Bjorn’s Corner: Aircraft lift

By Bjorn Fehrm

March 23, 2018, ©. Leeham News: In the last Corner, we finished our series about aircraft drag, by studying an airliner flying a mission and noting how the drag changed.

Before we leave the subject of airliner aerodynamics, we shall recap how lift is produced.

Figure 1. Computer Fluid Dynamic output of a Boeing 787 during cruise. Source: Boeing and Leeham Co.

Aircraft lift

The best way to describe how lift is generated on an aircraft and its wings has been debated over the years. There are two ways to explain it and they are the two sides of the same coin.

Aircraft lift explained with pressure

One can explain lift as the sum of the differences in pressure on an aircraft or a wing. Figure 1 shows the pressure distribution of a Boeing 787 during cruise.

This is a practical method, as static pressure working on an aircraft’s surface is easy to measure. Drill a small hole and connect a tube leading to a pressure sensor and you have the static pressure (if the flow is passing the hole and not blowing into it).

We will come to why the air creates different pressures on an airliner, but first the alternative method to explain lift.

Aircraft lift explained with Newton’s laws

We learned about Newton’s three laws in school. They rule how objects are reacting to force and are not complicated:

First law: An object either remains at rest or continues to move at a constant velocity unless acted upon by a force.

Second law: The force on an object is equal to the mass of that object multiplied by the acceleration of the object: Force = Mass * Acceleration

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Now we have our bodies: the aircraft and the air molecules. We think of air as light. It’s not really, it weighs 1.2kg per m3 at ground level (assuming we are close to sea level).

When the air is passing the aircraft, it’s forced to curve around the fuselage and the wings top and bottom surfaces. The curving means the air is accelerated, meaning the air’s mass plus the acceleration is exerting a force on the aircraft and the aircraft is exerting a force on the air molecules (Newton’s second and third law).

When the air is accelerated downwards over the wing, this acceleration is caused by the wings curvature forcing the air to curve downwards. The opposing force is the wings lift.

You can easily check this yourself. Put out your hand through the side window of the car at speed and angle it so it curves the air down or up. The mass of the air forces you hand up or down. Newton’s second and third law is at play.

The practical work with lift

In practice, it’s not easy to measure the minute acceleration the air’s molecules are subject to when curving around an aircraft. Therefore, the use of Newton’s laws and the fact one is flying on the downwash of air is seldom used as an explanation. As pressure and the speed of air is simpler to measure, one works with this method to explain and measure lift.

The pressure and speed of air are coupled. Air which is moving has kinetic energy (manifested by the dynamic pressure) and potential energy (manifested by the static pressure). The sum of these is constant (called Total pressure) if the aircraft is flying in non-compressible air flow (below M0.5).

So we can either measure the static pressure with the simple method I gave or we can measure the airflow’s speed and through:

static pressure + dynamic pressure = total pressure

we can calculate the other values. But the details of this is for the experts.

The simple rules we have to remember of all this are:

  • If the air is made to speed up (by curving around a convex surface like the wing’s topside), it lowers the static pressure.
  • If the air is slowed down (by hitting a surface head on or curving around a concave surface like the wing’s bottom side), it increases the static pressure.

Let’s now use this simple method to understand what is happening at the nose of the 787 in Figure 1. It’s a Computer Fluid Dynamic output picture with the colours showing different static pressures. Green shows the lowest static pressure and yellow the highest.

First, the air is hitting the nose head on. This slows the air down and the static pressure increases. We have yellow and gradually, as the air is more diverted along the nose, we have a lower orange and red pressure changing to violet regions before the crest of the nose.

As the air is forced to curve over the convex top of the nose, leading to the fuselage’s cylindrical part, it increases the speed as the curving is convex. We get a lower pressure region (blue and light blue). We have lift created by the aircraft’s nose, in the region where the curving of the air speeds up the airflow.

The same happens over the wings. Here the curving over-the-top is so strong we get a green colour, showing a very low pressure.

In the next Corner, we will dig a bit deeper into lift explained with pressure.

34 Comments on “Bjorn’s Corner: Aircraft lift

  1. Thanks Bjorn, maybe my physics marginal, but at higher altitude (thin) air is the differential pressure (percentage) the same above and below the wing as at sea level for example?

    If so the actual value is lower explaining decrease in field performance (lift) at higher altitudes with thinner air. I always thought that its just a decrease in engine performance?

    Thanks.

    • coffin corner. the place where stall from going over max available lift and Mach buffet meet for tea 🙂

    • Hi Anton,

      to some extent, yes, but the thinner air means less lift per unit wing area. So to keep lifting the aircraft’s weight, the angle against the air will have to increase (Alfa angle) which increases the speed of air over the wing and the deceleration of the air below the wing. This change of Alfa will affect the pressure profile over the wings cord (lengthwise cut), so the pressure profile is affected by flight altitude. We will look at it next Corner.

