West- East effect.

For simplicity I omitted the effect of earth rotation. You can include the rotation but it becomes a bit more complex. Let's not include any effects of the earth rotating around the sun, effects of the moon; these are negligible for these purposes but make it far more complex.


Flying eastward around the earth at the equator would yield 2.67 rotations around the earth centre when the circumvention takes 40 hours. One rotation for you flying around, 1.67 rotations the earth does by itself in the same time. The resulting rotational speed is one rotation every 15 hours.

Flying westward at the same speed would yield 0.67 rotations around the earth centre, still in the same directions as when one would fly eastward. The rotational speed is one rotation every 60 hours

In the latter case contribution to the lift would be negative because the rotation around the earth's centre would be slower than normal.

If you are standing still on the equator you are moving around the earth centre with a speed of approximately 462 m/s. That means that the "lift" you get from standing still is approx 0.34% of g.

Moving east at an additional 280 m/s would give a total of 740 m/s, resulting in 0.88% g centripetal force, which is a difference of 0.54% g from standing still. So in effect you need to produce 0.54% less lift than your weight.

Moving west at 280 m/s would give a total of 180 m/s, resulting in 0.05% g. So in effect you need to produce 0.29% more lift than your weight.

The difference in lift to generate is 0.83% between flying eastwards or westwards at the equator.


Moving north at the equator at 280 m/s gives a resulting speed of
sqrt(280^2 + 462^2 ) =~ 540 m/s
This results in a centripetal acceleration of 0.46% g, which is about 0.12% g more than when standing still at the equator. So flying north-south or south-north over the equator with 280 m/s requires 0.12% less lift than your weight at the equator.

Moving on the South-North-South track over the North pole also benefits from 0.12% centripetal acceleration when flying at 280 m/s. To counteract the Coriolis effect a bank angle of approximately 0.23 degrees to the left is needed, but this has no significant impact on the required lift.

[Capn Bloggs]

To counteract the Coriolis effect a bank angle of approximately 0.23 degrees to the left is needed
That in turn would have to be countered by a bit of rudder trim, would it not?

[misd-agin]

Earth's rotation is one of the considerations airport designers consider when locating park spots. West facing is safer.

[ATCast]

Earth's rotation is one of the considerations airport designers consider when locating park spots. West facing is safer.

In what sense is that safer? What are the risks mitigated by facing west? :confused:

That in turn would have to be countered by a bit of rudder trim, would it not?

:) Isn't there another thread on that subject?

[despegue]

I thought 01/04 had passed?:}

[crippen]

but what happened to the 'flat earth' and no global warming believers? Not a word off them. :}

[FCeng84]

A related issue that does require more consideration than lift is the angular rate impact of Earth's rotation. Earth rate is ~15 deg/hour (slightly less than 360 degrees in 24 hours). Depending on lattitude, heading, and speed an airplane will see quite a range of steady angular rates while at cruise. At the equator heading West pitch rate will be nose up. Turn to the East and pitch rate will be nose down and quite a bit larger. Head north and you will find right wing down roll rate to maintain wings level. Head south and left wing down roll rate is needed. There is a noticable difference between maintaining constant pitch and roll attitude and having the associated angular rates be zero.

[BOAC]

Makes you almost feel sorry for an IRS........................................:)

Then there is profile rate. Poor thing.

[haughtney1]

Good god, I thought this was going to be a thread about early model A340's....after reading it, I think I need to lie down...:uhoh:

[ATCast]

Head north and you will find right wing down roll rate to maintain wings level. Head south and left wing down roll rate is needed. There is a noticable difference between maintaining constant pitch and roll attitude and having the associated angular rates be zero.

You confuse me.
In my book if something is constant, that the associated rate is zero. Per definition...

Don't you mean the associated roll/pitch moment?

[ATCast]

I thought this was going to be a thread about early model A340'sThat's what I thought too! But then I decided to spin it in another direction. :}

[BOAC]

You confuse me.
In my book if something is constant, that the associated rate is zero. Per definition...
The devil is in the definition. I think you need to re-think your space-frames here. "constant pitch and roll attitude" in relation to the earth requires a constant input of attitude change in one or more axes in relation to space. Hence the 'IRS conundrum'

So - how does a 340 manage to fly, anyway?

