4
$\begingroup$

Aircraft speed is added to earth rotational speed when flying to the east, centrifugal force is increased compared to a westward flight. That means the aircraft weight is reduced = smaller lift, means flight with lower AoA = lower induced drag.

Can this in reality be used for less drag and greater speed or better fuel consumption?

If a plane flies east with speed of 1666km/h, centrifugal acceleration is 0.134m/s2, that means it has 1.37% less weight. If the plane weighs 78700 kg then the reduction in weight is 1078kg, when flying east!

If a plane flies westward at 1666km/h (same as earth's rotational speed) then looking from space (inertial frame) plane looks stationary, so centripetal force = zero.

This is the Eötvös effect:

enter image description here

$\endgroup$
4
  • $\begingroup$ Interesting concept. Though the original experiments were carried out with vehicles on the Earth’s surface. Even though these were marine vehicles, they were still greatly impacted by the Earth’s rotational speed. Would an aircraft in flight be impacted as much by this since it has no point of attachment to the Earth? The movement of the airmass in which it flies would have more of an impact. Thrust is acting upon the atmosphere, not the Earth, per se. Although, this would make perfect sense at takeoff, does the effect continue after the aircraft is airborne? $\endgroup$
    – Dean F.
    Sep 30, 2020 at 18:03
  • $\begingroup$ This experiment may prove that the Earth is cylindrical :) To prove that it is a sphere, you need to repeat the experiment at different latitudes and measure the reduction (of the already small) effect. But luckily, you don't even need to fly. Just weigh yourself at the equator and at the pole and see the difference. $\endgroup$
    – Zeus
    Oct 2, 2020 at 0:48
  • $\begingroup$ Generally, as you see yourself, the effect is negligible for practical airplanes, esp. compared to other effects. But ask artillerists: they will show you the correction tables for shooting east and west (and in other directions: this 'Eötvös effect' is just a trivial case of the Coriolis effect). $\endgroup$
    – Zeus
    Oct 2, 2020 at 0:54
  • $\begingroup$ @Zeus Yes Eotovos effect is just " vertical component" of Coriolis effect. $\endgroup$
    – user52248
    Oct 2, 2020 at 15:25

2 Answers 2

5
$\begingroup$

Technically yes. But as Jeffrey said, it's quite negligible. We can do the math knowing that the earth rotational speed is $360°$ per $24h$, you get $0.004°$ per second or $\omega = 7.27 \cdot 10^{-5} rad/s$. We can then calculate the centrifugal acceleration related to this speed assuming the earth radius is $r=6371km$ and neglecting flight altitude. $$a_c = \omega^2 r= 0.0337m/s^2$$ So if you're flying at a relative ground speed equal to the earth rotation, your centrifugal acceleration is either $0$ or $0.134m/s^2$ depending on which direction you are flying. Compare that to the gravitational acceleration $g=9.81m/s^2$ and you get $1.37\%$ of weight difference flying at Mach 1.5 with the earth rotation or against it.

Now remember that to have your weight reduced you need to fly with the earth rotation which means eastwards. And there you get a somewhat bigger problem reducing your performances in flight. Jet stream. Jet stream magnitude can be up to several hundreds of kilometer per hour meaning reduced ground speed around 10% are quite usual, resulting in 10% increase of flight time and fuel consumption thus destroying any opportunity to notice the 1.37% reduction of lift you're getting by flying east.

And even less useful when you know that the concorde used 2 tons of fuel to taxi from gate to Runway and 50 more tons to reach cruise speed and altitude in less than 45min....

$\endgroup$
6
  • $\begingroup$ No it means that the airplane is not moving. If your flying at exactly the earth rotation speed to the west, looking from outside the airplane would be stationary. Looking from the earth surface both flight are totally similar and the acceleration is the same in both directions, they follow the same curved path. $\endgroup$
    – MaximEck
    Sep 30, 2020 at 20:45
  • $\begingroup$ looking from space(inertial frame) plane is not moving.but looking from surface ,plane fly with earth rotational speed in curved path so it has centrifugal accelaration.in non inertial frame plane is moving with speed same as earth rotation so in this frame it has cetrifugal force.also centrifugal force dont exist in inertial frame $\endgroup$
    – user52248
    Sep 30, 2020 at 21:00
  • $\begingroup$ The centrifugal force is what's set you on a circular path. Name change depending on the frame but the physics stays the same. Your velocity vector changes direction, thus your momentum is changing and that's tanks to an acceleration. $\endgroup$
    – MaximEck
    Sep 30, 2020 at 21:17
  • $\begingroup$ So if you're flying at a relative ground speed equal to the earth rotation, your centrifugal acceleration is either 0 or 0.0674m/s2 You made mistake,it is 0.134m/s2, so when plane fly to east,his weight is 1.37% less, if plane has 78700kg then reduction of weight is 1078kg! $\endgroup$
    – user52248
    Oct 1, 2020 at 21:00
  • $\begingroup$ in numerator is 4π for plane which fly to east with same ground speed(1666km/h) as earth rotation...this plane will fly two earth circumference in 24h,because his speed from inertial frame(space) is doubled compare to earth speed.. $\endgroup$
    – user52248
    Oct 1, 2020 at 21:30
3
$\begingroup$

Yes, but the impact of the centrifugal force is negligible.

From https://en.wikipedia.org/wiki/Centrifugal_force#:~:text=Earth's%20gravity%20is%20a%20bit,produce%20the%20observed%20weight%20difference. we learn:

Note: In fact, the observed weight difference is more — about 0.53%. Earth's gravity is a bit stronger at the poles than at the equator, because the Earth is not a perfect sphere, so an object at the poles is slightly closer to the center of the Earth than one at the equator; this effect combines with the centrifugal force to produce the observed weight difference.

And you need to account that typical airplanes don't even go fast enough to full counter the earth's rotation. IIRC, it's more in the 800-900 km/h range for typical airliners.

Answering directly:

Can this in reality use for less drag and greather [sic] speed or better fuel consumption?

Less drag: not directly, drag is a function of speed, shape, and surface material. Less weight won't affect drag.

Speed is a function of thrust and drag, so not so much.

Better fuel consumption, I guess so. People with more aviation background can elaborate, but if you reduce weight, you can probably get a more efficient angle of attack as you need less force in the up direction, which may translate more or less directly in fuel savings.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy