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For a given airplane, are the minimum sink speed and maximum endurance speed the same?

Thankyou

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It depends on the characteristics of the engine.

Minimum sink speed is the speed for minimum power required. If your fuel consumption is generally proportional to power, then yes it should be very close to the maximum endurance speed. We call these 'power producing engines'.

However, if your fuel consumption is generally proportional to thrust, then no, your maximum endurance speed will be at best L/D - the minimum drag speed. We call these 'thrust producing' engines.

Both of these are idealizations and a detailed analysis will be slightly different.

In general, piston-propeller and electric-propeller aircraft are 'power producing' and jet aircraft are 'thrust producing'. Turboprop are often treated as power producing, but it gets messy.

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Minimum sink speed applies to gliding. It is based on the aerodynamic characteristics of the aircraft. Minimum sink speed is generally less than Vbg. The glider is not gaining distance as efficiently as Vbg but has a lower sink rate because of lower airspeed. V min sink is therefor useful in thermals, where the velocity of the updraft minus sink rate yields an altitude gain.

the glide slope at V min sink is steeper than at Vbg. This means the glider is in a higher drag configuration.

Mathematically, V min sink is calculated as sine angle of descent × airspeed

Notice how soaring birds have broad heavily cambered wings with multiple tip slats. These are not long distance gliders with streamlined high aspect wings like albatross.

the albatross will have a lower angle of descent but a higher airspeed, resulting in a greater rate of descent.

V max endurance will depend on what type of engine is on the aircraft. A jet will have its max endurance close to V best glide, which, not coincidentally, will also be the Vx of the aircraft. Graphically, this is where greatest excess thrust is found.

Propeller driven aircraft will have a slower V max endurance (also known as V min power) than V min sink because the prop affects the (aerodynamic) wind flow around the aircraft and the prop is more efficient at lower airspeeds. Even though drag may be slightly greater at the lower airspeed, less fuel is used (per unit of time) due to these greater efficiencies. No surprise that Vx is less than Vbg for prop driven aircraft.

It's important to understand that this is the source of differences between jet vs prop (or turboprop) V speeds, not because jets make thrust and props make power! All propulsion systems (that are any good) make thrust.

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