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As a glider pilot, we learn that Best L/D airspeed does not change with altitude. That is, the Indicated Airspeed (IAS) to fly in order to achieve Best L/D is the same no matter the altitude or air density. Additionally, that Best L/D does not change either.

Best L/D is calculated from the polar curve, which calls out a specific sink rate for that IAS. However, this sink rate only applies to standard atmospheric conditions, right? Since True Airspeed (TAS) increases with altitude (and thus ground speed, assuming no wind), in order for the same L/D to be achieved must sink rate also increase proportionally? Many discussions on glide performance discuss sink/lift/wind and speed-to-fly (i.e. MacCready), but seem to omit this detail which seems important to understand. Am I thinking about this correctly?

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Yes you are. The indicated airspeed and glide slope change little with altitude (until critical Mach number becomes a factor), but true airspeed does change.

Drawing the triangle of sink to horizontal distance gained, the hypotenuse is the glide slope. At a higher TAS, the ratio holds, therefore the sink rate and horizontal distance gained rate both increase.

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Yes, the indicated airspeed for best sink will be constant with altitude.

The true airspeed for best sink will increase with altitude.

Best sink happens at a particular $L/D$ (not best $L/D$, but a specific value for a given aircraft). If you think of that $L/D$ as the glide ratio -- or glide slope, it corresponds to an angle for the glide $\theta=\mathrm{atan}(L/D)$. You can think of this as a glide triangle -- it can be interpreted in either length (altitude, downrange) or speed (vertical and horizontal).

The hypotenuse of this airspeed triangle is the indicated airspeed for best sink -- it is constant with altitude. Framed as a true airspeed, it increases with the $\sqrt{\rho/\rho_0}$.

The vertical velocity behaves the same way (it is proportional to the square root of the density ratio).

Of course, a VSI (rate of static pressure change) does not operate in a similar manner to an airspeed indicator (pitot probe measuring dynamic pressure). So when we say 'indicated airspeed', the indicated does not have the same meaning for vertical airspeed.

The VSI suffers from lag and its own calibration issues. Suffice to say that when we talk about 'true' vertical speed, we're talking about what you would measure with a GPS on a day without thermals or other updrafts.

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