      • Thanks Bjorn, looking forward to that.

        Just realized as passenger you see whats going on at the top of the wing, however whats going on at the bottom at least equally as important.

        • Also keep in mind that an aircraft speeds are very different in

          1. Takeoff

          2. Climb to 10k (limited to 250 by reg if I recall right)

          3. Climb up from 10 k thorough to cruise altitude

          4. Highest speed at cruise at 35K +

  2. Having an airplane with a flat belly increases lift? Does a flat belly create other issues?

    • Bjorn’s corners are always interesting.

      Like otis, I find myself wondering if a flat belly (area around the wing roots / wheel wells) on an airliner influences the effective aspect ratio of the wings ? That is, just how much the drag/lift is affected by the size/shape of this area.

      I wonder if we will ever see ‘chines’ (SR-71) on commercial aircraft, if a) they were possible, b) the benefits outweighed any disadvantages.

      Kind of wish I had studied aeronautical engineering at university.

      • The body can generate lift and some Aircraft designs use this, however if the wings can generate Lift with less drag than the fuselage it is the preferred option.
        In some cases all Aircraft fuselages generate lift especially at high alfas like at rotation.
        Normally you want a cylindrical fuselage to take the hoop stress for the pressure difference at minimum mass, now that Boeing seems to again go away from the circular fuselage, the 747 section 41 was the last previous attempt, for the 797 we hope they can use the fuselage for some lift, make it very light with a small cargo hold and not get Section 41 problems when they transition from the nose section to the fuselage sections..

        • What would you do to the fuselage to make it generate a significant quantity of lift at an acceptable drag coefficient? What would body lift do to the pitching moment?

          Mind you, modern airliners do tend to cruise with the fuselage slightly nose up, which is surprising – one would think the least drag of a fuselage would be level and parallel to the line of flight – zero incidence, with the wings one or two degrees inclined developing all the lift.

          Any ideas?

          • It depends a bit on speed, for very slow aircrafts M<0.3 I assue you can design an efficient aircraft with a pretty effective lifting body fuselage.
            It has its applications like ground effect aircrafts like Beriev so well designs even though they do ususally fly faster and only use the fuselage a little bit to generate lift.
            The lifting fuselage can find its application for the pretty heavy short hop battery powered aircrafts that might fly part of its mission in ground effect to save energy, even though it can be a rough ride.

          • You blend it with the wing. Look up blended wing body designs.

          • Called lifting body

            Space Shuttle (vertical rocket powered glider)

            Various factors go into advantage vs disadvantage dependending on what it does and where it lives.

      • The Boeing Sonic Cruiser that never was (it became the 787 instead) had chines. Not sure what for.

        Not sure why the SR71 did either.

        • As far as I can make out (being an aerodynamicist, but with experience in the field of engines rather than aircraft) the chines introduce vortices (a swirling motion) that flow downstream/aft over the top of the wings.

          The swirling motion adds a rotational component to the air’s velocity (as viewed from the aircraft’s point of reference), increasing its total velocity and thus decreasing its pressure*, adding to the wings lift since the pressure difference over the wing increases.

          This would be the same effect offered by canard wings, for which SAAB fighter aircraft are famous (seen on the Eurofighter as well, and also the North American Aviation XB-70 Valkyrie, for example). Incidentally, the forward wing pair of a bumble bee creates vortices that extend over the aft wing pair, increasing its lift. It is why bumble bees can fly despite an actual wing area that seems to be on the small side.

          * Ptotal = Pstatic + Pdynamic
          where
          Pdynamic depends on the velocity, for compressible (high speed) flow approximately density*velocity^2

          Pstatic is the surface pressure, gives lift

          Ptotal is the sum of Pstatic and Pdynamic and is constant for the air around the aircraft.

          • Actually, one half rho vee squared is good only for INcompressible flow.

            For flowing air, this form of Bernoulli’s equation cannot correctly predict the magnitude of dynamic pressure. Not even for standard conditions = sea level & ambient temperature.

        • For best efficiency, ideally any air displacement should be down. Any air pushed sideways is wasted energy. I’d go with a rectangular fuselage with a flat bottom, with some downward fins or chines running on each side at the bottom corners to keep high pressure air from escaping around the corners.

    • It does by slowing down the air and by it creating a higher belly pressure if the belly has an angle to the flow. But using the belly or the fuselage in general as a lifting body is not effective. As Claes writes, it’s a lifting surface with a lousy aspect ratio (lousy wingspan to area ratio). It generates a LOT of induced drag. Better to leave the lifting to the wing with its high aspect ratio.

