Every treatise I read about propellers/fan blades/wings states that long, thin wings are more efficient than wide stubby ones.

So why is it that the blades in high-bypass turbofan engines fitted to commercial airliners -- that account for the vast majority of airmiles flown -- have, and continue, to get wider* as the planes to which they are attached have become progressively more cost efficient?

I would prefer an intuitive explanation rather than a deep mathematical dive, but I'd also like links to any papers that explore this phenomena.

* In both relative -- as a proportion of the circumference -- and absolute terms. Engines have gotten progressively larger in diameter, and have progressively fewer blades.

• Two instant thoughts, not sure how relevant they are: 1) those are not wings, they're compressor blades. Their job is to push air and keep it pushed. 2) efficiency for an airfoil is only part of the problem of overall system efficiency. Commented Sep 21, 2023 at 23:43
• And they are spinning very fast... Intuitively longer high aspect blades are better a slower speeds. Commented Sep 22, 2023 at 0:30

The improvement in efficiency has two roots:

1. Higher turbine pressure ratios. While the very early turbojets managed just 3.14:1, the most recent civil turbofans run at 50:1.
2. Higher bypass ratios. The first turbofan had a 0.3:1 BPR while the most modern ones run at 11:1.

Yes, the same number of more slender fan blades would help to increase efficiency, but they would never suffice to absorb the enormous power provided by the turbine. Like in a wing which needs a certain area to produce the desired lift, engine fans need enough fan area order to create thrust. Since the diameter of the engine can not grow indefinitely, all that area has to be provided within the given fan diameter. A larger fan would have higher tip speeds, and while the current large fans already run supersonically at the tips, the efficiency goes down if more of the fan runs at supersonic speed. Also, the size and drag of the fairing will go up, reducing the gains from a larger fan. Lastly, the fan still has to fit under a wing.

The ratio of the area of all fan blades relative to the area of the fan disk is called activity factor or solidity. With the same activity factor, a fan with more but more slender blades will have more friction drag because the Reynolds number of those blades will be lower compared to a fan with fewer and wider blades.

The historical fan blade had the same form as a compressor blade, Figure 3 and 4. The weight of the solid titanium blade stopped a wider cord design. The long and slender shape made it difficult to get the blades stable enough to avoid flutter (aero-elastic resonant deformation), therefore mid-blade clappers were needed. These caused efficiency losses due to shock waves that formed around the clappers.

As fan blades have a nacelle wall that stop tip streams, they don’t have to have a high aspect ratio to be efficient. As hollow titanium blades were developed, fewer wide-chord blades could be used. These are more robust and therefore could be made without clappers. Gradually the form was adapted to the different flow states over the blade.

• The original questioner requested an intuitive explanation. It's important to note that "We made the blades wider, thicker, hollow, changed the topology, all the time dancing around resonance issues- none of these changes could be made on their own, but together they give a 4% efficiency boost" is code for "You ain't gettin an intuitive explanation" Commented Sep 25, 2023 at 15:43

Long, slender wings impart a small momentum change to a large volume of air. Short, stubby wings impart a large momentum change to a small volume of sir. Small momentum changes generate less frictional losses so they are always favored for propellers and wings.

However, the centrifugal forces experienced by a rotating propeller blade scale as the square of the prop diameter and if too large, they will tear the blades off the hub. The strength of the blade material sets a limit on the prop or fan diameter for any given value of spin speed, and for high RPM fans the blades must be made shorter and wider (and thicker too) so they do not destroy themselves during operation.

Gliders utilize a long span, short chord wing design to achieve high efficiency as you described. This design enables them to accelerate the necessary mass of air downwards with the least amount of induced drag and skin friction.

The problem with engines is that they also need to accelerate a lot of air but the area constraints are strict: the required area of wing, the blade that is, has to be packed very very tightly and the remaining "deficit" is compensated by (rotational) speed.

As for the trend of fewer but wider blades: Modern materials and manufacturing methods allow the use of wider blades that are better in the sense that an air particle can be more gradually accelerated (backwards) along a wider blade, instead of forcing the same acceleration in a shorter distance. The profile of the wider blade can be designed to be "gentler" and more efficient.

