# Minimum Sink Rate in Sailplane

How do gliders ascend (either with an engine or thermal) at best rate of climb if it is very close to stall? Or they move up by sacrificing that best Rate of Climb. In image the best CL^3/CD is Minimum power required.

• Can you clarify what the question is? Commented Nov 27, 2023 at 12:04
• Glider (sailpane) pilots frequently thermal at "close" to the stall speed. Given the slow speed and high angle of bank, spins are a real risk if the aircraft is capable of spinning. This is one reason spin recovery - in the UK at least - is part of a glier pilot's annual check. Commented Nov 27, 2023 at 15:08

Usually, the designers make sure that the margin between the minimum sink speed and stall speed is larger. Take a look at a real example: the flight polar of the ASK21, one of the most common glider trainers.

The lowest sink speed when the glider is fully loaded (G/S is the wing loading) is marked with "ger. Sinken", and at 82km/h it is about 15km/h (+22%) larger than the stall speed (~67km/h). In gusty weather the pilots will fly at higher speeds, trading off performance against safety.

On a more general note, assuming constant zero-lift drag and parabolic induced drag, the mathematical equation to calculate the factor between the stall speed $$V_S$$ and the minimum sink speed $$V_{\textrm{min sink}}$$ would be the following one:

$$\frac{V_{\textrm{min sink}}}{V_S} = \sqrt{\frac{C_{L,max}\cdot k}{C_{D0}}} = \sqrt{\frac{C_{L,max}}{3\pi \cdot C_{D0} \cdot AR \cdot \epsilon}}$$

$$C_{L,max}$$ is the maximum lift coefficient attainable by your airplane,
$$C_{D0}$$ the zero lift drag, and
k the factor used for the quadratic term in the drag coefficient equation ($$C_D = C_{D0} + k\cdot C_L^2$$, which depends mainly on the aspect ratio AR of the wing and the oswald factor $$\epsilon$$)

• This is not really intentionally - the increase in sink rate close to stall is the result of growing flow separation. Without that, sink speed would decrease right up until stall. Commented Nov 27, 2023 at 18:03

How do gliders ascend at best rate of climb?

They do it by closely watching speed and stick forces.

You are right, when aspect ratio is high, the polar point of minimum sink is at a very high lift coefficient. If we use the parabolic drag equation, minimum sink c$$_\text{L}$$ over aspect ratio looks like this:

$$c_L = \sqrt{3\cdot c_{D0}\cdot\pi\cdot AR \cdot\epsilon}$$

With a minimum zero-lift drag coefficient of 0.008 and Oswald factor $$\epsilon$$ = 0.98 we get

 Aspect  | minimum sink rate at
ratio   | lift coefficient:
--------------------------------
15    |   1.053
20    |   1.216
25    |   1.359
30    |   1.489


With a standard-class glider the last polar point is probably not flyable at all. Flaps not only help to shift the laminar bucket up and down, but also allow high-performance designs to actually fly at their optimum polar points.

When thermalling I pay close attention to stick forces and have tried out stalling the glider before. Every type behaves differently, so I recommend to gain some altitude when flying a new type and then stalling it several times, with a variety of bank angles. In most cases control forces in roll become really low and some even will show stick forces into the circle right at stall. Depending on the airfoil on the outer wing, in that case you quickly pitch down a bit or throw the stick to the other side to support the stalling wing.

In sailing when you are close to the wind you should always play a bit with the rudder and watch the leech of the sail. If it starts to flutter, let go a bit on the rudder and then slowly tighten it again.

The same should be done when thermalling. When you know your plane, this will soon become second nature. Especially the most modern gliders can happily be flown down to very low speeds, but then their sink rate goes up because a lot of the wing has already separated airflow. Here it is better to fly at a faster speed: Controls are stiffer, control response is better and you circle at the same speed as everyone else in that thermal.

With weak and blue thermals (no clouds) you need to fly very tight circles because then thermals are narrow and climbing is only possible at steep bank and low speed. But this is hard work - most pilots fly for fun and happily accept a slightly lower climb rate but can fly at a lower bank angle and without paying close attention to speed at every moment.

• It’s worth clarifying that ‘what would give the minimum sink rate in static air’ is not the only, and not the most important factor that pilots take into account. Typically the pilot will try to spend a high proportion of their time in the areas of strongest lift. While the AoA might affect the glider’s performance by a few tens of feet per minute, staying in a strong thermal core can gain several hundred fpm in a climb.
– Frog
Commented Nov 27, 2023 at 18:59
• @Frog Yes - and where is the updraft strongest? At its center, which can be rather narrow. Which in turn requires tight circles. At high lift coefficients. If it weren't, gliders would mostly fly straight. Commented Nov 27, 2023 at 19:39

either with an engine or thermal?

Well, with an engine the best rate of climb is Vy. Lower angle of climb than Vx but faster. This results in a higher rate of climb.

With a thermal we use V min sinken because the rate of ascent is thermal updraft speed - sinken rate.

At V min sink the aircraft has a steeper angle of descent towards earth but a slower airspeed, resulting in a slower rate of descent.

This enables the updraft to increase altitude as much as possible, with the added benefit of slower airspeed allowing tighter turn radii to stay in the thermal.

Notice soaring birds, such as eagles, have broad, heavily cambered wings, with slatted tips, to fly as slowly as possible in thermals.