My aeroplane conundrum

A good while back, I had an interesting discussion with my dad. (I’ve had interesting discussions with him since. But they are not the subject of this post.)

I wondered why it is not significantly quicker to fly from London to New York than it is to fly from New York to London. He thought I was an idiot. (He may still think I’m an idiot. But that is not the subject of this post.)

My rationale was this. After take-off from Heathrow, the plane is, by definition, airborne. It is not in contact with the ground. Yet Earth is spinning beneath you, something that will be yet more apparent from Virgin’s new glass-bottomed plane. And it’s spinning from west to east.

Above LHR, Earth is rotating beneath you at a rate of 1,037 km/h, and 1,263 km/h above JFK. (That’s 790 mph to you New Yorkers.)

So let’s take the average of these two: 1,150 km/h. In an hour of westbound flight across the Atlantic, you will fly approximately 880 km (the rough speed of a commercial jet), but cover 2,030 km because of that spinning Earth. So you should be there in 2h 45m. Allowing for the time difference, you’ll arrive 2h 15m earlier than you set off. Like Phil Collins, but without Concorde.

Eastbound, your progress will be hampered as the earth spins in the same direction as the plane travels, and the journey back to London will take a staggering 20h 39m. More than a day wasted, once you’ve factored in the time difference. (The Gulf Stream will help a little, I guess.)

Why is it not so? Is it simply because the air is moving too? Or is something more complex—or indeed more simple—at play?

(I read recently that the reason for which a bumblebee doesn’t slam to the back of a plane/car is as yet unexplained by science. I have no idea whether that’s true. But maybe the same force is at play here.)

Comments

2 Responses to “My aeroplane conundrum”

  1. Rob on April 4th, 2013 09:21

    I recall having a similar thought when I was (a lot) younger with regards to a ball being thrown up on a plane – why does it not shoot to the back of the aircraft at 900km/h?

    Newton (clever chap that he was) covered this quite neatly in his 3 laws of motion. To take the bumblebee / ball on the plane scenario:

    The plane is travelling at 900km/h
    The ball (simpler than a bee as it has less propensity to move on its own) in your hand is moving at 900km/h
    When thrown up a new force and vector are introduced but the ball is still moving forwards at 900km/h!

    This is known as uniform motion under Newton’s first law.

    Now if you were to chuck the ball out of a window (unlikely I know but bear with me) the ball would be subjected to drag from the air outside the plane which is moving at considerably less than 400mph and would decelerate. Gravity would also have a bit to say in this situation.

    Taking your plane scenario:

    the plane on the ground is travelling at 1,150 km/h.

    To travel west the plane actually needs to decelerate by 900km/h (relative to the earth) a process that is hindered by drag of the air which is moving at a pretty happy deviation of 1,150km/h

    To travel east the plane needs to accelerate, through drag, to 2,050hm/h total speed to achieve it’s cruising speed.

    So in short you have a combination of inertia and air resistance making the flight to JFK more dependant on windspeed and direction than the movement of the Earth.

    Or to put it another way:

    “Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.”

    Of course if someone were to invent a method of nullifying Newton’s first law (an inertial damper if you will) and was daft enough to fit it to an aircraft then your 2hr flight time is perfectly doable.

  2. Iain on April 4th, 2013 13:23

    Rob is right…and so is your dad. However if the jetstream is in its normal position (right now its way off, hitting north Africa instead of the UK which is why its so bloody cold) then NY->LHR should be signicantly quicker than LHR->NY. Wind is not affected by the spinning planet, except that if the planet did not spin then temperatures would be static and as result there would be no jetstream…so in a very loose sense you could be considered to be right too!

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