QUOTE
Philae has been designed for compressive strengths between 2 kPa and 2 MPa. For a compressive strength less than 2kPa, Philae’s baseplate would touch the ground (but then effectively stopping further penetration) and the 360° rotation capability of the landing gear would be compromised. Still, all experiments could be performed. Only for compressive strengths < 100Pa (equivalent to tensile strengths of less than 5 . . . 10Pa) the mission objectives would be compromised.
Thanks Doug for these helpful figures. I was trying to visualize this in comparison to snow on Earth to get a feel for Philae's design tolerances, this is what I came up with. Please correct me if I'm making any bad assumptions here.
The minimum surface compressive strength Philae was designed for is 2kPa. This is comparable to snow/ice that can support the weight of a cube made of steel with 2.5cm (1") length sides (on Earth!). Qualitatively this is something like lightly compacted snow or snow with a icy crust, but definitely not fresh snow. The "mission objectives will be compromised" limit for surface strength is 100Pa. This is like snow that can support a sugar-cube-sized cube of ice with 1cm sides, or a cube of balsa wood with 6cm sides. These would still sink at least a bit in the freshest of powder snow, but that's really very little pressure - as a former Coloradan, I'd estimate this to be like wet snow, or fresh powder after sitting in the sun for an hour.
What this doesn't take into account is the fact that the compressive strength of the dusty layer could be very dynamic if it is compacted. Think of packing a snowball, it's easy at first but the more you compact it, the more pressure it takes. If compaction does play a part, it seems like it certainly won't hurt, as it can (presumably?) only increase compressive strength. However, compaction could introduce other effects like slippage if Philae lands on a (relative) slope. Anyway, thanks again for posting these numbers, finally helped me understand a bit more of what Philae was designed to handle.
-d
1 kgf/cm^2 = 98.0665 kilopascals.
density of (balsa wood, ice, steel) = (.0016, .00093, .008)
(((2.5^3) cm^2 * 0.008 kg/cm^3) / (2.5^2) cm^2) * 98 kPa/(kgf/cm^2) = 1.96 kPa
(((1^3) cm^2 * .000934 kg/cm^3) / (1^2) cm^2) * 98 kPa/(kgf/cm^2) = .091 kPa
(((6^3) cm^2 * .00016 kg/cm^2) / (6^2) cm^2) * 98 kPa/(kgf/cm^2) = .094 kPa