My professor mentioned that the contour of smaller airplanes changes more drastically than that of larger airplanes. In this context, he mentions the surface-to-volume ratio. But how does that relate to the more drastic change in a small plane's contour?
There'a value when discussing airframe icing called "collection efficiency". It's the proportion of supercooled droplets in given package of air that will penetrate the boundary layer of air and strike the surface instead of being carried around in the boundary layer.
Collection efficiency increases the smaller the leading edge radius is; that is, a sharp leading edge shape will collect more droplets in a given package of air. So it means smaller radiused flying surfaces and other shapes tend to collect more of a given volume of droplets than a blunt one of the same overall size.
The other factor is the total volume of supercooled droplets relative to the wing, and their ability to modify the airfoil contour. A very large wing is modified way less by ice accumulation for a given water droplet density, so it can tolerate more accumulation. The A-380's inboard leading edge is so large and with such a blunt radius, it doesn't need anti-icing at all.
On a side note, lots of jets don't use any anti-ice on the horizontal tail, because they basically over-size the surface so that it can generate minimum stability and trimming/control forces when loaded up with ice. When ice free, it's actually much larger than necessary.
Icing is critical on all aircraft for 3 major reasons.
- Loss of lift
- Added weight
- Increased drag
If we took an airfoil and scaled it down to 1/10th its original size, the contours are the same, but the professor is right because the Reynolds number will be different.
Reynolds Number = Chord x Velocity/Kinematic viscosity
Smaller aircraft generally have smaller chords and lower airspeeds. Relatively, the ice build-up will change the contour of the smaller wing more. But there is more to the story.
higher airspeed delays onset of turbulent airflow.
The second effect here is that less energetic airflow of the smaller plane will tend to separate earlier (even without icing). This can be seen on the Airfoil tools website with various Re numbers. They have a wide selection of airfoil types to study.
Another perspective: The “usual suspects” for why airframe icing is a problem are lift reduction, weight, and drag. As with many things about wings, that oversimplifies things… we’re misunderstanding the most significant danger to airframe icing.
By changing the shape of the airfoil and the airflow over it, you are moving the location of the CL (center of lift) and altering the angle of the lift vector as well. You may be producing enough lift, and little drag, and adding little weight, but unknowingly be changing pitch stability about the lateral axis outside of design parameters.
Small planes have surprisingly small CG envelopes of just a few inches whereas a transport category plane may have a significantly larger CG range. A Cessna 182 at gross weight has a CG range of 5” or 127mm.
In a fully loaded light aircraft I will often only be an inch or two from one of the CG limits. That means a 1” change in the location of the CL will put me out of envelope. And even more, I will likely be accumulating tail ice, which is a huge and under-estimated problem. Large transport aircraft rely on stabilizer trim, not elevator trim, giving them much more trim authority, thus more CG range, hence more options to adjust to a CL affected by ice accumulation.
What we may believe is a loss of lift, is actually a loss of sufficient elevator authority required to maintain an angle of attack that leads to level flight… and that lack of authority may be because icing lengthened the CL-CG arm, or reduced elevator downforce effectiveness, or both.
Some icing problems, like frost accumulation on the ground, will affect planes proportionally to their size. But aerodynamic icing in flight puts the aircraft with a smaller CG range and less pitch authority at much greater risk. Making matters worse, a “smaller” aircraft often has less climb capability (excess power) and a much lower ceiling (un-pressurized, less power, wing design, lack of turbocharging, etc) so we often can only descend out of an icing layer, not climb out of it. This cuts our escape options in half and requires us to descend back through the conditions that accumulated the ice if we were climbing.
So when we say “smaller” aircraft are more susceptible, “smaller” actually means airplanes with a narrower CG range, and/or less excess power, and/or less elevator/trim authority.