Why would larger aircraft have higher crosswind takeoff and landing limits than smaller aircraft?

Question

In a response to an earlier question about the paucity of runways at major British airports, a major theme was that the advent of larger, heavier aircraft with higher maximum-crosswind limits for takeoff and landing (combined with Heathrow’s relatively consistent windfield) reduced or eliminated the need for crosswind runways:

When Heathrow was opened as a commercial site it had THREE different runways in a triangle and by 1955 it had SIX runways - You can see them here: Wikipedia [sic] commons - arranged to allow parallel operation on any 2 runways no matter what the wind direction was.

But with the coming of larger transport aircraft having higher landing speeds and greater crosswind tolerances, the need for the extra runways was diminished - and by the end of the 1950s only the east/west runways were being used - they got extended into the 2 runways in use today, whilst the other runways were closed - they're used as taxiways today.

However, the things determining how much takeoff or landing crosswind an aircraft can handle are:

• First and foremost, the aircraft’s maximum rudder authority, which, most prominently, determines how rapidly the pilot can decrab the aircraft upon touchdown during a crosswind landing, in order to keep the main-gear tyres (which, for most aircraft,¹ are locked in a fore-and-aft orientation and cannot caster to align themselves with the aircraft’s direction of motion along the ground, unlike the nose gear) from being destroyed by the sideways forces generated by their being dragged down the runway askew; it also determines how much crosswind the aircraft can tolerate during its takeoff or landing roll before it starts weathervaning uncontrollably into the wind due to the force of the wind on the aircraft’s vertical stabiliser (although this is usually a secondary concern, as it generally requires less rudder authority than the large, high-rate yaw manoeuvre required to decrab the aircraft upon touchdown in a strong crosswind).
  • The aircraft’s maximum rudder authority, in turn, is determined by the ratio between, on the one hand, the amount of yawing torque the rudder is capable of exerting on the aircraft (a function of the rudder’s size, its effective moment arm, and [to a lesser degree] its maximum deflection angle) plus the additional yawing torque produced by the forward fuselage with the aircraft at a nonzero sideslip angle (a function of its size and effective moment arm, and of the aircraft’s sideslip angle), and, on the other, the amount of weathervaning torque produced by the vertical stabiliser and aft fuselage when the aircraft has a nonzero sideslip angle (a function of the size and effective moment arm of the aft portions of the aircraft, and of the aircraft’s sideslip angle); as all of the areas and effective moment arms involved would be increased or decreased in essentially equal proportion by a change in the aircraft’s overall size, a larger aircraft would not be expected to have significantly greater rudder authority than a smaller one.
  • A much more prominent factor in the rudder-authority department is, for multiengine aircraft with non-centerline thrust, the need to use the rudder to maintain directional control in the event of an engine failure during takeoff, with the good engine still at full power, at speeds down to far below those required to maintain flight;² the minimum airspeed at which the rudder has enough control authority to do so is referred to as V_MC (minimum controllable speed), and forms a hard lower limit on the aircraft’s range of allowable V₁ speeds (and, thereby, also on the amount of runway it requires for takeoff at a given weight). For non-centerline-thrust multiengine aircraft, this, rather than crosswind landings and takeoffs, is generally the critical case that defines the amount of rudder authority needed; thus, if there were to be a dichotomy in aircraft’s maximum rudder authorities, one would expect it to be between single-engine (and centerline-thrust multiengine) aircraft, on the one hand, and non-centerline-thrust multiengine aircraft, on the other, rather than between small aircraft and large aircraft per se.³ If anything, one would expect some small aircraft with wing-mounted engines to need more maximum rudder authority (and, thus, have greater crosswind capabilities) than some large aircraft with engines mounted close to the aircraft’s centerline!
• Secondly, the ability of the aircraft’s main-gear tyres to withstand the considerable sideways forces exerted on them before the aircraft is fully decrabbed; this determines the maximum crab angle at which the aircraft can safely touch down without tearing the tyres off its main landing gear, as well as the amount of time available for decrabbing the aircraft from a given angle before serious tyre damage occurs. If anything, smaller aircraft would seem to have an advantage here, as...
  • Smaller aircraft tend to land and take off at lower airspeeds, thereby minimising the sideways force on the main-gear tyres for a given crab angle, and, thus, presumably, increasing both the maximum safe touchdown crab angle and the safe time available for decrabbing from a given angle.
  • Smaller aircraft tend to have a lower tyre loading (less weight per unit tyre-contact-patch area) than larger aircraft, reducing the frictional force between the tyre tread and the runway surface, and, thus, the sideways forces on the main-gear tyres at a given airspeed and crab angle.

So why would larger aircraft have greater crosswind-takeoff-and-landing limits than smaller aircraft, rather than the other way around?

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¹: Although not all.

²: It is also generally considered desirable to maintain control of one’s aircraft in the event of an engine failure during cruise flight or when landing; however, these are much less critical situations in this regard, as...

• During cruise, an aircraft’s airspeed is generally much higher than during takeoff or landing (greatly increasing the rudder’s control authority), and its engines are at the considerably-lower-power cruise thrust setting (reducing the maximum thrust asymmetry - and, thus, the maximum rudder authority needed - should one fail en route), rather than the maximum-power TOGA (TakeOff/Go-Around) setting generally used during takeoff. (Some takeoffs are made light enough, and from long enough runways and/or into strong enough headwinds, to allow one to safely use a lower-power “flex” setting for takeoff, which decreases engine wear, fuel consumption, and noise production compared to using full TOGA power, at the expense of lengthening the aircraft’s takeoff roll and lowering the maximum allowable takeoff weight; however, even this setting still uses a much higher thrust level than the cruise setting.)
• During landing, the aircraft’s engines are generally spooled down almost to flight idle for the descent, greatly reducing the maximum thrust asymmetry (and, thus, maximum rudder authority required) in the event of an engine failure; even if TOGA power is needed (for instance, during a go-around or an encounter with strong windshear), the aircraft’s airspeed is still significantly higher than it is during the most critical portions of the takeoff ground roll (and the directional-control margins accordingly greater).

³: Granted, nearly all single-engine aircraft are also quire small... but so are many, many non-centerline-thrust multiengine aircraft, so it wouldn’t be just large aircraft having greater crosswind capabilities - many small aircraft would be expected to as well.

Answer 1

The overall trend has to do with speed. A rough check on the crosswind capability of an aircraft at a particular flap configuration is its sideslip capability, which roughly corresponds to the condition of a fully de-crabed crosswind landing. With a similar vertical tail volume and rudder chord ratio, two airplanes of very different sizes will have fairly similar sideslip capability.

Let's do a quick check:

• Cessna 172 has a final landing speed of approximately 61kt. It has a maximum demonstrated crosswind of 15kt. This corresponds to a sideslip of 14deg.
• B737-500 has a MZFW of 45 metric tons and a corresponding Vref of 122kt at Flap 40. It has a max demonstrated crosswind of 35kt. This corresponds to a sideslip of 16deg.

Disclaimer: do not use the above figures for flight. They are for references only.

Of course, a successfully demonstrated crosswind landing does not need to be fully de-crabed; landing gears have margin built in to cater for a crabbed landing and the associated lateral loads. Nevertheless, sideslip capability is a good first indication of a plane's crosswind capability. It's so important that steady-heading sideslip maneuvers are performed in development flight testing to ascertain stability at full pedal input prior to demonstrating maximum target crosswind.