Wing loading - positives and negatives

Surely this also depends on airspeed:

At 100KTAS, your 500fpm vertical gust gives a decrease in angle of attack of 2.8 degrees. At 320KTAS it gives only 0.8 degrees.

Using the lift formula (L = Cl * A * .5 * r * V^2) and assuming a starting angle of attack of 5º in both cases, the change in lift is:

• An extra 70% at 100KTAS
• An extra 19% at 320KTAS

Of course, a higher wing loading implies that the wing must be generating more lift. Assuming the same wing profile and speed, the only way to do this is to increase angle of attack. Taking a TB20 (141kg/m^2) and a PA28-140 (61kg/m^2) (and ignoring that they have completely different wings and speeds), the factor of 1.9 increase in angle of attack has a massive effect on the susceptibility to a gust:

Say the PA28 has an angle of attack of 4 degrees to maintain level unaccelerated flight at 100KTAS. The resulting change in lift from the gust would be an extra 87% and the corresponding change in lift for the TB20 would be an extra 50%. (yes, this is a silly example…)

Peter wrote:

a gust will hit you a lot harder at 320kt than at 100kt

Will it? I don’t see an intuitive reason why.

I think of a gust as a sudden change in the relative airflow. Our perception of turbulence is as accelerations, these accelerations happen because in the new relative airflow the aircraft is no longer in stable unaccelerated flight.

Taking your example of a vertical 500fpm gust, this has two immediate effects: the angle of attack is changed and the relative airspeed increases very slightly. Ignoring the relative airspeed change (which really is negligible – around 0.1knots at 100KTAS), the angle of attack change will immediately give the aircraft a whole lot more lift.

The hypothetical 100KTAS aeroplane would experience a 0.7g upward acceleration. This would of course be counteracted very quickly by the reduced downforce on the tail (angle of attack changes there too) pushing the angle of attack back towards its original value. The 320ktas plane would only experience an 0.2g acceleration.

Another interesting thought experiment is a head-on horizontal gust of, let’s say, 10knots.

The 100KTAS plane (which is probably quite light) will immediately have an increase in lift of 21%, while the 320KTAS plane will only have a 6% change in lift.

Drag varies as the square of (more or less) indicated speed. Assuming the same aeroplane flies at 100KIAS and 320KIAS at sea level, the additional drag force (and thus acceleration) from the 10KTAS wind speed will be just over double for the fast aircraft.

Most aircraft flying fast are much heavier, and so the additional horizontal force translates to a much lower acceleration. Interestingly, the lift component accelerations are independent of mass.

Peter wrote:

I know carbon wings are worse than metal because they are stiffer so they are worse for spilling gusts,

I have never thaught about “spilling gust” but carbon wings are generally more flexible than metal.

Peter wrote:

In heavy turbulence one slows down, both for Va and for comfort.

Perhaps this is mostly about horizontal gusts? The decreased speed has the intuitive effect on the horizontal accelerations.

Also Va decreases with a lower weight, because the objective is to achieve a wing stall before the max G is reached (typ +3.8).

This makes sense. Wings stall at more or less the same angle of attack over quite a wide speed and weight loading range. For a given speed, a higher weight will require a higher steady-state angle of attack.

Taking the lift formula and assuming a max G of 3.8 is allowed, shows that the stall angle of attack must be 3.8 times the steady state angle of attack:

When we decrease the weight we decrease the steady state angle of attack. We must correspondingly decrease the speed in order to increase steady state angle of attack to maintain the relationship of steady-state to stall angle of attack.

Of course, Va is not the same as Vno. Vno is defined in CS 23.1505 as:

(1) Not less than the minimum value of VC allowed under CS 23.335; and
(2) Not more than the lesser of –
(i) Vc established under CS 23.335; or
(ii) 0·89 Vne

Vc is design cruising speed. See CS 23.335 for the definition – basically its a number chosen by the designer which is greater than some number derived from the wing loading data.

Compliance with gust loading vertically of 25feet per second must be shown at Vd (max diving speed) and 50feet per second at Vc (design cruising speed).

Edited to remove assumptions, corrected below

I take it back, Vne and Vd are directly related in CS 23.1505:

Vne is:

(1) Not less than 0·9 times the minimum value of VD allowed under CS 23.335; and
(2) Not more than the lesser of –
(i) 0·9 VD
(ii) 0·9 times the maximum shown under CS 23.251.

So at Vne, your aircraft has been certified for a hypothetical 25fps vertical gust, with some safety margin. At Vno it has been certified for a hypothetical 50fps gust.

So I took the concrete examples of a TB20 and an RV-14, which have almost identical wing area (11.7m^2). Both cruise at similar speeds as well, around 155knots at similar age of max power settings. The RV-14 being a smaller aircraft (2 seater) with considerably smaller frontal area does this on 85 of the power of the TB20. Note that power required to overcome drag is directly proportional to frontal area or drag coefficient, so the RV-14 can be said to have 85% of the drag of the TB20.

Max weight for the TB20 is 1400kg, for the RV14 its 930. So the wing loading of the -20 is almost exactly 1.5 * the -14.

Lets assume for the moment that the TB20 is at an angle of attack of 4 degrees – then the RV-14 must be at an angle of attack of 2.6 degrees.

Assuming they encounter a head on gust of 30knots:

• The RV-14 and TB-20 will both experience a vertical acceleration of 1.42g
• The RV-14 will experience a horizontal deceleration 1.27 times stronger than the TB20 (TB20 decelerates faster because of its increased drag, but also slower because of its increased mass).

Assuming they encounter an upward-going gust of 25fps,

• The RV-14 will experience an upward acceleration of 3g
• The TB20 will experience an upward acceleration of 2.35g

So all other things being equal, more mass (equals more wing loading) does lead to a better ride by the dual effect of greater momentum damping out transient accelerations and the higher steady-state angle of attack lessening the relative effect of added alpha on vertical gusts.