• I would be interested to know what my nemesis finds to be untrue in this answer. As well as the others you have downvoted. Commented Sep 29, 2023 at 8:47
• I'm confused by "long, short span wing". How can a wing be both long and short span? Did a word or two get left out before the comma? Commented Oct 4, 2023 at 18:32
• Oops, that was supposed to be long span, short chord, glad someone caught it @FreeMan 🤣 Commented Oct 4, 2023 at 20:29
• I see no "nemisis". Your post is interesting; but less than authoratative.
– Buk
Commented Oct 27, 2023 at 20:24
• @Buk less authoritative does not justify a -1 vote. Negative votes are for bad answers that contain misconceptions or false information. Commented Oct 29, 2023 at 6:18

I would prefer an intuitive explanation rather than a deep mathematical dive

No equations, I promise! 😉

To answer this question, it has to be understood how the blades of a jet engine work (regardless of where they are mounted, i.e. on the compressor, on the turbine or on the stator). In particular, their main task is to bend as much as possible the airflow that passes over them. The following picture (source) shows how the airflow's velocity changes due to the blade's presence:

Being $$\beta_1$$ the angle of the airflow entering the blade and $$\beta_2$$ the angle of the airflow leaving the blade, a good blade design is where their difference (normally termed $$\epsilon = \beta_1 - \beta_2$$) is as big as possible, theoretically just equal the angles of the leading and trailing edge. To achieve this, the distance between two blades (called pitch, s) must be within a quite narrow value, around 1 to 0.5 the chord, c of the blade. Intuitively, this can be explained as a sort of "channel effect" that is created when two blades are close to each other and that helps the flow to follow the blade profiles. If the blades are too far apart, this channel effect vanishes and their efficiency too. Anyway they do not even have to be too close (pitch<0.5), otherwise a "blockage" effect results.

Now to answer your question: if the blades went out of the rotating axis just straight with a constant chord, then their pitch s would increase more and more moving away from the axis, losing that "channel effect" and efficiency. Increasing the chord of the blades proportionally to the distance from the axis, simply keeps the pitch within the optimal value.

long, thin wings are more efficient than wide stubby ones

Correct. Simplifying to the extreme, a blade or a wing work pushing air downward and receiving as a consequence, by virtue of the third Newton's law, a net "push" upward, that we call lift. Lift is proportional to the product of the speed at which the blade/wing pushes the air downward and to the mass of air being pushed. By simple energy considerations, it can be demonstrated that this process of generating lift is more efficient if a lot of air is pushed with a small speed. This is basically why a blade or a wing becomes more and more efficient the wider it gets and that's why helicopters and gliders tend to have lifting surfaces with very long span (technically they generate less induced drag).

why is it that... engines have gotten progressively larger in diameter?

The reason should be clear now: the longer their blades are, the more efficient they get. But why then jet engines didn't have a wide fan since the very beginning? Technological limitation: a rotating mass experiences a centrifugal force proportional to its distance from the axis of rotation and to the rotating speed squared. Just as a comparison, a jet engine rotor with its 15'000 rpm sees a centrifugal force which is 2'500 times higher than a helicopter rotor rotating at 300rpm! Structural strength limits the maximum diameter of a jet engine to a couple of meters and this structural limitation was even more strict back in the early days of jet engines: with the evolution of material technology the diameter has become increasingly bigger... anyway we are never going to see a jet engine with a fan as big as a helicopter rotor. Technological evolution also explains the fancier shape of the blades which now can be driven not only by mechanical requirements (it has to be straight to resist centrifugal force, full stop) but also by aerodynamics requirements.

why is it that... engines have gotten... progressively fewer blades?

This is not completely true. An old (1974) CFM56 had 24 blades on its fan, just like a modern (2003) RR Trent 900. An old RR Convey (first turbofan to enter service) had 20 blades, only 2 more than an ultramodern (2006) GEnx. So the number of blades is more related to the producer's in-house technical choices than to an historical evolution.

As promised, no math 👍

• ϵ=β1−β2 is an equation :) Commented Sep 29, 2023 at 8:45
• @Jpe61: you're right 😅 Commented Sep 29, 2023 at 8:56