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Is there a way to (safely) calculate the stall speed of an aircraft ($V_{S0}$) for anything below maximum weight? All the tables in the POH are valid for maximum weight only, and stall speed can drop significantly with a light load. As a consequence, if you're flying the published (max weight) $V_{ref}$ on final, you'll actually be carrying a significant amount of extra speed and thus increase the required landing distance, possibly in quite a dramatic fashion.

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All aerodynamic forces are proportional to the dynamic pressure, which is the product of air density $\rho$ and half of the square of flight speed $\frac{1}{2}v^2$. If your flight mass is reduced, reduce the dynamic pressure proportionally to keep all other parameters the same. To express this in terms of speed, you need to multiply the posted speed in the handbook with the square root of the mass ratio, like that: $$v_{reduced\,mass} = v_{full\,mass}\cdot\sqrt{\frac{reduced\,mass}{original\,mass}}$$

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  • $\begingroup$ While I'm pretty sure this is mathematically correct, could you elaborate how dynamic pressure relates to mass? Am I correct when I think you're saying that since the gravitational force is reduced, we need to reduce the amount of lift accordingly, and lift depends linearly on dynamic pressure? $\endgroup$ – falstro Jun 8 '14 at 9:11
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    $\begingroup$ @falstro: This is exactly right, I use the fact that lift force equals weight (mass times acceleration g) at a load factor of 1 (horizontal, unaccelerated flight). So I scale the dynamic pressure proportional to mass. Lift is dynamic pressure times area times lift coefficient, thus the dynamic pressure varies linearly with mass at a load factor of 1, when the others (area and lift coefficient) are kept constant. $\endgroup$ – Peter Kämpf Jun 8 '14 at 9:55
  • $\begingroup$ Ok, great. And the lift coefficient depends on the AoA, right? Thus if we adjust the dynamic pressure (and maintain a load factor of 1) as the weight is reduced to keep the lift coefficient constant, we'll have a constant AoA. That makes sense. Thanks! By the way, load factor of 1 is unaccelerated flight, not necessarily horizontal, approaches are usually descending :) $\endgroup$ – falstro Jun 8 '14 at 11:42
  • $\begingroup$ @falstro: Yes, you are correct, but the cosine of 3° (assuming this is your approach angle) is so close to 1 that I did not want to make the answer more complicated. The main thing is that the aerodynamics stay identical between the different mass cases (sloppy again: This is neglecting changes in Reynolds Number ;-) $\endgroup$ – Peter Kämpf Jun 8 '14 at 12:31
  • $\begingroup$ The small GA aircraft approach is usually 1000 feet in about a mile, so it's closer to 10 degrees on average but I suppose it's usually flattened out closer to the threshold, could this have a substantial effect on the maths? After the flare, it's practically horizontal so that's ok, but you don't want to end up in an accelerated stall in the flare. Also, Reynolds numbers. That triggers some deeply buried dark memories. <shiver> ;) $\endgroup$ – falstro Jun 8 '14 at 12:40

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