      This is also the motivation for the variable camber on the 787 and A350 wings (through spoilers and flaps which can do micro downward movements in flight, giving the wing more or less camber). It’s to increase the wing camber when the aircraft is heavy, with it aligning the fuselage for minimum lift in cruise. This lets the wing to the lift job, which it does so much better. The variable wing camber increases the global Lift/Drag ratio for the aircraft.

      • Makes me wonder, if a lifting body is a better idea over conventional wing and tube configuration, but how much lifting efficiency is lost with the lower aspect of the lifting body compared to wings.

        • I think experience has shown the thin wing wins out and to have the fuselage as a tube to carry passengers and cargo. Just look at the thickest airliner wing, that of the A380 and the size of cabin it can support.
          See the earliest jets, the Comet with its thick wing and buried engines and the 707 with thin wing. There was a clear winner there even though the Comet was faster.
          Even when it comes to some small executive jets, where they use best location of having the wing attachment at mid fuselage can be used , but only behind the cabin.

        • Ted , Bjorn answered you question about

          ” it’s a lifting surface with a lousy aspect ratio (lousy wingspan to area ratio). It generates a LOT of induced drag. “

          • Hence, if aspect ratio is a big factor, a blended wing aircraft is a lousy idea.

          • We will have an article in the coming weeks about blended wing.

      • Thank you Bjorn, that makes a lot of sense.

        I’m still wondering if there is an optimal wing sweep as most airliners seem to have a similar degree of sweep. I understand that greater sweep would reduce drag at higher speeds. I don’t know if airliners move fast enough for this to be a factor ?

        With the launch of the 777X we’ll see folding wingtips on airliners, is there a reason why wingtips wouldn’t be folded back (or forward !) in the same plane as the wing in order to increase wingspan/aspect ratio but still fit into a gate ?

        • Re wing sweep. You try to get away with the lowest sweep angle possible as large sweep angles build weight. With modern CFD you can build wing profiles which work efficiently at the desired Mach and still have a moderate sweep. Examples: The 747 cruises at M0.855 and has 37.5° quarter cord sweep as it was designed in the late 1960s before Whitcombe’s supercritical airfoil ideas. The with the supercritical profiles you have 787 M0.85 32°, A350 M0.85 31.9° while A330 has 30° but then only cruises at M0.82.

          The very dangerous wing flutter is affected by folding wing surface forward (or really angeling it forward) at the tip. Folding it backward more than Boeing’s rake tip (767-400, 787, 777X, P8) decreases its efficiency.

          • Thanks Bjorn. The wing sweep in the drawing of your NMA series looks “lowish” (28deg?), could it be part of weight savings and a compromise between short and medium haul applications?

  3. “First, the air is hitting the nose head on. This slows the air down and the static pressure increases.”

    That’s a bit confusing. The air should be not moving, no? It’s the aircraft that hits non-moving air. The air can’t really slow down, if it’s not moving in the first place, no?

    • The two cases are equivalent;

      The aircraft moving through still air, as in real life
      or
      The air being blown past a static aircraft at the same speed, as in a wind tunnel.

      So in reality you’re right, the air is static but suddenly accelerated to the speed of the aircraft.

      But the pressure is the same as if – within the frame of reference of the aircraft – it were standing still, and the air moving around the aircraft has been brought to a full stop.

  4. Björn,

    in your post above, you mention the non-compressible regime being Mach < 0.5. I'd put this at Mach 0.3 can still be achieved locally, e.g. at the suction peak of the wings since air is accelerated over the wing.

  5. I do not like the ‘air speeds up along the convex upper surface and lowers the pressure’ explanation for wing lift.

    This convex-concave conundrum is here just to confound us.

    If it were true, how would we explain inverted flight? It just does not make any sense.

    A wing is an air pump. As simple as that.

    It blows incoming air down. And generates lift up by doing so. This is not the ‘alternative’ lift explanation. This is THE explanation.

    A flat plate, or a brick, or a leaf, or a hand in the wind, all can generate lift. Given proper airspeed and angle of attack.

    • You answered your own question, airliners cant fly upside down!
      Those aerobatic planes that make a feature of inverted flight would have symmetrical wing foil.

      • But camber helps, less brute force.

        Some jets as I recall had reverse camber.

        It all has to do with what the machine is designed to do, its mission, where it lives most of the time and getting it off the ground and landed safety.

        That is a hugely complex set of contradictory needs.

        Bernouli anyone?

  6. Static Pressure: one without a velocity component.

    Fire Protection Sprinkler People have their own lingo, they call it residual.

    They tend to be odd though. Its really not Fire Protection, it is and should be facility protection from fire.

    Great series. I do miss Bournouli though and the arguments about lift and turning down wind!

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