[EMIT]

That's why we learned about Earth Rate Compensation and Transport Rate Compensation during those hours of ATPL theory. Yes, Inertial Systems are stable relative to space coordinate systems, indeed need to be perturbed to keep them stable relative to the Earth coordinate system that, itself, moves and tumbles through space.

[3holelover]

Surely "in relation to space" isn't what's relevant though... is it? Wouldn't "in relation to the direction of gravitational force" be more pertinent?

[EMIT]

Oh, and about the original question: the Russian planes are not supposed to fly by virtue of the rotation of the earth, the fly because of the aerodynamic lift produced by the wings. However, their climb performance is (jokingly) so abysmal, that their height increases mostly because the earth surface curls away from them.

[italia458]

And time goes faster at a higher altitude (general relativity), but it goes slower when you're moving (special relativity)! I think ATCast's time calculations are off... :}

[TURIN]

Aaaaaaaargh!


Posted from Pprune.org App for Android

[Natstrackalpha]

This is surely a post for the boffins on Jet Blast, it has a distinct Jet Blast ring to it. Talking of jet blasts and on a more serious note: Do we risk travel sickness due to the speed we are travelling (9oo kts on the EQ)?

Would we all fall over if the Earth suddenly stopped rotating.

Why don`t we build two giant jet engines to power the Earth around space?

We could place little buttons on lamp posts in the street so that people could ring the bell twice when they wanted to get off the Earth and visit a nearby constellation perhaps . . ?

If we are to fly the planet around the universe, would the pilots` licence be regulated by ICAO or would EASA have to stick their noses in?

Would an Earth type rating cost the Earth?

Re: Training. Where would the safest option be for a PFL?

Could we set up a roadside assistance team to repair the Earth in the event of a Terrestrial breakdown?

would it be possible to build special drive-thrus such as a burger joint with Earth size access - how high would the gantry have to be - ? "may I take your order please . .?"

"yes, thanks, 2 billion cheeseburgers, 14,750,000 1/4 pounders with cheese, 2,800,000 apple pies and 3 billion and 4 milkshakes and 200,000,000 coffes please . . ."

""would you like to make those a meal . . ?"

"oh, go on then . . "

"" . . do you want me to supersize that . . ?"

" . .wait a mo, I`ll just ask . . "

RESOUNDING CHORUS

" . . no thanks . ."

"" . Sugar for the coffees . . ?"

" . yeh, we`ll take . . 400,000,000 satchets . . "?"

" . .sorry, make that 399.999.998 as Emily doesn`t take sugar . . "

"" Thank you, that`ll be $34.75 billion and 7 dollars and 75 cents., please . . "

Please leave any countries entire wealth for our charity box
----------`Help Build A Planet`---------

"" . . Can you pay at the next window please, thank you, have a nice light year . .!"

<PA Announcemen>
"Would the Death Star in the parking lot, please make way for our customers, thank you!!"

[RAT 5]

The earth spins at approx 1000kts/hr. Concorde flies at approx 1000kts/hr. It takes off from JFK and flies towards LHR which is moving away at the same speed Concord is flying towards it. How does it ever arrive? Equally, it takes off from LHR and flies towards JFK, which is coming towards it at the same speed; i.e. they have a closing speed of 2000kts/hr. So why does it still take 3 hours?
Now I'll put the cork back in the rum bottle and try to stop the house spinning. Hopefully that will cause my brain to slow down too, relatively.

[BOAC]

Natstrack - don't forget to pick up a couple of Milky Ways for the kids.

Rat - what I have never understood is how, if the earth is 'stationary' (rotational only) at the poles but moving at 1000kts at the equator, there are not loud rending noises and shearing of the earth's surface - or is that what all these earthquakes are really about?

Leave the cork........................

[DaveReidUK]

What are kts/hr ?

[BOAC]

Ask a sailor.

[3holelover]

...a swing and a MISS! :p

[DaveReidUK]

Ask a sailor.Or a very industrious Boy Scout ?

[bucks_raj]

So if a Hot Air Balloon lifts off on a nil wind day and lands back say after an hour... It wouldn't land on the same spot where it got airborne from ....??

[RAT 5]

somebody is bound to fart and give thrust in one direction. Or perhaps a sneeze, if it's a lady.

You guys are too serious. Much long-haul flying? Strap an aluminium tube to your arse for too many hours and it addles your brain. Metallic osmosis with sweat.

[NSEU]

Follow link to previous discussion:

http://www.pprune.org/tech-log/10501-plane-lighter-going-west-than-going-east.html

[hawk37]

Bucks_raj

Not sure who you are asking the question to, however, making a bunch of assumptions, the simple answer would be no. Consider 24 hours and a spot on the equator. The balloon will have a certain translational speed and if it remains at this speed while increasing height then it has further to go in order to complete one rotation of the earth (larger radius from the earth's centre). So it will land further west than it took off from, the distance being some function of the height above ground and time that the balloon is airborne for.

[Gargleblaster]

Since someone mentioned "space" earlier in this thread:

With the universe, or a distant star as a reference, the earth doesn't rotate one revolution in 24 hrs, it actually goes a little further (1/365th of a rotation).

Since earth rotates counterclockwise around itself, while travelling counterclockwise around the sun, in one year, it'll have made an extra revolution. You can easily visualize this if you imagine a year only having 4 days, the earth moving one fourth of the way around the sun every day.

The earth's true rotation period (w.r.t. the background stars) is actually 23 hour 56 minutes. This is called the "sidereal" day.

Sidereal time - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Sidereal_day)

[Natstrackalpha]

No, guys listen, I am sure I`ve got it sussed.

Take a circle . . . .draw a circle. Let this be the Earth, say. Then imagine a point called . . .I dunno, London, say. Now draw a straight line from the centre of the Earth to the point called London. (on the surface of the circle)

Now go, say 50 degrees along the surface and call it 50deg West.

Draw a straight line from the centre of the circle, again to the point called 50deg West. Da-daaa!

See?!? Measure the Earth Surface distance from London to 50deg West, its so many centimetres on your drawing, right?

Now, measure the distance at a higher altitude above the surface, see?

Its further! Because the angle coming out of the centre of the Earth is getting wider and wider all the time . . . .so?

So, to do (60x50=3000) to do 3,000 on the surface is shorter than doing 3000 at a mega high altitude, for these purposes say 35000 feet.

That is why they have found discepencies in the time from London to East Coast of America and they assumed one`s body clock slowed down as we travel along.

ding!

So, had they have travelled at the same speed over the surface (they would have broken the land speed record and their backs!) there would not have been any discrepency in the time thing, thang . . .d`y`get what I mean . . ?

The maths is, even though you are travelling from A to B (London to 50 West) you are in fact travelling further when you are at altitude! So, pretending I cannot do the maths then (which is true) you have to work in dist/sp = T so, if we add more dist then it will take us longer . . . and yet we think we have only traveled from LON to 50W which is true, but we went round the houses to get there, even flying GCT.

So, whaddya say, hmm? The outside of a circle has further to travel than the inside. Its not relative, its simple.

[Natstrackalpha]

So if a Hot Air Balloon lifts off on a nil wind day and lands back say after an hour... It wouldn't land on the same spot where it got airborne from ....??

Yeh, it would apart from the odd draft. Why? Because the air in which the balloon is floating is in itself stuck to the Earth by gravity and therefore moves with it, the Earth rotates, the air is stuck to it, the ballon is in the air.

Job done.

Plus free gift!

Also, if there were no air, and you did the balloon trick, apart from it would not float, (or would it - thats another thing) so no air then . . . . . . It, the ballon, is travelling at the same speed as the . . . planet it is sitting on . . right? Yes it is.

Sooooo, if the surface of the planet is rotating at 900 kts/hr then said balloon is also travelling at the same speed, therefore same speed of the surface going up to altitude and same speed at the surface descending back down again. Not relative just p:mad:s easy.

Actually, balloon would blow up pretty fantastically, if there were no air . ..

[ft]

What are kts/hr ?

It's the new unit proposed to be used for acceleration by the NAECAMISA (North America Except Canada And Mexico International Standards Agency). It was decided that fathoms per forthnight per moment wasn't causing quite enough confusion. With this new unit, it is expected that 97.8% of all interplanetary space probes will be prevented from ever crashing into Mars as they will be on the wrong side of the sun entirely, on a trajectory roughly normal to the ecliptic. ;)

[Natstrackalpha]

Good god, I thought this was going to be a thread about early model A340's....after reading it, I think I need to lie down.

I know, I know . . . , don`t worry, my brain hurts too!