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In this comment a brief explanation is made of the differences between Max Glide Ratio and Min Sink Ratio:

Sink rate is how much altitude you lose over time, for example, how many feet per second. So minimum sink is the lowest sink rate you can get. Glide ratio is how much distance you can travel per given loss of altitude, for example, how many feet per feet. So max glide ratio is the shallowest angle you can glide at.

However, I don't understand how the lowest sink rate you can get isn't the same as the shallowest angle you can glide at. If I can design wing A to sink at only 1 foot per minute, wouldn't that automatically get me a longer glide ratio from altitude X than wing B that sinks at 2 feet per minute?

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No, because one is measured in time - the other is measured in distance. Just because you stay in the air longer doesn't mean you're going further. To me, it looks like the reverse of Vx and Vy. Or the difference between Best Endurance to Best Range. – Dan Feb 22 at 15:45
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Rotary wing pilot, so can't comment for fixed wings but on a helicopter, the sink rate and glide ranges are related to rotor efficiency. Max range is obtained when the rotor is at the bottom of it's power off range, typically 90%, and high airspeed. This results in a higher rate of descent than normal since you need more power from the rotor, which can only be got by falling quicker. Min rate of descent is typically 100% and 55 kts which is least power required and will keep you in the air longer, but covers a lot less ground horizontally. I imagine it's about efficiency on fixed wing also. – Simon Feb 22 at 15:54
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No, as Dan pointed out, the difference is time vs distance. If your theoretical wing that sinks at 2 fpm travels fwd 60 ft in that 1 minute, that would be a better max glide rate than your theoretical 1 fpm sink wing if it only travels 20 ft in that minute (glide ratio of 30:1 vs 20:1 respectively). – Jonathan Walters Feb 22 at 16:01
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Glide ratio is forward speed divided by sink rate. If I can double forward speed while increasing sink rate by a factor 3/2, that improves glide ratio and hurts sink rate. You are optimizing for different things, so it is not surprising the optimum conditions are different. – Ross Millikan Feb 22 at 21:36
    
If I can design one wing -- it should be noted that ALL AIRCRAFT have both minimum sink rate and max glide ratio. It's a matter of trim (mainly elevator trim because both are related to the wing's angle of attack). Glider pilots must know the correct trim for min-sink and max glide ratio. He'll use one to optimize flying in thermals and the other to fly great distances to discover new thermals. – slebetman Feb 23 at 1:57
up vote 10 down vote accepted

Glide ratio is the ratio of the distance a glider can travel horizontally to the altitude lost in transit. For instance, if a glider can travel 40 miles horizontally while losing one mile of altitude, the glide ratio is 40:1 (typical for a medium-high performance glider). The best glide ratio or maximum glide ratio is simply the best ratio a glider can achieve. Best glide ratio is achieved at a specific airspeed, which varies depending on the glider type. One flies at best glide speed in order to maximize the distance covered. When gliders are flying in a straight line and want to go as far as possible, they fly at best glide speed (typically 55-65kts).

Minimum sink is the minimum vertical speed the glider is capable of flying at in still air (typically 100-200ft/min). Minimum sink is also achieved at a specific airspeed, depending on the glider type (typically 40-50kts). One flies at minimum sink speed to maximize altitude gain when flying in lift. If you're circling in a thermal that is going up at 500ft/min, and your minimum sink speed is 100ft/min, then the glider will go up at 400ft/min.

To review, the key differences are:

  • Glide ratio specifies how "flat" the glide angle is
  • Minimum sink specifies the minimum vertical speed the glider can fly at
  • One flies at best glide speed to maximize the distance covered vs altitude lost
  • One flies at minimum sink speed to maximize altitude gain in lift
  • Best glide ratio is achieved at a higher airspeed than minimum sink

Any aircraft can be a glider with its engines out, so this applies to all aircraft.

However, I don't understand how the lowest sink rate you can get isn't the same as the shallowest angle you can glide at.

Remember that minimum sink comes at a lower airspeed than best glide. At minimum sink speed, the glide ratio is worse because even though the aircraft is sinking slower, it is also moving forward slower.

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That last paragraph is the best intuitive description I've heard so far. – slebetman Feb 23 at 1:59
    
Wow, this has been sitting without a check mark for a while... After rereading all the answers, I have to agree with @slebetman that your last paragraph finally sank in and made sense. Thanks! – FreeMan May 5 at 20:26
    
heh, based on my comment, I guess your answer had the minimum sink (in) rate.... /shows himself the door – FreeMan May 6 at 11:50

However, I don't understand how the lowest sink rate you can get isn't the same as the shallowest angle you can glide at.

Look at a Polar Curve: Polar curve

The lowest sink rate you can get is the maximum value of the curve, as illustrated in this image taken from the wiki article above:

enter image description here

The shallowest angle you can glide at is given by the tangent to the curve that passes through the origin (another image from the wiki article)

enter image description here

If I can design one wing to sink at only 1 foot per minute, wouldn't that automatically get me a longer glide ratio from altitude X, than another wing that sinks at 2 feet per minute?

As we see from the images above, the answer is not a clear yes/no, because it depends on the Glide Polar of the aircraft. Having a wing that sinks at 1 ft/min vs another that sinks at 2 fts/min is no guarantee that the polar is shifted upwards, giving you a better glide ratio. It will depend also on wing loading, as Peter wrote in this answer.

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You compare different things. Me can use your example. Wing sinks 1 foot minute and goes forward 10 foot. Another sinks 2 foot minute and goes forward 30 foot. You start with 10 foot. 10x10=100 and 5x30=150. You can see that second wing though sinking at 2 foot per minute was going faster and moved 150ft instead of 100ft. So the angle is shallower. The same is in real live. If you look at the glider manual it will have two speeds. Max Glide speed and Min Sink(endurance speed, always lower).

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